CN111884961A - Self-adaptive sparse predistortion structure based on compressed sensing algorithm - Google Patents
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Abstract
The invention discloses a self-adaptive sparse predistortion structure based on a compressed sensing algorithm. The method comprises the steps of carrying out compressed sensing sampling in a predistortion feedback loop, reconstructing five-order and high-order intermodulation signals by using an adaptive sparsity algorithm APSP, dynamically adjusting an initial value and a step length of sparsity according to the characteristics of the feedback loop signals to approach real sparsity, and then restoring the signals with high precision by using a subspace tracking algorithm to improve a coefficient estimation weight and improve the predistortion effect.
Description
Technical Field
The invention belongs to the technical field of predistortion structures, and particularly relates to a self-adaptive sparse predistortion structure based on a compressive sensing algorithm.
Background
The intellectualization, multi-frequency and low energy consumption of modern communication systems have emphasized the efficient use of radio spectrum resources. Digital Predistortion (DPD), a linearization method of a radio Frequency power Amplifier (RF PA) in a multi-carrier communication system, has gained wide attention from experts at home and abroad due to its high precision and good stability. In a study in the field of dual-frequency digital predistortion systems. In 2008, Roblin et al, by using a Large Signal Network Analyzer (LSNA) to obtain power amplifier parameters and then updating predistorter coefficients, a combination of a predistortion structure and frequency selectivity is generated. Further study by KimJhwo et al in 2012 extended the predistortion structure to five orders to obtain a more ideal linearization result. The feedback loop of Cidronali of Florence university combines with the undersampling technology, and proposes a dual-Frequency Intermediate Frequency predistortion structure (IF-DPD). Bassam et al perform nonlinear predistortion compensation on two separated frequency band signals respectively to provide two-dimensional digital predistortion. However, the acquisition of the output signal in the feedback loop of the dual-frequency predistortion system is severely limited by the sampling rate of the ADC (Analog-to-digital Converter).
Disclosure of Invention
Based on the defects of the prior art, the technical problem to be solved by the invention is to provide a self-adaptive sparse predistortion structure based on a compressed sensing algorithm, reduce the sampling rate to be close to an ideal linear power amplifier, and can be widely applied to the development of multi-band communication.
In order to solve the technical problems, the invention is realized by the following technical scheme: the invention provides a self-adaptive sparse predistortion structure based on a compressed sensing algorithm, which comprises a memory effect compensator of a double-frequency power amplifier predistortion model based on a piecewise linear function and an under-sampling reconstruction feedback loop part;
compressed sensing sampling is carried out in a predistortion feedback loop, a five-order and high-order intermodulation signal is reconstructed by using an adaptive sparsity algorithm APSP, the initial value and the step length of sparsity are dynamically adjusted according to the self characteristics of the feedback loop signal to approach the real sparsity, and then the coefficient estimation weight is improved by using a subspace tracking algorithm high-precision recovery signal.
Optionally, an input signal of the power amplifier in the structure is equally divided into two paths, one path of signal enters the dual-frequency power amplifier, and the other path of signal reconstructs an output signal of the concurrent dual-frequency power amplifier into an original signal containing lost out-of-band high-order intermodulation information before undersampling by using an adaptive sparsity APSP algorithm.
Further, P is defined as a Gaussian matrix, Yn(2) For undersampled output vectors, Yn(3) And (4) performing adaptive estimation on the sparsity to realize high-precision reconstruction for the reconstructed fifth-order vector under the condition that the sparsity is unknown.
Therefore, the self-adaptive sparse predistortion structure based on the compressive sensing algorithm has the following beneficial effects:
1. compared with the traditional predistortion method, the method has smaller distortion under the condition that the sampling bandwidth is smaller than the signal bandwidth, and can obtain better linearization performance so as to improve the reconstruction precision. Compared with the traditional predistortion, the NMSE of the undersampled double-frequency predistortion structure is improved by about 2-3dB compared with 2D-MP, 2D-DDR and 2D-CPWL, and meanwhile, the running time is saved due to the lower sampling rate.
