CN112769509A - 1-Bit compressed broadband spectrum sensing method based on sparsity self-adaption - Google Patents
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Abstract
The invention discloses a sparsity self-adaptive 1-Bit compressed broadband spectrum sensing method, which comprises the following steps of: the binary iteration hard threshold algorithm based on the pinball loss function is combined with the self-adaptive sparsity to construct an ASPIHT algorithm, then the signal sparsity is estimated in a self-adaptive mode by utilizing the fixed step length adjustment hard threshold value based on the ASPIHT algorithm, the original signal is recovered by utilizing the estimated signal sparsity, the 1-Bit compression broadband spectrum sensing based on the sparsity self-adaptation is realized, and the accuracy of the recovered signal is effectively improved.
Description
Technical Field
The invention belongs to the technical field of 5G mobile communication, and relates to a sparsity self-adaptive 1-Bit compressed broadband spectrum sensing method.
Background
In recent years, due to the rapid development of 5G technology, enormous data and information volume is generated, the requirement for signal broadband is higher and higher, and the broadband spectrum sensing technology faces the challenge of high sampling rate. In order to solve the problem, a cognitive radio broadband spectrum sensing technology based on a compressed sensing theory draws more attention. Compressed sensing consists of three parts, namely sparse representation of the signal, compressed observation of the sparse signal, and a recovery reconstruction of the compressed signal. The reconstruction algorithm is a key link for judging whether the theory can be practiced or not. However, the reconstruction algorithm for compressed broadband spectrum sensing is difficult to acquire the prior information of the signal when the signal is recovered, so that it is particularly important to perform blind sparsity research and improvement on the reconstruction algorithm.
For this reason, Tian et al first proposes and verifies the effectiveness of wideband spectrum sensing, and then proposes a wideband compressed spectrum sensing algorithm based on cyclic detection. Boufunos et al propose extreme quantization, i.e., 1-bit quantization, of the measured values, demonstrating that accurate and stable recovery can be achieved using only binary symbols of the compressed observations. The Binary Iterative Hard Threshold (BIHT) algorithm in the 1-bit compressed sensing can efficiently recover the original signal from the Binary compressed observed value. The BIHT algorithm has better reconstruction effect than other reconstruction algorithms, shows higher reconstruction signal-to-noise ratio and consistency, and has simple calculation process and low complexity. But the above algorithms all require known signal sparsity as a priori knowledge. In practical application, it is quite difficult to obtain the signal sparsity. And the reconstruction algorithm in the broadband spectrum technology has a serious dependence problem on the signal sparsity. This has been a problem to be solved in the field of signal processing. At present, however, most of the existing application perception research focuses on the reconstruction algorithm, and researches on how to improve the accuracy of the recovered signal and neglects the influence of signal sparsity information on the reconstruction effect.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a sparsity self-adaptive 1-Bit compressed broadband spectrum sensing method which effectively improves the accuracy of a recovered signal.
In order to achieve the purpose, the sparsity self-adaptive 1-Bit compressed broadband spectrum sensing method comprises the following steps of:
the binary iteration hard threshold algorithm based on the pinball loss function is combined with the self-adaptive sparsity to construct an ASPIHT algorithm, then the signal sparsity is estimated in a self-adaptive mode by utilizing the fixed step length adjustment hard threshold value based on the ASPIHT algorithm, the original signal is recovered by utilizing the estimated signal sparsity, and the self-adaptive 1-Bit compressed broadband spectrum sensing based on the sparsity is realized.
The method specifically comprises the following steps:
1b) obtaining a measurement vector y, an observation matrix phi, a maximum iteration number maxIter and a fixed step length m;
2b) setting x00, residual r0Y, iteration counter iter 0, estimated sparsity S m, stage index j 1, α>0；
3b) Recovery of the original signal is performed.
