In order to ensure the practicality of the scheme, the signal quality of the sur- rounding area can be estimated before set up the base station, and verify it by the ITU-RP.526 model. The result shows as Fig.4.
Fig. 4.Reconstructed result of prediction of ITU-RP.526 model, Pe = 0.0737.
The jammers are located at
1. 12.31342◦E, 50.23786◦N, frequency is 150.42 MHz, power is 40 W.
2. 12.30368◦E, 50.24468◦N, frequency is 150.61 MHz, power is 30 W.
3. 12.30154◦E, 50.22156◦N, frequency is 150.35 MHz, power is 20 W.
The useful receiver is located at 12.33161◦E, 50.23611◦N, frequency is 150.55 MHz, power is 30 W.
The results show that when sampling points are 25%, it is already clear to distinguish the area of high SNR from low SNR. It meets actual demand and proves the correctness of the scheme.
5 Conclusion
The paper introduced an estimate method based on compressed sensing. The method can solve the enormous data problems benefits from the advantage of compressed sensing, which works well on data reconstruction and compression.
The results show that the new algorithm meets our demand both in field mea- surement and model prediction. The future work is to solve the problem of the reconstruction error caused by terrain mutation.
References
1. Sharma, S.K., Lagunas, E., Chatzinotas, S., Ottersten, B.: Application of compres- sive sensing in cognitive radio communications: a survey. IEEE Commun. Surv.
Tutor.18(3), 1838–1860 (2016)
2. Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)
3. Tsaig, Y., Donoho, D.L.: Extensions of compressed sensing. Sig. Process.86(3), 549–571 (2006)
4. Dai, Q.H., Fu, C.J., Ji, X.Y.: Research on compressed sensing. Chin. J. Comput.
34(3), 425–435 (2011)
5. Bougher, B.: Introduction to compressed sensing. Lead. Edge34(10), 1256–1257 (2015)
6. Baraniuk, R.G.: Compressive sensing [lecture notes]. IEEE Sig. Process. Mag.
24(4), 118–121 (2007)
7. Candes, E.J., Wakin, M.B.: An introduction to compressive sampling. IEEE Sig.
Process. Mag.25(2), 21–30 (2008)
8. Zheng, H., Yang, F., Tian, X., et al.: Data gathering with compressive sensing in wireless sensor networks: a random walk based approach. IEEE Trans. Parallel Distrib. Syst.26(1), 35–44 (2015)
9. Shi, G.M., Liu, D.H., Gao, D.H., Liu, Z., Lin, J., Wang, L.J.: Advances in theory and application of compressed sensing. Acta Electron. Sin.5(37), 1070–1081 (2009) 10. Li, S., Ma, C.W., Li, Y., Chen, P.: Survey on reconstruction algorithm based on
compressive sensing. Infrared Laser Eng.42(s1), 225–232 (2013)
11. Baraniuk, R., Davenport, M., Devore, R., et al.: A simple proof of the restricted isometry property for random matrices. Constr. Approx.28(3), 253–263 (2008) 12. Liu, F., Wu, J., Yang, S.Y., Jiao, L.C.: Research advances on structured compres-
sive sensing. Acta Autom. Sin.39(12), 1980–1995 (2013)
13. ITU-RP.526-11: ITU International Telecommunication Union (2007) 14. ITU-R SM.337-6: ITU International Telecommunication Union (2008)
Distributed Compressive Sensing Based Spectrum Sensing Method
Yanping Chen1, Yulong Gao2(&), and Yongkui Ma2
1 School of Computer and Information Engineering, Harbin University of Commerce, Harbin, China
yanping1009@163.com
2 Department of Communications Engineering, Harbin Institute of Technology, Harbin, China
{ylgao,yk_ma}@hit.edu.cn
Abstract. For multi-antenna system, the difficulties of preforming spectrum sensing are high sampling rate and hardware cost. To alleviate these problems, we propose a novel utilization of distributed compressive sensing for the multi-antenna case. The multi-antenna signals first are sampled in terms of distributed compressive sensing, and then the time-domain signals are recon- structed. Finally, spectrum sensing is performed with help of energy-based sensing method. To evaluate the proposed method, we do the corresponding simulations. The simulation results proves the proposed method.
