A Broadband Spectrum Sensing Algorithm in TDCS Based on ICoSaMP Reconstruction

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1 MATEC Web of Conferences 73, 03073(08) SMIMA 08 A roadband Spectru Sensing Algorith in TDCS ased on I Reconstruction Liu Yang, Ren Qinghua, Xu ingzheng and Li Xiazhao Inforation and Navigation College, Air Force Engineering University, Xi an, China Abstract: In order to solve the proble that the wideband copressive sensing reconstruction algorith cannot accurately recover the signal under the condition of blind sparsity in the low SNR environent of the transfor doain counication syste. This paper use band occupancy rates to estiate sparseness roughly, at the sae tie, use the residual ratio threshold as iteration terination condition to reduce the influence of the syste noise. Therefore, an I(Iproved Copressive Sapling Matching Pursuit ) algorith is proposed. The siulation results show that copared with algorith, the I algorith increases the probability of reconstruction under the sae SNR environent and the sae sparse degree. The ean square error under the blind sparsity is reduced. INTRODUCTION Transfor doain counication syste (TDCS) is one of the candidate technologies of cognitive radio. ecause of its good counication and anti-jaing perforance in low SNR environent and the advantages of flexible spectru access ode, it has a good developent prospects []. TDCS is very suitable for the field of ilitary counication interference due to its strong antijaing perforance. However, existing hardware can't bear the pressure of high sapling rate which broadband signals bring, at the sae tie, in the process of electronic warfare, the interference between hostile parties is usually accurate interference, including single tone interference, ulti-tone interference, narrowband interference and roadband interference, etc. On the other hand, TDCS counication environent is a low signal to noise ratio of the broadband environent. the wireless spectru has obvious sparse characteristics, so the copressed sensing theory is used into the field of TDCS broadband spectru sensing. Reconstruction algorith is one of the key technologies of copressed sensing. The greedy algorith in reconstruction algorith is widely concerned because of its siple structure and high reconstruction probability. The classical reconstruction algoriths include Matching Pursuit algorith [], Orthogonal Matching Pursuit [3] and Copressive Sapling Matching Pursuit [4] algorith. In paper [5], a double threshold orthogonal atching pursuit algorith is proposed. y double screening the selected atos, the signal can be reconstructed in the case of blind sparseness, but the axiu nuber of iterations in the iteration terination condition in the algorith is not introduced; In order to iprove the perforance of the reconstructed algorith based on the noise, a kind of copressed sensing denoising based on selective easureent is proposed in paper [6], However, the algorith ust know the a priori inforation of the signal sparseness, so the scope of its use is liited. In paper [7], a ulti-candidate singular orthogonal atching pursuit algorith is proposed for the proble that the recovery accuracy of greedy algorith is not high. However, the algorith also needs the priori inforation of sparseness, so the scope of use is liited. At present, the copressed sensing theory is applied to the field of TDCS broadband spectru sensing at hoe and abroad.in paper [8], a MIMO-TDCS copressed-sensing inforation feedback ethod based on tie-frequency two-diensional copression is proposed. In paper [9], a ethod for constructing the deterinistic ebedded chaotic sequence-cyclic Toeplitz structure copressed sensing observation atrix is proposed for the liitations of rando observation atrix in TDCS. these algoriths is based on the preise that the signal sparseness is known. However, the signal sparseness is usually unknown during the actual TDCS transission. In view of the above probles, Authors propose an I (Iproved Copressive Sapling Matching Pursuit) algorith. The algorith uses the frequency occupancy rate to estiate the sparsity of the signal and use the residual ratio threshold as iteration terination condition to reduce the influence of the syste noise. * Corresponding author: a9070@63.co, xubzheng@sina.co The Authors, published by EDP Sciences. This is an open access article distributed under the ters of the Creative Coons Attribution License 4.0 (

