International Journal of Antennas and Propagation

Volume 2015, Article ID 136826, 6 pages

http://dx.doi.org/10.1155/2015/136826

## Sidelobe Suppression with Null Steering by Independent Weight Control

^{1}Department of Electronic Engineering, IIU, H-10, Islamabad 44000, Pakistan^{2}Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock Campus, Attock 43600, Pakistan^{3}School of Engineering and Applied Sciences, ISRA University, Islamabad Campus, Islamabad 44000, Pakistan

Received 20 April 2015; Accepted 18 May 2015

Academic Editor: Vincenzo Galdi

Copyright © 2015 Zafar-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 uniform linear array of antenna elements can steer up to nulls. In situations where less than nulls are required to be steered, the existing algorithms have no criterion to utilize the remaining weights for sidelobe suppression. This work combines sidelobe suppression capability with null steering by independent weight control. For this purpose, the array factor is transformed as the product of two polynomials. One of the polynomials is used for null steering by independent weight control, while the second one is for sidelobe suppression whose coefficients or weights are determined by using convex optimization. Finally, a new structure is proposed to incorporate the product of two polynomials such that sidelobe suppression weights are decoupled from those of null steering weights. Simulation results validate the effectiveness of the proposed scheme.

#### 1. Introduction

Null steering for adaptive beamforming is an important area of research due to its military and commercial applications [1–6]. Null steering techniques can broadly be classified as Direction of Arrival (DOA) based beamformers and optimal adaptive beamformers [1]. Existing DOA based null steering techniques either control the excitation of elements’ amplitude only [2, 3], phase only [4, 5], or both [6]. There are also techniques that achieve null steering by changing the position and/or elevations of the array elements [7–10].

Elements’ phase and amplitude excitation techniques are slow for large arrays because even if a single null changes its position, the whole set of weights is required to be reevaluated which is obviously time consuming and complicated. On the other hand, null steering by controlling the excitation amplitude only is easy to implement and less sensitive to quantization error but reduces the number of steerable nulls [2, 3]. The techniques like phase only and position perturbations of the array elements are nonlinear problems and cannot be solved directly by analytical methods [11]. Besides, position perturbations methods require servo motors for the movement of the elements and, in case of large arrays, the complexity to control element position increases due to increase in computational time to find new position perturbations.

The solution for this problem is the null steering by independent weight control where if a single null changes its position, only the weight set corresponding to that null is evaluated and changed [3, 6]. Unfortunately, these DOA based beamformers do not have sidelobe suppression capability. Although this problem has been addressed for optimal adaptive beamforming algorithms [12, 13] the method cannot be used in DOA based beamformers because in these algorithms pattern synthesis weights are not determined by using optimization techniques.

This paper presents a technique where the array factor is transformed as product of two polynomials such that one polynomial denoted by provides independent steering of all available nulls while the other denoted by suppresses sidelobes by utilizing remaining weights. The coefficients of are determined by forcing the zeros of to lie on unit circle in the complex plane [6] while the coefficients of are evaluated using convex optimization. Furthermore a structure is presented to implement this array factor where the sidelobe suppression weights are decoupled from the weights meant for independent null steering. Therefore the coefficients of will not be required to change with the change in position of any interference.

The rest of the work is organized as follows. Section 2 presents problem formulation, while proposed technique and structure are discussed in Sections 3 and 4, respectively. Simulation results are given in Section 5. Finally, conclusion and future work recommendation are given in Section 6.

#### 2. Problem Formulation

Consider a uniform linear array (ULA) of omnidirectional elements. Let be the element spacing, the progressive phase, and the angle of arrival of the plane wave impinging on the array. Figure 1 shows the path difference of this wave on the adjacent elements of the ULA; that is, . The output of the array elements is multiplied by the properly selected coefficients to steer the nulls in the directions of interferences. We take the first element (element 0) of the array as reference and , where is known as wave number. The signal at element 2 is the delayed version of the signal at element 1 and is expressed as . Let ; then the array factor can be given asThis is the -degree polynomial and has roots (nulls) dependent on coefficients . In factorized form, (1) becomeswhere are zeros forced to exist on the unit circle in the complex plane [2, 3, 6, 14] and their position on the circle depends on coefficients .