Keywords: Distributed compressive sensingSpectrum sensing Joint sparse modelTime-domain detection
1 Introduction
Spectrum sensing is the base of cognitive radio. At present, some known methods mainly conclude Energy-based algorithm, cyclostationary detection and eigenvalue- based algorithm [1,2]. Generally speaking, these methods are applied in the individual antenna case. However, with the growing requirements of date rate and the improve- ment of wireless communication technologies, multi-antenna technologies have already been applied in many wireless communication systems. Subsequently, spectrum sensing under the multi-antenna circumstances become a problem to be solved. Cur- rently, some multi-antenna based spectrum sensing methods were proposed, such as random matrix based methods and GLRT (generalized likelihood ratio test) methods [3–7]. For random matrix based methods, the signals sampled from multiple antennas are comprised of a random matrix, and then some parameters, such as eigenvalue, are extracted to perform spectrum sensing.
GLRT-based methods are a kind of technologies as solving the problem of multi-antenna spectrum sensing. In [4–6], some eigenvalues of sampled covariance matrix are used as test statistic. In literature [7], GLRT is exploited directly as test statistic, and the idea is evaluated in OFDM and MIMO system. It is well known that multi-antenna technology bring some advantages for the wireless communication. On the other hand, some disadvantages have also been introduced inevitably, such as too much
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https://doi.org/10.1007/978-3-319-73564-1_24
data and high sampled frequency. Fortunately, compressed sensing provides a practical idea to deal with these difficulties. In 2006, compressed sensing is proposed [8], and then it has been fast applied to manyfields, including the wireless communication, signal processing and image processing. In the view of compressed sensing, sample and compression are performed simultaneously, and the signal is sampled based on the signal sparsity but not the bandwidth used in the Nyquist sampling theorem, which can alleviate the computational complexity and hard cost. Meanwhile, in order to fully exploit the correlation of inter-signal and intra-signal, the framework of distributed compressed sensing is built on the base of the joint sparse model [9,10], which bridge between multi-antenna based wireless communication and compressed sensing. More impor- tantly, computational complexity is further reduced because of the correlation structure.
In this paper, we obtain the sampled signals in terms of distributed compressed sensing, which can reduce the hard cost and further decrease the subsequent compu- tational complexity, and then the energy-based spectrum sensing is adopted. Because of the utilizing of the correlation of multiple antennas, the sparsity in single antenna case is extended to the multiple antenna case by virtue of joint sparse model. It follows that higher reconstruction probability is obtained with the constriction of the same sensing measurement.
2 The Description of the Proposed Method
2.1 Distributed Compressive Sensing
We suppose that the number of antennas isJ, and the received signal ensemble can be expressed asXẳẵx1 x2 xJT, wherexi2RN. In the framework of distributed compressive sensing, the compressed measurements are written as
Y ẳUX ð1ị
where Y ẳẵy1 y2 yJT, Uẳ
U1 0 0
0 U2 0
... ... .. . ...
0 0 UJ
2 66 64
3 77
75. For the individual sig-
nal,yiẳUixi, whereyi2RM; Ui2RMN.
It is well known that the concept of common sparsity is built on the single signal.
For multiple antennas, however, the multiple signals possess intra-signal and inter-signal correlation. Joint sparse models (JSM), called common/innovation com- ponent JSMS, were introduced to describe these characteristics, which includes three specific models, named JSM-1, JSM-2 and JSM-3. Therefore, in the framework of distributed compressive sensing, JSM is written uniformly as
XjẳZCỵZj; j2 f1; 2 Jg ð2ị where ZC denotes the common component, and Zj is the innovation component.
Specifically, they can be sparsely represented as
ZC ẳWCHC; kHCk0ẳKC
ZjẳWjHj; Hj 0ẳKj ð3ị wherek k 0denotes thel0-norm, e.g., the number of nonzero values of signal vector. In this setting, the signal ensemble X can be rewritten as
XẳWH ð4ị
whereWẳ
WC Hj 0 0 WC 0 Hj 0
... ... ... ... ...
WC 0 0 Hj
2 66 64
3 77
75,HẳHTC HT1 HT2 HTJT .
The different sparsity assumptions regarding the common and innovation compo- nent correspond to different models. When both of the common and innovation com- ponents are sparse, we call it JSM-1 model. When there exist no common components in the signal ensemble, we refer to it as JSM-2 model. In this model, each innovation component of signal ensemble is sparse, and all the signals possess the same sparse support but have different nonzero values in the same locations. A practical scenario well-modeled by JSM-2 model is MIMO communication system we often encounter in this paper. If the common component is not factorized sparsely, we name the model as JSM-3 model. It is widely recognized that the signal ensemble from multiple antennas of MIMO satisfy the condition of the common and innovation component. It follows that we restrict out attention on JSM-2 model. Currently, the recovery algorithms in the framework of JSM model are categorized into trivial pursuit and iterative greedy pursuit, such as DCS-SOMP arisen from conventional OMP algorithm.
