Journal of Sensors

Volume 2016, Article ID 6139802, 8 pages

http://dx.doi.org/10.1155/2016/6139802

## Detection of Defective Sensors in Phased Array Using Compressed Sensing and Hybrid Genetic Algorithm

^{1}School of Engineering & Applied Sciences, ISRA University, Islamabad 44000, Pakistan^{2}Electrical Department, Air University, Islamabad 44000, Pakistan^{3}Electronic Department, International Islamic University, Islamabad 44000, Pakistan

Received 3 February 2015; Revised 12 June 2015; Accepted 14 July 2015

Academic Editor: Manuel Pineda-Sanchez

Copyright © 2016 Shafqat Ullah Khan 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

A compressed sensing based array diagnosis technique has been presented. This technique starts from collecting the measurements of the far-field pattern. The system linking the difference between the field measured using the healthy reference array and the field radiated by the array under test is solved using a genetic algorithm (GA), parallel coordinate descent (PCD) algorithm, and then a hybridized GA with PCD algorithm. These algorithms are applied for fully and partially defective antenna arrays. The simulation results indicate that the proposed hybrid algorithm outperforms in terms of localization of element failure with a small number of measurements. In the proposed algorithm, the slow and early convergence of GA has been avoided by combining it with PCD algorithm. It has been shown that the hybrid GA-PCD algorithm provides an accurate diagnosis of fully and partially defective sensors as compared to GA or PCD alone. Different simulations have been provided to validate the performance of the designed algorithms in diversified scenarios.

#### 1. Introduction

Nowadays array testing is of great interest in the research community. Moreover, the estimation of the power pattern and detection of faulty sensors in antenna arrays are an important issue in radar, remote sensing, and mobile and satellite communications [1–3]. There is a possibility of getting one or more antenna elements defective which results in degradation of radiation pattern of the array [4–6]. Prior to the correction of the patterns, it is necessary to first diagnose the defective antenna element in the array. Several traditional techniques are available to detect the number and the positions of faulty elements from the observation of healthy array and damaged power pattern [7, 8]. The most commonly used techniques for array detection are matrix method [9], back propagation algorithm [10], and exhaustive searches [11]. However, these techniques are computationally expensive as they require that the number of measurements should not be less than the number of antenna elements in the array.

In array diagnosis, the purpose is to locate the faulty elements in linear array. The sparse vector is defined as the deviation between the weights of the healthy reference array and the array under test [12]. In practical scenario, the number of defective elements is small. Thus the new array is very sparse with a small number of active elements, allowing a less number of measurements for the detection of faulty elements. The failure detection problem using the recovery techniques of signals in compressed sensing allows the harmonic estimation of sparse signals using a small number of data [13, 14]. The measurement matrix must satisfy the restricted isometry property to avoid information in the actual signal from distortion. In such a framework, an inventive turnup for the detection of defective linear arrays from far-field measurement has been proposed [15] enchanting the benefit of the compressed sensing technique.

Compressed sensing (CS) is a signal processing technique, in which one can recover a signal from a set of linear measurements instead of a signal itself, where the number of the measurements is less than the signal. As a consequence, the original signal has to be recovered from the measurement matrix, which is ill-posed due to the reduced dimension. CS technique [16–19] states that it possible to recover the underlying signal from less number of measurements below the Nyquist sampling rate, under the suitable conditions such as restricted isometry property (RIP). In literature several techniques are available for solving the ill-posed recovery problem. These techniques can be classified into a number of algorithm families with their problem varying approach [20–22].

Among the researchers in engineering, GA and PCD algorithm have required special attention. GA is bioinspired technique that has been used successfully for different optimization problems in numerous fields of engineering [23–25]. On the other hand, PCD, with the idea taken from coordinate descent method, is also used for different minimization problems.

In this paper, taking into account the promising performance of GA and PCD, we have introduced a CS based array diagnosis technique. This technique is based on the measurement data of the far-field pattern. The system relating the difference between the field measured using the healthy reference array and the field radiated by the array under test is solved using GA, PCD algorithm, and GA hybridized with PCD algorithm. The major advantage of this hybrid technique is the avoidance of slow and early convergence of GA. The performances of all of these algorithms have been compared with each other in terms of convergence and mean square error (MSE). The GA-PCD algorithm provides an accurate diagnosis of fully and partially defective sensors as compared to the individual GA or PCD algorithm alone. Different simulations have been provided to validate the performance of the designed algorithms.

The remaining of paper is organized as follows. The problem formulation is discussed in Section 2, while in Section 3, we have designed GA, PCD, and hybrid GA-PCD. Section 4 describes the simulations and results, while Section 5 concludes the work and recommends some future directions.

#### 2. Problem Formulation

Let us consider a linear array of elements along -axis, whose far-field patterns are given as [1]where is the weight vector of the th antenna element, is the wave number, is the th measurement pattern, and is the distance between the consecutive elements. The noisy far-field pattern of the array under test is expressed aswhere is the th sample of an additive zero mean complex Gaussian noise with variance and is the th weight vector of the array under test. In (2), is given aswhere is the fraction of faulty elements. The original and noisy faulty Chebyshev power pattern with and SLL = −35 dB are shown in Figure 1. The normalized Chebyshev weights of the original and faulty array with 8th and 15th elements not working are depicted in Figure 2. The difference field pattern between the ideal and the array under test is given [11] by the following equation:or it can be written as follows: where and is the th element of the array under test failure vector which is given by