Jingjing Yang ^1，3 ，Dezhang Chen ² ，Hao Tang ² ，Jiang Yu ¹ ，Ming Huang ^1*

1.Wireless Innovation Lab of Yunnan University，Kunming 650091，China

2.Radio Monitoring Center of Yunnan Province，Kunming，650228，China

3.Kunming Key Lab of Spectrum Sensing and Radio Monitoring，Kunming 650091，China

*E－mail：huangming＠ynu.edu.cn

Abstract： Detection and direction finding of illegal emission source is the core issue of radio monitoring network.However，the performances of traditional fixed stations and mobile stations which are based on energy detection and work individually are often compromised with multipath fading and shadowing in urban environment.To mitigate the impact of these issues，a cooperative compressed spectrum sensing model which consists of several sensing nodes and a fusion node is proposed in this paper.The maximum minimum eigenvalue based detection method is applied to the sensing model.Simulation results show that cooperative compressed sensing provides an efficient way to sense radio signal which is sparse at frequency domain.

1 Introduction

Radio spectrum is the essential natural resource for wireless communication.In order to share this resource the spectrum allocation policy which provides fixed allocation to license user has been adopted for long time，and it is the mission ^［1］ of radio spectrum management department to identify and eliminate illegal emissions，as well as ensure radio spectrum safety.As thus，spectrum monitoring platforms from stand alone systems to completely automated nationwide networks have been established.Taking Yunnan Province as an example，a spectrum monitoring network ^［2］ containing more than 130 stations，covering 178 000 square kilometers has been established in the second and third phase of the monitoring network construction projects.However，with the development of wireless communication and urbanization，electromagnetic environment is becoming more and more complex，which has put a great challenge to radio spectrum monitoring.For example，due to the rapid increase of tall buildings in modern cities，the coverage of traditional monitoring station is decrea sing，which has seriously affected the direction finding ability；some stations even lost the associated location functionality.Developing grid monitoring network，of which the sensing nodes work cooperatively，is the best solution to these problems.Although the grid network has been firstly proposed in some ITU documents in the 90's of the 20th century，it remained in concept in that time due to a combination of limitations such as the RF technology，processing ability of computers，network capacity and information processing techniques.Nowadays，the maturation of software defined radio and high performance computer systems makes the development of grid radio monitoring possible.Recently，cooperative sensing，which is the basis for grid radio monitoring network becomes a research hotspot.For example，the task of spectrum sensing in a cognitive network is to detect spectrum holes licensed to primary users；although sensing can be performed by each secondary receiver in a non cooperative fashion，cooperative spectrum sensing has been demonstrated to be able to combat multipath fading，shadowing and mitigate the receiver uncertainty problem，which gives raise to a combined decision more accurate than the individual decisions ^［3，4］ .

Generally，increasing the sensing node in acooperative sensing network will give raise to a much more accurate detection.But this will increase the network transmission burden at the same time.In this paper，a cooperative compressed spectrum sensing model is proposed，and its performance is simulated and analyzed.The rest of the paper is organized as follows.In section 2，framework of the sensing model is given and the eigenvalue based cooperative compressed sensing technique is introduced.Simulation results are shown in section 3 and conclusions are made in section 4.

2 The Cooperative Compressed Spectrum Sensing Model

A diagrammatic sketch of the sensing model is depicted in Figure 1.It consists of several sensing nodes（SN）and a fusion node（FN）.The sensing nodes are supposed to be equipped with software defined radio platforms such as USRPs which are responsible for receiving the signal transmitted from the illegal emission source（S）.Signal samples received at these sensing nodes are compressed and then transmitted to the fusion node（FN）which takes charge of signal reconstruction and cooperative detection.The fusion node is connected to the monitoring center，which is capable of controlling the working status of the whole system.Location of the emission source is supposed to be displayed in real-time on an electronic map，and then authorized to the mobile terminal，guided by which the target emission source could be found out flexibly.In what follows，the cooperative compressed sensing process is simulated.