2.2 The Proposed Algorithm
In order to interpret the proposed method, wefirst show the block diagram in Fig.1.
We canfind from Fig.1 that the proposed method consists of DCS, DCS-JOMP and energy-based detection algorithm. We will introduce them in the following section, respectively.
RF
RF
DCS DCS- SNR Judge
JOMP x1
x2
xJ
1 1 1
y = Φx
2 2 2
y = Φ x
J J J
y = Φ x
1' y
2' y
J'
y threshold
H0
H1
Fig. 1. The block diagram of the proposed method
For multi-antenna signals, the received signals fit with JSM-2 model. Therefore, distributed compressed sensing can be applied to sample the multi-antenna signals.
Supposed that the sparsity of signal is K, the sampled signals in the framework of compressed sensing can be expressed as
y1ẳU1x1ẳU1Wh1
y2ẳU2x2ẳU2Wh2
yJẳUJxJẳUJWhJ 8>
><
>>
: ð5ị
wherexi; iẳ1; ; Jdenotes the received signal fromithantenna.Ui; iẳ1; ; Jis measurement matrix,Wis the sparse basis, andh1is sparse representation in the sparse basis.
Joint reconstruction of distributed compressed sensing (DCS-JOMP) is described as follows:
(1) Initialize.kis the times of iteration,Xis the space spanned by coefficients vector to be reconstructed.rj;kis the residual error. LetXẳ ẵ,rj;0ẳyj.
(2) Judgment of the correlation. The column corresponding to the biggest correlation withrj;k1 is picked out fromUjW, i.e.,nkẳarg max
n2f1;2...Ng
PJ
jẳ1rj;k1;/j;n. Then the spaceXis be updated to Xẳ ẵXnk.
(3) Updating of residual base, Kj;kẳUj;X. Where Uj;X is the group of the selected column of measurement matrix based onXẳ ẵXnk.
(4) Updating of the residual error. The sparse representation after the each iteration is denoted as hj;kẳ ðK0j;kKj;kị1K0j;kyj, so the residual error is expressed as rj;kẳyjKj;khj;k.
(5) Stopping the iteration. Whenk[K, we stop the iteration.
By exploiting DCS-JOMP algorithm, we obtain the time-domain signals. And then the error and noise are estimated to compute the SNR, further set the threshold. Finally, energy-based method is employed to perform spectrum sensing. Specific process is described in the following section.
For the conventional energy-based method, the test statistic is Zẳ2PTW
nẳ1x2ðnị.
Where 2TW is the length of the received signals,Tis the time interval, andWis the bandwidth. The received signal isxðnị ẳsðnị ỵwðnị.
For simplification, but without loss of generality, we normalize the received signal by the noise covariance, i.e.,w0ðnị ẳwðnị=rw, s0ðnị ẳsðnị=rw. Therefore, the test statistic reduces toZ ẳPN
nẳ1y0ðnị2. In this situation, the binary hypothesis test can be expressed in the form
Z ẳ X2TW
nẳ1
w0ðnị2; H0
X
2TW nẳ1
s0ðnị ỵw0ðnị
ð ị2; H1
8>
>>
><
>>
>>
:
ð6ị
By analyzing (6), we can conclude that the received signal follows the central chi-square distribution when no signal exists. Inversely, the received signal follows the non-central chi-square distribution with the non-central parameter
d ẳ X2TW
nẳ1
s0ðnị2 ẳ X2TW
nẳ1
sðnị rw
2
ẳ P
2TW nẳ1sðnị2
r2w ẳ 2TWPs
Pn ẳ 2TWc ð7ị Correspondingly, we can compute the detection probability and the false-alarm probability
Pd ẳPðZ[kj ị ẳH1 Quð ffiffiffi pd
; ffiffiffi pk
ị ð8ị
Pf ẳPðZ[kj ị ẳH0 Cðu;k2ị
Cðuị ð9ị
whereCð:ịis Gamma function,Cð:; :ịis the incomplete gamma function,Quð:; :ịis the generalized MarcumQfunction, the kis the predetermined threshold.uẳTW is the production of time and bandwidth. Generally speaking, we refer to the false-alarm probability as constant, i.e., constant false-alarm probability, and then compute the decision threshold. Finally, substitution of threshold into (8) yields the detection probability.
3 Numerical Simulation and the Corresponding Analyzing
Wefirst analyze the reconstruction error of compressed sensing and distributed com- pressed sensing for the various number of antennas. In the simulation, we assume that the signal is spare in the discrete cosine base, the lengthN= 64, the sparsityKis 4. The noise follows the Gaussian distribution, SNR = 10 dB. The times of Monte Carlo is 500. The reconstruction algorithm of compressed sensing and distributed compressed sensing are OMP algorithm and DCS-JOMP algorithm. The results are shown in Fig.2.
