Xiang Gao, Zeyu Sun^*

*Corresponding author

School of Computer and Information Engineering, Luoyang Institute of Science and Technology, Henan, China

 

 

 

 

 

CSSC: A Compressed Sensing Spares Channel Bayesian Estimate in Sensor Networks

 

KEYWORDS: wireless sensor networks, Bayesian estimation, compressed sensing, greedy algorithm.

 

ABSTRACT: Wireless communication system performance usually by shadow fading and frequency selective fading and multipath effect Ring, the channel environment, unlike cable channel, uncertainty and great randomness, and unpredictable .So the design of receiver put forward more requirements, such as distortion caused by the signal at the receiving end Correction, need to know the order number of channel in a wireless channel, the Doppler frequency shift and channel impulse Response parameters, etc. Channel estimation accuracy will directly influence the whole performance of the system, access to details of the channel Information to achieve accurate demodulation receiving end, is an important indicator to measure the performance of wireless communication system, and is also in phase Correlation detection, demodulation and equalization the basis of communication technology. Therefore, the channel parameters estimation is the realization of wireless communication a key technology in the system, on the study of channel parameter estimation algorithm is also an important significance Work. Actual measurements have shown that in many cases, the wireless channel is a channel with sparse. In order to use the Bayesian channel estimation algorithm to estimate channel, using sparse characteristic of the channel at the same time, the paper improved the search method of support set in SABMP algorithm .In the process of dominate search support set introduces the ideas of Viterbi decoding path, eventually reduce the computational complexity of the algorithm. Theoretical analysis and simulation results verify the effectiveness of the improved algorithm.

 

 

INTRODUCTION

 

The traditional channel model was generally supposed that channel vector of each element is subject to independent identically distributed random variables, it is generally believed to obey Gaussian distribution, but look from actual observations, in many cases show a sparse characteristics of wireless channel is channel vector elements of value is very small, can approximate to zero. For sparse channel estimation problem is currently a hot research topic in the field of communications. Compressed sensing algorithm can make full use of the sparse characteristics of the channel, can obtain superior than the traditional least squares (LS) method estimates of performance, at the same time also does not have a lot of increase their algorithm complexity. Compressed sensing principle of estimation is to estimate the signal projection onto random observation matrix, by the sparse observation vector to estimate target signal (1).Bayesian channel estimation algorithm is also a kind of traditional estimation algorithm, Bayesian estimation to estimate the channel with channel mathematical expectation, the estimation error is minimal. To the sparse characteristic of channel, is used to calculate the mathematical expectation of random variable, can be a few can ignore small probability event, leaving some big probability event, to take advantage of bayesian estimation algorithm, to calculate the relative probability of each major event, target was calculated by the relative probability to the expectation of a random variable. If enough small had probability events, the difference between the two estimates can be ignored. In literature (2) a Bayesian channel estimation algorithm is proposed and is called DABMP algorithm, the algorithm of channel does not require the distribution of random variables can be used for any distribution channel estimation. Thesis on the basis of the original algorithm, an improved algorithm to keep the original algorithm of random variable distribution, on the basis of wide adaptability(3), the selection of big probability event has made the improvement, by setting a threshold, will be much fewer big probability events are preserved, and improve the search to the actual the possibility of a big probability event set, so as to improve the performance of channel estimation. Paper compares the improved algorithm and DABMP algorithm performance; the simulation results verify the effectiveness of the improved algorithm (4).

 

 

RELATED WORKS

 

There have been a large number of research results on data fusion privacy protection technology in wireless sensor networks, such as the literature (5). These mostly depend on to credible and communication process of security of sensor nodes, but in practical application, sensor nodes are typically deployed in untrusted environments, the security of nodes is cannot be guaranteed, there is probable capture, an attacker can obtain the session key and decrypt of privacy aware data. The papers (6) introduces the method of building shared key between sensor nodes, which ensures the security of the communication process, A data fusion scheme is proposed to prevent tampering and steal private data in (6). Before sending the data, the lower node must encrypt its privacy data, so the intermediate nodes need to carry out the decryption operation of the received data frequently. In order to reduce the operation cost of the decryption operation. The papers (7) proposed an encryption scheme based on the ideal lattice. In this scheme, the intermediate nodes do not need to decrypt the received data, so the data fusion can be directly carried out, and the encrypted data can be transmitted to the upper node. The paper (8) proposed data fusion algorithm PDA (Data Aggregation Privacy-preserving), which contains two algorithms CPDA and SMART. CPDA algorithm using data perturbation techniques, in the privacy of data to add a secret random number of ways to hide sensitive information; In SMART, the original data is divided into J slices, randomly selected in the neighborhood of J-1 neighbor nodes and exchange data with them, each node on all received sections do SUM processing as their data. Two algorithms have better protection of privacy, but CPDA uses the algebraic properties of the polynomial, the computational overhead is relatively large, and the SMART of the data in a split mode leads to a larger amount of data traffic. Yang Geng presents a low energy consumption method of privacy protection ESPART, On the basis of SMART algorithm, the algorithm is a random time slice for nodes, which avoids the collision between the same layer data and reduces the impact of data loss on the fusion results. The paper (8)proposed PASKIS and PASKOS algorithms by using the method of adding auxiliary information in secret data, and the computational complexity of is O(1), It can effectively prevent internal and external attacks, but need to send a large number of supplementary information, will inevitably increase the burden of communication. At the same time, the integrity detection for wireless sensor networks is also gradually being studied by researchers.

 

In this paper, Compressed Sensing Spares Channel (CSSC) based on the detection of failure nodes is proposed. Comprehensive consideration of the data fusion of privacy, confidentiality, fusion result accuracy design target, the algorithm before the deployment of sensor nodes, each node distribution random number, using perturbation techniques in the raw data to add random numbers to real data hiding, to hop by hop encryption (hop by hop) on the fusion processing of the data encryption transmission, reduce the possibility of external attack, using two rounds of fusion process network performance detection of node failures and to calculate the fusion results.

 

SPARSE CHANNEL MODEL

 

Digital signal in our daily life occupy the important position, many data operation and delivery the core is information from analog to digital conversion. Analog-to-digital conversion device to convert the physical information data flow, through complex software program to realize digital processing, at the same time, require hardware can fast when need accurate measurements Speed and stable capture the changing input signals. With the progress of technology, increasing. The amount of data on modulus conversion equipment and the subsequent digital signal processor, and storage requirements are the more To the higher. And traditional signal processing theory with sampling theorem for signal processing principles, the mining Sample theorem dominate all signal and image acquisition, processing, storage and transmission, must be greater than the sampling rate Or equal to twice the signal bandwidth, so as to bring great pressure signal processor. In this case, the pressure Sensing theory arises at the historic moment. Compressed sensing is based on the matrix analysis, theory of probability statistics, optimization and operations research, and many other mathematical theories On the basis of the description and processing of a new theoretical framework. Compressed sensing theory can be very low Rate of realization of signal sampling and processing, while reduce the cost of data storage, transfer, reduce the signal Time and calculate the cost. On the other hand, the ideology of compressed sensing also brings new high-dimensional data analysis. The direction of theory itself is a question of will transform coding and underdetermined linear equation and the sparse solution of the problem With highly incomplete measurement for signal reconstruction problems related topics together. Since 2006,Have been proposed, the compressed sensing theory in information theory, signal/image processing, medical imaging, pattern recognition, geology Exploration, optical/radar imaging, wireless communications, and other fields has been developed rapidly. Especially in the aspect of image processing, In the face of a huge number of pixel information to a signal transformation after compression, in a minority of absolute value is larger The sparse signal component part with sparse signal component of the zero or near zero, only information storage and transmission parts can still very good reconstruction signals, namely is the best interpretation of compressed sensing theory in this field[11-13].The advantages of compressed sensing theory is to break through the bottleneck of the Shannon sampling theorem, the reconstruction of the original signal is needed Amount of observation data is far less than the traditional sampling method need the amount of data, make high resolution signal acquisition Possible. CS theory research mainly revolves around three core issues, including signal sparse, Signal sparse observations (or called sparse measurement) and the signal reconstruction.

h=h_a*h_b(1)

 

H is a channel vector, N long  is the product of had award, ha is of length N, obey a certain distribution of random variables, h_b is the vector of length N, each of these elements are independent identically distributed variables, and obey the parameters for the Bernoulli distribution of P. In order to reflect the sparse nature of channel, there are many zero elements in h, so P values smaller (9-12).

 

If the pilot signal transmitter launch, pilot signal matrix with a Gaussian random variable signal matrix, has related literature prove Gaussian probability matrix is very satisfying RIP (Restricted Isometry Property) properties. Observations of the observation vector y can be expressed as:

y=h+n(2)

 

Formulas of  is M*N observation matrix, the launch of the pilot signal can be understood as a matrix, n is subject to a plural additive white Gaussian noise of Gaussian distribution. Based on compressed sensing theory, as long as h enough sparse, then use a dimension is small, the observation vector can be restored dimension vector h, namely can do M*N.

 

According to the theory of probability knowledge, the mathematical expectation of h Africa zero position number is NP. Channel vector h in the zero position number and nearly equal to the probability of NP relatively large. So please mathematical expectation when these things to consider. The above analysis is based on the prior probability distribution of the conclusion, after receiving the pilot signal response situations happening probability and changed. An estimate of signal under test is to use mathematical expectation instead of the estimated signal expression can be expressed as follows:

(3)

 

The is expressed as received y and know the location under the premise of the non-zero channel's expectations, use pseudo-inverse matrix multiplied by the observation vector y instead of ;Said the expectations in premise for received y channel’s is support set, namely the zero set position.

 

For any support set, the denominator is p(y), to compare the time can be neglected. P(s) is the prior probability, obey the Bernoulli distribution. Key is p(y/s), y is on  by h projection and additive Gaussian white noise, and Gaussian distribution is a superimposed on a non-Gaussian variable, if remove non Gaussian component, will get a Gaussian distribution of the variables. Therefore the y projections to orthogonal complementary space are:

(4)

 

isorthogonal complement matrix here. CC to obey Gaussian distribution. Ignore some subtle influence and the probability of the exponential, the resulting in literature [12] the size of a probability measure is:

(5)

If the node receives the information d_i at the t time, the data fusion model can be defined as:

f(t)=f(d₁,d₂,...,d_i,...,d_n)     (6)

 

According to the definition of fusion, the other typical data fusion function calculation formula is as follows:

 

MINIMUM: f(t)=min{d_i  i=1,2,...,n} (7)

MAXIMUM: f(t)=max{d_i  i=1,2,...,n}  (8)

COUNT: f(t)= {d_i  i=1,2,...,n}  (9)

 

 

SUPPORT SET SEARCH ALGORITHM AND SIMULATION

 

But at the time of every search, the first big probability and may be very small compared to the probability that the second big difference, and that there is a lot of probability search to the wrong results. That is in front of the search results as long as there is one step wrong, the end result would not be right. In order to reduce the happening of this kind of situation, the literature rounds of search, search in the first round to the column position assumed POS1, when the first position for the second round of the search will exclude POS1, search in the position of the remaining set. This adds to the search of computation. In order to solve this problem, the thesis applies the ideas of the viterbi decoding path to search process. Sparse channel length is N, every position with zero and not two kinds of state, each state may be regarded as the 0 s and 1 s of binary code. If not considering channel vector elements of specific values, channel estimation is to long for N binary code. All search is corresponding to the path of the path length is N decoding, SABMP algorithm is quite so the path of the path length of 1 decoding. The longer the path length, had decoding the more accurate, the greater the algorithm complexity. In order to both equilibrium and path length is set to 2.And the probability of two paths only when the difference is small to decode with path length 2, if the difference is very big decoding is used by position.

 

Searches for the first position, the position of each non-zero probability from big to small order, compare the first and the second number, if the ratio of the first and second values greater than the threshold, can retain maximum probability corresponds to the location, otherwise keep corresponding to the location of the two probabilities. Searches for the second and subsequent position, if there are two locations to retain the last time, it respectively on the basis of their reserve position search add position, and then put all the probability from big to small order, to determine whether the ratio of the two largest probability is greater than the threshold th, more than just keep two kinds of circumstances, otherwise, they only keep a situation. And then calculates retained the relative probability of all cases, finally calculate the approximate mathematical expectation.

 

Procedure G(,y,p,²,pos)

Initialize L{1,2,…,N}, i1

Initialize empty sets Smax,s_d,p(s_d/y),E[x/y,s_d]

L_iL

While ipos do

{Smax∪{,1},

Smax∪{,2}, …Smax∪{|L_i|}|,kL_i

Compute {V(S_k)|S_k

V(S₁)maxj V(s_j), V(S₂)maxj {V(S_j)/V(S_i)}

s_d{s_d, s₁}

compute {p(s₁/y),E[x/y,s1)}

P(s_d/y)  {P(s_d/y), P(s₁/y)}

E[x/y,s_d]  { E[x/y,s_d], E[x/y,s₁]}

Smaxs₁

L_i+1Ls₁

ii+1

compute {p(s₁/y),E[x/y,s₁)}, {p(s₂/y),E[x/y,s₂)}

P(sd1/y)  { P(sd/y), P(s1*/y)}, P(sd2/y)  { P(sd/y), P(s2*/y)}

E[x/y,sd1]{E[x/y,sd],E[x/y,s1*]},E[x/y,sd2]{E[x/y,sd], E[x/y,s2*]}

smax1s1*,smax2s2*

L1,i+1Ls1*, L2,i+1Ls2*

ii+1

End if

End while

Return sd1, P(sd1/y), E[x/y,sd1]

End procedure

 

In order to facilitate the research, the CSSC algorithm gives the following definitions and theorems:

Definition 1: 2^ is a common attack structure. If the  is satisfied:

, (10)

 

Definition 2: The general attack structure  on the set of P is given, and the corresponding maximum attack structure is:

_max{B  B ，} (11)

 

Definition 3: Set P={P₁,…,P_n} is a limited set of participants; K is the system secret, the secret sharing scheme for K can be expressed by ：Kg(P₁)…g(P_n), g(P_i) is a collection of all the shares assigned to P_i. is a secret sharing scheme to achieve the attack structure β; it must satisfy the following two properties:

 

the characteristics of secret reconstruction: XP, if X, then:

H(K{g(P_i)  P_i X})=0 (12)

 

H() is entropy function.

 

the security characteristics:

, H(K{g(P_i)  P_i X})= H(K {g(P_i)  P_i X}) (13)

 

K represents any element in a secret space.

 

Theorem: S_iS, if S_i S, if S_i={P_j,P_k}, then: Any one of the elements of the K, in addition to the elements K:

H(Kg(P_j), g(P_k))=0

 

Prove: The share of P_j is g(P_j)={K_tP_jS_t,1tm+m}, the share of P_k is g(P_k)={K_tP_kS_t,1tm+m}.So S_i={P_j, P_k}, we know that K_ig(P_j) and K_ig(P_k),namely: in S_i, any participating parties are not able to collect K_i.

Because K is a different element from K in the main secret space of the system. Given a division {K₁,…,K_m+m}on K, obviously, {K₁,…,K_i-1,K_i+K-K,…,K_i+1,…,K_m+m}is a division on K. Therefore, the P_i and P_k can reconstruct the probability of the share of K and K. If g_k(P_j) and g_k (P_j) are the share of K and K respectively, then: H(K{g(P_i)  P_i X})= H(K {g(P_i)  P_i X}).

 

Simulation parameter Settings are as follows: channel length N=256, number M=64 observations, the sparse degree of P₁=0.05, the signal-to-noise ratio of 20 db, SABMP D=10 cycles in the algorithm, the improved algorithm cycles D=1.The simulation result of both methods is shown in figure 1:

 

Figure 1. 200*200m², Comparison of fusion accuracy.

 

Figure 2. 400*400m², Comparison of fusion accuracy

 

Seen from the simulation results of two kinds of algorithm can restore the original signal very well. Calculated under two kinds of algorithm to estimate the signal and original signal mean square error (mse) is 19.56 dB and 20.18 dB, respectively, the differences between the two is very small, and because of the improved algorithm cycles is one over ten of the original, the computation is reduced greatly.

 

 

CONCLUSION

 

 

This article mainly elaborated based on pilot symbol aided channel estimation, the first detailed introduction based on pilot assisted LS, MMSE channel estimation algorithm, and in the Matlab simulation platform of LS, MMSE channel estimation are compared, and the simulation Although the MMSE channel estimation performance is better, but in the solving process to compute inverse matrix, increase the computational complexity, right In some high real-time demand system, MMSE is generally not used; LS algorithm is simple, and don't have to know first. Check information, better estimation performance, so to be able to use a wide range of; finally based on the LS channel estimation algorithm for noise sensitivity. The shortcomings of feeling, by adopting wavelet packet to the LS algorithm to estimate the channel response value for noise reduction processing, optimized the LS. Channel estimation algorithm, the simulation results show that the improved LS channel estimation effectively reduce noise to estimate the channel response value make the LS channel estimation algorithm, the influence of the performance got obvious improvement.

 

ACKNOWLEDGEMENT

 

 

The study was supported by the Henan Province Education Department Cultivation Young Key Teachers in University of Under Grant (No. 2016GGJS-158), and Henan Province Education Department Natural Science Foundation under Grant No. (No.15A413016, 17A520044).

 

REFERENCES AND NOTES

 

1. Zeyu Sun, Yongsheng Zhang, et al. “EBKCCA: A novel energy balanced k-coverage control algorithm based on probability model in wireless sensor networks”, KSII Transactions on Internet and Information Systems, 10(8),3621-3640 (2016).
2. Kanu Geete, Piyush Kumar Shukal, et al. “A survey on Grey Hole Attack in wireless sensor networks”, International Journal of Computer Applications, 95(23),23- 29 (2014).
3. Ahmadi Ali, Shojafar Mohammad, et al. “An efficient routing algorithm to preserve  k-coverage in wireless sensor networks”, The Journal of supercomputing, 68(2),599-623 (2014).
4. Kushal Mukherjee, Shalabh Gupta, et al. “Statistical-mechanics-inspired optimization of sensor field configuration for detection of mobile targets”, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 41(3),783-791 (2011).
5. Chih Cheng Hsu, Ming Shing Kuo, et al. “Joint design of asynchronous sleep-wake scheduling and opportunistic routing in wireless sensor network”, IEEE Transactions on Computers, 63(7),18740-1846 (2014).
6. Teddy M Cheng, Andrey V Savkin. “A distributed self-deployment algorithm for the coverage of mobile wireless sensor networks”, IEEE Communications Letters, 13(11), 877-879 (2009).
7. Hougbo Jiang, Shudong Jin et al. “Prediction or Not? An energy-efficient framework for clustering-based data collection in wireless sensor networks”, IEEE Transaction on Parallel and Distributed Systems, 22(6), 1064-1071 (2011).
8. Qun Zhao, Gurusamy Mohan, “Lifetime maximization for connected target coverage in wireless sensor networks”, IEEE/ACM Transaction on Networking, 16(6),1378-1391 (2008).
9. Xiaohua Xu, Xiangyang Li, et al. “A delay-efficient algorithm for data aggregation in multihop wireless sensor networks”, IEEE Transactions on Parallel and Distributed Systems, 22(1),163-175 (2011).
10. Jie Wu, Fei Dai, Ming Gao et al. “On calculating power-aware connected dominating sets for efficient routing in ad hoc wireless networks”, Journal of Communications and Networks, 4(1),59-70 (2002).
11. Yourim Yoon,  Yonghyuk Kim. “An efficient Genetic Algorithm for maximum coverage deployment in wireless sensor networks”, IEEE Transactions on Cybernetics, 43(5),1473-1483 (2013).
12. Huanzhao Wang, fanzhi Meng etal. “Energy efficient coverage conserving protocol for wireless sensor networks,” Journal of Software, 21(12),3124-3137 (2010).