Patent Application
20240413844
This relates to RF signal processing, and in particular, a multi-loop signal processing architecture.
Tunable radio frequency (RF) filters have used tunable filters in wireless communication as part of the overall processing of received RF signals to extract signal information. Inversely, such tunable filters have been used as part of the process of encoding information onto an RF signal as part of wireless communications.
One type of resonator is an LC tank, although other types of resonators are also known. Within an LC tank, the resonant frequency may be controlled by changing the capacitance, for example via a continuously adjustable capacitor, such as a varactor controlled by a variable bias voltage, or a via a discrete set of capacitances, such as a bank of switched capacitors, or a combination of continuous- and discrete-value capacitances. Other LC resonator implementations that may have a variable L may also be applicable as resonators may also consist of distributed components. Fundamental to a resonator is a structure that can store energy in multiple modalities and that the characteristics of the resonator are a result of the mechanisms for exchanging this energy between these modalities.
Tunable RF filters are generally characterized by control inputs to adjust the center frequency and bandwidth of the resonators that comprise the filter. Issues of operating center frequency, bandwidth, tuning range, resonator stability, and intrinsic noise sources are but a few of the important aspects describing the performance of these tunable RF filters. Additional control of such external factors as temperature or time related component aging needs to be considered.
An RF signal generally refers to a signal that is relatively narrowband such that it can be associated with a carrier frequency that is relatively high. Baseband frequency (BB) is used to imply any frequency that is relatively low. Typically, an RF frequency is at least 10 times that of a BB frequency.
Available wireless radio architectures consist largely of interchanging discrete modules that are designed to meet a required radio frequency (RF) band and process the incoming RF signal. These modules are designed for a discrete frequency range. In general, the carrier frequency may be anywhere from 1 MHz on the low end to 100 GHz on the high end, but this is not limiting.
Current radio architectures for the discrete band RF frequency modules deploy direct-sampling software to process the incoming RF signal and commonly known as a Software Defined Radio (SDR). A direct-sampling software defined radio (DSDR) 10, shown in
Antenna 12 as shown in
This existing SDR 10 architecture is enabled by state of the art ADC 14 and DSP 20 signal processing hardware that has emerged with clock rates available up to several tens of GHz. Hence a DSDR 10 can be realized for the range of radio frequencies from 1 MHz to 40 GHz, with essentially only firmware changes via frequency band specific module insertions.
In the ideal DSDR 10 of
DSP 20 is one problem but generally the bigger problem is that ADC 14 has to have sufficient dynamic range such that, at the lower end, the quantization noise does not contribute to the receiver NF, and at the upper end, it does not saturate due to the large number of undesired interference signals mixed in with the desired signal.
This has been mitigated to an extent with the recent advent of chip based bandpass filters 22 (BPF) in a front-end module as shown in
According to an aspect, there is provided a signal processing circuit for processing a signal, comprising a bandpass filter having a passband, a signal processing block downstream of the bandpass filter, a first feedback path that extends from between the bandpass filter and the signal processing block to upstream of the bandpass filter, and a second feedback path that extends from downstream of the signal processing block to upstream of the bandpass filter wherein, in operation, the first feedback path reinforces the signal in the passband and the second feedback path conditions the signal at an output downstream of the bandpass filter.
According to other aspects, the signal processing unit may comprise one or more of the following features, alone or in combination: the first feedback path may be a positive feedback path, the second feedback path may be a negative feedback path, and wherein the negative feedback path may suppress internal noise generated downstream of the bandpass filter; a central frequency, a frequency selectivity, or both a central frequency and a frequency selectivity of the bandpass filter may be tunable; the signal processing circuit may further comprise an adjustable scaling block in the first feedback path, the second feedback path, or both the first feedback path and the second feedback path; the signal processing block may apply a first domain transformation, and the negative feedback path may comprise a second processing block that applies a second domain transformation that is the inverse of the first domain transformation; the signal processing block may comprise an analog-to-digital converter (“ADC”), and the second processing block may comprise a digital-to-analog converter (“DAC”); the internal noise may comprise quantization noise from the ADC; the signal processing circuit may further comprise a digital signal processor that conditions a signal in the negative feedback path; an output of the ADC may be connected to a digital signal processor as a receive channel of a software defined radio; the signal processing circuit may comprise a phase control element in the first feedback path, the second feedback path, or each of the first feedback path and the second feedback path; the signal processing circuit may comprise a plurality of bandpass filters connected in series and a plurality of first feedback paths, each bandpass filter comprising a corresponding first feedback path; the signal processing circuit may comprise a plurality of second feedback paths connected in parallel from downstream of the signal processing block to upstream of the plurality of bandpass filters and between adjacent bandpass filters; each of the first feedback paths and the second feedback path may further comprise a gain element; the first feedback path may be a positive feedback path, the second feedback path may be a negative feedback path, and the signal processing circuit may further comprise a controller programmed with instructions to adjust the gain block of the positive feedback path to cause the bandpass filter to self-oscillate, and then adjust the gain block of the negative feedback path to stabilize the bandpass filter; the signal processing circuit may comprise a plurality of bandpass filters and positive and negative feedback paths; the signal processing block may be controlled to control one or more poles of a transfer function of the signal processing circuit; the bandpass filter may comprise an acoustic wave resonator and an adjustable phase control element; and the signal processing may comprise a plurality of acoustic wave filters and a switch that selects a desired one of the plurality of acoustic wave filters
According to an aspect, there is provided a signal processing circuit, comprising a first signal loop having a first signal processing block and a first feedback path that extends around the first signal processing block, the first signal processing block having a frequency dependence that causes the first signal loop to generate a passband. A second signal processing block is downstream of the first signal loop. A second feedback path extends from downstream of the second signal processing block to upstream of the first signal processing block. In operation, the first feedback path reinforces a signal in the passband and the second feedback path conditions the signal at an output downstream of the first signal processing block.
According to other aspects, the signal processing circuit may include one or more of the following aspects: the first feedback path may be a positive feedback path, the second feedback path may be a negative feedback path, and the negative feedback path may suppress internal noise generated downstream of the first signal processing block; the first signal processing block may comprise a resonator; a central frequency, a frequency selectivity, or both a central frequency and a frequency selectivity of the resonator may be tunable; there may be an adjustable scaling block in the first feedback path, the second feedback path, or both the first feedback path and the second feedback path; the second signal processing block may apply a first domain transformation, and the second feedback path may comprise a third processing block that applies a second domain transformation that is an inverse of the first domain transformation; the second signal processing block may comprise an analog-to-digital converter (“ADC”), and the third processing block may comprise a digital-to-analog converter (“DAC”); the internal noise may comprise quantization noise from the ADC; there may be a digital signal processor that conditions a signal in the second feedback path; an output of the ADC may be connected to a digital signal processor as a receive channel of a software defined radio; the first processing block, the second processing block, or both the first processing block and the second processing block may comprise at least a phase control element; the first processing block may comprise a plurality of bandpass filters connected in series, each bandpass filter comprising a corresponding first feedback path; there may be one or more further second feedback paths connected in parallel from downstream of the second signal processing block to between adjacent bandpass filters of the plurality of bandpass filters; the first feedback path may be a positive feedback path, the second feedback path may be a negative feedback path, and there may be a controller programmed with instructions to adjust a positive gain block of the positive feedback path to cause the bandpass filter to self-oscillate, and then adjust a negative gain block of the negative feedback path to stabilize the bandpass filter; the second signal processing block may be controlled by a controller; the first signal processing block may comprise an acoustic wave resonator and an adjustable phase control element; the first signal processing block may comprise a plurality of acoustic wave filters and a switch that selects a desired one of the plurality of acoustic wave filters; there may be a signal input upstream of the first signal loop; there may be a signal input between the first signal processing block and the second signal processing block, the second feedback path comprising a negative gain block.
A method of processing a signal using a signal processing circuit that comprises a first signal loop comprising a first signal processing block and a first feedback path that extends around the first signal processing block such that the first signal loop comprises a passband, a second signal processing block downstream of the bandpass filter, and a second feedback path that extends from downstream of the signal processing block to upstream of the first signal processing block, the method comprising the steps of
According to an aspect, there is provided a dual loop signal processing architecture that may be used, for example, for data extraction in a front-end module (FEM), or for other suitable applications. The dual loop architecture may include a set of fixed components whose configuration and operation may be controlled by software. For some examples of a FEM connected to the antenna, the architecture may applicable for both receive and transmit functions.
According to an aspect, there is provided a signal processing circuit for processing a signal, comprising a bandpass filter having a passband; a signal processing block downstream of the bandpass filter; a first feedback path that extends from between the bandpass filter and the signal processing block to upstream of the bandpass filter; and a second feedback path that extends from downstream of the signal processing block to upstream of the bandpass filter. In operation, the first feedback path reinforces the signal in the passband and the second feedback path conditions a signal at an output downstream of the bandpass filter.
In other aspects the signal processing circuit may include one or more of the following aspects, alone or in combination: the first feedback path may be a positive feedback path, the second feedback path may be a negative feedback path, and the negative feedback path may suppress internal noise generated downstream of the bandpass filter; a central frequency, a frequency selectivity, or both a central frequency and a frequency selectivity of the bandpass filter may be tunable; there may be an adjustable scaling block in the first feedback path, the second feedback path, or both the first feedback path and the second feedback path; the signal processing block may apply a first domain transformation, and the negative feedback path may comprise a second processing block that applies a second domain transformation that is the inverse of the first domain transformation, and the signal processing block may comprise an analog-to-digital converter (“ADC”), the second processing block may comprise a digital-to-analog converter (“DAC”), the internal noise may comprises quantization noise from the ADC, there may be a digital signal processor that conditions a signal in the negative feedback path, and an output of the ADC may be connected to a digital signal processor as a receive channel of a software defined radio; there may be a phase control element in the first feedback path, the second feedback path, or each of the first feedback path and the second feedback path; there may be a plurality of bandpass filters connected in series and a plurality of first feedback paths, each bandpass filter may comprise a corresponding first feedback path, there may be a plurality of second feedback paths connected in parallel from downstream of the signal processing block to upstream of the plurality of bandpass filters and between adjacent bandpass filters, each of the first feedback paths and the second feedback path may further comprise a gain element, and where the first feedback path is a positive feedback path and the second feedback path is a negative feedback path, the signal may further comprise a controller programmed with instructions to adjust the gain block of the positive feedback path to cause the bandpass filter to self-oscillate, and then adjust the gain block of the negative feedback path to stabilize the bandpass filter; there may be a plurality of bandpass filters and positive and negative feedback paths; and the signal processing block may be controlled to control one or more poles of a transfer function of the signal processing circuit.
According to an aspect, there is provided a method of processing a signal using a signal processing circuit that comprises a bandpass filter having a passband, a signal processing block downstream of the bandpass filter, a first feedback path that extends from between the bandpass filter and the signal processing block to upstream of the bandpass filter, and a second feedback path that extends from downstream of the signal processing block to upstream of the bandpass filter, the method comprising the steps of filtering a signal in the bandpass filter and reinforcing the signal ins the passband using the first feedback path; processing the filtered signal using the signal processing block downstream of the bandpass filter; and conditioning an output signal at an output downstream of the bandpass filter.
According to other aspects, the method may further comprise one or more of the following elements, alone or in combination: the first feedback path may be a positive feedback path, the second feedback path may be a negative feedback path, and wherein conditioning the output signal may comprise suppressing internal noise generated downstream of the bandpass filter; reinforcing the signal and conditioning the output signal may comprise controlling a gain factor, a phase, or the gain factor and the phase in each of the first feedback path and the second feedback path; the method may further comprise the step of controlling the bandpass filter by tuning a central frequency, a frequency selectivity, or both a central frequency and a frequency selectivity of the bandpass filter; the signal processing block may apply a domain transformation, and the negative feedback path may comprise a second processing block that applies a second domain transformation that is the inverse of the first domain transformation, the signal processing block may be an analog-to-digital converter (“ADC”), and the second processing block comprises a digital-to-analog converter (“DAC”), the internal noise may comprise quantization noise from the ADC; a plurality of bandpass filters may be connected in series with a plurality of positive feedback paths, each bandpass filter comprising a corresponding positive feedback path, and there may be a plurality of negative feedback paths connected in parallel from downstream of the signal processing block to upstream of the plurality of bandpass filters and between adjacent bandpass filters; the method may further comprise the step of adjusting again of the positive feedback path to cause the bandpass filter to self-oscillate, and then adjusting a gain of the negative feedback path to stabilize the bandpass filter; and there may be a plurality of bandpass filters and positive and negative feedback paths.