The specific operation of step 3b) is:
1c) calculating aiter+1＝xiter-αΦTgiter；
2c) Calculation of biter+1＝ηS(aiter+1) Updating the residual riter+1＝y-sign(Φbiter+1)；
3c) Calculating the energy difference of the signal estimation value when biter+1-xiter||2If the condition of not less than epsilon is not satisfied, turning to the step 4c), otherwise, turning to the step 5 c);
4c) judge riter+1||2≥||riter||2Whether the condition is satisfied or not, when | | | riter+1||2≥||riter||2If the condition is true, updating the iteration index j ═ j +1, iter ═ iter +1, updating the parameter S ═ j × m, and going to step 7 c); otherwise, go to step 5 c);
5c) let xiter+1＝xiter；
6c) Let r beiter+1＝riter；
7c) When iter is less than or equal to maxIter, turning to step 2c), otherwise, turning to step 8 c);
8c) outputting the recovery result
And an estimated sparsity S of the signal, wherein,
the invention has the following beneficial effects:
in the specific operation of the sparsity-adaptive-based 1-Bit compressed broadband spectrum sensing method, a binary iteration hard threshold algorithm based on a pinball loss function is combined with adaptive sparsity to construct an ASPIHT algorithm, then the hard threshold is adjusted by a fixed step length to recover an original signal based on the ASPIHT algorithm, and in the actual operation, exact sparsity information is not needed, the sparsity of the signal is estimated in a self-adaptive manner, the signal recovery is realized by the estimated sparsity, and meanwhile, the method is not easily influenced by the step length, so that an effective path is provided for the application of the actual 1-Bit compressed sensing theory.
Drawings
FIG. 1 is a reconstruction diagram of the SABIHT algorithm;
FIG. 2 is a graph of the reconstructed signal-to-noise ratio of a Bernoulli signal under BIHT and ASBIHT algorithms under noise-free conditions;
FIG. 3 is a reconstructed SNR graph of a Gaussian signal under BIHT and ASBIHT algorithms under a noise-free condition;
FIG. 4 is a graph of the reconstructed signal-to-noise ratio of a Bernoulli signal under BIHT and ASBIHT algorithms under noisy conditions;
FIG. 5 is a graph of reconstructed SNR for a Gaussian signal under BIHT and ASBIHT algorithms under noisy conditions;
FIG. 6 is a comparison graph of reconstructed SNR of PIHT algorithm and ASPIHT algorithm under different initial step sizes
FIG. 7 is a comparison graph of reconstructed SNR for different initial step sizes of the ASPIHT algorithm;
FIG. 8 is a graph comparing the number of iterations of the ASPIHT algorithm at different initial step sizes;
FIG. 9 is a graph of four algorithm reconstructed SNR;
FIG. 10 is a graph of the four algorithms reconstructed mean angular error contrast;
FIG. 11 is a comparison graph of mean Hamming errors reconstructed by the four algorithms.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
The invention introduces self-Adaptive Sparsity into a BIHT algorithm, provides a Sparsity self-Adaptive Binary Iterative Hard threshold (SABIHT) algorithm, and accurately reconstructs signals with unknown Sparsity by learning signals and noise, thereby solving the problem of dependence of the BIHT algorithm on the Sparsity of the signals. The SABIHT algorithm is obtained by fusing a sparsity self-adaption strategy under a BIHT framework, the BIHT is an adaptation algorithm of an Iteration Hard Threshold (IHT), and the goal of the BIHT algorithm is to find a formula phiTThe minimum estimated value of (y-sign (phi x)) is mapped to a unit spherical surface through a hard threshold function after the minimum estimated value is found by using a gradient descent method, and the size of the signal sparsity K determines the size of a threshold in the hard threshold function;
the BIHT algorithm is mainly calculated as:
xiter+1＝ηK(aiter+1) (2)
wherein,
the term is convex single side1Norm j (x) ═ ye Φ x]_||1Thus the BIHT algorithm tends to reduce the objective function j (x) during each iteration, e representing the hadamard product, representing the result of multiplying two spaced corresponding elements, [ g [, g ] ]]Denotes a negative function, i.e. if ui<0, then [ u ]i]_＝uiOtherwise, [ u ]i]_0. J (x) is convexFunction, so J (x) ═ Σ J existsi(x) At the same time each Ji(x) Can be given by formula (3):
wherein phi isiRepresents the ith row of the observation matrix phi, and Ai(x)＝sign(<φi,x>)。
When in use<φi,x>Not equal to 0, then Ji(x) The gradient of (d) is:
when in use<φi,x>If 0, then the gradient will have a differential subset instead:
thus, after i is accumulated, get
Thus, the improved BIHT algorithm can be understood as attempting to solve the following problems:
