The present invention relates generally to simulation of signal processing systems, and more particularly to simulation of RF signal processing systems.
Wireless communication circuits and systems are becoming increasingly common. Wireless communication circuits and systems are often tested by simulation before fabrication to ensure correctness of operation and to help categorize wireless device components. Simulation of wireless communication components allows designers to investigate new designs and to test design changes without expending time and money in producing physical samples.
Non-linear blocks are often present in wireless communication systems. For example, low noise amplifiers (LNAs) are often limited by voltage sources having upper and lower bounds which limit the dynamic range of the LNA. Mixers are often subject to leakage from local oscillators, with self-mixing potentially occurring with the RF signal. In addition, both active and passive devices of all blocks may introduce non-linearities at the device level.
Non-linearities may introduce additional spectral components in the form of undesired harmonics of input signals, intermodulation, and gain compression, for example. The undesired harmonics may negatively affect circuit operation. Intermodulation, particularly of undesired harmonics in a multi-tone system, may distort a signal being processed, as well increase system complexity by requiring DC offset cancellation circuitry or complex filters. Non-linearities also may result in reduced gain, through clipping or other effects.
Accordingly, preferably simulation of wireless communication systems and components includes simulation of non-linear blocks or elements. However, simulation of non-linear elements may be difficult. Simulation of non-linearities may be extremely expensive from a computational perspective, with for example extraneous signal components spread about the continous spectrum. This computational expense is further increased if the non-linear blocks include memory.
The invention provides a simulation system and method for simulating RF systems including non-linear elements.
One aspect of the invention provides a method of simulating radio frequency signal processing circuitry, comprising forming a compressed vector based equivalent of a signal;
performing processing on the compressed vector based equivalent to simulate radio frequency circuitry operation, the processing forming a processed compressed vector based equivalent of the signal; and forming an output signal using the processed compressed vector based equivalent of the signal.
Another aspect of the invention provides a method of modelling circuitry, comprising converting first signals to compressed equivalent signals; processing the compressed equivalent signals to form further compressed equivalent signals; and converting the further compressed equivalent signals to second signals.
Another aspect of the invention provides a system for performing RF signal processing modelling, the system comprising signal generator blocks forming compressed vector based equivalent signal representations; RF signal processing blocks processing compressed vector based equivalent signal representations; and conversion blocks converting compressed vector based equivalent signals to RF signal representations.
These and other aspects of the invention are more fully understood in view of this disclosure.
The RF signal may be viewed as similar to RF signals often encountered in wireless communication systems. For example, a wireless communication system may utilize a carrier frequency, represented in
Accordingly, aspects of the invention may be viewed as using only frequency bands of interest in simulation of a device, or of non-linear blocks of a device. In
As an example, consider a 900 GSM 900 MHz application. The application has a carrier frequency of 900 MHz. In the example, the application has a third order non-linearity, so that three harmonics are of interest. The total signal bandwidth is therefore 2.7 GHz. If a sampling frequency is 1 KHz, a vector of length 2,7000,000 defines the sampled signal. If, however, the channel bandwidth is 6 MHz a significant portion of the vector contains information not of particular importance.
Creation of vectors containing information for frequency bands of interest, for example in a matrix form, allows for significantly reduced, or compressed, vector size. As the three harmonics are of interest in the example, four vectors may be formed, each defined by samples formed using a 1 KHz sampling frequency in the frequency bands of interest. Each band provides a vector of length 6,000, and the four frequency bands of interest therefore provide a matrix with 24,000 entries, as opposed to 2,700,000 entries otherwise provided. A reduced number of computations may be performed in view of the reduced matrix size.
In aspects of the invention, summation, multiplication, and convolution operations are also modified so as to provide operations for the translated signal components that are substantially equivalent to those operations for untranslated signals. In aspects of the invention, these operations are defined as follows.
A discrete signal x[n] is a Piecewise Non-Zero (PWNZ) signal if it can be described as follows:
A discrete signal x[n] is a Equally Piecewise Non-Zero (EPWNZ) signal if it is PWNZ with the following properties:
NiH−NiL+1=LP
∀iε[1,M] (2)
Using the compressed vector terminology of above, a compressed vector-based (CVB) equivalent of an EPWNZ signal is:
Summation of CVB equivalent signals may be considered as:
Given zvp[n] as the summation of xvp[n] and yvp[n] (i.e. zvp[n]=xvp[n]+vpyvp[n] where “+vp” is a symbol of summation of two CVB equivalent signals), then
Where xi, yi, and ziεR1×L
Subtraction of CVB equivalent signals may be considered as:
Given zvp[n] as the subtraction of xvp[n] and yvp[n] (i.e. zvp[n]=xvp[n]−vp yvp[n] where −vp is a symbol of subtraction of two CVB equivalent signals), then
Where xi, yi, and ziεR1×L
Multiplication of CVB equivalent signals may be considered as:
Given zvp[n] as the multiplication of xvp[n] and yvp[n] (i.e. zvp[n]=xvp[n] Xvp yvp[n] where “Xvp” is a symbol of multiplication of two CVB equivalent signals), then
Where xi, yi, and ziεR1×L
Division of CVB equivalent signals may be considered as:
Given zvp[n] as the division of xvp[n] and yvp[n] (i.e. zvp[n]=xvp[n]÷vp yvp[n] where “÷vp” is a symbol of division of two CVB equivalent signals), then
Where xi, yi, and ziεR1×L
Scalar multiplication of a CVB equivalent signal may be considered as:
Given zvp[n] as the scalar multiplication of xvp[n] with the scalar á (i.e. zvp[n]=á.vpxvp[n] where “.vp” is a symbol of a scalar multiplication of a CVB equivalent signal with a scalar), then
Where xi, and ziεR1×L
Convolution of CVB equivalent signals may be considered as:
Given zvp[n] as the convolution of xvp[n] and
In which xFi and yFi are flipped version of xi and yi respectively (i.e. xFi(n)=xi(length(xi)−n)). M is the maximum number of sub-pieces taken into account, and {circle around (x)} is as follows:
In some aspects of the invention, xi{circle around (x)}yj is substituted with a regular convolution if yj(F−f)=yj(f−F).