According to an aspect, there is provided a receive module for a digital communication device, the receive module comprising a bandpass filter having a passband; an analog-to-digital converter (“ADC”) downstream of the bandpass filter, the ADC having an output connected to a processor of the digital communication device; a positive feedback path that extends from between the bandpass filter and the signal processing block to upstream of the bandpass filter; and a negative feedback path that extends from downstream of the signal processing block to upstream of the bandpass filter, the negative feedback path comprising a digital-to-analog converter (“DAC”); wherein, in operation, the positive feedback path reinforces the signal in the passband and the negative feedback path suppresses internal noise generated downstream of the bandpass filter. The digital communication device may comprise a software defined radio.
According to an aspect, there is provided a signal processing circuit for a digital communication device, comprising: an outer signal loop comprising an input, an output, and a transformation block adapted to perform a signal transformation operation on a signal being processed; and an inner signal loop comprising a tunable bandpass filter, the inner signal loop being nested within the outer signal loop such that the tunable bandpass filter is connected within each of the inner signal loop and the outer signal loop, and the transformation block is connected outside the inner signal loop.
According to other aspects, the signal processing circuit may comprise one or more of the following alone or in combination: a central frequency, a frequency selectivity, a Q factor, or combination thereof, of the bandpass filter may be adjustable; the bandpass filter may comprise a plurality of resonator outputs; the transformation block may comprise a processor block that is programmed with instructions to individually control poles of a transfer function of the outer signal loop; the transformation block may be adapted to apply a domain transfer to at least one of the resonator outputs; the transformation block may receive the plurality of resonator outputs in parallel; the outer signal loop may be a negative feedback loop and the inner feedback loop may be a positive feedback loop; the transformation block may be in a signal path of the outer signal loop or in a feedback path of the outer signal loop; the inner signal loop may comprise a positive feedback path and the outer signal loop comprises a negative feedback loop, such that the positive feedback path reinforces the signal in the passband and the negative feedback path suppresses internal noise generated downstream of the bandpass filter; the signal processing block may apply a first domain transformation, and the negative feedback path comprises a second processing block that applies a second domain transformation that is the inverse of the first domain transformation; the signal processing block may comprise an analog-to-digital converter (“ADC”), and the second processing block may comprise a digital-to-analog converter (“DAC”); the internal noise may comprise quantization noise from the ADC; there may be a digital signal processor that conditions a signal in the negative feedback path; the outer signal loop may comprise an output connected to a transmit device; and the inner signal loop may comprise an input upstream of the tunable bandpass filter outer signal loop that is connected to a receive device.
Other aspects of the circuits and methods described above will be apparent from the discussion below.
These and other features will become more apparent from the following description in which reference is made to the appended drawings, the drawings are for the purpose of illustration only and are not intended to be in any way limiting, wherein:
A signal processing circuit, generally identified by reference numeral 30, will now be described with reference to the drawings.
Referring to
Inner loop 40, which may also be referred to herein as an upstream loop, with an upstream processing block 42 that has a frequency dependence, and an inner feedback path 45 that extends around upstream processing block 42. In many practical implementations, upstream processing block 42 may be a resonator or bandpass filter. Other components that have a frequency dependence may also be used, which, in combination with feedback path 45, produce a passband. Bandpass filter 42 may be a continuous time tunable RF bandpass filter that enables independent tuning of the filter center frequency and/or the filter bandwidth using Q control. Inner loop 40 may have a positive feedback variable gain block 44 on inner feedback path 45 that reinforces the input signal as an active feedback filter (AFF). The various components in inner loop 40, such as processing block 42 and variable gain block 44, may be variable or tunable to control the output of inner loop 40.
Outer loop 50 has a second, or downstream, signal processing block 54 and an outer feedback path 55 that extends from downstream of the inner loop 40 to upstream of processing block 42. In one example, signal processing may be conducted by a discrete time digital signal processing (DSP) block 52 that may involve domain transfers (ADC 54 and DAC 56). Outer loop 50 also incorporates inner processing block 42 as one leg of outer loop 50. There may be more than two outer loops 50, but the loops are in parallel with inner loop 40, each of the possible multiple outer loops 50 sharing the same inner loop tunable RF bandpass filter 42. Outer loop 50 may include a gain block (not shown).
In some cases, the dual loop architecture, which may be referred to as dual parallel loop processing (DPLP), may be used to suppress internally-generated noise. In this example, inner loop 40 may be a positive feedback loop that reinforces the signal within a desired passband, while outer loop 50 may be a negative feedback loop that is conditioned to negatively interfere with internally-generated noise in the passband. In other examples, the DPLP architecture may be designed with and without a gain block in the outer loop. Signal processing circuit 30 may have a top-level architecture providing a digitized signal output 34, shown in
The dual loop architecture 30 may be a parallel combination of mixed signal processing that may combine both analog RF processing and digital RF processing. The depicted example includes a digitized signal output 34. In some examples, this mixed signal, dual parallel loop processing (DPLP) may be implemented into the front-end module (FEM) of a wireless communication architecture, and may be used in a software defined radio (SDR).
The function of inner loop 40 will be considered first, after which the function of outer loop 50 will be considered, both with and without a gain block in outer loop 50.
While various filter designs may be used in inner loop 40, to maintain simplicity in this description, only the arrangement of inner loop 40 shown in
In some examples, processing block 42 may be a resonator, such as a tunable bandpass filter (BPF), which typically relies on resonator processing control to refine the frequency selectivity of the filter when processing a signal. Generally, the processing relates to the ability to adjust the center frequency and the bandpass region. Also, in general, to control the bandwidth of the signal processing, active feedback in the form of a feedback gain element has been widely used to provide this bandwidth control in a method called Q-enhancement.
As will be understood, methods involving bandwidth control generally refer to the movement of the resonator pole or poles in the s-plane, which are a point of focus in design analysis. As will be recognized, a resonator may have more than a single pole.
By way of example, the context of the discussion herein will be this more complex active feedback resonator signal processing. While the discussion focuses primarily on this active feedback filter (AFF) in signal processing, other tunable filters may also be used, such as those that do not have active feedback, or other types of processing blocks alone or in combination with a resonator.
Referring to
Referring again to
In one example, bandpass filter 42 may be an active positive feedback filter (PFF) within the signal loop 40 that both 1) tunes the center passband frequency, and 2) allows for Q enhancement or Q spoiling of a resonator. The Q control is sufficient to allow for the realization of narrowband radio frequency, microwave, and RF millimeter wave (RFMM) bandpass filters. This may be used with resonators 46 in a network as discussed above with respect to
Relevant variants of the PFF of
Referring to
When more than one pole exists in the s-plane, there may be a dominant pole that is nominally located at the center of the pass band. Other poles tend to be less significant, nonetheless important, in determining the response of the resulting bandpass filter. Herein, when a single pole is referenced in a resonator network 46 response, it is the dominant pole that is being addressed.
Next consider a resonator that contains P>1 poles, with P=3 shown in
The minimum sampling rate that may be had using the multi-pole bandpass filter 42 will now considered. Consider a data communications signal that is composed of a sequence of contiguous symbols. Parameters of these symbols (eg. amplitude or phase) contain the data bits or information. In theory, if an analog filter is provided that is ‘matched’ to the communications signal in terms of the symbol shape and the Nyquist condition for ‘zero inter symbol interference’ (ISI), then only one sample is needed per symbol. Other components may be incorporated, such as fixed frequency up and down conversion may be used that reduces the sampling rate required.
To have the reduced ADC, and subsequently reduced DSP requirements, sampling rate is a key consideration in that it is necessary that the ADC have an aperture time that is small in comparison with the period of the highest frequency component to be digitized. Referring to
An additional problem is the nonlinearity of FET gate 72 in that the channel resistance depends on the input signal voltage and the capacitor 76 voltage. Further, the timing jitter of FET gate 72 is of significance. The gate comes from a clock synthesizer with an output emerging from logic gates. The timing jitter of dt will add an uncertainty of (dv/dt)dt to the eventual sample, where dv/dt is the slope of the incoming voltage. This results in a sample uncertainty that is related to the signal through the slope of the signal which is noisy. Hence jitter related noise may be mitigated by a low phase noise clock synthesizer and high current logic, which is a dissipation issue. Jitter may be reduced with DSP if the sampling is highly redundant such that the sampling rate far exceeds the Nyquist rate commensurate with the signal bandwidth. If the sample redundancy is not significant, then DSP may be incapable of improving on the noise resulting from timing jitter.
The smaller the aperture time of the SH, the fewer electrons related to the signal make it into the capacitor. Space charge in the FET channel of the switch is an additional source of electrons that contribute to the capacitor charge depending on the drain and source voltages during the aperture time which contributes to switching noise.
This section will cover complex concepts involving signal processing loops incorporating both real time and digital time processing. It will be shown that, among other features, the dual loop processing concept reduces or eliminates self-generated noise from the processing, such as quantization noise. These concepts are illustrated in
Inner loop 40 has been discussed above, dealing primarily with the benefits to be achieved by the positive feedback filter architecture. However, there is another purpose of the positive feedback loop and that is to modify the Nyquist Resonator Curve (NRC) of the resonator in the upstream signal loop, which may be referred to as an upstream receiver. In this way the negative feedback gain of the outer loop can be set to higher negative gain values. This leads to the ability to suppress downstream receiver processing noise in a controllable way. An example the effect of the negative feedback in outer loop 50 is shown in
The outer loop 50 with negative feedback leads to an effective reduction of the reinforcement of desired signal 85 in the inner loop 40 with positive feedback. Hence to compensate for this effective reduction in inner loop 40 gain from the negative outer loop 50 feedback gain, the positive feedback within inner loop 40 may be made stronger. In fact, the gain of inner loop 40 may be Ginner>1 without loss of stability as the effective gain of inner loop 40 is reduced by the negative feedback gain Gouter<0, leaving an effective Ginner eff<1 again.
The two loops therefore are interactive. For a specific case of a signal of given bandwidth, the net signal reinforcement is commensurate with the signal bandwidth. Inner loop 40 reinforcement may be strong enough to change the shape of the NRC of the upstream receiver such that sufficient negative feedback can be applied without risk of loop instability.
As used herein, s represents the complex frequency such that A(s) in block 92 represents the frequency response of the upstream inner loop filter processing. Between the upstream and downstream sections 91 and 94 is a tap point 98 shown for reference. Tap point 98 may be used as the notional input of any noise 99 that may be introduced by the downstream outer loop processing 94. Noise 99 is represented by Q(s).
The discussions of outer loop 50 above have noted that a gain element may or may not be present, although
A(s) may be a number of different things.
B(s) includes a component for a domain transformation. A domain transformation may be, for example, an input continuous time signal transformed to an output that comprises digitized samples, such as by using an ADC B(s) may be a transformation in frequency such that the input to B(s) is different than the frequency at the output. Part of the processing in the feedback path of outer loop 50 may includes a domain transformation (not shown in
Output 100 of the receiver, denoted as Y(s), is a frequency spectral representation. This is meant as a representation only as the output is likely a discrete time sampled signal. Also, as I(s) and Q(s) are random processes, then strictly speaking only the statistical properties of Y(s) are definable. Hence Y(s) should be understood as being a representation of the output which is convenient for discussion. It is not meant as a precise description of the output.
In one example, the processing in
The output signal Y(s) therefore represents the domain transformed variant of the input signal V(s) that is accompanied by some residual noise. It is understood that additional post detection processing is required in order to retrieve and extract the relevant information from the digitized Y(s) data as contained in V(s). Therefore, a post detection processing block D is added as shown in
It will be shown that the architecture of
In an implementation of significance for a receiver, inner loop 40 is a positive feedback loop with a gain of G1 and outer loop 50 with a negative feedback loop gain of G2. The objective of the positive loop is to enhance the desired signal V(s) relative to the noise and interference of I(s) by narrowing the effective signal bandwidth through the upstream processing such that it is more compatible with the bandwidth of V(s). It shall be shown that the objective of the negative feedback loop around both the upstream and downstream receiver sections is to reduce the presence of the noise source of Q(s) in the output Y(s). The operation of this is evident if the transfer functions are considered.