s.t.||u||0＝K,||u||2＝1 (6)
the specific process of the ASBIHT algorithm comprises the following steps:
1) obtaining a measurement vector y, an observation matrix phi, iteration times maxIter and a residual error proportion gamma, wherein gamma is more than or equal to 0 and less than or equal to 1;
2) initialization: x is the number of00, 0 is the iteration counter iter;
xiter+1＝ηγ(aiter+1) (8)
ηγ(aiter+1) For retaining vector aiter+1In2Norm greater than gammah| u | | non-woven phosphor2The other elements are set to be 0;
3) when iter +1 is not more than maxIter, turning to step 1); otherwise, turning to the step 4);
4) obtain the output result
Comprises the following steps:
x in the formula (8)iter+1＝ηK(aiter+1) By selecting the K elements with the largest coefficients, for xiter+1A sparsity constraint is added. The conventional BIHT algorithm is in the iterative calculation process, xiter+1Approaching to real x step by step, x being sparse in signaliter+1Is concentrated in some minority elements and thus can pass through vector xiter+1The energy possessed by the element(s) in (b) distinguishes between the noise and signal components contained therein. The ASBIHT algorithm selects a vector xiter+1To zero the remaining elements to an energy greater than the vector xiter+1Gamma xiter+1||2. The ASBIHT algorithm differs from the conventional BIHT algorithm in that: in the conventional method, the BIHT algorithm needs the signal sparsity K as prior information because elements whose number is equal to the signal sparsity K in the signal vector are reserved and other elements are set to zero. The ASBIHT algorithm can concentrate energy on the characteristic of few elements for utilization, and the elements occupy the vector l2The ratio of norms imposes a sparsity constraint on the resultant vector.
Method two
The method combines a binary iteration hard threshold (PIHT) algorithm based on a pinball loss function with self-adaptive sparsity to construct an ASPIHT algorithm. The hard threshold is adjusted by using a fixed step length to realize the signal sparsity self-adaptation of the algorithm, and the problem of unsatisfactory reconstruction effect caused by unknown signal sparsity is solved.
The invention summarizes the specific implementation process of the fixed step length method into the following three steps:
1a) determining the size of a fixed step length m to enable the size to meet the condition that m is less than or equal to K;
2a) taking the size of the step length m as the initial value of a hard threshold in a reconstruction algorithm to perform spherical mapping, calculating the energy difference and the residual error of the signal estimation value in the adjacent two iteration processes, simultaneously judging whether the residual error is reduced along with the increase of the iteration times, and calculating whether the energy difference of the two signals meets | | xiter-xiter-1||<ε；
3a) When the residual error is reduced along with the increase of the iteration times, and the energy difference of the two signals meets | | xiter-xiter-1||<And e, recording the size of the hard threshold at the moment, and performing signal recovery by taking the hard threshold at the moment as the estimated signal sparsity.
After the adaptive sparsity method is introduced into the PIHT algorithm, the implementation process of the algorithm is improved as follows:
1b) obtaining a measurement vector y, an observation matrix phi, a maximum iteration number maxIter and a fixed step length m;
2b)x00, residual r0Y, iteration counter iter 0, estimated sparsity S m, stage index j 1, α>0；
1c) Calculating aiter+1＝xiter-αΦTgiter；
2c) Calculation of biter+1＝ηS(aiter+1) Updating the residual riter+1＝y-sign(Φbiter+1)；
3c) Calculating the energy difference of the signal estimation value when biter+1-xiter||2If the condition of not less than epsilon is not satisfied, turning to the step 4c), otherwise, turning to the step 5 c);
4c) judge riter+1||2≥||riter||2Whether the condition is satisfied or not, when | | | riter+1||2≥||riter||2If the condition is true, updating the iteration index j ═ j +1, iter ═ iter +1, updating the parameter S ═ j × m, and going to step 7 c); otherwise, go to step 5 c);
5c) let xiter+1＝xiter；
6c) Let r beiter+1＝riter；
7c) When iter is less than or equal to maxIter, turning to step 2c), otherwise, turning to step 8 c);
8c) outputting the result
And an estimated sparsity S of the signal, wherein,
as is known, the PIHT algorithm has a good reconstruction effect when the parameter τ in the pinball loss function is-0.2, so that the parameter τ values in the following experiments are all-0.2.
