Research Article
Joint Angle-Amplitude Estimation for Multiple Signals
with L-Structured Arrays Using Bioinspired Computing
Fawad Zaman
Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock Campus, Punjab, Pakistan
Correspondence should be addressed to Fawad Zaman; fawad@ciit-attock.edu.pk
Received 28 July 2016; Revised 10 October 2016; Accepted 24 October 2016; Published 15 January 2017
Academic Editor: Donatella Darsena
Copyright © 2017 Fawad Zaman. Tis 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.
Te aim of this work is to estimate jointly the elevation and azimuth angles along with the amplitudes of multiple signals impinging
on 1-L- and 2-L-shape arrays. An efcient mechanism based on hybrid Bioinspired techniques is proposed for this purpose. Te
global search optimizers such as Diferential Evolution (DE) and Particle Swarm optimization (PSO) are hybridized with a local
search optimizer called pattern search (PS). Approximation theory in Mean Square Error sense is exploited to develop a ftness
function of the problem. Te unknown parameters of multiple signals transmitted by far-feld sources are estimated with the
strength of hybrid DE-PS and PSO-PS. Te efectiveness of the proposed techniques is tested in terms of estimation accuracy,
proximity efect, convergence, and computational complexity.
1. Introduction
Parameter estimation such as Direction of Arrival (DOA)
of electromagnetic signals for multiple sources is one of the
vital areas of research in array signal processing from the
last few decades. Te DOA estimation ensues in adaptive
beamforming to place the nulls in the direction of jam-
mers or unwanted signals, while placing the main beam
in the desired direction [1–3]. Terefore, various schemes
are investigated for DOA estimation in literature but mostly
limited to one-dimensional (1D) DOA estimation of sources
impinging on linear array [4–6]. Te 1D DOA estimation
is comparatively straight forward because it only involves
the angle of elevation as function of DOA. However, 2D
DOA estimation is relatively complicated as it involves both
elevation and azimuth angles [7–11]. 2D DOA estimation
has engaged the interest of research community in the feld
of radar, sonar, wireless communication systems, and so
forth [12]. Te estimation failure, pair matching between
elevation and azimuth angles, and computational complexity
are the major problems observed in 2D DOA estimation. Te
diferent array confgurations have been proposed to address
the 2D DOA estimation problem [13–15] but lack the requisite
resources to resolve the aforementioned problems. In [16],
Propagator Method (PM) with parallel shape array is used
to overcome the computational complexity of [15], but the
estimation failure and pair matching problems still exist. In
[17], the PM is applied with L-shape array to surmount the
drawbacks of [16] but requires a large number of snapshots
and sensors.
In the present scientifc society era, the signifcance of
Evolutionary Computing Techniques (ECT) that include
Genetic Algorithm (GA), Particle Swarm Optimization
(PSO), and Diferential Evolution (DE) cannot be vilipended.
Tese techniques are not only easy to implement but also have
the signifcant ability of hybridization with other heuristic
and nonheuristic techniques. Terefore, the signifcance of
these techniques is realized in diferent varying nature of
applications [18–22].
In this paper, DE and PSO are hybridized with PS to
jointly estimate the amplitude and 2D DOA of far-feld
sources impinging on 1-L- and 2-L-shape arrays. In this
hybridization process, DE and PSO act as global search
optimizers, while PS is used as rapid local search optimizer.
Te best individual results of DE and PSO are given to
PS for further tuning. Te performance criterion is devised
on the basis of Mean Square Error (MSE) that is applied
as an objective evaluation function. Tis ftness function is
Hindawi
Wireless Communications and Mobile Computing
Volume 2017, Article ID 9428196, 12 pages
https://doi.org/10.1155/2017/9428196