The signal transfer function is defined as
when Q(s)=0. The “quantization noise” transfer function is defined as
when V(s)=0. The noise of the downstream receiver is referred to here as quantization noise as it typically is associated with a quantizer/sampler. However, it is not limited to quantization noise and may include any noise that can be approximated as being additive as described earlier.
To simplify the calculation of the transfer functions the loop is reorganized as shown in
As an example, let A(s) represent a single pole of an equivalent complex bandpass. This is a valid approximation if the response of the front end receiver is of relatively narrow bandwidth. The simplification allows a closed form expression of the transfer functions to facilitate the present discussion. Therefore, the form of A(s) is
where p is a positive real value. With this C(s), in block 110, becomes
Then C(s) is substituted back into the transfer functions, resulting in
The zero at s=p(1−g1) appears in HQTF but not in HSTF. Consequently, if V(s) is of narrow bandwidth with a bandwidth realistically comparable with p, then the first order noise cancellation is evident. This is the basis of the action of the feedback receiver of
In summary, with the inner and outer feedback loops arranged in the manner shown in
It is evident that A(s) can be any processing function that has some dependence of frequency in the vicinity of the band center of the desired signal V(s). In this way positive feedback of the inner loop can be used to narrow the bandwidth of A(s). For example, A(s) could be any fixed or tunable bandpass filter as will be shown.
These expressions may be expanded on with an assumed transfer function of B(s). However, the point is that the insertion of the zero into HQTF is the key feature.
The concept of the dual loop feedback may also be expanded to an architecture as shown in
Letting A1(s) and A2(s), corresponding to blocks 92a and 92b, respectively, be two first order bandpass filters given as complex bandpass equivalents as
Then it can be shown that the closed loop for HQTF(S) will have two zeros corresponding to the q enhanced poles of p1 and p2.
Referring to
The closed form expressions become more unwieldy. However, the general structure of positive and negative feedback paths can result in the general architecture with multiple zeros in the passband of HQTF.
There are additional modifications that can be done for enhanced performance and flexibility of implementation. The gain blocks 97a and 97b of {g1, g2, . . . } in
A further flexibility is that the outer loop negative feedback paths can be changed to positive feedback paths and then with processing applied to the feedback paths an arbitrary set of passband poles may be realized. In this way the passband frequency response can be arbitrarily shaped. Hence the resulting frequency response resulting from the upstream and downstream receivers along with the feedback paths can be spectrally shaped and sufficiently frequency selective such that no further post detection processing is required.
The generalized feedback transfer functions of {g1, g2, . . . } can be configured dynamically such that the receiver can respond optimally to a variety of disparate input signal formats and noise contributions. These feedback transfer functions of {g1, g2, . . . } can be implemented in a DSP processor or FPGA processor resulting in a very flexible form of a software definable radio.
The feedback processing presented herein may be used to control the position of P poles 140 on an individual pole-by-pole basis as shown in
As will be understood based on the discussion here, it may be possible with feedback processing to simultaneously place each of the resonator poles individually in the s-plane, individually controlling both the bandwidth of the resonator (pole movement parallel to the horizontal axis) and the resonator frequency (pole movement parallel to the vertical axis).
There will now be considered the feedback processing of the active feedback filter (AFF) which may be used to achieve an active multi-pole placement AFF. Generalized control theory concepts will be introduced, applied to the feedback processing functions with control made possible in different processing domains that may characterize an observable, such as frequency or phase, out of the resonator. The signal in the AFF loop is in the RF analog domain. The resonator output will be referred to as an RF analog signal also with domain A.
A characteristic of signal processing circuit 30 (or DPLP) may include the state space domain transformation within the feedback loop as shown
As shall be shown in detail below, the result of a DPLP enabled three pole resonator, may be used to provide significantly increased bandwidth as shown in
In the DPLP, the domain A may be RF analog. Domain B may be different than domain A, of which there are several possibilities, including but not limited to:
An advantage of this domain transformation may be that the feedback processing in a different domain than that of the RF signal domain A is often simpler and more practical to implement. For instance, if domain B is digital, then the feedback processing may be implemented in digital signal processing (DSP) 52. Complex processing functions may be readily implemented in DSP that are not practical to implement in analog RF.
A typical application of the AFF may include narrow bandwidth filtering of a wireless signal intercepted by the antenna prior to down conversion and digitization. Interference and noise outside of the desired signal bandwidth may swamp the desired signal such that the desired signal may be irreversibly corrupted in the down conversion and digitization process. Hence a bandpass filter commensurate with the desired signal bandwidth is necessary to suppress this interference and noise. With the DPLP, more complexity in the feedback signal may be robustly implemented.
Additionally, DPLP may tolerate the large signal amplitudes that may be present in filters of high Q poles as the pole energy storage becomes large. This allows for feedback synthesis to be based on multi-dimensional state-space processing. As will be developed, this allows for the plurality of resonator poles to be simultaneously Q enhanced and arbitrarily placed in the s-plane with a single feedback loop. Thus, complex tunable multi-pole bandpass filter responses may be synthesized.
As noted previously, while the discussion herein is in terms of a dual loop architecture, this is for convenience as there may be a plurality of observations emanating from the resonator which are linearly independent, and which may be simultaneously transformed in parallel into a plurality of domains and acted on by a plurality of feedback domain processors, which may be referred to as multiple parallel loop processing (MPLP). It will be understood that, where a DPLP is described and depicted for ease of understanding, the principles may also be incorporated into an MPLP architecture. These pluralities of linearly independent signals, produced by the plurality of parallel feedback processing paths, may be simultaneously fed back into the resonator after transformation back into domain A. For example, low Q requires a low latency in the DSP which may not always possible. However low latency may be achieved in an analog domain.
An example of MPLP is illustrated in
An example of signal processing circuit 30 of
The RF feedback gain 178 is for latency mitigation and low Q-enhancement of the received input signal. The loop with DSP 52 is for both higher Q-enhancement and general signal processing for data extraction.
Referring to
Resonator Pole Placement with the DPLP
Let P be the number of poles of the resonator (with positive complex natural mode frequencies). To set the P poles to arbitrary locations represents 2P constraints as each pole has a real and an imaginary component, and the feedback processing has a minimum of 2P degrees of freedom (DOF) when acting on the N inputs to produce the M outputs.
Furthermore, it is assumed that the resonator of P poles may be adjusted by externally setting the natural resonance frequency of the individual poles. Hence this is P DOF which implies that the feedback processing needs P additional DOF.
Regardless of the details of the feedback processor, it will require forming approximate derivatives and integrations of the N observables and the forming linear superpositions of sets of variables to form the M outputs. Such linear operations are trivial to provide if the domain B is DSP. However, if the domain B is analog processing at baseband or RF, then the implementation of linear analog operations quickly becomes unwieldy as P increases beyond P=1. Again, the domain transformation within the DPLP feedback loop between the domains of A and B allows for domain A to be RF and domain B to be DSP. The DSP allows for a practical implementation of the feedback processing such that the P poles may be placed arbitrarily and simultaneously.
Based on this, there may be, for example, a multipole resonator with P=3 in the DPLP with the feedback processor computing the feedback signal that places these three poles as a Chebyshev bandpass filter of order 3. The Chebyshev poles may be placed close to the jω axis to provide a narrowband filter of high frequency selectivity as illustrated in
There will now be provided a discussion of an example analysis of signal processing circuit 30 (or DPLP), shown as a closed loop in
A resonator has a transfer function in terms of poles and zeros that may be expressed as
where N(s) is a numerator polynomial in s (which is the complex frequency of continuous time). D(s) is denominator polynomial in s.
In DPLP, an active feedback filter (AFF) is added that has a transfer function of
Where Hfp(s) may contain active gain elements. The closed loop is illustrated in
The closed loop is given as
The denominator polynomial (DB-NA) has roots which are the closed loop poles. By design of the feedback polynomials of A and B, the poles may be moved to wherever desired.
Hence the objective of DPLP is to solve for A and B such that the roots of
are at the desired s-plane locations.
It happens that the implementation of
is not easily done in continuous time RF space. However, a domain transformation to discrete time space (generally from RF to digital) may be implemented to achieve an equivalent version of the continuous time Hfb (s) in the discrete time Hfb (z), where the coefficients A and B may be easily changed for different tuning as it is a digital implementation. This process is shown in
Given Hres(s) the feedback transfer function of Hfb(z) may be determined such that the desired closed loop passband response is obtained.
Referring to the DPLP block diagram in
The DPLP 30 has two parallel feedback paths:
In this way some preliminary Q enhancement of the Hres(s) block 202 is possible, providing additional mitigation against potential ADC block non-linearities.
Inner loop 40 may include a tunable resonator that has a varactor or a switched capacitor bank for resonance frequency tuning based on a resonant LC tank. However, a varactor of high Q-factor and linearity may be difficult to integrate into a chip circuit. There may also be issues with the bias tuning voltage which may be moderately high to minimize distortion effects. Consequently, one implementation for changing capacitance of the analog LC tank may be via switched capacitor banks 233. Other types of resonators with different considerations may be used.
The DPLP domain transformation provides the ability to accommodate a resonator that may only be tunable in discrete steps. An example is a resonator using switched capacitors for tuning.
A switched capacitor resonator with K switches provides 2K discrete natural frequencies of the analog resonator using different combinations of switch positions. As an example, suppose there are capacitors with values of C, 2C, and 4C arranged in parallel with three switches. Then the capacitance values of the set {C, 2C, 3C, 4C, . . . 7C} may be realized by setting the three switches appropriately. A general problem with this switched capacitor resonator is that it does not allow for tuning of the frequency except for 8 discrete steps.
However, with the DPLP domain feedback processing 3, the pole of the switched capacitor resonator may be moved over a small range relative to the capacitor switch settings, but this may be sufficient so that the next switch setting may be used in the RF resonator, enabling continuous frequency changes slightly larger than the frequency band covered by each basic switched capacitor settings.
As will be shown, this may result in continuous frequency tuning over a large range with a continuous change in the DPLP feedback processing.
A digital resonator may be used as a phase shifter and shift the resonance frequency slightly, but this may be sufficient so that the next switch setting may be used in the RF resonator. An example of a block diagram of the analog resonator switched capacitor bank 232 with four capacitors and feedback processing 48 and gain block 234 is shown in
One specific example of feedback processing is a digital resonator. While a digital resonator may be implemented in a variety of ways, the DPLP may provide a digital resonator within outer loop 50. In one example, the DPLP may use feedback processing with digital domain B to produce a feedback signal from the superposition of the state variables in such a way as to tune the DPLP pole continuously in frequency. This may be extended to a resonator consisting of P poles along with the K sets of switched capacitors.
This principle may be further generalized. Consider a resonator of a plurality of poles that has N different switch settings that may attach or detach a reactive component to the multipole resonator at different and arbitrary points in the resonator. There may be 2N combinations of switches and therefore 2N different arrangements of analog resonator pole positions. In principle, a feedback processor function may be determined for every requirement of DPLP pole positions from each of the 2N resonator configurations. However, there may be a specific resonator configuration for which the feedback signal amplitude is minimal. This is the switch configuration that is selected for the desired output DPLP pole position pattern.
The open loop bode is plotted in
The ten percent change in the digital resonator will cause the DPLP center frequency to change about 4 percent. Hence if there are 4 switched capacitors for 16 states, then this is about a 64 percent change in the DPLP tuning frequency.
Finally it may be noted that the amplitude dips slights when the digital resonator is detuned away from the RF resonator. It may be necessary to compensate this with a small increase in G to maintain the precise level of Q enhancement, an adjustment made by the DPLP.
This section will consider a state space formulation of the DPLP feedback processing of signal processing circuit 30 that will enable simultaneous placement of multiple poles. In the typical case the multi-pole resonator structure is implemented as a two-port subsystem with a single input and a single output (referred to herein as a Single Input Single Output (SISO) network. From the single output, the DPLP processing makes sufficient observations to form the single feedback to Q enhance or place multiple poles at a time. While the single feedback is in principle sufficient to move the multiple poles to desired locations, a practical implementation of the DPLP will allow for the resonators to be adjusted simultaneously. This reduces the amplitude of the feedback signal necessary. However, the resonator frequencies do not need to be tuned precisely or with high resolution. Hence switched capacitors may be used for the tunable resonator.
It is also possible to consider the general resonator with multiple input ports and multiple output ports or a Multiple Input Multiple Output (MIMO) network. However, as SISO works adequately for DPLP, there is little impetus for added complexity. However, MIMO should be considered for the DPLP in the most general form.