Fig. 1 shows an asbit algorithm reconstruction diagram, and the specific process is as follows:
firstly, selecting a fixed step length s as an initial hard threshold parameter, judging whether an estimated hard threshold meets requirements through test conditions, controlling the hard threshold parameter to gradually approach a signal sparsity k by taking the step length s as the step length, and finally recovering the signal according to a BIHT principle by using the estimated hard threshold parameter.
The test conditions of the ASBIHT algorithm comprise the energy difference of adjacent two-stage reconstruction signals and the magnitude of residual energy, and the ASBIHT algorithm is combined with the theory discussed above, so that the ASBIHT algorithm realizes coarse estimation of sparsity and initialization of iteration variables, and a sparse adaptive iteration part under a BIHT framework.
Example one
Sparsity self-adaptive method simulation based on BIHT algorithm
In order to prove that the performance of the ASBIHT in the aspect of signal recovery is effective and objective, experimental simulation is carried out through an MATLAB program, and the comparison of the algorithm in the aspect of signal reconstruction performance under the influence of no noise and noise is carried out respectively, wherein the specific environments of the experiment are as follows: the configuration of the computer is Intel Core i5-5200U 4 Core CPU, the main frequency is 2.20GHz, the memory is 8GB, the operating system windows 1064 bits, and the software is Matlab R2018 a. The signal recovery performance index mainly takes a mainstream evaluation index as a standard, and comprises the following steps: reconstructed signal-to-noise ratio (SNR) and average reconstruction angle error (AAE).
Without the influence of noise
First, a random gaussian matrix is adopted as the sensing matrix Φ, wherein the length of the simulation signal is fixed to be N-256, and the number of observations M is increased from 50 to 600 by the step size 50. The average reconstructed signal-to-noise ratio of the BIHT algorithm with the proposed adaptive BIHT algorithm at sparsity K20, 40,60 is compared. In the simulation experiment process, the signal sparsity of the traditional BIHT algorithm is manually input, and when the simulation signal is changed, the updated accurate signal sparsity value is simultaneously input, but the signal sparsity is not given by the algorithm provided by the invention under the same experiment condition. Each of the simulation experiments was performed 100 times under different observation conditions.
Fig. 2 shows the results of the reconstruction performance test using bernoulli signals, where the sparsity of the signals is 20,40, and 60, respectively, the reconstruction signal-to-noise ratios of the two algorithms are gradually increased with the increase of the number of observations for the sparse bernoulli signals, and the adaptive BIHT algorithm that does not need to acquire the sparsity of the signals in advance has almost the same effect as the conventional BIHT algorithm in terms of reconstruction effect.
The simulation signal of fig. 3 is a classical gaussian sparse signal, and it can be seen from fig. 3 that the reconstruction results of the signals of the two algorithms under different experimental conditions are similar, and the reconstruction signal-to-noise ratio stably rises with the increase of the number of observed values.
Conditions influenced by noise
The sensing matrix phi adopts a random Gaussian matrix, wherein the length of an original simulated signal is fixed to be N-256, the number M of observed values takes three values of 300, 350 and 400, and the symbol inversion of a certain observed value symbol caused by the influence of noise is assumed to exist in a signal vector. And comparing the average reconstruction signal-to-noise ratio of the BIHT algorithm and the proposed adaptive BIHT algorithm under the condition that the sparsity is respectively 10,20,30,40,50 and 60. Each of the simulation experiments was performed 100 times under different observation conditions.