It can be seen that the reconstruction error reduces with the increasing of the number of sensing measurements, whichfit with the theoretical analysis. Additionally, for distributed compressed sensing, the reconstruction error is inversely proportional to the number of antennas. For example, for M= 20, the reconstruction error is 33.8%
when compressed sensing is adopted, the reconstruction error is 10.6% and 7.4% for 2 antennas and 4 antennas when we exploit distributed compressed sensing.
To further evaluate the performance of the proposed method under the different antennas, we as before take 2 antennas and 4 antennas as the example. SNR is 3 dB. In the simulation, we use the detection probability under constant false-alarm probability to measure the performance of the proposed algorithm. The simulation results are illustrated in Fig.3.
It is obviously observed that the detection probability of multi-antenna distributed compressed is higher than that of compressed sensing, and the detection probability varies with the number of antennas. For example, whenM= 20, the detection prob- ability is 82.1% when compressed sensing is adopted, the reconstruction error is 97.3%
and 99.4% for 2 antennas and 4 antennas.
In the following, we evaluate the detection probability under the different SNR.
The SNR varies from−15 dB to 10 dB. In addition, to compare with the conventional energy-based detection algorithm, its detection probability is also provided. In this simulation, the false-alarm probability is 0.05, the number of antenna J is 4. The number of sensing measurements is M= 16, and the sparsity is 4. We compute the threshold using (8), and then obtain the detection probability illustrated in Fig.4.
It can been seen from Fig.4 that the detection probability increases with the increasing of SNR. Generally, the performance of the conventional time-domain detection algorithm outperforms that of the proposed method. This is because that compressed sensing leads to the wastage of the signal energy. For example, when the detection probability reaches 100% for the conventional time-domain detection, SNR is 5 dB, and the sampled number is 64. For the proposed method, however, the number of antennas and sensing measurements are 4 andM = 13 respectively when the detection probability reaches 100%.
5 10 15 20 25 30 35
0 0.2 0.4 0.6 0.8 1 1.2 1.4
The number of measurements M
Reconstruction error
CS
2-antenna DCS 4-antenna DCS
Fig. 2. The relationship between the number of measurements and the reconstruction error
4 Conclusions
To solve the problem of high sampling rate and hardware cost, we exploit the intra-signal and inter-signal to sample the MIMO multi-antenna signals, which obvi- ously decrease the sampling rate and hardware cost. Combining with energy-based sensing method, we proposed a novel spectrum sensing. The proposed method perform the nearly similar to the conventional time-domain spectrum sensing.
5 10 15 20 25 30 35
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
The number of measurements M
Detection Probability
CS-Pd CS-Pf
2-antenna DCS-Pd 2-antenna DCS-Pf 4-antenna DCS-Pd 4-antenna DCS-Pf
Fig. 3. The relationship between the number of measurements and the detection probability
-15 -10 -5 0 5 10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
SNR/dB
Detection probability
DCS-Pd DCS-Pf
Non-compressive-Pd Non-compressive-Pf
Fig. 4. The relationship between SNR and the detection probability
Acknowledgments. This work is supported by National Natural Science Foundation of China (NSFC) (61671176).