Consider the DPLP with N/2 resonators. Converting the resonator transfer function to the Z domain results in an Nth order transfer function as
The coefficient b0 is zero as there is no through connection. Also aj is always normalized to 1. The numerator and denominator are multiplied by z in preparation for the state space notation, giving
Next this may be considered as a cascade of two transfer functions as shown in
The all-pole section given as
results in a difference equation of
The set of state variables are
Consequently, the difference equation may be written as
Hence the state space A matrix is given as
And the B matrix is
The numerator transfer function is given as
Write the difference equation as
The feedback is also given by
The feedback transfer function may be written as
The loop 262 for the general DPLP is now fairly simple consisting only of a filter 264 for the feedback processing 266 as shown in
The state space formulation of the DPLP feedback processing for a single pole resonator will now be considered. Then this is expanded to the multi-pole resonator.
Start with the ideal single resonator that has a transfer function of
The general state space formulation is
where x is the vector of state variables and u is the input. A is the system matrix and B is the input matrix. Let z(t) be the input and y(t) be the output. The state vector is selected to be
which results in the system matrix of
Note that the state variables selected are not unique and that different system matrices may result. However, the system modes are invariant to the choice of the state variables. The choice of state variables allows for a simple signal flow diagram consisting of a pair of integrators as in
For simplicity, the derivative operator in the numerator of H(s) is separated out and u(t) is taken as the input. Then the input matrix is
For the system to be controllable the controllability matrix of [B AB A2B . . . ] is determined, which is of full rank. In this case it is as
The system is controllable and hence the pole may be fully moved with feedback based on a linear superposition of the two state variables. However, there is only access to the state variable x1. In this simple example, x2={dot over (x)}1. Therefore, if x1 is observed then x2 may be derived by a linear operation. Therefore, a full state feedback may be provided, and then as the resonator is controllable, place the closed loop poles at an arbitrary desired location. For a higher order system, this may not be so obvious that all the state variables may be observed from the single output. A method of determining if this is possible is to consider the observability of the system. If the state space system is observable, then all the state variables may be derived by linear operations and superpositions of the available outputs. The output of the state space is represented as
where in this case x1 is observed at the output such that
C=[1 0]
The observability matrix is
which is of full rank. In this case the observability matrix is
which has a rank of 2.
Next, the weighting vector for the feedback may be formed, denoted as k and the input is then
Therefore, the state space of the closed loop AFF is
The new closed loop poles are given as the eigen values of the matrix (A−Bk). Hence the weight or control law vector of k may be determined, which will set the desired poles. That is, if the pair of {A,B} is controllable, then the eigenvalues of (A−Bk) may be any arbitrary desired set.
As the derivative operator has been separated from the numerator, the feedback may be added to the input so that the feedback is adjusted by (1/as) implying an integration, giving:
and the feedback is F(s)X1(s). If ωr is adjusted, then k1 may become zero. Hence what is left is that the feedback to the input is proportional to x1(t).
The state space formulation is therefore a powerful tool in considering any form of resonator and positing an existence query as to whether all of the poles of a multi-pole resonator may be individually Q modified (enhanced or spoiled) to desired locations in the s plane.
Note also that the resonator ωr may not need to be adjusted for the desired closed loop pole: it may be sufficient to adjust k. As will be shown, it may be possible to adjust ωr after determining k such that the magnitude of k may be minimized. Or it may be possible to set coefficients in k to zero by changing ωr. This is beneficial as the processing to determine the state variables may then be simplified as some are weighted by zero in the feedback.
With switched fixed capacitors for frequency tuning, it is not possible to smoothly tune the capacitor in state space. Hence, the state variables may be approximated from the output. With the controller version of the state space this is straightforward as
Consequently, the feedback is:
It may be better to change the order of the processing such that the derivative x2 is after the state space processing with a numerator of one in order to have an estimate of x2 that may be scaled and integrated to form the feedback required for a Q enhanced resonator that is then adjusted in frequency such that k1=0. This reversal in state space is shown in
The optimal determination of the weighting vector of k is based on A and B. A caution is that the state variables are now based on this modified transfer function. Note that assuming the numerator derivative to be in front changes B, and hence changes the weighting vector k as well as the state variables. This may be compensated for in the DPLP feedback processor.
DSP processing may be added as shown in a Simulink model 320 depicted in
While this is a demonstration that the DSP processing is both efficient and simple to implement, the conversion from continuous time to discrete time is not the best approach. It is better to model the resonator in Z domain resulting in a more direct DSP implementation.
A relatively simple example of a continuous time AFF implementation of signal processing circuit 30 in state space is shown in
Inner loop 40 filter may be a bypass such that HLF(s)=1. There is a variable delay 340 of Td with a gain block 342 with a gain of G. There may be a simple DPLP, based on a single pole resonator, that may provide an arbitrary continuously variable delay in DSP that may be modelled as an infinite series of poles plus a gain factor such that arbitrary tuning may result.
The open loop response evaluated on the jω axis is
such that the Nyquist resonance curve (NRC) is a closed circuit of unit radius. The operating point is on the real axis at 1/G such that if G>1 then the operating point will be encircled and the AFF is unstable. For the range of −1<G<1 there is Q enhancement of the set of frequencies where ωTd=nπ where n= . . . −2, −1, 0, 1, 2, . . . . Hence there may be a periodic frequency response with multiple Q enhanced poles and multiple passbands. This is shown in
Next consider a DPLP where the sampling interval is T and the delay is Td=nT. A Simulink model 360 is shown in
The method of analysis is to convert the loop components into Z domain and to approximate the quantization as an independent noise source added at the point of the ADC conversion.
As in the continuous domain there may be an open loop response of
Instead of evaluating on the s=jω axis as in the s-plane the unit circle of z=ejωT may be evaluated in the Z plane. Hence the NRC is a unit circle, and the Nyquist stability analysis may be considered as before. In this case there is no continuous time transfer function in the loop and hence the entire loop may be disregarded as sampled such that the closed loop response is
Note the comparison of the continuous time closed loop response of
which is equivalent provided that 2T=Td. The difference is that the closed loop response assumes a time sampled signal. Hence an equivalent DPLP Simulink model 380 is shown in
The DPLP considered has a delay that is an integer number of sampling intervals, which is preferably variable. One possibility is to implement a delay with a passband response with wo=0.2 (normalized), D=0.1, Td=0.1, and T=1.0. The bode plot of continuous time and discrete time is shown in
A Simulink simulation model 400 of the discrete filter placed in the loop is shown in
With the transfer function of Hd(z) given as
the difference equation may be determined directly. It may be shown that the implementation in DSP involves 5 coefficient multiplications and 5 additions.
In this example, a single continuous time pole (P=1) resonator, or first order resonator, is considered as a Simulink model 420 depicted in
The open loop Nyquist plot is calculated based on converting the resonator into a discrete time sampled transfer function and then cascading this with the discrete time transfer function. The resulting NRC curve is shown in
This two pole DPLP resonator Nyquist resonator curve (NRC) looks similar to a 2-pole frequency space resonator NRC because there are effectively two poles in this DPLP state space resonator: one as a continuous time resonator and the other as a digital domain resonator.
Clearly the continuous time resonator may be tuned and then the DSP resonator/phase shifter may be determined to provide a desired Q enhanced response.
A second resonator may be added to make a second order resonator. A Simulink model 440 is shown in
The open loop Nyquist plot is calculated based on first converting the continuous time resonator into a discrete time sampled transfer function, as above, and then cascading this with the discrete time transfer function. The resulting NRC for this P=2 DPLP is seen in
An RF resonator may be chip integrated or implemented with distributed off-chip components. Consider the fixed frequency resonator for certain applications, represented perhaps as a SAW or a BAW device. The generally passive fixed frequency resonators may perform this filtering task effectively with no power requirements and may be designed to tolerate the large interference signals, albeit at a fixed center frequency.
A fixed frequency resonator may be generally a fixed set of poles—poles which may be Q enhanced or Q spoiled as well as frequency shifted as desired following the above principles. A SAW or BAW has a common characteristic of spectral regrowth which may be mitigated following the above principles.
Further, the SAW/BAW may have several passband poles of moderately high Q. However, an issue with the SAW is that it is difficult to control the passband ripple and slope with frequency. Feedback processing necessary for multi-pole placement becomes unwieldy and unreliable if implemented with RF circuitry. Yet such processing is almost trivial to implement in a digital domain where the signals are digitized. Hence the loop should consist of two domains: the RF domain for the resonator, and the digital domain for the feedback processing.
By using the DPLP feedback, the multiple poles of the SAW may be moved to more desired locations to provide an even higher Q passband response with very small passband variation, and in the process, suppress spectral regrowth as well. The feedback signal in the DPLP loop may also be large in comparison to the input signal.
With the development of very high speed digital processing, ADCs, and DACs, such a mixed signal loop may be practical to implement. A potential weakness is that the transition from the RF domain state space A to the state space domain B may involve frequency down conversion, sampling, and ADC quantization. These processes may have a relatively high noise figure (NF) and may be susceptible to out of band noise.
The resonators remove a large amount of the out of band noise and interference as it propagates in the loop prior to the domain A to domain B transformation components. The transformation of domain B to domain A involves up-conversion, and DACs which may generate significant out of band frequency spurs and quantization noise. This is largely removed by the resonators before circling back to the A and B domain transformations.
As a final example consider the practical implementation of signal processing circuit 30 as shown in
A DPLP pole placement algorithm may then be used to determine the processing required to get the pole placement that will result in the objective passband response. In the Chebyshev case, the objective is a flat passband response over a desired −1 dB bandwidth.
The resulting response is shown in
As another visualization of what the DPLP algorithm is doing for this Chebyshev bandpass filter example, consider
This response, as shown in
Identical methods are used to achieve a Butterworth passband response.
As the number of resonators 462 increases, it may become numerically more of an issue to work with the transfer function in terms of poles and zeros directly. Alternatively, it is possible to work with the Nyquist resonator curve (NRC). The NRC includes all frequency dependent components of the open loop response. Representing the open loop response graphically makes it easier to achieve desired characteristics of the closed loop response by deforming the NRC around the operating point.
Let Hres(z) be the transfer function of the resonators in the z domain. This may be determined directly from the frequency measurements of the resonator or it may be a pole zero transfer function model of the resonator that is converted into the discrete time domain. Hfb(z) is the DSP processing which is an exact representation of what is implemented with the exception of the signal digitization. The NRC is then formed from the open loop response of Hres(z)Hfb(z) which is plotted in the complex z-plane.
The NRC sketched for a one pole equivalent open loop is shown in
The frequency response is given approximately by the inverse of the phasor connecting the operating point to the frequency point on the NRC. As observed here, the phasor length grows as the frequency moves away from the closed loop resonance point. The closed loop resonance point is defined as the intercept point of the NRC and the real axis.
The objective is to optimize Hfb(z) such that the NRC has the desired shape. An example of this is shown in
Combined Frequency Translation and Signal Digitization with DPLP
The DPLP transformation from domain A to domain B may involve both frequency translation and signal digitization with DSP used for feedback processing 48 as an example of the parallel processing paths indicated in
The first step is to create the continuous time model of the resonator that is subsequently converted to a discrete time model as was discussed above and modeled and shown in
Assume uk is the input and partition the model into the denominator part and the numerator part.
Let yk be the output of the first transfer function and define the state variables as
This then sets up the state space of A and B where vk is the output.
Next decide on the Q enhanced poles and determine the k vector. The feedback is given by
The output is observable as vk which is related to the state variable as:
which is expressed in terms of the state variables as:
The advantage of the controller state space model is that the state variables are all direct delayed versions. Hence a simple delay tapped line is implemented. This is shown in a Simulink model 530 depicted in
Next consider the DPLP with two resonators. The same steps as before may be followed to determine the DSP processing that is required. The first step is the continuous time model of the resonator, followed by conversion to a discrete time model. This two pole resonator was previously discussed and modeled as previously shown in
It can be shown that this results in a z-transform model as
The coefficient of ai is always 1 this may be pulled out, rewriting the transfer function as
Now multiply by z−3 to get
Assume uk is the input and then partition the model into the denominator part and the numerator part as
Let yk be the output of the first transfer function and define the state variables as
This then sets up the state space of A and B, where vk is the output. Next decide on the Q enhanced poles and determine the k vector. It can be shown that the feedback is thus given by
The output is observable as vk which is related to the state variable as:
which is expressed in terms of the state variables as
The advantage of the controller state space model is that the state variables are all direct delayed versions. Hence a simple delay tapped line is implemented. This is shown in a Simulink model 540 depicted in
The design principles discussed above can be extended to other architectures that involve a down conversion, such as a bandpass delta sigma circuit. Delta Sigma (DS) is a digital signal processing technique that is incorporated into ADC architectures to reduce the quantization noise in generic receivers. Bandpass DS (BDS) is an extension of DS that may be used to suppress the intrinsic noise of the down conversion process in addition to the quantization noise. A chip integrated version of BDS, such as those that operate above 1 GHz, may be difficult to implement as a resonator with a sufficiently high Q is required, which is difficult to produce using conventional integrated circuitry. Using the variable filter technology of this disclosure, a high Q, stable resonator, such as a resonator with a Q over 1,000, that may be integrated onto a chip.