2 MATEC Web of Conferences 73, 03073(08) SMIMA 08 The siulation results show that the I algorith has a significant iproveent in the reconstruction probability copared with the algorith under the sae SNR and sparsity. The ean square error of the I algorith is lower than that of the algorith under the blind sparsity. This section ainly focuses on the background, probles, purpose and significance. Section ainly introduces the odel of this paper. Section 3 ainly analyses the algorith. Section 4 ainly introduces the solution of the probles. Section 5 introduces and analyses the I algorith this paper proposes. Section 6 ainly siulates the perforance of the I algorith. Section 7 ainly suarizes the full text. MODEL DESCRIPTION Set the working bandwidth of TDCS as. authorized users randoly occupy part of the band. the rest of band is idle, therefore, the broadband signal has soe sparsity in the frequency doain. As shown in Figure. Figure : roadband spectru sensing odel. In the front of the TDCS, the broadband copressed sensing fraework is built, and it is shown in figure. TDCS electroagnetic environent roadband analog signal x (t) AIC Observati on data Signal reconstruction Threshold decision Aplitude spectru vector Figure : TDCS roadband Copression sensing Fraework. AIC is an analog inforation converter, which is based on the copressed sensing theory. It can directly copress signal while sapling, therefore, we can get the observation vector y is: y = Φx () Where y is the M diensional observation vector, and each of the M values contains ost of the inforation of the original signal. Therefore, solving equation () belongs to NP proble. In the context of TDCS broadband spectru sensing, we can take advantage of the sparsity of x in the frequency doain, perforing fourier Transfor on x s = Fx () Where F is an N N discrete Fourier transfor atrix, s is the spectru of x, having K nonzero values, and K <M, It is called the sparseness of the signal s. Substituting equation () into equation () - y = ΦF s (3) y = Θs (4) Aong the, Θ is an M N-diensional observation atrix, which needs to satisfy the conditions such as RIP, Incoherence. For the solution of Eq. (4), the spectru s is usually reconstructed by solving a proble based on the iniization of the e 0 nor, and then the signal x is solved by using equation (). in s s 0 st.. y = Θs (5) x = F - s (6) The solution obtained by this solution is optial, but solving equation (5) is still an NP proble. The ain ethod of this ethod is to transfor the e 0 nor iniization proble into e nor iniization proble, and use the idea of linear prograing to solve the signal reconstruction [0]. The paper [] shows that the iniu nor of e and e 0 iniu nor are equivalent under certain conditions. Thus equation (5) can be written as in s s st.. y = Θs (7) At present, this paper ainly uses the greedy algorith as a fast and effective algorith to solve the above-entioned reconstruction proble. At present, it ainly includes atching pursuit algorith (MP), stagewise orthogonal atching pursuit algorith (St), orthogonal atching pursuit algorith () and copressive sapling atching pursuit algorith () and so on. 3 COSAMP ALGORITHM Copared with other greedy algoriths, the advantage of algorith is that it can identify ultiple atos in each iteration process, and can converge quickly. At the sae tie, we add the idea of "back check", which iproves the reconstruction precision and avoids the threshold selection proble. The algorith pseudo code is as follows. Input: observation atrix Θ, easured value y, sparse degree K. Output: rebuild signal ˆx. Initialize: x ˆ0 = 0, residual r = 0 y, iterations identify = 0, and the index Λ0 set is epty. () = +. () generate the interediate agent signal T u = Θ r, find u in the K large coponent of the location set Ω. (3)update Λ = Λ Ω and update the colun collection Θ=[ Θ- Θ ]. (4) reconstruct the signal, through the least squares estiation, get x = Θ y and retain the K axiu coponent, then get ˆx. (5) update the residual, r y Θx ˆ. =

3 MATEC Web of Conferences 73, 03073(08) SMIMA 08 (6) terinate the decision, if <K, then return (), otherwise (7). (7) output ˆx. In the above equation, Θ is called Θ s pseudo inverse. Although algorith has the advantages of fast convergence and good anti-noise perforance, its biggest flaw is that it needs to know the a priori inforation of signal sparseness, so its practical application potential is very liited. 4 ITERATION TERMINATION CONDITION OF RESIDUAL RATIO THRESHOLD In order to solve the shortcoing of the traditional iterative terination condition, a new iterative terination condition is proposed by the paper [], which solves the shortcoing of the traditional iteration terination condition under low SNR. First, the easured value y can be decoposed into y = y + e + e (8) Aong the, y is the noise-free interference signal. e is the noise for the bandwidth. e is the outside the noise for the bandwidth. e and y are independent of each other, then the th iteration r ( y ) can be written in the following for ( y) = ( ) y + e + e r r Siilarly, ( y) = ( ) y + e + r r e (9) + ( y) r is + ( y) = + ( y + e ) + r r e (0) With the increase in the nuber of iterations, the change of the r ( y+ e ) will be saller and saller, which is not enough to change becoe the ain factor of the ipact in r ( y ), then e r ( y ). Accordingly, the difference between the residuals of the two iterations is ore likely to reflect the iteration, and thus the iterative terination condition is r r f = () r In this equation, = r r is the residual coefficient, which can reduce the influence of rando noise and enhance the robustness of the algorith. θ is the set threshold and is independent of channel characteristics and noise. In this paper, the algorith based on the above ideas is iproved, and an I algorith is proposed. 