The present invention relates generally to wireless communication systems that employ polar modulation methods to transmit non-constant envelope signaling waveforms. More particularly but not exclusively, the present invention relates to systems and methods for bandwidth reduction through pulse insertion.
Signal modulation has historically been impressed on an intermediate frequency (IF) or radio frequency (RF) carrier by using a rectangular coordinate system. The rectangular coordinates are normally referred to as the in-phase (I) and quadrature-phase (Q) components. The I-channel is used to directly modulate a cosine-carrier signal and the Q-channel is used to directly modulate a sine-carrier signal. The modulated carriers are then summed and amplified to form the desired transmit signal. This approach is very general and can in principle be used to create any transmit waveform of interest. It is hereinafter referred to as IQ modulation in this disclosure.
Polar modulation is an alternative modulation method which is mathematically identical to IQ modulation. Polar modulation is capable of exhibiting much better power amplifier efficiency than IQ modulation and is of great interest in the low-power communications industry for that reason.
Modern communication systems make substantial use of digital signal processing methods. The I- and Q-channel modulation signals are normally represented by a series of synchronous discrete time samples that can be represented by the sample pairs (Ik, Qk). The equivalent polar representation of this same signal is given by Rk∠θk, in which Rk is the magnitude of the signal modulation and θk is the phase of the modulation. Mathematically, the IQ modulation and polar modulation coordinate samples are related by:
Rk=√{square root over (Ik2+Qk2)}
θk=tan−1(Qk,Ik) (1)
and
Ik=Rk cos(θk)
Qk=Rk sin(θk) (2)
One of the most severe problems associated with polar modulation is that the signal bandwidth of the polar modulation is normally much larger than the bandwidth of the IQ modulation system. This is especially true for the phase component. Although the mathematical relationships given by (1) and (2) are exact, they are also highly nonlinear, leading to severe bandwidth expansion in application. A bandwidth-limited IQ modulation signal does not in general create a bandwidth-limited polar signal.
One of the major causes of this problem is modulation signal trajectories that pass near the origin of the signal constellation. Such signal trajectories can produce severe spiking behavior in the phase channel, resulting in severe bandwidth expansion. In order for systems to effectively employ polar modulation and exploit its benefits in the power amplifier area, bandwidth reduction of the polar modulation waveforms is very desirable if it can be accomplished without causing other serious impairments to system performance.
Methods and systems for modifying polar modulation signals to improve performance and reduce bandwidth demands for associated signal processing are disclosed. These methods and associated systems are also denoted herein as the STM method or STM approach for purposes of brevity. In accordance with aspects of the invention, problematic signal trajectories may be detected and corrective signals may be inserted to improve performance by modifying the signal trajectories.
Embodiments of the present invention may allow for tradeoff of major transmit system performance parameters of polar modulation including signal bandwidth, signal fidelity in the form of Error Vector Magnitude (EVM), and adjacent channel leakage ratio (ACLR), to achieve a wide range of performance characteristics.
The foregoing aspects and the attendant advantages of the embodiments described herein will become more readily apparent by reference to the following detailed description when taken in conjunction with the accompanying drawings wherein:
The methods and systems disclosed herein are applicable to any digital communication system that employs polar modulation or derivatives thereof to communicate digital communication waveforms. These waveforms may be generally described mathematically as a superposition of pulse-like waveforms such as for EDGE and WCDMA (see, e.g. Proakis, J. G., Digital Communications, 4th Ed., McGraw-Hill Book Co., 2001, “Digital Cellular Telecommunications System (Phase 2+) Modulation,” ETSI TS 100 959 V8.4.0(2001-11), and “3rd Generation Partnership Project; Technical Specification Group Radio Access Network; User Equipment (UE) Radio Transmission and Reception (FDD),” 3GPP TS 25.101 V6.7.0(2005-03).
The balance of this disclosure will address WCDMA applications, but it will be apparent to those of skill in the art that the techniques employed herein are applicable to a variety of other systems and applications and therefore are not intended to be limited merely to WCDMA applications.
Embodiments of the Signal Trajectory Modification (STM) methods and systems described herein (also denoted herein for brevity as the STM approach or S™ method) and in related U.S. Provisional Patent Application Ser. No. 60/884,164, incorporated by reference herein in its entirety, may be used to augment the normal IQ-based transmit signal with an additive bandlimited signal such that the bandwidth and precision demands of the augmented signal represented in polar form may be dramatically reduced. Although in some embodiments the addition of this bandlimited signal may cause some degradation to the transmit EVM, any degradations may be more than offset by potentially significant benefits such as improved adjacent channel leakage rejection (ACLR), reduced requirements for digital to analog converter (DAC) clock rates and bit-widths, and ultimately lower power consumption.
