International Journal of Antennas and Propagation

Volume 2015, Article ID 654958, 7 pages

http://dx.doi.org/10.1155/2015/654958

## Compressed Measurements Based Spectrum Sensing for Wideband Cognitive Radio Systems

^{1}Department of Electrical Engineering, University of Tabuk, Tabuk 71491, Saudi Arabia^{2}Department of Electrical Engineering, Assiut University, Assiut 71516, Egypt^{3}Electrical Engineering Department, King Khalid University, Abha 62529, Saudi Arabia

Received 4 August 2015; Revised 8 December 2015; Accepted 10 December 2015

Academic Editor: Stefano Selleri

Copyright © 2015 Taha A. Khalaf 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 the most important component in the cognitive radio (CR) technology. Spectrum sensing has considerable technical challenges, especially in wideband systems where higher sampling rates are required which increases the complexity and the power consumption of the hardware circuits. Compressive sensing (CS) is successfully deployed to solve this problem. Although CS solves the higher sampling rate problem, it does not reduce complexity to a large extent. Spectrum sensing via CS technique is performed in three steps: sensing compressed measurements, reconstructing the Nyquist rate signal, and performing spectrum sensing on the reconstructed signal. Compressed detectors perform spectrum sensing from the compressed measurements skipping the reconstruction step which is the most complex step in CS. In this paper, we propose a novel compressed detector using energy detection technique on compressed measurements sensed by the discrete cosine transform (DCT) matrix. The proposed algorithm not only reduces the computational complexity but also provides a better performance than the traditional energy detector and the traditional compressed detector in terms of the receiver operating characteristics. We also derive closed form expressions for the false alarm and detection probabilities. Numerical results show that the analytical expressions coincide with the exact probabilities obtained from simulations.

#### 1. Introduction

There is a remarkable growing demand on wireless devices and services that use the electromagnetic spectrum for communication. In static license regime, the spectrum bands are assigned to licensed holders on a long term basis for large geographical regions. However, a large portion of the assigned spectrum remains underutilized [1]. Cognitive radio (CR) can utilize the spectrum more efficiently in an opportunistic fashion. CR allows a secondary user (SU) to use a specific spectrum band as long as its licensed primary user (PU) is protected against harmful interference. The Federal Communications Commission (FCC) defined the CR as follows:* a radio or system that senses its operational electromagnetic environment and can dynamically and autonomously adjust its radio operating parameters to modify system operation* [2]. The main functions for CRs are spectrum sensing, spectrum management, spectrum mobility, and spectrum sharing [3].

One key component of the CR system is spectrum sensing (SS), by which a SU radio can detect the presence or absence of the PUs and identify the available white spaces in the spectrum [4]. In order not to affect the performance of the PU, the SS process has to meet the sensing speed and accuracy requirements set by the FCC [2]. The problem becomes more challenging, particularly in wideband systems where the sampling rate has to be higher than or equal to the Nyquist rate. Consequently, the complexity and the cost of the hardware circuits as well as the power consumption would be high [5–7]. Moreover, the timing requirements for rapid sensing may only allow the acquisition of a small number of samples which may not provide accurate information about the existence of the PU.

Recently, compressive sensing (CS) is used to solve the high sampling rates problem in the CR systems. CS allows the sensing of sparse signals at sub-Nyquist sampling rates and a reliable recovery of the signal via computationally efficient algorithms [8, 9]. In CS, the signal can be recovered from a small number of projections over a sensing basis (measurements) as long as it is sparse over the representation basis that is incoherent with the sensing basis. Examples of the sensing basis matrices are Gaussian, Bernoulli, partial Hadamard, and partial Fourier matrices. In order to reconstruct the signal, the sensing basis should satisfy the restricted isometry property (RIP) [10]. Signal reconstruction is the solution of an -norm optimization problem to recover the high dimensional data from the low dimensional measurements.

In previous work of using CS in CR applications, SS is completed in three steps: sampling using an analog to information converter (AIC) at a sub-Nyquist rate, reconstructing the Nyquist rate signal or reconstructing the PU frequency response, and then applying one of the spectrum detection techniques on the reconstructed signal [11–13]. The SS process can be considered as a binary hypothesis test, where the detection algorithm has to decide which one of the two hypotheses is probably true. The mostly used detection schemes are matched filter detection [14], energy detection [15], and feature detection [16]. Although the algorithms proposed in [11–13] reduce the hardware complexity of acquiring the signal, they increase the computational complexity through the reconstruction process. The fundamental task of SS is to detect the presence of the PUs. Therefore, the full reconstruction of the wideband signal is not necessary as long as the PU existence can be accurately detected from the compressed measurements. In [17], it was shown that the detection and estimation problem can be solved using the compressed measurements without reconstructing the original signal. However, the observation matrix chosen is the random observation matrix which serves the purpose of the reconstruction process not the detection process. The authors showed that the detection probability increases as the number of the compressed measurements increases. The analytical results of [17] show that the traditional detector outperforms the compressed measurements based detection algorithm in terms of the detection probability and the proposed detection algorithm will provide the same performance as the traditional detector only when the number of the compressed measurements equals the number of Nyquist rate samples.