5 ICOSAMP ALGORITHM 5. ALGORITHM ANALYSIS According to the analysis of algorith in Section 3, its biggest drawback is that we need to know the prior inforation such as signal sparseness and use it as the nuber of iterations, which greatly reduces its potential in practical application. In the fourth section, for the shortcoing of the traditional iteration terination condition, a residual ratio threshold iteration terination condition is proposed, which overcoes the influence of the process of reconstructing the signal at lower SNR. Fro the above analysis, the residual ratio threshold iteration terination condition can be applied to the algorith as an iteration terination condition without relying on the signal sparse degree K. that is, the iteration can be calculated once for each tie the residual ratio f, and then with the set threshold θ is copared, if f <θ, the iteration stops and outputs ˆx, otherwise iterates until f <θ. For the algorith in the iterative process of the sparse degree K, can be estiated by the occupation of the band. In TDCS practical engineering applications, the K of the signal is difficult to obtain, but the occupancy rate of a band is very easy to obtain, usually through the spectru detection equipent in a certain area to detect a band, or through The relevant spectru anageent departent to obtain long-ter survey results. after getting the band occupancy rate, the signal can be a slight estiate of the degree of sparseness. for exaple, the relevant US research departents on the 30MHz ~ 3GHz frequency band within the spectru of occupation, The result is 5.% ~ 3.%, so the range of sparseness of this band is N 5.% ~ N 3.%, where N is the Nyquist sapling frequency and the sparsity estiate K can be taken in this range. 5. ALGORITHM FLOW The code of the I algorith is as follows. Input observation atrix Θ, observed value y, estiation of sparsity K. () initialization: x ˆ = 0, residual r 0 = y, the nuber of iterations identified = 0, the index 0 set is epty. () = +. (3) generate the interediate agent T signal u = Θ r, find u in the K large coponent of the location of the collection Ω. (4) update Λ = Λ Ω and update the colun collection Θ =[ Θ- Θ ]. (5) reconstruct the signal, by least squares estiation, getting x = Θ y and retain the K largest coponents. Then get ˆx. (6) update the residual, r y Θx ˆ. = 3

4 Reconstruction probability Reconstruction probability MATEC Web of Conferences 73, 03073(08) SMIMA 08 (7) iterative decision, if f, ipleent (8), otherwise return (), the threshold value range is usually 0. to 0.5. (8) output ˆx. The algorith ends. In the iproved I algorith, do not need to know the signal sparse degree K, which is a priori inforation. we just need to know the frequency band of the study instead, and this paraeter in the actual application process is easy to obtain. In addition, another advantage of the algorith is the fusion of residuals ratio threshold iteration terination conditions and then the step (7) iterative decision process, instead of the signal sparsity of this iteration terination condition. Which solves the proble that algorith can not reconstruct the signal accurately under TDCS blindness. 6 SIMULATION ANALYSIS 6. RECONSTRUCTION PROAILITY ANALYSIS In order to verify the reconstruction effect of the I algorith, especially the difference in the reconstruction probability between I algorith and other algoriths in the lower SNR of TDCS. We use MATLA siulation platfor for verification. select Gaussian rando Measureent atrix as easureent atrix. Nyquist sapling frequency points N = 56, the nuber of observations M = 8, band occupancy rate = 0%, decision threshold = SIMULATION ANALYSIS OF RECONSTRUCTION PROAILITIES WITHOUT NOISY CONDITIONS Figure 3 shows the coparison of the reconstruction effects of, R, St, and I algoriths without noisy 信号稀疏度为 conditions. K 时的重构概率 (M=8,N=56) R St I Sparseness Figure 3: Coparison of reconstruction probabilities of different algoriths without noisy conditions. sparseness is lower than 3, each algorith can reconstruct the original signal with the probability of nearly 00%. When the signal sparseness is between 5 and 40, The reconstruction probability of and R began to decrease obviously, while and I algorith can reconstruct the original signal with the probability of nearly 00%. When the sparse degree is greater than 45, the reconstruction probability of and I algorith begins to drop even lower than that of the previous Several algoriths. This ay be due to and I algorith need to select ore atos as a support set and resulting in over atch in the higher sparse degree. so in the lower sparse degree, the perforance of I algorith reconstruction is obvious. 6.. SIMULATION ANALYSIS OF RECONSTRUCTION PROAILITIES UNDER NOISY CONDITIONS. The working environent of TDCS transission syste is the low SNR environent, therefore, it is ore significant to copare the perforances of each algoriths reconstruction probability in the low SNR environent. The experiental results are shown in the following figure. 