2. The method can reconstruct the five-order intermodulation signal by utilizing compressed sensing sampling and an adaptive sparse algorithm APSP, is applied to a predistortion feedback loop, not only improves the accuracy of the reconstructed signal and the coefficient estimation weight, but also improves the predistortion effect while greatly reducing the sampling rate, and has higher accuracy when being applied to a flexible model compared with the traditional predistortion method. The output power of the predistortion system is returned to about 1dB, and ACPR can be improved to-49 dBc, which is close to an ideal linear power amplifier.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly understood, the present invention may be implemented in accordance with the content of the description, and in order to make the above and other objects, features, and advantages of the present invention more clearly understood, the following detailed description is given in conjunction with the preferred embodiments, together with the accompanying drawings.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings of the embodiments will be briefly described below.
FIG. 1 is a schematic structural diagram of an adaptive sparse pre-distortion structure based on a compressive sensing algorithm according to the present invention;
fig. 2 is a reconstruction algorithm for adaptively estimating the sparsity of a signal according to the present invention.
Detailed Description
Other aspects, features and advantages of the present invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, which form a part of this specification, and which illustrate, by way of example, the principles of the invention. In the referenced drawings, the same or similar components in different drawings are denoted by the same reference numerals.
Referring to fig. 1 to 2, the present invention utilizes a Compressed Sensing (CS) technique to compress a signal, so as to effectively reduce the sampling pressure at the radio frequency front end, for the problem that the sampling rate of an acquired output signal in a feedback loop of a dual-frequency predistortion system is severely limited. The CS theory is different from the traditional Nyquist sampling theorem, and when the signals are sampled, all N-dimensional signals do not need to be processed any more, but linear measurement is carried out by using an M-dimensional observation matrix far smaller than N.
The CPWL function can characterize the nonlinear behavior of a strong nonlinear system, and the piecewise linear function containing the memory effect is as follows:
where C (n) and O (n) are the inputs and outputs, respectively, of the nonlinear system. a isi，brAndriare coefficients of a piecewise linear function. b represents the dc offset and can be neglected in digital predistortion. M represents the memory depth of the model, and R represents the number of segments of the piecewise linear function. Beta is arR/R denotes a threshold value for defining the boundary of the piecewise linear function.
Through the processing of the lattice segmentation and omitting the direct current offset term, (1) can be expressed as a form that the output and the coefficient are in linear relation:
where θ (n-i) is the phase of C (n-i). Definition of
And
input signals of frequency band one and frequency band two respectively, the center frequency is omega1＝2πf1And ω2＝2πf2(assume ω2＞ω1)。C1n (i-) and C2(n-i) represents the baseband complex envelope. Definition of ω ═ ω (ω)2-ω1) /2, dual frequency in discrete time domain [14]The baseband equivalent signal is as follows:
C(n)＝C1(n)e-jωnT+C2(n)ejωnT(3)
where T is nT and T is the sampling interval. (3) The formula (2) can be substituted by the formula (1):
O(n)＝O1+O2(4)
the specific indirect learning structure of the nonlinear system:
define C on main roadn、OnRespectively nonlinear system input and output signals, on the branch, input signal
M after output of the inverse modelnCoupled signal dn(dn＝xn) And mnComparing and making difference, using error enOptimization and adjustment of inverse model systemAnd (4) counting. In order to realize the non-correlation between the fifth-order and high-order intermodulation signals and the power amplifier input signals, namely further improve the power spectral density of the equivalent nonlinear model of the concurrent dual-frequency power amplifier, an input power spectrum in an inverse model is defined as shown in a formula (7):
The nonlinear system is equivalent to a modified linear system and a modified nonlinear system, and the ideal acquisition of high-order intermodulation signals is demonstrated by using frequency spectrum, namely
When the value is equal to zero, the transmission function can stably and accurately represent the performance of the inverse model. However, the bandwidth of the feedback loop in the predistortion architecture is limited and it is inevitable to lose the high order intermodulation signal that needs to be acquired, i.e.
Not equal to zero. These missing high-order intermodulation signals affect the weight solution in the adaptive algorithm, so that the minimum mean square optimal solution cannot be obtained, and the acquisition error of the inverse model gradually increases, so that it can be seen that the feedback loop reconstructs the missing high-order intermodulation signals of the fifth order and the like, which has great influence on the predistortion effect.