In the case of a circuit that involves a down conversion, the down conversion may be a significant source of noise. A tunable dual loop implementation for frequency up and down conversion noise mitigation is shown in
Signal processing circuit 30 can provide a notch filter but with input 34 applied at a different point in the loop. This is shown in
Note the transfer function from input 32 g(t) to output 34 port is the same as that of the downstream noise that was considered before. The transfer function will have a notch at the location of the dominant pole of the Q enhanced bandpass filter 42 with filter block 572 and gain block 574. Negative feedback gain 576 will determine the depth of the notch. Note this version is in RF.
There may also be a version that is a baseband processing variant with quadrature sampling as shown in
A notch filter can be used to null out a narrow band interference. It can also be used to form a zero of a complex filter using both poles and zeros, such as an RF elliptic bandpass filter.
As a numerical example, first consider a catalogue variable bandpass whose response is shown in
Note that the optimum bandpass delta sigma axis is coincident with the trough of the NRC at s=0 such that the feedback gain can be larger (to separate the pole from the zero). However, it is difficult to determine this angle so that a practical implementation would have the delta sigma axis at 180 degrees from the peak. That is, the peak may be determined for further Q enhancement easily, but the bandpass delta sigma axis is more difficult. In that case, the maximum delta sigma negative outer loop feedback is less.
Given the NRC, there is a point on the outer encirclement boundary of the trajectory that has maximum modulus referenced to the origin, and a point that has minimum modulus as referenced to the origin. For the NRC of a SAW that is Q enhanced, these points are roughly on opposite sides. The maximum is suitable for positive inner loop feedback Q enhancement, and the minimum is suitable for Q spoiling in the negative feedback outer loop.
Next a modest Q enhancement is applied by a factor of Qen=10. The closed loop NRC is shown in
The bandwidth of the STF can be restored by increasing this signal reinforcement gain of the inner loop. However, the zero gets pushed toward the jω axis for a narrower notch. To widen the notch bandwidth, a second order bandpass delta sigma may be implemented providing two poles and two zeros. Further widening of the notch bandwidth is achieved by implementing a higher order bandpass delta sigma.
The loop can be expanded to two poles such that there are two signal-reinforcement Q enhanced poles that can be realized in the upstream receiver. The negative feedback loop can have two loops also as described above.
As discussed above, the bandpass filter 42 of inner loop 40 (or resonator A(s) or block 92 of upstream processing 91 shown in
Acoustic wave SAW/BAW devices will now be discussed, and in particular the SAW which is analogous to a BAW.
For the dual loop, this SAW filter network is part of bandpass filter 42 and may include a saw filter 642, a gain block 644, and a phase shifter 646. A positive reinforcement feedback loop 45 may be provided around this which will do two things:
To achieve a deeper notch of the downstream receiver noise transfer function a higher negative feedback gain is required. By shaping the NRC of the closed loop upstream receiver stability can be assured.
An acoustic resonator, such as a SAW, may provide high frequency selectivity as bandpass filter 42. The NRC of the SAW is generally not suitable for outer loop 50 noise shaping as there are several poles. However, the SAW response can be Q enhanced with an inner loop 40 and then the NRC will change sufficiently such that the negative feedback can be applied with arbitrary gain for an arbitrary level of suppression. A block diagram of a SAW implementation as the resonator in the upstream receiver is shown in
SAW filter 642 can be any bandwidth SAW filter where the passband includes the passband of the desired signal. Referring to
In the quadrature sampling, the signal phasor of real and imaginary components is extracted. This is multiplied by a complex number with a real and an imaginary component. The resulting phasor is changed in both angle and magnitude which is regarded herein as complex scaling. The resulting phasor is then converted back to RF with a quadrature DAC 56 and frequency upconversion 652.
The system in
The concept of a tunable bandpass sigma delta will be described in detail below.
By way of an example, a Taiwan Semiconductor Manufacturing Company (TSMC) SAW will be considered.
Next consider the signal reinforcement applied to the SAW filter in the positive feedback inner loop at the frequency of maximum modulus. The inner loop gain is denoted as G and is real. This corresponds to the loop gain when all the other components in the loop have unity gain at the frequency corresponding to the maximum modulus of the open loop NRC. In
The NRC may be adjusted to be more circular and with the origin moving closer to one side of the outer encirclement of the NRC for a specific frequency within the general passband of the SAW. In
The frequency plot of the Q enhanced SAW is shown in
Next, the outer loop of the negative feedback is added in, and in particular, the signal transfer function (STF) from the input to the output of the outer loop, and the noise transfer function (NTF) that is from the output of the inner loop Q enhanced SAW to the output of the outer loop.
In
In
To narrow the signal passband, the inner positive feedback loop gain can now be increased. In this case it is increased to G=0.93. The NRC of this further Q enhanced SAW is shown in
A point of emphasis is that both loops can be jointly and collaboratively adjusted to achieve the desired reduction of noise, as well as the desired narrow passband for the STF.
The desired signal is referred to herein as S with the interference and noise as N. As shown in
A problem is that the digitizer block A has
Hence some of the information of S is destroyed as it passes through the transformation of the digitization A.
In more abstract terms, the input to the digitizer A is a continuous signal of an infinite number of different states. The output is a finite number of discrete states. With large N, most of these states are used to map the variability of N with only a few effective output states of A for mapping S. Hence much of the information of S is lost. As a tangible example consider the digitizer A to be an ADC that samples the signals with Nq quantization levels. The mapping is of the input continuous signal of S+N to the output discrete category. The mapping of the infinite number of continuous states to the finite Nq categories represents a loss of information. To see this, if N>>S then the entropy or uncertainty of the mapping of S to the output category is large. Therefore, the mutual information between the input S and the ADC output is low. Herein, mutual information refers to a 1:1 correspondence between sender and receiver on a bit level—sender and receiver mutually agree that the bit sent is identical to the bit received.
In the digitization process, there is a mapping of a region of the continuous signal space to the quantized output that is irreversible. Once the region has been collapsed into one output category this cannot be undone and there is loss in the mutual information. This loss in mutual information can be quantized.
To illustrate this, consider the difference in the receivers in
In both circuits, A is responsible for the information loss because of quantization noise. After the quantization of A, it is possible to construct a DSP wherein further loss in mutual information is negligible.
For
The argument being made is that the process that does the mapping from the continuous valued signal to the discrete valued signal is the key component where mutual information is irreversibly lost. Generally, the quantizer may be thought of as an ADC with Nq levels. However, it can be more:
However, the concept is straight forward: take a signal in continuous time and continuous amplitude and map this into a finite number of discrete categories in the digitization process.
The objective is to apply this abstraction to the signal processing circuit 30 such as shown in
The best that can be achieved is a continuous time matched providing a filter output symbol that corresponds perfectly to the symbol of the incoming signal. As an example, consider BPSK that is uncoded and a single bit ADC used. The mutual information loss of the ADC can be zero in this case (depending on the probability density function PDF of S and N). The matched filter provides the signal conditioning, or the ‘protection of the ADC’, such that there is no loss of mutual information in the ADC, and this is for an ADC that is only a single bit.
The ADC may be fixed with a given sampling rate and a fixed number of quantization levels. The BPF resonator may be of fixed modest Q with a bandwidth that is broader than that of S.
Consider that the signal out of BPF 42 can be recirculated back to the beginning for a number of times as shown in
The effect is to reinforce S with the positive feedback so that it grows in amplitude at the output of the BPF while N only grows where it is in-band. By controlling the amplitude gain of the feedback signal the effective number of times that S goes through the BPF may be effectively controlled. Hence into the quantizer A S is added to S that has gone through the BPF twice and S that has gone through the BPF 3 times and so on up to the effective number of circulations. This is roughly equivalent to the Q enhancement of the feedback resonator BPF that will be denoted as Qe. Note that N is limited to about one pass through the BPF as the subsequent passes contribute much less. However, the spectral portion of N that is within the BPF close to fc will become enhanced just as S is.
The benefit is then that the quantization levels of A can be adjusted to best accommodate the larger S. With the reinforcement, S has grown relative to N such that the quantization is dominated by S. Note the limit of this can be that the passband narrows as Qe increases to the point that some of S is lost at the outer band edges of S. For an isolated symbol of S there is actually no loss of having an arbitrarily high Qe implying a very narrow bandwidth that can be less than the bandwidth of S. However, when a consecutive stream of symbols is considered, this is no longer true as the symbols will begin to mutually interfere. This conflates adjacent symbols leading to information loss.
To avoid this loss, multiple BPF resonators may be used.
An issue is that the recirculating BPF requires gain which comes with noise. Also, the loss through the BPF represents a NF (“noise factor”) due to the thermal noise affecting the components in the loop. This in-band thermal noise is amplified in the same way by reinforcement as S. Hence the NF may be minimized so as not to erode the mutual information of the filtered version of S.
Nonlinearities are interesting as they do not directly lead to information loss. Hence, gain compression that is just a new mapping of S to the output can be had. However, the compression does not result in a conflation of states by itself. However, if the compressed signal is such that quantizer results in conflation of states then there is a loss in information. Also, different frequency components of the signal can be considered. As these are mixed due to a nonlinearity then this is equivalent to conflation of states again leading to information loss
A limitation is that S also sees the feedback path which spoils some of the gain such that the bandwidth of the BPF is effectively broadened. However, it is a balance of the Qe and positive feedback gain G. This can be quantified by evaluating the transfer functions.
This may be extended to having more than one resonator in the loop. Consider two BPFs in series. If the BPFs are at the same center frequency, then one frequency will be emphasized slightly more than any other frequency. After Qe times through the loop then this frequency component will be strongly emphasized, and the overall Q enhance response will appear as a single pole.
If the BPFs are the same then this is roughly equivalent to going through one BPF 2×, 4×, 6× . . . Qe2× as opposed to 1×, 2×, . . . Qe×. Roughly this is equivalent to having a single BPF but with twice the Q.
If the BPFs are tuned differently, they will still not differ that much as the BPF bandwidth is assumed to be much broader than the Q enhanced bandwidth. Hence there is still going to be one frequency with slightly higher gain that the rest.
If a two pole response is desired, two loops may be used, one around each BPF 42 as in
Now assume that this second order filtering with first and second BPFs 42 are such that the feedback loops favor two different frequencies. Now it can be seen that the Q enhanced response will result in a two pole response. The poles can be placed favorably as described above.
For now, just assume that the two loops are identical. S going through effectively (roughly) Qe BPFs in series and then will go through Qe BPFs in the second. Again, roughly equivalent to the single BPF having twice the Q. By this approximate equivalence it can also be seen how the overall response can be a two pole response if the BPF loops are tuned slightly differently.
Now consider the negative feedback of the error signal shown in
This gives effectively a double integration of the error signal as the negative feedback goes through the two BPFs 42. To get better control of the negative feedback, the negative feedback 576 can be input at both sum blocks 780 as shown in
This architecture can be generalized into N BPFs 42 with positive feedback and the N negative feedbacks 576 as shown in
For the higher order loops, the feedback analogy still applies as it is evident that N passband poles can be placed arbitrarily with tuning. The concept of the negative feedback of the quantization error can be seen to cancel the injected quantization error with a rough equivalence of N integrations. Hence the more BPF poles that are transformed into zeros, then the more control may be had over where the quantization noise is nulled in frequency.
Redrawing
Here the input is the sum of the desired signal 782 denoted by S which is assumed to reside within the passband of the bandpass filter. The interference and noise signal 784, denoted by N which is assumed to be distributed over a broader range of frequency that S. These signals propagate through band pass filter (BPF) 42. The output of BPF 42 is digitized in the ADC 54, which may contribute quantization noise, and then there is DSP 52 to extract the information from desired signal 782.