Suppose that there arem sensing nodes in the system，each one collecting N samples of the received signal from the illegal emission source，and we denote it as X∈ ^N×1 .Generally，radio signal is sparse in the frequency domain and hence，it is compressible.So that，X can be approximated in a given domainψ∈ ^N×K ，as x≈ψv，where K is the sparsity defined as maximum non zero elements，v is the sparse vector.We assume that the received signal at each sensing node is compressed to X′＝ΦX.Here，Φis a measurement matrix with size M×N（M＜＜N），following Gaussian distribution；the compressive ratio is denoted asδ＝M／N.Considering that these samples are arranged in a matrix Y′∈ ^δN×m at the fusion node.Similarly，consider that the transmitted sig nal samples from the illegal emission source are compressed and arranged in a matrix X′∈ ^δN×1 .Let H∈ ^1×m be the channel matrix with elements｛h _i ｝，i＝1，2，...，m，representing the channel gain between the i th sensing node and the illegal emission source.Finally，let V and V _IN ∈ ^δN×m be the matrices contain thermal noise and impulse noise sample that corrupt the received signal.The matrix of the collected sample is then Y′＝X′H＋V＋V _IN .The reconstructed matrix is denoted as Y∈ ^m×N .Signal reconstruction algorithm comes in two main varieties ^［5］ ，convex optimization algorithm and greedy algorithm.The greedy algorithm basically measures inner product through repetitive structure，and selects a column of that has the highest correlation with signal X.There are some kind of greedy algorithm such as MP，OMP，CoSaMP，and IHT.OMP algorithm ^［6］ is adopted in the paper.

At the fusion node，the covariance matrix R＝YY ⁺ of the reconstructed signal samples is obtained，and the eigenvalues｛λ ₁ ≥λ ₂ ≥...λ _m ｝of R are then computed.Here，（.） ⁺ represents the complex conjugate and transpose.The spectrum sensing can be formulated as a binary hypothesis test problem，i.e.H ₀ ：Primary signal is absent，H ₁ ：Primary signal is present，where H ₀ is called null hypothesis，meaning that there is no illegal emission in the spectrum band，and H ₁ is the alternative hypothesis，which indicates the appearance of illegal emission.Two important parameters associated with the spectrum sensing performance are the detection probability，P _d ，and the false alarm，P _fa ，which are defined as P _d ＝Pr｛decision＝H ₁ ｜H ₁ ｝＝Pr｛T＞＝λ｜H ₁ ｝，P _d ＝Pr｛decision＝H ₁ ｜H ₀ ｝＝Pr｛T＞＝λ｜H ₀ ｝，where Pr（.）is the probability of a given event，T is the detection dependent test statistic andγis the decision threshold.Test statistic T is determined by different detection techniques.There have been several sensing algorithms including the energy detection，matched filtering，and the cyclostationary feature detection，each having different operational requirements，advantages and disadvantages ^［7］ .Energy detection is the most popular method among spectrum sensing techniques due to its simplicity，and it does not need any information of the signal to be detected and is robust to unknown dispersive channel.However，energy detection relies on the knowledge of accurate noise power，and inaccurate estimation of the noise power leads to high probability of false alarm as well as miss detection.To overcome the shortcomings of energy detection，the detection method based on the eigenvalues of the covariance matrix of received signal is developed by Zeng et al. ^［8］ .It is shown that the maximum minimum eigenvalue detection（MMED）performs well even in noise environment.As thus，MMED is adopted in this paper，and the test statistic T is calculated as T＝λ ₁ ／λ _m .