Attention is now directed to
This direct modulation approach relies on linear gain modules throughout, which results in substantial inefficiency in power amplifier (PA) sections because the output power from the PA must always be maintained well below the PA's maximum output power capability in order to have sufficiently good linearity.
As an alternate to direct modulation, polar modulation may be used.
In some embodiments source (2.1) can be identical to source (1.1) in
The amplitude and phase corresponding to each output sample pair Rk∠θk can be related to the input (Ik,Qk) sample pair by equations (1) and (2). The Rk samples may be handled fairly simply, as illustrated in the embodiment shown in
In a PLL-based polar implementation, the phase processing path can be considerably more complicated than the amplitude path. Ultimately, the phase modulation may be imposed on a voltage-controlled oscillator (VCO) within the PLL (2.8) as frequency modulation (FM). In order to interface correctly with the VCO, the phase samples θk may be differentiated by (2.11) to create instantaneous-frequency samples (IFM). All of the synchronicity may be orchestrated by a precision clocking source (2.12). The IFM samples may be converted to analog voltage/current by DAC (2.10) and the output lowpass filtered by (2.9) to adequately reduce sampling images. The IFM may then be impressed on the PLL (2.8) by using one- or two-point modulation. The output from the PLL (2.7) is ideally a phase-only modulated signal that when combined with the amplitude signal in (2.6) results in the desired reconstructed transmit signal. Gain block (2.5) may be used to provide additional signal level adjustment as desired.
An expanded view of one embodiment of the IQ to Polar Conversion (2.2) is shown in
The rectangular to polar conversion may be performed by (10.11) utilizing equation (1) in a COordinate Rotation DIgital Computer (CORDIC) implementation. The FM samples that are provided at the FM DAC (10.10) input may be created using a simple differentiator like (2.11) shown in
An output transmit signal IQ plot for one embodiment of a system as shown in
Behavior of Polar Signal Components
The baseband bandwidth of the I- and Q-channel signals for the WCDMA example is approximately 4 MHz. Due to the square-root raised-cosine chip-shaping used in WCDMA, there is ideally no signal energy present at larger offset frequencies for the IQ rectangular signal representation.
In contrast, the bandwidth extents of the AM and FM signal paths at the output of the rectangular-to-polar conversion block (10.11) in
STM Approach
Embodiments of the STM approach are designed to address problems associated with these problematic signal trajectories. According to certain aspects, the STM approach involves sacrificing a portion of EVM performance in return for lower bandwidth and precision requirements needed for the FM path. The reduced requirements on the FM path may be exploited to address a number of design issues, including (i) reducing the required number of D-to-A converter bits required for the θ signal for a specified spectrum performance level, (ii) reducing the high-frequency content of the θ(t) signal thereby allowing lower sampling rates to be used, and (iii) reducing the dynamic range requirements imposed on the power amplifier (PA) because the technique can be used to avoid an annular region centered at the constellation origin if desired.
In certain embodiments, improvements(s) in the FM signal path come at the expense of EVM performance. More specifically, the STM approach involves introducing a small, precisely controlled additive signal contribution wherever portions of the otherwise ideal WCDMA signal trajectories would fall too close to the constellation origin, thereby creating bandwidth issues for the FM signal path. Certain attributes that may provide one or more advantages will be described in greater detail in the following sections (as well as in Appendix 3 of related U.S. Provisional Patent Application Ser. No. 60/884,164, incorporated by reference herein in its entirety) and include:
General STM Methodology
In one exemplary embodiment, an STM module as shown in
Certain embodiments of the STM implementation consist of the following aspects as shown in
STM Approach RMS Approximation
In certain embodiments, an approximation of the RMS value of the input (Ik,Qk) sample-pair stream may be determined as shown in (11.11) in
RMSk=max(|Ik,|Qk|)±0.375(|Ik|,|Qk|) (5)
The accuracy of this approach is very attractive given its simplicity, however, it will be recognized by one of skill in the art that other methods may be used for RMS approximation if desired.
The RMS Approximation block may be followed by a simple first-order recursive infinite impulse response (IIR) filter that may be used to reduce the variance of the RMS calculation to a desired level. In one exemplary embodiment, the recommended processing for this IIR filter is given in (6) by
RMSFk+1=γLPFRMSFk+(1−γLPF)RMSk (6)
where RMSFk represents the smoothed low-variance RMS estimate for the input (Ik,Qk) sample-pair stream. In this form, 0<γLPF<1. The −3 dB frequency of this filter is given by (7) as
where Fs is the sample-pair rate of 26 Msps in the present embodiment. The WCDMA chip-rate is 3.84 MHz and this value is used below in Table 2 to estimate the number of chip-times required before the filter responds. In some embodiments, useful values for γLPF may range from roughly 0.90 to 0.99.