Fig. 4 adopts a sparse bernoulli signal, fig. 5 adopts a sparse gaussian signal, and the reconstruction results of the two algorithms show that the reconstruction effects of the two algorithms are good when reconstructing sparse signals with different signal sparsity under the noise condition, and the signal reconstruction signal-to-noise ratio is increased. Therefore, the self-adaptive BIHT algorithm in the 1-Bit compressed sensing can accurately reconstruct sparse signals under the condition that the signal sparsity is not acquired under the noise condition, and the problem of reconstruction accuracy reduction caused by the fact that the signal sparsity cannot be acquired can be solved.
Fixed step length PIHT algorithm performance test
After the fixed step length method is introduced, the reconstruction performance of the BIHT algorithm is greatly influenced by the difference of the value of the step length m. Therefore, in this embodiment, after the step length m is introduced through experimental investigation, the influence of the selection of the value m on the reconstructed signal-to-noise ratio of the adaptive PIHT algorithm is considered.
In the first experiment, a sparse bernoulli signal is adopted, the signal length N is 256, the number of observed values M is 300 to 600, the interval size is 50, the sparsity K is 20, the step length M is M1, 5 and 10, 10% of symbol value inversion exists in the signal, 100 simulation experiments are respectively performed under each initial step length and the number of observed values, and the observed matrix is a gaussian random matrix. The experimental result is shown in fig. 6, when the fixed step length m is 5 and 10, the reconstructed signal-to-noise ratio of the adaptive PIHT algorithm is higher than that of the conventional PIHT algorithm, and when the number of observed values is greater than 400, the reconstructed signal-to-noise ratios of the adaptive PIHT algorithm and the conventional PIHT algorithm are almost the same, but the reconstruction effect of the adaptive PIHT algorithm is slightly better than that of the data when the fixed step length is 5 when the step length is 10.
Experiment two, the simulation signal adopts sparse bernoulli signal, the length of the signal is fixed to be N-256, and the number M of observed values in this experiment is fixed to be 300, the sparsity selects different values K-10, 20,30,40,50,60, the step length M is respectively the value M-1, 5, 10% sign value inversion exists in the signal, and the observation matrix is gaussian random matrix. The simulation results are shown in fig. 7 and 8, when the step size value m is 10, the reconstruction performance of the two algorithms is the closest, the difference between the iteration times of the adaptive PIHT algorithm under different step sizes is relatively large, and when the step size m is 1, the iteration times of the algorithm are too high. And when the step size is m-10, the iteration number of the algorithm given in this chapter is even lower than that of the traditional PIHT algorithm, and the reconstruction performance is equivalent at the moment. The simulation experiment shows that the larger the value of the fixed step length is, the fewer the iteration times of the algorithm is, and meanwhile, the reconstruction effect of the algorithm is acceptable because the values of the step length are different. Because the accurate signal sparsity cannot be obtained in advance in practical application, the iteration times can be reduced by increasing the step length, and the calculation complexity is reduced. However, when the step size is large, a relatively large estimation error is likely to occur, and therefore, in the following experiments, a fixed step size m is selected as 10.
And a third experiment is used for verifying the reconstruction performance of the adaptive PIHT algorithm under the noise condition and comparing the reconstruction performance with the experiment result of the adaptive BIHT algorithm under the same experiment condition. In this experiment, it is assumed that the original signal length N is 256 and the sparsity K is 20, 10% symbol value inversion exists due to noise influence, the signal-to-noise ratio is 50dB, the number M of observed values is 300 to 600, the initial step value M is 10, and the observation matrix is a gaussian matrix.
Fig. 9 shows the variation of the reconstructed snr of the four algorithms under different numbers of observation values, and it can be seen from the experimental results that the average snr of the reconstructed signal of the (noisy) BIHT algorithm is significantly lower than that of the PIHT algorithm under the same experimental conditions. In the process that the number of observed values is increased from 300 to 600, the average reconstruction signal-to-noise ratio difference value of the two algorithms is increased from 2dB to about 4dB, so that the PIHT algorithm has the advantage of obvious reconstruction signal-to-noise ratio due to higher robustness under the influence of noise. And the average signal-to-noise ratio difference can reach about 1dB at most. Therefore, for the evaluation criterion of the reconstruction signal-to-noise ratio, the adaptive PIHT algorithm can completely reach the reconstruction performance of the traditional PIHT algorithm under the prior condition of not needing the signal sparsity, and even can exceed the performance of the traditional PIHT algorithm with a large probability.