Moreover, in the conventional predistortion structure, the sampling rate requirement of the converter is high, and the frequency band of the output signal of the power amplifier is wideDegree, interval of each band are all related, and the bandwidth of the output end of the power amplifier is (f)2-f1)+5×1.2max(B1，B2) And (3) sampling the MHz signal to obtain 5-order in-band quadrature and cross modulation products. Therefore, in order to improve the predistortion effect and reduce the sampling rate, an under-sampling digital predistortion system for reconstructing lost five-order and high-order signals with high precision is provided, namely, compressed sensing sampling is utilized in a predistortion feedback loop, and an adaptive sparse algorithm APSP is utilized to reconstruct five-order intermodulation signals, so that the sampling rate is reduced by utilizing the compressed sensing characteristic, the reconstruction signal precision is improved, the coefficient estimation weight is improved, the predistortion effect is improved, and the structure is introduced in detail.
The overall undersampled dual-frequency predistortion structure (as shown in fig. 1) mainly comprises a dual-frequency piecewise function memory effect compensator and an undersampled reconstruction feedback loop part. The double-frequency piecewise function memory effect compensator mainly comprises the following conversion processes:
since both the CPWL function and the polynomial function can be used to describe the non-linear characteristics of the power amplifier, it is assumed here that by a reasonable choice of the order of the polynomial function, the polynomial function can approximately replace the CPWL function, i.e.:
the memory effect compensator based on the dual-frequency piecewise function power amplifier model in the solid frame in the graph II is obtained by taking the formula (8) into the formula (6) as follows:
wherein, C1(n-i)e-jωnt+C2(n-i)ejωntAnd y (n) are respectively a model input signal, a model memory effect compensation signal, in which structure Ji(. for) a non-linear function, vq，iIs a transfer function WiThe coefficient of (·), Q is the highest order of the digital predistortion polynomial, and M is the length of the memory effect consideration.
And the other part mainly applies a compressed sensing self-adaptive sparse reconstruction algorithm to a feedback loop of the predistortion system. Namely, compressed sensing sampling is utilized in a predistortion feedback loop, and a five-order intermodulation signal is reconstructed by utilizing an adaptive sparse algorithm APSP. Input signal O of power amplifier in structurenEqually divided into two paths. One-path signal Xn(1) And entering a dual-frequency power amplifier. The other path utilizes the APSP algorithm of the self-adaptive sparsity to reconstruct the output signal of the concurrent double-frequency power amplifier into an original signal X containing the lost out-of-band high-order intermodulation information before undersamplingn(3). Defining P as a Gaussian matrix, Yn(2) For undersampled output vectors, Yn(3) For the reconstructed fifth-order vector, the algorithm is mainly used for adaptively estimating the sparsity under the condition that the sparsity is unknown, so that high-precision reconstruction is realized. Aiming at a double-frequency main signal, a five-order and high-order out-of-band intermodulation signal, the signal fusion is understood as a compressed sensing problem, and an APSP algorithm is utilized to reconstruct a complete signal, so that an undersampled predistortion structure is realized, the reconstruction precision of the out-of-band five-order signal is improved, the influence of the lost five-order and high-order signals on the least mean square solution of a weight in an identification algorithm is reduced, and the effect of a self-adaptive sparsity predistortion structure is improved.
The common indicators for evaluating the digital predistortion performance are the adjacent channel power ratio ACPR and the normalized mean square error NMSE. ACPR is defined as the power ratio of the adjacent channel output signal to the in-band carrier:
where Y (f) is the power spectral density, fneighborFor adjacent channel signal frequency, fmainIs a primary frequency channel
Normalized mean square error, NMSE:
wherein, ymeasure(α) is an input measurement signal, ymodelAnd the alpha is an output signal of the double-frequency power amplifier, and the beta is the number of sampling points.
Adaptive sparse signal reconstruction
Reconstruction of a condition M from compressed sensing>KlogN (where M, N is the rows and columns of the measurement matrix P and K is the sparsity) sets the sparsity initial value to (0-0.1) M, sets the measurement matrix P to the value given by the parameters (K,K) Satisfy RIP (RIP) limited isometricPropety, i.e., define if P satisfies:
wherein Y isn(2) Is K sparse signal, ifkIf the value is less than 1, the measurement matrix P is said to satisfy the RIP of K order. If K is0More than or equal to K, namely the sparsity estimated value is greater than the true value, then
The condition is true. Setting the thresholds T1 and T2 differentiates the energy into fast and slow dropping phases: greater than T1 is the region with larger energy difference, i.e. when the energy difference of the reconstructed signals in two adjacent stages is
Increasing the step length and reducing the reconstruction time; the region with smaller energy difference is larger than T2 and smaller than T1, i.e. when the energy difference of the reconstructed signals in two adjacent stages is
And the step length is reduced to improve the reconstruction precision.