3 Simulation Results and Discussion

It is supposed that anamplitude modulated（AM）signal x＝（A＋x ₀ ）cos（2πf _c t）is generated by the illegal emission source.Here，x ₀ ＝A ₀ cos（2πft）is the waveform that the message is to be transmitted，A（A ₀ ）andf _c （f）represent the amplitude and frequency of the carrier wave and message wave.In the following simulation，parameters of the AM signal are set to be A＝2，A ₀ ＝ ，f _c ＝10Hz andf＝2Hz；time t is supposed to vary from 0 to 1s with an interval of 1／N，N is an integer which represents the length of the signal collected at the fusion node.Since the AM signal is sparse in frequency domain，compressed sensing is applicable.A comparison between the original AM signal and the recovered signal using OMP algorithm is shown in Figure 2.The measurement matrix is the Gaussian matrix with a size of M×N＝23×26.After 500 times simulation，we get the average error rate is approximate to zero，which indicates that the original signal with a length of 256 can be compressed to 1％of its real size in the absence of channel interference.However，the signal received at each sensing node is a superposition of noise and effective signal.To investigate the performance of the algorithm in noise environment，we suppose the signal received at each sensing node experienced Rayleigh fading，interfered by thermal noise and impulsive noise.The original signal and the recovered signal is plotted in Figure 3（a）.Results indicate that the error rate is about 0.52 when SNR＝5 andδ＝0.5.Generally，for a given compression ratio，error rate decreases gradually with increasing SNR，as shown in Figure 3（b）.So that to ensure the error rate is less than 0.5，SNR should be great than 5dB.Besides，for a specified SNR，error rate decreases with increasing compression ratio，and a saturation status can be achieved in the range ofδ＝0.2 toδ＝0.9.

Figure 4 shows the probability density（histograms）of the test statistic generated from simulation for SNR＝－5（left）and SNR＝20（right）.The histograms depict the hypothesis of no illegal emission（H ₀ ）and illegal emission present（H ₁ ）when m＝6 and N＝256.One can notice that P _d will increase with increasing SNR for a fixed threshold，since the area of the histogram on the right of a given threshold under H ₁ increases，and it separate from that ofH ₀ .The net result is an increased P _d for a given P _fa or a reduced P _fa for a given P _d .

The ROC curve which depicts the relation between P _d and P _fa for different values of SNR is shown in Figure 5（a）.Length of the signal observed at the fusion point is set to be 256，the compression ratio isδ＝0.5.The threshold rangeγis 0 to 20 for SNR＝20dB，1 to 12 for SNR＝15dB，and 1 to 10 for SNR＝10dB.The more a ROC curve bends toward the upper left，the better is the detection performance since a higher P _d and lower P _fa is achieved.It reveals that a high SNR willgive rise to a performance improvement.For example，when SNR＝20，P _d approximates 1 at the point of P _fa ＝0.1；while for SNR＝10，P _d saturates at a much higher P _fa which is about0.75.From these analysis，we find that the signal transmitted to the fusion node cannot be totally reconstructed due to the impact of noise.To investigate whether it will degrade the performance of the whole system，ROC curves of the spectrum sensing network are compared to the one without compressed sensing.Figure 5（b）shows the simulation results for SNR＝5 and SNR＝20.It is seen that the ROC curves for the system with and without compressed sensing overlap well.This indicates that the compressed sensing block added to the spectrum sensing network does not affect the performance of the system，but it could save the transmission resources from the sensing nodes to the fusion node.

4 Conclusion

A cooperative compressed sensing model for regional radio monitoring is proposed.The received signal is compressed at each sensing node and then transmitted to the fusion node，at which OMP algorithm is adopted to reconstruct the signal.When the SNR is 20dB，a detection probability of 95％could be achieved at the compression ratio of0.5.Interestingly，we find that although the received signal cannot be recovered completely under noise environment，it doesn't affect the performance of the system.Due to compressed sensing is integrated into the detection system，transmission resources can be saved to a great extend.But on the other hand，this will increase the workload of the fusion node，which is in charge of both the signal reconstruction and cooperative sensing.As thus，the study of parallel algorithm for enhancing the signal processing efficiency at the fusion node and implement of the system based on USRP remains our future work，and more results will be published latter.

Acknowledgments

This work was supported by the National Natural Science Foundation of China（Grant Nos.61161007，61261002，61162004），the Specialized Research Fund for the Doctoral Program of Higher Education（Grant Nos.20125301120009，20125301120009），China Postdoctoral Science Foundation（Grant No.2013M531989），and the Key Program of Natural Science of Yunnan Province（Grant No.2013FA006）.

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本文发表在国际会议31st URSI General Assembly and Scientific Symposium（p.16－23，Aug.，2014，Beijing，China），发表时有删改。 ZldlV2sA7u2+UijZaCtc9BAnZavdj9ds47VKto2qqjadYoQLi071WIOawNGjzZdc