Fig. 10 shows the variation of the average angle error of the four algorithms under different numbers of observed values, and from the experimental results, it can be seen that the reconstruction angle error of the PIHT-based algorithm (including noise) under the same experimental condition is smaller than that of the BIHT-based algorithm, and the adaptive average reconstruction angle error at each number M of observed values can reflect the advantages of the adaptive PIHT algorithm provided by the present invention, which can have better reconstruction performance in the recovery of the original signal, and the adaptive PIHT algorithm provided by the present invention has objectively improved performance.
Fig. 11 shows the variation of the average hamming error of the four algorithms under different numbers of observed values, and it can be seen from the experimental results that the average error of the (noisy) PIHT algorithm under the same experimental condition is significantly smaller than that of the BIHT algorithm, and the improved PIHT algorithm and the sparsity adaptive BIHT algorithm of the present invention exhibit the advantage of noise immunity with the increase of the number of observed values.
The invention has the following advantages:
different from the traditional BIHT algorithm, no matter in the noise-free condition or in the noise condition, the invention can adaptively estimate the signal sparsity without exact sparsity information, realizes signal recovery by utilizing the estimated sparsity, has the performance equivalent to that of the BIHT algorithm with the known sparsity, and can better realize reconstruction.
According to the ASPIHT algorithm, a fixed-step sparsity self-adaptive method is introduced into the PIHT algorithm, and the problem that reconstruction accuracy of a traditional PIHT algorithm is reduced when sparsity signals are unknown under a noise condition is solved. Simulation experiment results show that reconstruction performance of the PIHT algorithm under the noise condition is obviously superior to that of the BIHT algorithm, and compared with the situation that reconstruction performance of the traditional PIHT algorithm is reduced under the condition that signal sparsity information is unknown, the adaptive PIHT algorithm can realize accurate reconstruction of signals under the same condition.
Claims (3)
1. A sparsity self-adaptive 1-Bit compressed broadband spectrum sensing method is characterized by comprising the following steps:
the binary iteration hard threshold algorithm based on the pinball loss function is combined with the self-adaptive sparsity to construct an ASPIHT algorithm, then the signal sparsity is estimated in a self-adaptive mode by utilizing the fixed step length adjustment hard threshold value based on the ASPIHT algorithm, the original signal is recovered by utilizing the estimated signal sparsity, and the self-adaptive 1-Bit compressed broadband spectrum sensing based on the sparsity is realized.
2. The sparsity-adaptive-based 1-Bit compressed broadband spectrum sensing method according to claim 1, specifically comprising the steps of:
1b) obtaining a measurement vector y, an observation matrix phi, a maximum iteration number maxIter and a fixed step length m;
2b) setting x00, residual r0Y, iteration counter iter 0, estimated sparsity S m, stage index j 1, α>0；
3b) Recovery of the original signal is performed.
3. The sparsity-adaptive-based 1-Bit compressed broadband spectrum sensing method according to claim 1, wherein the specific operation of step 3b) is as follows:
1c) calculating aiter+1＝xiter-αΦTgiter；
2c) Calculation of biter+1＝ηS(aiter+1) Updating the residual riter+1＝y-sign(Φbiter+1)；
3c) Calculating the energy difference of the signal estimation value when biter+1-xiter||2The condition that the epsilon is less than or equal to not satisfied,go to step 4c), otherwise, go to step 5 c);
4c) judge riter+1||2≥||riter||2Whether the condition is satisfied or not, when | | | riter+1||2≥||riter||2If the condition is true, updating the iteration index j ═ j +1, iter ═ iter +1, updating the parameter S ═ j × m, and going to step 7 c); otherwise, go to step 5 c);
5c) let xiter+1＝xiter；
6c) Let r beiter+1＝riter；
7c) When iter is less than or equal to maxIter, turning to step 2c), otherwise, turning to step 8 c);
8c) outputting the recovery result
And an estimated sparsity S of the signal, wherein,
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