International Journal of Antennas and Propagation

Volume 2015 (2015), Article ID 542614, 11 pages

http://dx.doi.org/10.1155/2015/542614

## Efficient DoA Tracking of Variable Number of Moving Stochastic EM Sources in Far-Field Using PNN-MLP Model

^{1}Faculty of Electronic Engineering, University of Niš, Aleksandra Medvedeva 14, 18 000 Niš, Serbia^{2}Singidunum University, Danijelova 32, 11000 Belgrade, Serbia

Received 9 August 2015; Accepted 1 December 2015

Academic Editor: Ahmed T. Mobashsher

Copyright © 2015 Zoran Stanković 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

An efficient neural network-based approach for tracking of variable number of moving electromagnetic (EM) sources in far-field is proposed in the paper. Electromagnetic sources considered here are of stochastic radiation nature, mutually uncorrelated, and at arbitrary angular distance. The neural network model is based on combination of probabilistic neural network (PNN) and the Multilayer Perceptron (MLP) networks and it performs real-time calculations in two stages, determining at first the number of moving sources present in an observed space sector in specific moments in time and then calculating their angular positions in azimuth plane. Once successfully trained, the neural network model is capable of performing an accurate and efficient direction of arrival (DoA) estimation within the training boundaries which is illustrated on the appropriate example.

#### 1. Introduction

Signal source localization by employing passive antenna arrays is widely used technique in different areas such as communications, radars, acoustics, and medicine. Important step in this spatial determination of source location is to perform an angular direction of arrival (DoA) estimation of a signal radiated from the source. Among other things, the purpose and nature of the signal have to be taken into account while performing the DoA estimation, as signals can be considered either desired and deterministic or interfering both deterministic (unintentional interference) and stochastic (random function in time). In wireless communications, once the angular positions of desired/interfering electromagnetic (EM) source are found by using DoA estimation, the adaptive beam-forming algorithm can be employed to optimize the radiation pattern of antenna array so that it allocates the main beam towards the user of interest and generates deep nulls in the directions of interfering signals from mobile users in adjacent cells.

A number of DoA estimation algorithms have been proposed in the literature taking into account the statistical properties of source signals, geometry of the antenna arrays at the receiver end, multiplexing schemes, and so forth. Majority of these algorithms rely on the processing of a spatial covariance matrix of received signals at antenna array elements. Multiple Signal Classification (MUSIC) [1] is one of these techniques, widely used due to its superresolution capabilities. However, it is of high computational complexity as it requires a demanding spectrum search procedure, resulting in some cases in a longer run time not suitable for real-time applications. Artificial neural networks (ANNs) [2–4] represent an alternative faster approach to the MUSIC and other intensive superresolution DoA algorithms. ANNs are very convenient as a modeling tool since they have the ability to learn from the presented data and therefore they are especially useful in solving complex problems or those not fully mathematically described. In other words, ANNs are able to map dependence between two datasets. The learning process is an optimization procedure through which parameters of the ANN are optimized to have the ANN outputs as close as possible to the target values. This ability qualifies ANNs as very suitable tool for estimating the angular positions of source signals [4, 5].

In [6] a new approach based on combination of the Multilayer Perceptron (MLP) [3, 4] and the Radial Basis Function (RBF) ANNs [3, 4] is developed for two-dimensional, in azimuth and elevation planes, DoA estimation of deterministic signals radiated from narrowband EM sources. In [7, 8] and in [9], which was extended version of [8], an ANN approach, realized by the MLP neural model, has been presented to provide a high-resolution DoA estimation of stochastic signals. Since no amplitudes can be defined for the numerical values of stochastic signals, the characterization of stochastic signals differs from the characterization of deterministic signals. It requires considering the correlation between any two spatial points of the stochastic source in order to provide an estimation of spatial covariance matrix. A network-based methodology for the numerical computation of stochastic electromagnetic (EM) fields excited by spatially distributed noise sources with arbitrary spatial correlation was presented in [10, 11]. Based on stochastic source radiation model developed from [10], the MPL models from [7–9] were able to efficiently perform mapping from the space of stochastic signals described by the correlation matrix to the space of DoA in angular azimuth coordinates. However, their application was limited to the cases of only few stochastic narrowband EM sources in the far-field, at the fixed mutual distance. In [12–14], the developed MLP models were extended to allow an efficient DoA estimation of a number of mutually arbitrary positioned uncorrelated stochastic EM sources in far-field.

Both the superresolution algorithms and previously mentioned neural models have one limitation when performing the DoA estimation. The number of EM sources presented in the observed sector has to be known in advance in order to preserve model validity and its sufficient accuracy for angular positions determination. If the model is developed for particular number of sources assumed to be present in the observed sector during the model operation, in cases when the actual number of present sources is smaller or higher than assumed number, it is possible that model will incorrectly identify sources angular positions. Therefore in this paper, two-stage neural model, based on combining the probabilistic neural network (PNN) [15, 16] and the MLP network, is proposed in order to overcome this limitation. The PNN-MLP model is capable of performing an efficient and accurate DoA estimation of stochastic EM sources whose number is changing in time and sources are also moving fast in the observed sector. The example presented in the paper demonstrates the accuracy and suitability of the proposed neural network model for real-time applications.

#### 2. Stochastic Source Radiation Model

Stochastic source radiation model, presented in [7–9, 12–14] and also used in this paper, starts from the assumption that each source radiation in far-field can be represented by linear uniform antenna array with elements mutually separated by , , where is observed frequency in far-field (Figure 1). In general, the degree of correlation between antenna elements feed currents, described by vector , is arbitrary and it can be expressed by the correlation matrix [10, 11]:By employing the Green function marked with vector , where and are azimuth and elevation angles determined with respect to the first antenna element, the level of electric field radiated from the antenna array representation of stochastic source, at some sampling point in the far-field, can be calculated as is the radiation pattern of antenna array, is the distance of far-field point to the centre of array, is free-space impedance, is the phase constant (), and are the distances of considered far-field point from the first to the th element of antenna array. For observation points in the far-field, we use a more general notation in order to describe the antenna array elements distance from particular points in far-field. For example, in Figure 1 represents the distance between th element () in the antenna array and th point in the far-field ().