In various aspects of the invention the CVB signals are in terms of dB, while in other aspects of the invention other scales are used.
In the CVB processing block of
In various embodiments the simulation blocks may be considered as combinations of the operations described above. For example, the simulation blocks may be Linear Time Invariant without memory (LTI) blocks, Linear Time Invariant with memory (LTIM) blocks, Non-Linear Time Invariant without memory (NLTI) blocks, and Non-Linear Time Invariant with memory (NLTIM) blocks. These blocks may in turn be used to form low noise amplifier blocks, mixer blocks, and other blocks.
As a notation convenience, an input to a block may be considered to be x(t) and an output of a block may be considered y(t). Also as a notation convenience X(f) and Y(f) may be considered Fourier tranforms of x(t) and y(t), respectively.
For an LTI operation y(t)=á1x(t) and Y(f)=á1X(f), where á1 is a constant scalar. The CVB equivalent representation of the LTI operation, the LTI block, in the frequency domain is Yvp(f)=á1.vpXvp(f).
For an LTIM operation
where H(f) is the
Fourier transform of the impulse response h(τ).
The CVB equivalent representation of the LTIM operation, the LTIM block, in the frequency domain is
where Hvp(f) is the CVB equivalent of H(f).
For an NLTI operation,
y(t)=a0+a1x(t)+a2x2(t)+a3x3(t)+ . . .
Y(f)=a0δ(f)+a1X(f)+a2X(f)*X(f)+a3X(f)*X(f)*X(f)+ . . .
Where a1, a2, . . . are coefficients representing non-linearity of a device and * indicates convolution of two signals. The coefficients may be extracted, for example, by performing curve fitting on a curve relating inputs and outputs of the device. The CVB equivalent representation of the NLTI operation, the NLTI block, in the frequency domain is
In some embodiments NLTIM blocks are modeled as combinations of NLTI sub-blocks and LTIM sub-blocks. In other embodiments a Volterra series method is used. In a Volterra series an nth order non-linear operator is described as
in which x(t) is the input, y(t) is the output, and hn(τ1, . . . τn)=0 for any τJ<0 j=1, . . . , n).
Further information may be found in Schetzen, M., “The Voleterra and Wiener Theories of Nonlinear Systems” (1980), the disclosure of which is incorporated by reference.
Simulation may be computationally expensive when convolution operations are performed in the frequency domain. Accordingly, in some embodiments of the invention CVB equivalent signals in the time domain are used, allowing for, for example, multiplication in the time domain instead of convolution in the frequency domain. A real time domain signal s(t) has a Fourier transform S(f). Svb(f) is a CVB equivalent representation in the frequency domain. The CVB equivalent representation in the time domain is svb(t), with
which utilizes an approximation function, and where fc is the the carrier frequency and B is the bandwidth of interest. For the frequency domain
CVB equivalent systems are formed using a combination of frequency shift blocks and samplings. For example f(x)=x2,
may be implemented as shown in
As an example, the input signal is a GSM900 standard Interference signal.
The system of
y(t)=a0+a1x(t)+a2x2(t)+a3x3(t)
With the non-linear coefficients derived from curve fitting, with curves generated for example using tools from Cadence corporation. In the example described the coefficients are
a0=0 a1=1 a2=0.27 a3=−4.5.
Similarly, the mixer may be modeled as a non-linear block. In the example described, the mixer is modeled in accordance with the block diagram of
y(t)=a0+a1x(t)+a3x3(t)
The coefficients are derived using curve fitting, with for example curves generated using tools from Cadence Corporation. In the described example, the coefficients are
a0=0 a1=1 a2=0.32 a3=−3.21.
Simulation results are shown in the graphs of
Accordingly, the invention provides a modeling system and method using compressed vectors. Although the invention has been described in certain embodiments, it should be recognized that the invention encompasses the claims supported by this disclosure and the their equivalents.
This application claims the benefit of the filing date of U.S. Provisional Application No. 60/428,432, filed Nov. 21, 2002, entitled “Compressed Vector-Based Spectral Analysis Method and System for NonLinear RF Blocks”, the disclosure of which is incorporated by reference herein.
Filing Document | Filing Date | Country | Kind | 371c Date |
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PCT/US03/37298 | 11/21/2003 | WO | 5/19/2005 |
Number | Date | Country | |
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60428432 | Nov 2002 | US |