The only purpose of the receiver is to process the combination of S and N such that information 832, denoted by I, can be extracted. This information I is related to what is unknown about S that is of interest. For example, in a communications signal sending a sequence of symbols. The symbol carrier frequency fc, symbol shape (and hence its frequency bandwidth) is known. The amplitudes of the symbol corresponding to different bit values are also known. What isn't known is the bit value of the symbol which carries this information. Hence all the processing of the receiver is about abstracting I from the receiver input sample of N+S and I in this case is the bit value.
Given {S+N} there is the theoretical mutual information of IM which is less than I. That is, I is the information of S that could be extracted if there was no N. However due to N there is residual uncertainty in the information abstracted from S which is IM. Note that IM is independent of the receiver processing and that the actual information abstracted from S by the receiver, denoted by IR is less than IM. The optimum receiver is one in which IR=IM. The inefficiency of the receiver is the loss in the information such that could form a FOM of the receiver as FOM=IR/IM. It is necessary to consider the impairments of the receiver components as they contribute to the degradation of the FOM. This leads to the impairment budget for the receiver that lets to tangible specifications for the receiver components. However, the receiver architecture and processing should be evaluated based on the degradation of the FOM and not on an individual specification such as linearity and noise figure.
The performance or merit of the signal processing circuit 30 architecture of
Note that for a practical realization of the positive and negative feedback loop, the loop gain and frequency response has to be designed and managed. Hence positive feedback and negative feedback are concepts related to signal enhancement or reinforcement and loop noise suppression respectively. The output of ADC 54 also goes to a processing block, such as DSP 52, that extracts the information of the signal. Also, BPF 42 is general in that it could be a resonator, multipole filter, filter with poles and zeros. The only real requirement is that it does not have a null within the passband of the desired signal of S and it has some amplitude and phase variation with frequency. It could be for example a delay line with only variation in phase with frequency and no amplitude variation.
In
The dual loop concept can be generalized such that there are two types of receiver self-noise that affects the degradation of the FOM. These two types will be denoted here as the upstream and the downstream self-noise. Noise that is generated upstream from the tap point of the positive feedback loop is upstream noise 844 (Nu). Noise that is generated downstream of the tap point of the positive feedback loop is downstream noise 846 (Nd). The Nu noise that is outside the bandpass of S can be reduced by the positive feedback loop. The Nd noise that is within the bandwidth of S can be suppressed based on the negative feedback loop. This is illustrated in
This can be generalized further as BPF 42 can be any of the filter components prior to the loop tap point 842 or upstream from the loop tap point 842. It may therefore be assumed an upstream receiver that encompasses BPF 42. Again, as long as the upstream receiver has some phase variation with frequency it can respond appropriately to the positive feedback loop. The upstream noise is N+Nu and Nu can be absorbed into N which will be assumed moving forward. Downstream components 850 can be the remaining receiver components which can consist of further filtering, ADC, frequency translation and so forth. ND is the equivalent noise source being the superposition of all of these sources of downstream noise 846. This is shown in
Signal processing circuit 30 may have a general architecture that has an upstream receiver portion and a downstream receiver portion separated by tap point 842. A signal reinforcing positive feedback path 45 is around the upstream portion and a negative feedback path 55 is around the upstream and downstream portions with a downstream tap point 852 at the output of the downstream components 850.
A further generalization is that the DSP processing block 52 operating on the digitized signal can have two general outputs: one optimized for the negative feedback path 55, and the other being the output leading to the information extraction of the signal S. The equivalent downstream tap point 852 may therefore be within the DSP processing block.
However, the operation of the negative feedback loop is to suppress noise generated within the downstream receiver. The subsequent DSP that takes advantage of the noise suppression also has to pass through downstream tap point 852 of where the feedback signal is taken.
However, there may be additional processing between downstream tap point 852 and the DAC that is not necessarily shared with the processing for the extraction of the information. Therefore, the DSP processing becomes split into two portions. There may be two separate DSP elements incorporated herein. It is possible to perform both functions within a single physical DSP, but the logic would be doing two different functions.
A final generalization realizes that the upstream portion of signal processing circuit 30 may be subdivided with multiple tap points 842 and a sum block 780 at the tap points 842 where portions of the positive and negative feedback loops can be fed back to the input signal loop. This is shown in
The mixed signal processing may rely upon both positive and feedback loop, with the BPF sharing a common leg of both loops:
The essence of the disclosure is the apparatus of these two nested mixed signal processing loops and the methodology of how to use them. By balancing these two loops the information of the desired signal can be optimally preserved.
An efficient anti-aliasing filter (AAF) 870 with decimation is the cascaded integrator comb (CIC) filter 872, an optimized class of finite impulse response (FIR) filters combined with an interpolator or decimator. An example of a CIC 872 implemented architecture is shown in
The advantage of anti-aliasing filter 870 is that the integrators are simple to implement and require no overload logic. The CIC 872 implementation can be generic as there are few configuration parameters to vary. However, the few configurable parameters also implies that the filter is not very tunable for specific RF signal modulations. Additionally, it is located after the ADC 54 which does not reduce the ADC 54 processing load. Hence this is limited to the AAF implementations which have to be highly efficient and are generally followed with an equalization filter post-decimation. As will be discussed below, the complexity of this CIC implementation may not be warranted.
To implement rudimentary receive side anti-aliasing in current DSDR architectures, one can add low pass filters (LPF) before the ADC of the DSDR architecture of
Note that antenna 12 is not effective for low frequencies and hence the combination of the antenna and LPF in the receive side provide a broad bandwidth filter prior to digitization. In the transmit side of
Additionally, on the transmit side, the system DSP 20 of
The positive feedback loop of
It may be advantageous to have the anti-aliasing filter at baseband as complex coefficient multiplication is not required and it is the pre-decimation operations that generally dominate the overall DSP related power requirements, although the CIC integrators are very efficient and can be used in general. However, this is not always possible due to band mapping in the down conversion that can be a significant contributor to overall noise. The final decimation ratio can be high enough that subsequent DSP is at a much-reduced clock rate and hence less of a concern in terms of power dissipation.
An attribute of the positive feedback loop is that it can form the stable high Q pole necessary for avoiding all aliasing noise and reducing the band mapping complexity prior to down conversion using an anti-aliasing filter, is the use of band-folding illustrated in
Band folding is based upon the Nyquist frequency Nf=1/Δt, where t is the time increment between observations. Note that the Nyquist frequency is a property of a discrete-time system, while the Nyquist rate is a property of a continuous-time signal.
Any accumulation of excess noise in the folding can be looked at. In the ADC sampling where frequency bands that are multiplies of the sampling frequency are folded, the sampling output is a superposition of the aggregate of these folded bands. However, as only one of the folded bands contains signal, there is no accumulation of excess noise.
To avoid aliasing noise, it is necessary that:
Hence the ADC does not have to expend additional quantization and dynamic range on these unwanted signals.
The limitation with
Every DSP operation prior to bandpass filtering to remove the out of band frequency content will add quantization noise and will degrade the dynamic range. Hence these initial DSP processing steps can be very intensive.
On the transmit side, the signal samples are generated at the RF passband and converted to analog. This is a highly intensive DSP process because the DAC only has the subsequent LPF to remove conversion artifacts. Hence the DSP and DAC may process samples of low quantization noise which again implies a moderate number of bits. This limits the processing of
For the objective SDR to become a reality, without excessive performance required of the ADC, DAC and DSP, typically a dynamic range, a tunable narrow passband filter architecture is desired which provides active Q enhancement that is robust and stable to enable desired signal extraction and mitigate nearby interferers.
The upstream signal loop may be programmed and controlled to provide an arbitrarily high Q of several thousand. Hence, all the filtering can be done in this tunable high Q bandpass filter to isolate the desired signal and eliminate all of the out of band interference, prior to band digitization and the DSP.
The distortion of the SH and gate clock jitter become very critical in realizing an SDR of acceptable performance. The matched filter output will have a high rate of change of signal voltage with time (dv/dt) during the aperture time. This requires a very short aperture time for adequate sample definition which significantly restricts the clock jitter that can be tolerated. For instance, take a GPS signal wherein the bandwidth is about 1.2 MHz, and the data is at a 50 Hz rate such that T is 20 msec. With a suitable SH capable of operating at the carrier of 1.5 GHz, the ADC and DSP can be provided by a very slow processor such as an Arduino as the symbol rate is only 50 Hz. However, if the signal were to be sampled at the rate of 1/T, the dv/dt at the sampling point is related to a signal with a bandwidth of 1.2 MHz. Hence the aperture time of the ADC sampling the baseband GPS chip level matched filter output can only be several 10s of nsec. But this requirement pales in comparison with the 1.5 GHz carrier rate in the DSDR that changes significantly in a few tens of psec. It is the aperture time jitter that ultimately limits what can be achieved with reduced rate sampling.
Referring to
The LO shown is an impulse train at the same rate as the carrier. The jitter is independent from one LO impulse to the next which leads to voltage noise in the samples of (dv/dt)dt. However, as these are independent then in the LPF following the downconversion, the jitter is averaged out. As an example, consider a carrier of 10 GHz and a LPF bandwidth of 10 MHz. Then the down conversion is equivalent to an averaging of 1000 jitter sourced noise samples leading to virtually an elimination of the sampling jitter issue. The remaining noise is the low frequency phase noise of the LO clocking.
Jitter reduction may also be achieved by oversampling the ADC. This is the same function as the frequency down conversion. Say the 10 GHz carrier signal is sampled at 10 GHz and then average the ADC samples and decimate. Again, there are 1000 samples of jitter sourced noise that is averaged for an elimination of the jitter noise.
But an over-sampling ratio of 1000 is generally excessive in terms of eliminating jitter noise. Instead a reduced ADC sampling rate of say 1 GHz for a 100 sample averaged may be considered. Hence the RF BPF can be set to only include the 10 MHz bandwidth of the desired signal. This eliminates any excess noise due to band folding. The ADC sample rate can be set as low as 1/T if the upstream signal loop may be a sufficient matched filter and if sampling jitter is not a problem. If jitter is a problem, then the ADC rate can be increased such that sufficient averaging of the jitter can be achieved to meet a specification. This specification is going to be loose for simple modulations such as BPSK (Binary Phase Shift Keying) and QPSK (Quadrature Phase Shift Keying) but tight for complex QAM constellations of high order.
Consequently, the upstream signal loop may potentially provide an adequate matched filter response such that the sampling rate can be as low as 1/T. For cases where sampling clock jitter is an issue, the ADC sampling rate can be increased beyond 1/T to allow for sample averaging. Also, the upstream signal loop may be used in conjunction with an LO down conversion prior to the ADC sampling which achieves a similar effect. As an example, the LO down conversion to a baseband signal and commensurate ADC sampling is equivalent to high-speed sampling at once per RF cycle and then averaging with a ratio of the carrier frequency to the bandwidth of the desired signal. In other words, the inclusion of the upstream signal loop in the DSDR allows for setting the ADC sampling rate depending on the clock jitter reduction required to help meet overall SNR requirements, more typically expressed as the Eb/No requirement.
There is more to the matched filter concept in that the quantization requirements of the ADC can be significantly reduced. Consider BPSK as an example where it is of interest if the symbol amplitude is positive or negative. Referring to
In more sophisticated receiver processing, coding would be applied over a set of BPSK symbols. For higher performance it is necessary to use schemes such as soft decoding and in this case the ADC may be needed that has a few quantization levels. An AGC feedback is required in this case. However, the number of ADC levels is no larger than the advantage gained by the soft decoding. That is 4 levels of quantization may be sufficient and that adding more is diminishing returns. Also, if jitter is excessive then a down conversion can be added in front of the ADC eliminating this issue, or simply sampling the comparator faster and averaging.
Next consider QPSK which is just two orthogonal channels of BPSK. A 2/T aggregate sampling rate may be used to provide for the quadrature sampling required. This can be conveniently implemented with a hybrid device at the output of the upstream signal loop that gives the in-phase and quadrature phase components. For the QPSK comparators can still replace the ADC as the base signal is BPSK. Extending this if an N by N QAM constellation is considered then only an N level ADC is need of log2(N) bits.