In this paper, we propose an algorithm that enables the detection of the PU existence from the compressed measurements directly without going into the intermediate process of reconstructing the signal. This can be realized by designing a compressive sensing process that guarantees that the information used in the detection process is preserved in the compressed measurements. To achieve this, the sensing matrix has to be designed with constraints different from those used in the conventional CS [10] and the detector proposed in [17]. The algorithm we propose in this paper is based on the well-known energy detection techniques. Therefore, the sensing matrix should preserve the energy of PU signal. The discrete cosine transform (DCT) [18] has the property of energy compaction where most of the energy of the time domain signal will be concentrated in few samples of the DCT domain signal. Therefore, we adopt the DCT matrix as the sensing matrix in our algorithm. In addition to the reduction in the computational complexity due to the elimination of the reconstruction process, the results show that the proposed algorithm provides a better performance than the traditional energy detector that uses the Nyquist rate signal and accordingly the compressed detector proposed in [17]. Moreover, the detection algorithm we propose does not require a priori knowledge or estimation of the PU signal sparsity. We also derived closed form expressions for the detection and false alarm probabilities. Simulation results are provided to validate the derived expressions.

The remainder of this paper is organized as follows. The system model and the detection algorithms are described in Section 2. The derivation of the false alarm and detection probabilities is provided in Section 3. Section 4 presents the numerical results and discussions. Finally, the conclusions are drawn in Section 5.

#### 2. System Model and Detection Algorithms

In this section, we present the system model, compressive sensing based energy detection (CSBED) algorithm, and the compressed measurements based energy detection (CMBED) algorithm. Let us first summarize some notations and definitions that will be used through the paper:(i): it is the null hypothesis which states that there is no transmission from the PU in the band under consideration,(ii): it is the alternative hypothesis which states that there is a transmission from the PU in the band under consideration,(iii): the SU accepts after applying the detection algorithm,(iv): the SU rejects after applying the detection algorithm,(v): it is the probability that the SU decides that the PU exists while it does not (probability of false alarm).

##### 2.1. System Model

In this paper, the primary network is assumed to be the television broadcasting system. According to the IEEE 802.22 WRAN standards [19], the PU signal is transmitted using orthogonal frequency division multiplexing (OFDM) with the following specifications: 54 MHz: main carrier frequency, 4.45 Mbps: data rate, 16-QAM: payload modulation, and 2048 FFT: size. The channel is modeled as an additive white Gaussian noise (AWGN) channel. The hypothesis model is defined as follows:where is the signal received by the SU, is the PU signal with bandwidth , and is an (AWGN) with zero mean and one-sided power spectral density of . The received signal is sensed using CS to get the low dimensional data vector which has a sub-Nyquist sampling rate and is given bywhere is an vector which represents the Nyquist rate samples of , is the compressed measurements vector, and is an sensing matrix ().

##### 2.2. Compressive Sensing Based Energy Detection Algorithm (CSBED)

In CSBED, the Nyquist rate signal is reconstructed from the compressed measurements vector** y** of (3) and then the energy detector is applied to the reconstructed signal. The reconstruction process is a linear inverse problem with sparseness constraint. It was shown that this problem is an NP-hard [21]. Basis Pursuit (BP) [22] is a reconstruction technique that transforms the problem to a convex optimization problem that can be solved by linear programming as follows:

Several reconstruction techniques have been proposed in the literature. Examples of these techniques are Matching Pursuit (MP) [23] and Orthogonal Matching Pursuit (OMP) [24]. These techniques differ in the computational complexity and memory requirements. For instance, the computational complexity and memory requirements of the OMP algorithms as a function of the iteration number are summarized in Table 1. In QR-1, only after the final iteration does OMP find the solution [20]. The accuracy of the reconstructed signal depends on the number of compressed measurements and the number of iterations. In order to detect the existence of the PU, the energy of the reconstructed signal is calculated and compared with a predetermined threshold as follows: