Journal of Electrical and Computer Engineering

Volume 2018, Article ID 4782718, 9 pages

https://doi.org/10.1155/2018/4782718

## A Sequential Compressed Spectrum Sensing Algorithm against SSDH Attack in Cognitive Radio Networks

Correspondence should be addressed to Yong Bai; nc.ude.uniah@iab

Received 10 February 2017; Revised 11 August 2017; Accepted 1 November 2017; Published 2 January 2018

Academic Editor: George S. Tombras

Copyright © 2018 Zhuhua Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Spectrum sensing is one of the key technologies in wireless wideband communication. There are still challenges in respect of how to realize fast and robust wideband spectrum sensing technology. In this paper, a novel nonreconstructed sequential compressed wideband spectrum sensing algorithm (NSCWSS) is proposed. Firstly, the algorithm uses a sequential spectrum sensing method based on history memory and reputation to ensure the robustness of the algorithm. Secondly, the algorithm uses the strategy of compressed sensing without reconstruction, which thus ensures the sensing agility of the algorithm. The algorithm is simulated and analyzed by using the centralized cooperative sensing. The theoretical analysis and simulation results reveal that, under the condition of ensuring the certain detection probability, the proposed algorithm effectively reduces complex computation of signal reconstruction, significantly reducing the wideband spectrum sampling rate. At the same time, in the cognitive wideband communication scenarios, the algorithm also achieves a better defense against the SSDF attack in spectrum sensing.

#### 1. Introduction

Cognitive radio (CR) technology can increase the efficiency of spectrum utilization for wideband wireless communications [1]. Aiming at detecting spectrum holes, spectrum sensing is the precondition for the implementation of CR [2].

To detect the spectrum holes more effectively over a wide bandwidth in Cognitive Radio Network (CRN), traditional wideband spectrum sensing acquires the wideband signals with a high-speed analog-to-digital converter (ADC) and then uses digital signal processing techniques to detect spectral opportunities. However, it is very often limited by the capability of ADC hardware and unable to meet high-speed sampling rate stated in Nyquist sampling theorem for wideband spectrum sensing [3]. An effective solution to address the challenge is spectrum sensing technology based on the compressed sensing (or called compressed sampling, CS) theory. CS can maintain the structure and information of the original sparse signal far below the Nyquist sampling rate. There have been many research achievements in this field. Tian and Giannakis applied the CS to the research of wideband spectrum sensing and verified its effectiveness [4]. Collaborative spectrum sensing from sparse observations in CRNs is studied in [5] by applying matrix completion and joint sparsity recovery to reduce sensing and transmission requirements. In order to reduce computational cost, spectrum holes can be obtained by means of partial reconstruction. Hong [6] presented a method of detecting the primary users (PUs) based on Bayesian compressed sensing, which can estimate important parameters of the primary user’s signal directly from compressed sampling without the need for complete reconstruction. Thus it greatly reduces the computational complexity, but it still needs some parameters’ distribution information of the original sparse signal. Actually, partial and complete signal reconstruction may not be required in many spectrum sensing applications. A method was proposed in [7] for nonreconstruction compressed detection of random signal under the maximum likelihood criterion. A new method for blind detection of signals by using nonreconstruction compressed sampling without prior knowledge was proposed in [8].

In compressive observation, the redundant observation is usually contained. In order to effectively reduce the number of observations, the sequential theory was introduced into the wideband spectrum sensing, and sequential compressive spectrum sensing algorithm was proposed in [9, 10]. The algorithm can make the compressive ratio adjusted adaptively according to the signal sparsity, which can reduce the sampling number, but this method still needs to reconstruct the original signal. In [11], according to the maximum interference endured for PU, the optimal false-alarm probability is set, which can obtain the largest throughput for second users (SUs) by improving the threshold method. However, the detected signal is still the deterministic signal, whose sparsity is known in [9–11]. In [12], nonreconstruction compressed sampling method combined with sequential testing for random signals was presented. In [12], only AWGN (Additive White Gaussian Noise) channel is considered, and the robustness of the algorithm was not guaranteed with malicious users (MUs) under the SSDF (Spectrum Sensing Data Falsification) attack [13].