QAM modulation is very common for high rate communications signals. For such schemes there is information impressed into the amplitude and single bit quantization is not sufficient. However, the ADC can be implemented for a QAM scheme wherein the number of ADC levels is equivalent to the number of QAM levels. Hence for 64 QAM only an 8 level ADC and DAC is necessary with is 3 bits. This can be achieved with a high speed flash convertor, an example of which is shown in
A key point is that the upstream signal loop may be a resonator that is sufficiently narrow that only the desired signal, with some in-band noise and interference, makes it to the quantizer. The symbol decoder is therefore the output of the quantizer/accumulator/decimation process. If equalization is required for minimizing ISI and providing a matched filter response, then the upstream signal loop can be tuned directly. In this case, an additional DSP based equalizer may not be required.
There exist modulation signals where such an ADC/DAC with few fixed quantization levels is not sufficient. For example, consider the LTE modulations where multiple signals are superimposed, and the signal amplitude sample has more of a gaussian distribution. For such signals, more quantization levels may be necessary especially if the SNR in-band is quite high. In this case the quantization noise may become a dominant contribution to the overall noise and unrecoverable distortion which is undesirable.
In summary, the reduced sampling rate of 1/T has been considered while the carrier frequency can be arbitrarily high. The Jitter issue with the noise sensitivity of (dv/dt)dt has been considered as a limitation. A further limitation that needs consideration is the sample and hold (SH) device. There are practical limitations in the SH as the ratio of the sample hold time to aperture time cannot be arbitrarily large. Advanced SH devices use a cascade of switches and holding capacitors to increase this ratio but with the penalty of contributing to the overall sampling noise and distortion. As the ratio becomes large it may be necessary to use a faster ADC with an aperture time that is commensurate with the limitations of the SH.
Once the faster ADC is included then the sampling rate can be increased at the modest expense of a faster DSP clock. A multi-stage circuit 940 for increasing the ratio of hold time to aperture time is shown in
While the matched filter can in principle be achieved with a set of poles of the upstream signal loop, there may be limitations. Creating an all-pole approximation to the root raised cosine filter is achievable but creating a barker code impulse response of a spread spectrum signal is not possible without zeros. Zeros can be generated in the upstream signal loop by placing some components in parallel. However, controlling the position of the zeros may be difficult. Hence the matched filter may be split into an analog and a digital component. Take the Barker code as an example. The matched filter corresponding to the chip is done in the upstream signal loop and the barker correlation is done in the DSP. The sampled bandwidth in this case is the chip rate and not the symbol rate.
Consider the spread spectrum code as consisting of a small segment convolved with a larger segment. A simple example is the Manchester code which is often used to guarantee a zero average value regardless of the data. An example is shown in
Consider a communications receiver where there is an incoming data modulated symbol which is subjected to noise and interference. The receiver needs to process this signal by aligning to the symbol component of the incoming signal while remaining ideally orthogonal to the noise component. This is easily visualized in the signal space where the processing of the receiver is along the symbol basis function. The noise is assumed to be equally distributed over all the orthogonal signal basis function of the signal space. This leads to symbol correlation in the time domain and a frequency matched filter in the frequency domain perspectives.
The most complex symbol of phase and amplitude data modulation of duration T implies the minimum sampling rate of 1/T. Note that the symbol time is not necessarily inversely related to the bandwidth of the individual symbol pulse shape signal and can, in fact, be less. For example, a spread spectrum coded symbol as used in CDMA can have a significantly larger bandwidth than 1/T.
An additional utility of the disclosed architecture is that the poles of the upstream signal loop may be positioned such that the frequency response or impulse response of the filter is matched to the data symbol resulting in a matched filter as discussed above. The ADC can sub-sample at the lowest possible rate of the data signal symbol rate. Note that the symbol rate of 1/T can be lower than the actual Fourier bandwidth of the data symbol itself. However, this low sample rate is only possible if the RF filter is precisely centered on the desired signal. Such accuracy is achieved with the upstream signal loop through calibration and run-time adaptive feedback tuning.
Removal of Self-Generated Processing Noise from RF Signal Processing Using a Negative Feedback Outer Loop
There will be considered a dual loop architecture as described above and depicted in, for example,
The positive feedback loop (or upper loop 40), which may consist of multiple resonators, may act as a tunable bandpass filter based on active feedback. Loop components may have a high linearity when based on switched reactive components, in comparison with varactors that may introduce non-linearity effects. The resonators are placed upstream of the down conversion and ADC which are vulnerable to large out of band signals and broadband noise. The resonators may be operated to provide poles of moderate Q of around 100 that provide for very effective bandpass filtering to suppress most of the undesired noise and interference entering the down conversion and ADC.
Turning to the negative feedback loop of
For reference, signal processing circuit is shown in
The key aspect of quantization noise removal may be to implement a variable bandpass delta-sigma modulation approach which moves the quantization noise out of the signal frequency band. Delta-sigma modulation (DSM) is a well-known fixed frequency scheme.
Down converting the signal+noise input to baseband yields the baseband delta-sigma with an integrator providing a pole at s=0 is prior art. When operation of the direct sampling is shifted using a bandpass filter with a center frequency of fc, the integrator is now replaced with a resonator centered at frequency fc. This results in a bandpass delta-sigma modulator (BP-DSM).
A problem for a broadband BP-DSM to get a tunable resonator with sufficient Q. Because current BP-DSM implementations are at fixed bandpass center frequency and thereby not tunable, the BP-DSM is not currently used at RF/microwave frequencies. However, the upstream loop changes this when provided with a tunable resonator that can change frequency while providing a high and stable Q independent of the frequency change. In this implementation, the resonator may be shared by both the positive feedback and the negative feedback loop, creating a variable bandpass frequency delta-sigma modulation (VBP-DSM) scheme 970.
Referring to
A feedback path may be used for implementing a variable bandpass delta-sigma. In this case the pole of the upstream signal loop becomes a zero of the QNTF. The movement of the dominant resonator poles in the VBP-DSM is illustrated in
It is important to note that with negative feedback (Q spoiling) the pole may be moved to the left, hence separating the upstream signal loop pole from the zero. The system effect of the negative feedback loop will be further discussed later.
The effect is that the QNTF zero now reduces the response in the middle of the passband. As also observed is that it is necessary that the pole has a high Q prior to forming the feedback loop. This is what limits the application of delta-sigma. However, with the upstream signal loop, the Q may be increased such that the QNTF zero becomes relevant.
Consider the VBP-DSM with a general bandpass filter of
The closed loop response of the filter is given as
where G denotes the feedback. The transfer function of the quantization noise is given as
which shows the poles of the filters being mapped into the QNTF zeros as discussed before. However, consider the ratio of the closed loop signal to the quantization noise:
which is just the filter transfer function that is independent of the feedback level G. It can be seen that increasing G decreases both a) the level of the signal reaching the ADC as well as b) the quantization noise. Hence the important result that the VBP-DSM allows a reduction of the signal level into the ADC without an increase in the effective NF of the receiver.
The negative feedback loop will nominally have a very narrow passband. Hence the analysis can be simplified as an equivalent complex envelope analysis. The integrator pole is shifted from the origin along the real axis into the LHP.
As the upstream signal loop pole is moved more to the left with the negative feedback, then the efficacy of the delta-sigma in terms of reducing the quantization noise is reduced. In this case:
with simulation results shown in
Adding in saturation of the ADC mitigation, as discussed below, there is a Simulink model 1020 of
Next consider how the negative feedback loop is implemented to realize a first order VBP-DSM 970 with one upstream signal loop 972 as shown in
Clearly the ADC/DAC do not have to be direct sampling and may include frequency translation, with the following considerations:
A second order loop with two upstream signal loops 972 is possible as shown in
With the saturation at 0.5 and −0.5, and the input gain set at 0.5, the second order loop provides good attenuation of the quantization noise as shown in
Add an AGC-like control that that operates to reduce the gain if saturation of the ADC is sensed. As before, the gain is reduced ahead of the ADC which has the same effect as increasing the quantization step but allowing the saturation level to increase.
Next consider the possibility of adding additional poles in H(z) in the ΔΣ. Let
be the delta-sigma filter that is mapped into the s domain. Now the signal path is given as
Now the QNTF is given as
From this it is clear that additional zeros in the QNTF can be contributed by the VBP-DSM filter. Also, the ratio is
as before. Hence, additional poles may be added in the VBP-DSM filter that will provide different closed loop responses without affecting the ratio of the input signal level to the quantization level. This provides additional design flexibility.
Delta-Sigma Modulator with Variable Frequency and Q
The dual loop circuit may be represented by upstream signal loop 970 acting as a BPF with a positive feedback gain 1072 (G>0) in the feedback path 1074, and a negative feedback loop 974 as shown in
The ADC may optionally be direct sampling which does not require down conversion. In this discussion, direct sampling ADC has been assumed for most of the analysis. However, this can imply a down-conversion prior to the ADC. There are several variations possible that may also be included in the analysis and development of a dual loop architecture. As discussed, the principle of the dual loop may be considered independently of how the down conversion and digitization is done. Therefore, what is considered for direct sampling may also be applicable for a general down conversion and digitization scheme.
Upstream signal loop 972 also provides the required bandpass poles of moderately high Q that are necessary for implementing a VBP-DSM 970 loop. The main objective of VBP-DSM 970 is to suppress the quantization noise of the digitization process within the narrow band of the desired signal. This is achieved by actually shaping the noise spectrum of ADC 54 quantization noise to frequencies outside of the band of the desired signal.
In an ideal case, an effective VBP-DSM 970 with further Q enhancement of the resonator poles would simultaneously result in higher frequency selectivity of the desired signal. However, to achieve the desired noise spectrum shaping, Q spoiling of the upstream signal loop components may be required. Hence the proposed VBP-DSM implementation may be considered a compromise with a primary objective of achieving the highest SNR output of the digitization process possible. The dual loop may use the negative feedback loop DSP filtering to achieve the final passband shaping of the desired signal, as will be discussed.
The generalized dual loop architecture 1080 may be as shown in
VBP-DSM 970 may be used to shape the noise of the components after upstream signal loop 972 so that they are outside of the bandwidth of the desired signal. This may result in a much lower NF of this section of the circuit. With this, the signal level into this portion of the circuit may be reduced by scaling the overall signal. This is the function of scaling block 1084 in
The analysis of VBP-DSM 970 may be difficult due to the mixed signal modelling required. This is simplified by approximating the bandpass operations as equivalent baseband below. This allows for efficient time domain simulation. Secondly, the nonlinear behavior of the digitization process can be linearized allowing for Laplace LTI analysis. This is the first step is to justify the baseband modelling as representative of the variable bandpass dual loop system. Then the baseband VBP-DSM can be described by introducing the simultaneous transfer function of the signal and the noise and considered as a first and second order VBP-DSM in the negative feedback loop of the dual loop architecture.
In this section the equivalence of a bandpass pole as a first order low frequency pole will be considered to justify the baseband model as being used to represent the bandpass system of the variable bandpass delta-sigma. Consider the input impedance of a parallel RLC resonator which is given as
Specifically consider the expansion around ω=ωo+Δω. This may be written as
which can be approximated as
which is valid provided that
Hence this approximation only refers to operating around resonance and not the Q of the pole itself. Using since
which can be simplified as
Finally normalize this as
which is only dependent on the bandpass pole parameters of {ωo, Q}. Hence the bandpass pole at
is equivalent to the low pass pole at DC. Consider the expression of
Hence the pole is on the negative real axis at
which is expected.
Referring to
From the perspective of the ADC quantization noise, the transfer function is H(s)=s/(s+G), and from the input signal perspective, the transfer function is H(s)=1/(s+G). Hence the ratio of the signal to noise transfer functions is 1/s. Note that this ratio is independent of G. This hides the fact that the signal bandwidth increases with a decrease in the VBP-DSM negative feedback loop G as the negative feedback loop BPF pole moves away from the jω axis.
In an example shown in
The limit of G<0 can be seen when delay is included in positive feedback loop 1100. To analyze this, it is necessary to switch into discrete time analysis where the pole trajectory would eventually cross the unit circle and the positive feedback loop becomes unstable.
Positive feedback loop 1100 provides a narrow band Q enhanced pole for input signal 32, thus protecting ADC 54. For the quantization noise of ADC 54, it provides a zero close to the jω axis which is effective in reducing the quantization noise around the band of the desired signal.