References
1. Haykin, S.: Cognitive radio: brain-empowered wireless communications. IEEE J. Sel. Areas Commun.23(2), 201–220 (2005)
2. Axell, E., Leus, G., Larsson, E.G., et al.: Spectrum sensing for cognitive radio:
state-of-the-art and recent advances. IEEE Sig. Process. Mag.29(3), 101–116 (2012) 3. Wang, L., Zheng, B., Cui, J., Meng, Q.: Cooperative MIMO spectrum sensing using free
probability theory. In: The 5th International Conference on Wireless Communications, Networking and Mobile Computing (WiCom 2009), pp. 1–4 (2009)
4. Wang, P., Fang, J., Han, N., Li, H.: Multi antenna-assisted spectrum sensing for cognitive radio. IEEE Trans. Veh. Technol.59(4), 1791–1800 (2010)
5. Taherpour, A., Nasiri-Kenari, M., Gazor, S.: Multiple antenna spectrum sensing in cognitive radios. IEEE Trans. Wirel. Commun.9(2), 814–823 (2010)
6. Zhang, R., Lim, T.J., Liang, Y.-C., Zeng, Y.: Multi-antenna based spectrum sensing for cognitive radios: a GLRT approach. IEEE Trans. Commun.58(1), 84–88 (2010)
7. Font-Segura, J., Wang, X.: GLRT-based spectrum sensing for cognitive radio with prior information. IEEE Trans. Commun.58(7), 2137–2146 (2010)
8. Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory52(4), 1289–1306 (2006) 9. Duarte, M.F., Sarvotham, S., Baron, D., Wakin, M.B., Baraniuk, R.G.: Distributed
compressed sensing of jointly sparse signals (2005)
10. Baron, D., Duarte, M.F., Wakin, M.B., Sarvotham, S., Baraniuk, R.G.: Distributed compressive sensing (2009).https://arxiv.org/abs/0901.3403v1
Recent Advances in Radio Environment Map:
A Survey
Jingming Li1(&), Guoru Ding2,3, Xiaofei Zhang1, and Qihui Wu1
1 Department of Electronics and Information Engineering,
Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China lijingmingjlu@163.com, zhangxiaofei@nuaa.com,
wuqihui2014@sina.com
2 College of Communications Engineering,
PLA University of Science and Technology, Nanjing 210007, China dr.guoru.ding@ieee.org
3 National Mobile Communications Research Laboratory, Southeast University, Nanjing 210018, China
Abstract. Electromagnetic spectrum, the main medium of wireless communi- cation has been over-crowded. Accompanied by the arrival of big data era, the problem of the spectrum scarcity has received people’s attention. The emergence of cognitive radio improves the utilization of the spectrum and provides an effective solution to break the limitations of the traditional static allocation.
Radio Environmental Maps (REM) is an enabling technology of cognitive radio which can be intuitive, multi-dimensional display of spectrum information. It provides a visual basis while accessing dynamic spectrum and sharing spectrum.
In this paper, the various aspects of REM are studied from the perspective of cognitive radio. Based on the concept of REM, the recent research progress of REM is summarized, and a series of challenges in the construction of spectrum pattern are also highlighted.
Keywords: Cognitive radioRadio environment mapSpectrum trend Spectrum dynamic accessSpectrum sharing
1 Introduction
With the rapid development of radio technology and business, the demand for radio spectrum resources is exploding. The mobile traffic is expected to increase by a factor of 1,000 over the next decade. In order to meet the huge traffic growth, the next generation mobile network is expected to achieve 1,000 times the capacity growth compared with the current wireless network deployment [1]. So the work of radio spectrum resource management is becoming complicated. National radio management departments have been fully aware of the important resources of spectrum, the eco- nomic and social development, and national defense construction. The Federal Com- munications Committee (FCC) established the Spectrum Task Force in 2003 and formally approved the use of dynamic spectrum access equipment in 2010. The Next Generation (XG), funded by the Defense Advanced Research Project Agency
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https://doi.org/10.1007/978-3-319-73564-1_25
(DARPA), studies dynamic spectrum management throughflexible spectrum policies.
In addition, DARPA has introduced an advanced radio map to achieve real-time sensing of the radio spectrum in frequency, space and time [2].
At present, the existing spectrum allocation mechanism is static which is at the division of the partition. Each segment of the spectrum isfixedly assigned to different authorized users. Most of the spectrum resources have been exhausted. It is difficult for new business to provide a large section of available spectrum resources. So, the dynamic sharing of spectrum resources and promoting the integration of heterogeneous networks of cognitive wireless technology are considered to improve the spectrum utilization of promising ways [3]. The term Cognitive Radio (CR) is proposed by Dr.
Joseph Mitola in 1990. In general, CR allows unauthorized sub-users to access the unoccupied spectrum of the authorized primary user [4]. The core purpose of cognitive radio is to detect the free spectrum of the radio environment and use these idle spec- trums intelligently without affecting the main user system to achieve the effect of improving the spectrum utilization. Therefore, we need to build and manage the spectrum database to obtain time, space and other multi-dimensional spectrum avail- ability information [5]. Radio Environmental Maps (REM) is a promising tool for the realization of cognitive radio network (CRN). REM is an integrated database that includes information about the radio frequency (RF) signal environment, the relevant laws and regulations, the strategy, the physical location of the equipment, the available services and relevant historical experience [6]. With REM, the primary user and the secondary user can better understand their radio environment, help secondary users access the main user free frequency band, reduce the hidden node problem, improve the overall network performance. In this paper, we summarize the recent research progress of REM, and we elaborate the various aspects of REM in detail through the whole view in order to provide a comprehensive framework for how to use REM for spectrum dynamic access and spectrum management.
As shown in Fig.1, the structure of this paper is as follows: The second part defines REM and generalizes the application scenario of REM. The third part introduces the theory and method of spectrum trend from several key technologies of spectrum trend,
Fig. 1. Various aspects of REM