信号稀疏度为 K 时的重构概率 (M=8,N=56) Sparseness R St I Figure 4: Coparison of reconstruction probabilities for different algoriths at SNR = Figure 4 shows the relationship between the reconstruction probability and the sparseness of the algorith under the low SNR. It can be seen fro the figure that the reconstruction probability of each algorith is affected by different degree in the environent of lower SNR. The reconstruction probability of I algorith is better than that of other algoriths. The calculation probability of I algorith is about 0% higher than that of algorith in the sae SNR environent. This is because I algorith uses the difference between adjacent iterations and the residual ratio coefficient to weaken the influence of rando noise, and then iprove its anti-noise perforance. Therefore, the advantages of I algorith in the lower SNR environent is ore obvious. It can be seen fro the figure that the reconstruction probability curve of I algorith is better than that of the previous algorith. When the signal 4

5 MSE MATEC Web of Conferences 73, 03073(08) SMIMA MEAN SQUARE ERROR (MSE) ANALYSIS In order to test the recovery accuracy of I algorith in TDCS low signal-to-noise ratio (SNR), this paper use ean square error (MSE) siulation analysis, signal sparseness K=5, spectru occupancy rate =0%, the easureent atrix selects the Gaussian rando easureent atrix, Nyquist sapling frequency points N=56, the nuber of observations M=8, the decision threshold = 0.. The siulation results are shown in the following figure I SNR Figure 5: Coparison of signal recovery MSE for different algoriths Figure 5 shows the curve of MSE value with the signal to noise ratio. ecause TDCS still has good perforance at lower SNR, the siulation environent in this paper is lower SNR. It can be seen fro the figure that the MSE is reduced with the increase of the SNR, and the MSE of the I algorith is slightly better than the algorith. This is due to the I algorith treats the residuals of the adjacent two iterations as the iteration terination condition and increases the residual ratio coefficient. These iproved easures ake the I algorith have soe antinoise perforance, so the accuracy of the recovered signal is higher than that of the algorith in the TDCS lower SNR environent. 7 CONCLUSIONS In the TDCS low SNR environent, the signal in the frequency doain has obvious sparse characteristics, so use the copressed sensing technology to sense TDCS front spectru environent. In practical engineering applications, the sparsity of the signal is difficult to obtain, and the traditional algorith in the use of the signal reconstruction needs to know this priori inforation. In this paper, the sparse degree of the signal is estiated by spectru occupancy situation, and the algorith is iproved by using the residual ratio threshold as an iteration terination condition, so the I algorith is proposed. The siulation results show that I algorith is ore accurate than algorith, and its anti-noise perforance is stronger, which is significant for wideband spectru sensing in TDCS low SNR. REFERENCES. T. C. XIE, X. Y. Da and Z. Y. Chu, An estiation algorith of basis function synchronous paraenters of Transfor Doain Counication Systes based on Frobenius Nor Journal of Air Force Engineering University, vol. 5(), Feb. 04, pp S. G. Mallat and Z. Zhang, Matching pursuits with tiefrequency dictionaries IEEE Transactions on Signal Processing, vol. 4(), 993, pp J. A. Tropp and A. C. Gilbert, Signal Recovery Fro Rando Measureents Via Orthogonal Matching Pursuit IEEE Transactions on Inforation Theory, vol. 53(), 007, pp D. Needell and J. A. Tropp, : Iterative Signal Recovery Fro Incoplete and Inaccurate Saples Applied & Coputational Haronic Analysis, vol. 6(3), 009, pp X. Y. Liu, Z. G. Zhao and H. X. Lv, Double threshold Orthogonal Matching Pursuit algorith Coputer Science, vol. 44, June. 07, pp L. Y. Pei, H. Jiang and R. L. Ma, Denoising recovery for copressive sensingbased on selective easure, Journal on Counications, vol. 38, February. 07, pp J. P. Tian, X. J. Liu and Y. P. Liu, Multi-candidate Set of Generalized Orthogonal Matching Pursuit Algorith Journal of Applied Sciences, vol. 35(), 07, pp C. L. Gao and Q. H. Ren, Study on MIMO-TDCS tiefrequency copressed sensing feedback schee Seiconductor Optoelectronics, vol. 35 june. 04, pp N. Li, Q. H. Ren and Y. Z. Su. Constructive ethod of CS easureent atrix in TDCS Coputer Engineering & Design, vol. 38, Jan. 07, pp Q. Li and X. Zhao, Adaptive Algorith for Wideband Spectru Sensing Journal of Jilin University, vol. 33, Mar. 05, pp A. M. MADNI, A systes perspective on copressed sensing and its use in reconstructing sparse networks IEEE Systes Journal, vol. 8(), 04, pp F. H. Fan and H. L. Ruan, Non-convex copressive sensing ultra-wide band channel estiation ethod in low SNR conditions Acta Electronica Sinica, vol. 4(), Feb. 04, pp Y. Chen and Z. QIN, Gradient-based copressive iage fusion Frontiers of Inforation Technology & Electronic Engineering, vol.6(3), 05, pp J. S. Dong, J. Y. Yin and C. F. LI, A gradient-based steering kernel reconstruction strategy for sei-rando Fourier easureents in copressed reote sensing Journal of Infrared & Millieter Waves, vol. 34(6), 05, pp J. Y. Zhuang, C. Qian and W. J. He, Iaging through dynaic scattering edia with copressed sensing Acta Physica Sinica, vol. 65(4), 06, pp

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