When a priori knowledge of signal and sparsity is unknown, in order to agilely and robustly find out the spectrum holes not occupied by PUs, this paper presents an enhanced novel nonreconstructed sequential compressed wideband spectrum sensing (NSCWSS) algorithm. Firstly, a weighted sequential spectrum sensing method based on history memory model is designed. The method assumes that, in collaborative sensing environment, the initial credibility value of each secondary user is the same. After the end of each sensing, the value of credibility of corresponding users will be updated. Then the sensing results of secondary user are assigned with different weights corresponding to its credibility and history accuracy in the final fusion, which can improve the antijamming ability of the algorithm to launch SSDF attacks. In addition, the algorithm uses a compression sensing method without reconstruction, which combined with the theory of sequential detection; thus it can ensure the least average computation for signal detection.

#### 2. The Process of Nonreconstructed Compressed Detection

In Cognitive Radio Network, SUs need to judge whether PUs exist or not for dynamic access without affecting the normal communications of the PUs. The compressed detection model can be expressed as

Under the fading channel, Corresponding to the cases that the PU does not exist or exist, a binary hypothesis testing model can be established as follows:where is the sequence of samples of random sparse signals, is the channel fading gain of the th sensing link, and is the sequence of the samples of noise of the sensing link, which is independent and identically distributed (i.i.d) with one-sided power spectral density . Here, we assume that and are independent of each other; is the sampling number, and is the observation matrix with dimension . Normally, is required, where is the signal sparsity.

Considering fading channels, Rayleigh and Rician distributions do, in many cases, model the envelope of the signal through the fading channel very well. However, in the actual wireless communication environments, it is found that the Nakagami distribution provides better matching degree with the actual test [14]. In comparison with the Rician distribution, the Nakagami distribution does not need to be assumed in terms of direct conditions. Thus, the sensing links are assumed to be subject to a Nakagami-*m* fading; then the received power of th CR user obeys a Gamma distribution. The probability density function (PDF) of is given by [14–17]where denotes the severity of fading, is the Gamma function, is the local-mean power of , and denotes the received instantaneous signal level. As increases, the level of fading decreases. When or , the sensing channel is subject to one-sided Gaussian fading and the Rayleigh fading, respectively. When , the Nakagami fading can be approximately equivalent to the Rician fading. is given by [16]where is the average SNR of the th sensing channel and is the expected local-mean power of the PUs under assumption.

In the nonreconstruction approach we can test the two assumptions in (2) by directly processing the observation vector . Here, denotes the number of observations, and we assume that each observation is statistically independent of each other. Then, with assumption, the observation sequence is Gauss random vector with mean 0 and variance . While the observation sequence is Gauss random vector under condition, its mean is , and the variance is .

According to the Neyman-Pearson theorem [18], given a false-alarm probability , the detection probability is maximized with the test

The threshold is determined by

Putting the probability density function of into (5) and taking the logarithmic transformation [3], we can get

Thus, the detection statistic for random signal based on nonreconstructed compressed sampling is expressed as

Formula (8) contains all the information needed for signal compressed detection. In addition, if , it shows no compression capacity. That is to say, it is converted into the convertional energy-detection based spectrum sensing. The detection statistics follow distribution [12]. Then we can get where the right tailed distribution of the random variables in distribution is

Further, to simplify calculation, by using approximate expression method of distribution, we can get

From the above analysis, the relation equation between and can be given by

In (13), .

is the average SNR related to the th sensing channel, and then

Obviously, Because the function is strictly monotonically decreasing, will increase with the increase of SNR and observation number under given . From (9), the theoretical observation number required by the compressed detection algorithm can be given as

#### 3. System Modeling

Centralized collaborative spectrum sensing can be seen as a series of processes of voting, decision, and fusion of binary decisions. Such a system is mainly composed of PU, SUs, malicious users, and fusion center (FC). The system model is shown in Figure 1.