Consider what this means for input signal 32. There is positive feedback loop 1100 at the top in parallel with negative feedback loop 974 at the bottom. Therefore, the net Q enhancement can remain the same if the feedback loop 1100 is compensated for the gain of negative feedback loop 974. It is the total feedback gain that is of significance as the pole is being pushed toward the jω axis. This becomes the zero for VBP-DSM 970 and negative feedback loop 974. In other words, the dual loop allows for independent control of the position of the pole and the zero.
The positive feedback loop 1100 gain can now be greater than 1. Without negative feedback gain 576, a positive feedback loop gain G>1 would become an unstable feedback loop and oscillate. The outer negative feedback loop gain can be increased from a low value to a higher value such that the oscillation ceases. This provides a zero that can be close to the jω axis and a pole that is moved away from the jω axis giving the required and stable bandwidth for the desired signal.
The outcome of the previous section was justification for modelling VBP-DSM 970 as the baseband delta-sigma module (BB-DSM) provided that the Q of the bandpass pole is sufficiently high. This is convenient as the BB-DSM is easier to develop and analyze. Consider first a continuous time loop 1110 as shown in
Let the Signal Transfer Function (STF) denotes the transfer function from the input to the output and let the Quantization Noise Transfer Function (QNTF) denote the transfer function from the source of the quantization noise at the output of the ADC to the output port.
There may be considered an arbitrary mapping in the ADC and DAC from analog to digital and digital to analog each with a gain of 1. There is then an additional loop gain associated with the integrator such that the transfer function is G/s. Based on this the transfer functions can be written as.
Hence the STF is a first order low pass filter with a pole at s=−G and the QNTF is a high pass filter with a pole also at s=−G. The important bit is that the QNTF has a zero at s=0 (refer to
This is the central concept of VBP-DSM which is simply that at low frequency the signal passes through with no loss while the quantization noise is suppressed.
At higher frequency though, this desirable characteristic fades. Therefore VBP-DSM is applicable where the ratio of the ADC sampling rate to the Nyquist rate of the bandpass signal is large.
In the STF and QNTF for continuous time given above, if G increases then the pole moves along the real axis into the LHP and the cut-off frequency increases. Hence the frequency region over which the VBP-DSM is effective increases. However, the limitation is the ADC sampling frequency.
Now consider a signal g(t) at a frequency of ωs<<G and interference v(t) at ωv<<<G such that both components are passed through the loop with unity gain. Hence the output will be approximately g(t)+v(t). The noise added is q(t) but this is attenuated by approximately ωs/G at the signal frequency and ωv/G at the interference frequency. It may be assumed that there is subsequent filtering after the VBP-DSM loop to remove the higher frequency interference.
The point here is that the VBP-DSM is not about suppressing the interference relative to the desired signal. Rather it is about suppressing the quantization noise at the frequency of the desired signal. The actual form of the quantization noise at the interference frequency may be disregarded as it can be assumed that a subsequent DSP band pass filtering around the desired component suppresses the interference.
Next the approximate equivalence of the integrator may be considered as being replaced by the discrete time accumulator. This is done with the mapping as
which has a pole at
For the QNTF the zero remains at z=1. In a real ADC, there is a latency with the conversion such that an additional z−1 may be included in the open loop transfer function:
which has a pole at z=1−GT.
When GT exceeds 2, the pole exits the unit circle and the VBP-DSM at that point becomes unstable. Also, it should be clear that the effect of the zero in the QNTF at z=1 only has effect for frequencies that are low in frequency relative to the sampling frequency.
First Order Delta-Sigma Example with Signal Sampling at 100 Hz
The following is an example of a first order VBP-DSM with a sampling rate of 100 Hz and an ADC that quantizes at a resolution of 0.2. Four input sinusoidal signals are used at different frequencies in Simulink model 1120 as shown in
The spectrum is shown in
A note is that it may seem that the gain required is significant which is an issue in a closed loop. However, this gain is associated with an integrator and therefore the gain is illusory and more about how fast a capacitor integrator can be charged by a current source as in a physical circuit. Note that making the capacitor smaller is equivalent to increasing the gain. The integrator can also be replaced with a discrete time accumulator, as shown in a Simulink model 1140 as depicted in
First Order Delta-Sigma Example with Weak Tone Signal at 1 Hz
In the next simulation, the signal is at 1 Hz and an amplitude of 0.1 and some higher frequency interference with amplitudes of 1 each. Results are shown in
Turn now to the second order VBP-DSM 970 as shown in
The advantage of the second order is that it provides a second zero in the passband of the desired signal for the quantization noise. In the complex baseband this can be modeled with a pair of integrators 1172 (representing 1/s1 and 1/s2) as in
If the movement of the closed loop poles of this circuit is analyzed, the result is the locus as in
The utility of the additional positive feedback loops of the second order VBP-DSM 970 is that the bandpass poles can be placed anywhere in the LHP, providing significant design flexibility. For example, the gains G1 and/or G2 may be adjusted such that the two positive feedback loops are unstable and oscillate. G3 and/or G4 may then be increased until the oscillation ceases. In this way there may be more control of the positions of the poles, and they may be placed arbitrarily close to the jω axis. This gives flexibility in configuring the VBP-DSM for both the desired signal passband and the VBP-DSM noise suppression.
Further suppression of the quantization noise can be had with a second order system. This has two 1/s integrators as shown in
Remarkable results, with an ADC that only has six quantization levels of {−0.5,−0.3,−0.1,0.1,0.3,0.5}, are seen in
At this point, saturation of the ADC has been avoided by reducing the input gains to the ADC but add scaling at the output of the ADC.
To aid in visualization of the signal flow in negative feedback loop 974, consider outer loop 50 of
Next, the sampling rate of the ADC will be considered. Let the sampling interval be T such that the sampling frequency is 2π/T (rads/sec). If this frequency is much higher than ωs or ωv then the effects of frequency folding need not be considered. Then G can be increased such that quantization noise becomes negligible. This is equivalent to a high oversampling ratio. Typically, it may be assumed that there is some up-front fixed filtering that is commensurate with the ADC sampling rate such that frequency folding does not occur.
Next, the saturation effects of the ADC are considered. If the input signals are large such that the ADC saturates then the SNR is reduced significantly. Saturation negatively impacts the SNR and is to be avoided. It can never be avoided completely as a number of interference signals are generally superimposed at the input with the combined amplitude being statistical. It is more that the backoff of the signal into the ADC is based on the RMS of the composite signal and then the SNR degradation can be determined by approximating the probability density function of the combined amplitude to be Rayleigh. However, managing the saturation with a backoff of the input signal implies an increase in the equivalent noise figure (NF) for this portion of the receiver. As the receiver is a careful balance of NF and linearity this is an issue. To calculate this, the step size of the ADC in relation to kTB thermal noise may be considered.
If the input is scaled by a ratio of (1/R), then it follows directly that 20 log(R) higher interference power can be tolerated with the same probability of ADC saturation. In the VBP-DSM it is considered that the transfer gain of the quantization noise is ωs/G. It follows therefore that R=G/ωs can be set and then the level of quantization noise to the desired signal level is the same as if there was no scaling (R+1) and no VBP-DSM loop. However, an increase of the interference power level of 20 log(G/ωs) dB can be tolerated which can ameliorate the issue of ADC saturation.
Stating another way, if ADC has a fixed sampling interval of T, the power spectral density of the quantization noise will be proportional to 1/T. Furthermore, if a VBP-DSM loop is implemented then the input can be scaled by a factor of R=G/ωs with no degradation in the output SNR due to the quantization noise of the ADC. For the first order VBP-DSM, G is not limited. All that happens is that the pole moves towards the center. However, if the delay of the ADC is added then G will have a limit, but it is not overly significant.
In one example, the dual loop architecture may involve A VBP-DSM to take advantage of the oversampling rate of the ADC to reduce quantization noise that subsequently allows for a signal reduction into the ADC that then results in a higher tolerance for interference.
Why does this benefit not result with Q enhancement? With Q enhancement the pole at ωs would be placed closer to the jω resulting in a larger gain at the desired frequency. At the interference frequency there is no enhanced gain. But this means that while the desired signal is grown relative to the interference signal, it is not the case that the interference signal is suppressed. Hence at the input to the ADC there is now a larger desired signal and the same size interference signal. But now it would seem that the input to the ADC can be reduced, but this just reduces the loop gain which may be maintained for Q enhancement. Having the signal scaling outside of the loop triggers an increase in the NF which can be seen by taking the quantization noise and replacing it with an equivalent noise source at the input to the loop. Here now the quantization noise competes directly with the desired signal which is now attenuated due to the scaling.
ADC Saturation Effects with Scaling Following Tone Input Mixing
Next consider the effect of ADC saturation. Here the saturation of the ADC is set at ±1. The effect is shown in
To fix this, a scaling can be applied prior to the loop as in the following simulation. 6 dB of attenuation, as shown in a Simulink model 1220 depicted in
However, this is not a viable solution as the NF of the integrator will have a moderate NF and the 6 dB of loss will add directly to the integrator NF.
ADC Saturation Effects with Scaling Before ADC
A better approach is to apply the scaling in front of the ADC as shown in a Simulink model 1240 depicted in
The delta-sigma loop gain can be obtained again by adding a larger scaling after the ADC. If a feedback gain of 2.5 is added after the ADC, then the equivalent of the loop gain back to 50 is received and the quantization noise improves as ‘G’ has increased from 20 to 50.
6 dB of the desired signal is lost into the ADC due to the attenuator required to eliminate the saturation. However, 20 dB is gained due to the VBP-DSM and hence the noise floor is improved by about 14 dB. If the input frequency was even lower, then the SNR could be further improved as evidenced in
One utility of the DPLP processing is direct frequency translation discussed above that may also be achieved in a DSP which additionally provides signal digitization using discrete time sampling and quantization discrete time sampling of the signal and subsequent reconstruction where the feedback processing may be precisely implemented.
For application of signal processing circuit 30 to the SDR, additional taps may be added to signal processing circuit 30 discussed above, as shown in
A more detailed view of the dual loop mixed signal processing architecture in the transmit mode is seen in
The loop is connected to an antenna 1280, a T/R switch 1281, and an LNA 1283 as shown. The forward signal path, digitization, and DSP may be existing components of an SDR as shown in
In
In the standard SDR transmit mode, DSP 52 generates the transmit baseband signal with the DAC 56 and up-conversion 1286, but now the signal is passed to the power amplifier T/R switch 1281 and to the antenna 1280. In this way there is little additional hardware required for the DPLP function. Bandpass filter 1288 after up conversion 1286 is a broad bandwidth designed to remove some of the spurious DAC components such as the noise components of DAC 56. However, this is hampered as DAC 56 is within the loop and contributes noise.
For this an additional active RF feedback 1290 may be required as shown in
Many SDR options are relevant here, some of which include:
As an example, three single-pole resonators may be provided with an active feedback signal loop with a variable gain block to form a bandpass filter in the RF domain. When the feedback gain is increased, the center pole of the three resonators moves toward the jω axis, while the flanking poles move a smaller amount away from the jω axis, thus creating Q-enhancement.
Inversely, if the feedback gain is reduced, the center pole of the three resonators moves away from the jω axis, while the flanking poles move a smaller amount toward the jω axis, thus creating Q-spoiling.
With the DPLP state space feedback, however, each of the three s-plane poles may be independently moved toward the jω axis simultaneously for Q-enhancement or away from the jω axis for Q-spoiling. As long as no single pole moves across the jω axis into the right hand s-plane from the left-hand plane, then this active feedback 3-pole BPF is always stable.
One could have the active feedback BPF enabled, and then disable this active feedback BPF path and enable the DPLP state space feedback path. Additionally, referring to
The DPLP feedback processing may include up-conversion for use with a slower rate DAC or may be at the signal frequency for a high sampling rate DAC. While DPLP is capable of Q enhancing all three poles simultaneously, latency in DSP processing may be introduced if the BPF bandwidth is too broad.
Referring to
In this patent document, the word “comprising” is used in its non-limiting sense to mean that items following the word are included, but items not specifically mentioned are not excluded. A reference to an element by the indefinite article “a” does not exclude the possibility that more than one of the elements is present, unless the context clearly requires that there be one and only one of the elements.
The scope of the following claims should not be limited by the preferred embodiments set forth in the examples above and in the drawings, but should be given the broadest interpretation consistent with the description as a whole.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/CA2022/050824 | 5/24/2022 | WO |
| Number | Date | Country | |
|---|---|---|---|
| 63211268 | Jun 2021 | US | |
| 63192055 | May 2021 | US |