According to a number of experimental results.
T1Selecting:
T2selecting:
the effect is better. To reduce the likelihood of overestimation, steps are taken hereLong S initial value S0＝M/[2log2(N)]. According to the above conditions, a reconstruction algorithm for adaptively estimating the sparsity of a signal, specifically a reconstruction algorithm for adaptively estimating the sparsity of a signal (as shown in fig. 2), is proposed herein for a feedback loop signal in an indirect learning predistortion structure.
The algorithm flow is as follows: firstly, setting a proper sparsity initial value K according to a compressed sensing reconstruction condition0The number of iterations can be reduced. Next, the initial value K is judged0In relation to the true value K when
Then K0And the estimation is larger than or equal to K, namely, the over-estimation or under-estimation phenomenon is prevented from being generated. Finally, when the initial value is smaller than the true value, a step S is added to the initial value.
Otherwise, one step S is decreased. For the selection of the step length S, in order to reduce the reconstruction time, the dynamic adjustment can be performed according to the energy difference of the reconstruction signals of two adjacent stages. Firstly, giving an initial value to S, if the adjacent signal energy satisfies
The step length needs to be increased by half of the original step length; if the adjacent signal energy satisfies
It is indicated that the energy difference between the two adjacent stages is small, the step size needs to be reduced by half.
The invention relates to a self-adaptive sparse predistortion structure based on a compressed sensing algorithm. In recent years, a Compressed Sensing (CS) technology is emerging in applications of signal compression, and can effectively reduce sampling pressure of a radio frequency front end. The CS theory is different from the traditional Nyquist sampling theorem, and when the signals are sampled, all N-dimensional signals do not need to be processed any more, but linear measurement is carried out by using an M-dimensional observation matrix far smaller than N. The design firstly understands signal fusion as a sampling reconstruction problem of compressed sensing through a memory effect compensator based on a piecewise polynomial model, namely reconstructs lost fifth-order and high-order intermodulation signals at high precision by using an adaptive sparse algorithm in a predistortion feedback loop, so that the least mean square solution of a coefficient weight approaches the optimum, reduces an acquisition error and improves a linearization effect. The method comprises the steps of carrying out compressed sensing sampling in a predistortion feedback loop, reconstructing five-order and high-order intermodulation signals by using an adaptive sparsity algorithm APSP, dynamically adjusting an initial value and a step length of sparsity according to the characteristics of the feedback loop signals to approach real sparsity, and then restoring the signals with high precision by using a subspace tracking algorithm to improve a coefficient estimation weight and improve the predistortion effect. Compared with the traditional predistortion, the undersampled double-frequency predistortion structure reduces the sampling rate, simultaneously improves the NMSE by about 2-3dB compared with 2D-MP, 2D-DDR and 2D-CPWL, enables the output power of the predistortion system to return by about 1dB, improves the ACPR to-49 dBc, is close to an ideal linear power amplifier, and can be widely applied to the development of multi-band communication.
While the foregoing is directed to the preferred embodiment of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
Claims (3)
1. A self-adaptive sparse predistortion structure based on a compressed sensing algorithm is characterized by comprising a memory effect compensator of a double-frequency power amplifier predistortion model based on a piecewise linear function and an under-sampling reconstruction feedback loop part;
compressed sensing sampling is carried out in a predistortion feedback loop, a five-order and high-order intermodulation signal is reconstructed by using an adaptive sparsity algorithm APSP, the initial value and the step length of sparsity are dynamically adjusted according to the self characteristics of the feedback loop signal to approach the real sparsity, and then the coefficient estimation weight is improved by using a subspace tracking algorithm high-precision recovery signal.
2. The adaptive sparse predistortion structure based on compressed sensing algorithm of claim 1, wherein the input signal of the power amplifier in the structure is equally divided into two paths, one path of signal enters the dual-frequency power amplifier, and the other path of signal utilizes the APSP algorithm of adaptive sparsity to reconstruct the output signal of the concurrent dual-frequency power amplifier into the original signal containing the missing out-of-band high-order intermodulation information before undersampling.
3. The adaptive sparse predistortion structure based on compressed sensing algorithm of claim 2, wherein P is defined as Gaussian matrix and Y is defined asn(2) For undersampled output vectors, Yn(3) And (4) performing adaptive estimation on the sparsity to realize high-precision reconstruction for the reconstructed fifth-order vector under the condition that the sparsity is unknown.
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