International Journal of Antennas and Propagation

Volume 2018, Article ID 2054271, 7 pages

https://doi.org/10.1155/2018/2054271

## AOA, Delay, and Complex Propagation Factor Estimation for the Monostatic MIMO Radar System

Al-Zaytoonah University of Jordan, Amman, Jordan

Correspondence should be addressed to Saleh O. Al-Jazzar; oj.ude.juz@g.helas

Received 19 June 2018; Revised 29 August 2018; Accepted 12 September 2018; Published 22 November 2018

Academic Editor: Giorgio Montisci

Copyright © 2018 Saleh O. Al-Jazzar and Sami Aldalahmeh. 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

In this paper, we propose a solution to find the angle of arrival (AOA), delay, and the complex propagation factor for the monostatic multiple-input multiple-output (MIMO) radar system. In contrast to conventional iterative computationally demanding estimation schemes, we propose a closed form solution for most of the previous parameters. The solution is based on forming an approximate correlation matrix of the received signals at the MIMO radar receiver end. Then, an eigenvalue decomposition (EVD) is performed on the formed approximate correlation matrix. The AOAs of the received signals are deduced from the corresponding eigenvectors. Then, the delays are estimated from the received signal matrix properties. This is followed by forming structured matrices which will be used to find the complex propagation factors. These estimates can be used as initializations for other MIMO radar methods, such as the maximum likelihood algorithm. Simulation results show significantly low root mean square error (RMSE) for AOAs and complex propagation factors. On the other hand, our proposed method achieves zero RMSE in estimating the delays for relatively low signal-to-noise ratios (SNRs).

#### 1. Introduction

Multiple-input multiple-output (MIMO) radar is becoming increasingly popular due to its ability to overcome the fluctuation in the received power caused by varying radar cross section [1]. Thus, it is proposed in the literature as a tool to estimate the location of different targets [2–8]. Radar signals are transmitted from multiple transmitter antennas; then, they are reflected off targets and received back at the radar, hence providing the required receiver diversity. However, this operation requires estimating the angle of arrivals (AOAs) and delays of the received signals, which is usually done via a maximum likelihood (ML) method [9]. Nonetheless, the ML is computationally expensive because of its iterative nature. Worse yet, it might converge to a local minima leading to erroneous estimated parameters, providing inappropriate initial values fed to the ML algorithm. As a result, a need rises to provide a closed form solution to the estimation problem, which might also serve as an appropriate initial guess for the ML.

Several articles in the literature proposed direction finding methods for the bistatic MIMO radar system where the transmitter and receiver are located in different positions such as in [5]. On the other hand, many MIMO radar models were proposed in the literature such as in [6], which utilize the monostatic MIMO radar model where the transmitter and receiver are colocated. In this paper, we utilize the monostatic MIMO radar model in [6] with some extensions to fit the proposed solution. The proposed method starts by computing an approximate correlation matrix upon which we apply eigenvalue decomposition (EVD) to find the AOAs from the corresponding eigenvectors. However, it is noticed that when the received signal is stacked in a matrix form, a specific number of columns at the beginning of the matrix should be ideally zeros. The number of these columns is related to the delay of the received signal reflected off the nearest target. This property is used to independently estimate the delays. Then, the estimated AOAs and delays are used to form structured matrices which are utilized to find the complex propagation factors for each target. These estimates can be used as initializations for other adaptive MIMO radar estimating methods as in [6].

The rest of the paper is organized as follows: Section 2 presents the problem formulation part, Section 3 contains the proposed solution, and Section 4 shows simulation results. Finally, we conclude in Section 5.

#### 2. Problem Formulation

In this section, we present the system model for the monostatic MIMO radar which is similar to the one used in [6]. Assume that the radar consists of colocated and transmitting and receiving uniform linear array (ULA) antennas, respectively. Let the transmitting antennas transmit a pulsed signal that is modulated by the sequences (for ), having a period of and consisting of chips. These signals are uncorrelated over time, and antenna elements, i.e., where is the expectation operator and is some delay.

For targets, the manifolds of the transmitted and received signals are, respectively, where is the transpose operator, are the coordinates of transmitting antennas, are the coordinates of receiving antennas, is the carrier frequency used, is the speed of light, and is the AOA of the th target (it is worth mentioning that we are considering the azimuth angle only in this paper).

Neglecting the clutter effect, the radar signal is reflected off the targets, hence experiencing different propagation factors and delays. Therefore, the received signal vector at time is represented as where is the Hermetian operator and with is the complex propagation factor, which includes the path loss and reflection coefficient factor off the th target. Also, is the delay for the th target, is a complex Gaussian noise vector of zero mean, and covariance matrix, with is identity matrix. The radar system is shown in Figure 1.