The output from the γLPF filter may be weighted by the parameter λ, which sets the upper limit for the magnitude of the STM insertions. In some embodiments, the useful range for λ may be 0≦λ<0.20.
STM Approach Event Detection
In certain embodiments detecting dθ/dt may be done by monitoring whether a candidate signal trajectory invades a specific annular region about the origin of the signal constellation plane. However, in some embodiments a more attractive, simple, and reliable detection metric may be used based on the quantity Δθ/Δt, where Δt is the digital sampling time interval and Δθ can be computed based on (Ik,Qk) input sample pairs alone. Using a detection metric that is based on dθ/dt may be preferable since the FM signal path is typically the most problematic. Based on the annular region that is carved out in the WCDMA constellation (see, e.g.,
In some embodiments, phase differentiation may be implemented by simply taking the difference between the phases of adjacent (Ik,Qk) sample pairs. In other embodiments, improved performance may be obtained by applying different methods to implement phase differentiation.
It can be shown (see, e.g. Appendix 3 of related U.S. Provisional Patent Application Ser. No. 60/884,164, incorporated by reference herein in its entirety) that the phase difference between two time-adjacent (Ik,Qk) sample-pairs is given by (8)
Assume that the maximum Δθk that is acceptable after application of the STM approach is given by φ. After substituting this into (8) and re-arranging the equation, the result can be written as (9) (see also Appendix 4 of related U.S. Provisional Patent Application Ser. No. 60/884,164, incorporated by reference herein in its entirety).
tan(φ)[IkIk−1+QkQk−1]−[QkIk−1−Qk−1Ik]≧0 (9)
Substitution of Λo for tan(φ) provides one exemplary embodiment of an Event Detection algorithm. Applying this algorithm, an Event Detection may be declared if the conditions of (10) are met (see also Appendix 6 of related U.S. Provisional Patent Application Ser. No. 60/884,164, incorporated by reference herein in its entirety).
C2≦0
or
C1−Λo|C2|≧0
for
C2=IkIk−1+QkQk−1
C1=|QkIk−1−Qk−1Ik| (10)
STM Approach Event Screener
In some embodiments it may be necessary to prevent consecutive Event Detections from all being passed through to the subsequent signal processing (see, e.g., Appendix 6 of related U.S. Provisional Patent Application Ser. No. 60/884,164, incorporated by reference herein in its entirety). This process may be done in a variety of ways, including through application of logic that screens for successive events and produces a corresponding output, including output logic that blocks subsequent detection signaling until a preset number of detections has occurred. The number of successive Detection Events screened may be denoted as the sample-depth. At a 26 Msps (Ik,Qk) sample rate, a recommended sample-depth for this screening action is 4. It will however be recognized by one of skill in the art that other sample-depths may be used depending on the application. The logic diagram of
STM Approach Determination of Normal Vector
In some embodiments correction signals to be combined with a transmit signal should be additive in nature to the IQ signal components of the transmit signal. The STM approach signals that are added to the original (Ik,Qk) sample streams as shown in
In order to provide the greatest benefit in reducing |dθ/dt| for a given amount of introduced additive signal modification (i.e., EVM degradation), the original signal trajectory shown in
If the available discrete-time (Ik,Qk) sample-pairs that are nearest to the Event Decision are used in a linear point-intercept formula (e.g., y=m×+b), it can be shown that the (Ip,Qp) coordinates for the point of closest-approach to the origin are given by (11) (see also Appendix 4 of related U.S. Provisional Patent Application Ser. No. 60/884,164, incorporated by reference herein in its entirety).
Precise calculation of the point's coordinates is, however, unnecessary since all that is required is knowledge of which quadrant the point resides in. It can be shown that the point (Ip, Qp) has the quadrant behavior listed in Table 3 with the following definitions (12) applied (see also Appendix 5 of related U.S. Provisional Patent Application Ser. No. 60/884,164, incorporated by reference herein in its entirety).
d1=Ik+1−Ik−1
d2=Qk+1−Qk−1
d3=Qkd1−Ikd2 (12)
Based on the signs of IP and QP, the quadrant of the point can be readily determined, and when the unit-normal n is computed for |d1| and |d2| placing it in the first-quadrant as (nx, ny), the so-called Flip-logic amounts to directly applying the signs of IP and QP to nx and ny respectively.
The optimal phase orientation for the signal trajectory modification signals is given by the unit-normal vector to the signal trajectory at point P. When the voltage change between adjacent samples dI and dQ is restricted to the first-quadrant for illustrative purposes, the unit-normal vector n can be computed as in (13).
This unit-normal vector can be more easily calculated by using a CORDIC-like iterative algorithm based on the dot-product between (nx, ny) and (dI, dQ) (see, e.g. Appendix 5 of related U.S. Provisional Patent Application Ser. No. 60/884,164, incorporated by reference herein in its entirety). Extending the result to all 4-quadrants may be done by following the guidelines provided previously in Table 3. For (dI, dQ) confined to the first-quadrant, the pseudo-code for a CORDIC-like computation is as shown below in Table 4.
STM Approach Signal Insertion Amplitude
In some embodiments, in order to further reduce the impact on EVM performance, the magnitude of the insertion signal may be made proportional to the scaling parameter λ as well as proportional to the amount by which the Event Detection event exceeds the threshold level given by Λo. It will be recognized by one of skill in the art that other variants of this amplitude proportionality may be adopted if desired, however, the following method may provide advantages based on simplicity of implementation.
When the fully-developed unit-normal vector is given by (ny, ny), and with λ and Λo as defined earlier, the signal insertion amplitudes applied to the I and Q pulse-insertion (
where Λ is the metric computed in the Event Detection algorithm. Although not stated elsewhere, the value of Λ is strictly positive and is limited to a maximum value of π.
STM Approach Pulse-Shaping Filters
Non-zero outputs from the unit-normal calculations can occur at any time, separated by as few as NH time samples. With this perspective in mind, it may be desirable to assemble the signal modification signals using a convolution of the unit-normal vector samples and the desired pulse shape in order to accommodate the superposition of multiple events.
A wide range of pulse-types may be considered for this role. In certain embodiments one choice would be to use the same pulse shape as used for the WCDMA chips themselves (i.e., square-root raised-cosine pulses with β=0.22). However, in some embodiments this would lead to a slowly-decaying time-pulse which could result in additional gate-count both in the pulse-shaping FIR filters as well as in the time-delays. Since the inserted pulses may only be applied intermittently and with a fairly low amplitude, wider pulse spectrums which decay more quickly in time may be used to reduce the gate-count in this area. Owing to its more rapid time-decay compared to the square-root raised cosine pulse, one exemplary approach is to use a raised-cosine pulse shape with an excess bandwidth parameter of 0.50. The shorter pulse shape of this approach may also result in less EVM degradation.
Example STM Approach Results for WCDMA Single Voice-Channel
A cursory comparison of one embodiment of the polar modulation method as shown in
The improvement in spectrum levels at 3.5 MHz and 8.5 MHz is substantial as shown. The signal trajectory behavior for the transmit signal with the STM approach applied is shown in
In some embodiments, use of the STM approach may degrade the EVM performance of the transmitter slightly as shown by the histogram in
STM Approach Design Parameter Choices
A number of different design parameters may enter into the resultant performance and benefit assessment of using the STM approach. In order to limit the tradeoff considerations to a reasonable scope for example purposes, the parameters considered in the embodiment described here include only the signal insertion amplitude parameter λ, the maximum allowed dθ permitted per sample (at 104 Msps rate), and the threshold parameter Λo. All other parameters are otherwise left as described in Table 1 and
In some embodiments, implementation of the STM approach may be particularly advantageous if either the maximum phase change per sample is limited to a practical level like 45° and/or the number of FM DAC bits is less than 10. The limitation on maximum theta is considered below in Table 7.
In situations where the number of FM and AM DAC bits is limited to only 8 effective bits, the STM approach leads to spectrum performance that is otherwise completely unattainable without its use, as shown below in Table 8. Under the illustrated conditions, use of the STM approach can provide on the order of 10 dB improved sidelobe level at 8.5 MHz offset at a very acceptable EVM performance level.
The foregoing description, for purposes of explanation, used specific nomenclature to provide a thorough understanding of the invention. However, it will be apparent to one skilled in the art that specific details are not required in order to practice the invention. Thus, the foregoing descriptions of specific embodiments of the invention are presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed; obviously, many modifications and variations are possible in view of the above teachings. The embodiments were chosen and described in order to best explain the principles of the invention and its practical applications, they thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated. It is intended that the following claims and their equivalents define the scope of the invention.
This application is a continuation application under 37 C.F.R. §1.53(b) of patent application Ser. No. 11/971,790 filed on Jan. 9, 2008, now abandoned entitled PULSE INSERTION SYSTEMS AND METHODS FOR POLAR MODULATION. This application also claims the benefit of priority under 35 U.S.C. §119(e) to United States Patent Application U.S. Provisional Patent Application Ser. No. 60/884,164, entitled PULSE INSERTION SYSTEMS AND METHODS FOR POLAR MODULATION, filed on Jan. 9, 2007, the contents of which is hereby incorporated by reference herein in its entirety for all purposes.
Number | Name | Date | Kind |
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20060227895 | Booth et al. | Oct 2006 | A1 |
20080007346 | Jensen et al. | Jan 2008 | A1 |
Number | Date | Country | |
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60884164 | Jan 2007 | US |
Number | Date | Country | |
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Parent | 11971790 | Jan 2008 | US |
Child | 12119279 | US |