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Performance evaluation of direction-of-arrival (DOA) estimation algorithms has continuously drawn significant attention in the past years. Most previous studies were conducted under the situation that antenna element separation is about half wavelength in order to avoid the appearance of grating lobes. On the other hand, recent developments in wireless communications have favoured the use of portable devices that utilize compact arrays with antenna element separations of less than half wavelength. Performance evaluation of DOA estimation algorithms employing compact arrays is an important and fundamental issue, but it has not been fully studied. In this paper, the performance of the matrix pencil method (MPM) that applies to DOA estimations is investigated through Monte Carlo simulations. The results show that closely spaced emitters can be accurately resolved using linear compact array with an array aperture as small as around half wavelength.

Direction-of-arrival (DOA) estimation is one of the most important applications in array signal processing. In the context of array signal processing, these algorithms can be grouped into three categories: conventional methods, subspace methods, and maximum likelihood techniques [

The DOA estimation problem is about estimation of undamped exponentials based on the measured samples of the signal from an array. Performance evaluations of subspace methods and the corresponding Cramer-Rao Lower Bound (CRLB), which gives the lower bound on the variance of any unbiased estimator, have been well studied for the estimation of a single damped/undamped exponential (e.g., [

In the last two decades, there has been significant interest in reducing the physical dimensions of existing electronic devices with the rapid development of the electronics industry. In line with this development, recent applications in antenna arrays have been focused on compact array design [

In view of this, this paper aims to characterize the effect of (i) changes in the array aperture with a fixed number of elements and (ii) changes in the number of elements in a fixed aperture on the accuracies DOA estimations with signals corrupted by Additive Gaussian White Noise (AGWN) using a Monte Carlo approach. In particular, the MPM will be considered. The focus of this study is on the effect of variations of the array aperture on the MPM algorithm under the ideal sensor condition. A brief review of MPM is first given followed by the Monte Carlo simulations and discussions towards the end of the paper.

Consider a space where there are

Once

This section presents Monte Carlo simulations of DOA estimations using ULAs with different array apertures and different number of elements. Three cases are presented to illustrate our findings. First, a four-element ULA with different apertures under the illumination of two closely spaced emitters is studied. Then, ULAs with fixed apertures but different numbers of elements are considered. Lastly, DOA estimations of three closely spaced incoming signals using arrays with a fixed aperture but different numbers of elements are studied.

A ULA with four ideal isotropic sensors is studied. The objective is to investigate how the accuracy of DOA estimation is affected by the reduction of the array aperture. The separation of the array elements is changed from

Two equal-power and equal-phase coherent sources come from the azimuth angles of

The results are shown in Figure

Next, we study the effect on the performance of MPM when the incoming signals are not of equal power and equal phase. The entire procedure is repeated for the DOA estimation of

To investigate the performance of MPM for DOA estimations when the incoming signal direction changes, DOA estimation problems with the two signals coming from the directions of

Summary of DOA estimations using MPM for a four-element ULA with interelement separation varying from

Summary of DOA estimations using MPM for a four-element ULA with interelement separation varying from

Average Bias

Bias of Signal 1 and 2

Summary of DOA estimations using MPM for a four-element ULA with interelement separation varying from

In the previous case, when the two closely spaced emitters approach to the endfire directions, it was found that the array aperture of the four-element ULA has to be ≥

The array apertures of

Now, the same estimation procedure is repeated with an array aperture of

The previous results show that for a fixed small array aperture (especially for the cases of

When the array aperture is further increased to

Summary of DOA estimations using MPM for a four-element ULA with the number of array elements varying from 4 to 20. Two equal-power incoming signals are from the directions of

In the last case, we consider DOA estimation problems of three closely spaced, equal-power, and equal-phase signals with an SNR of 5 dB come from the directions from

Lastly, the incoming signals of the same DOA problems and the array aperture are increased to

Summary of DOA estimations using MPM for a four-element ULA with the number of array elements varying from 6 to 20. Three equal-power incoming signals are from the directions of

In this paper, we have investigated the performance of MPM in DOA estimations using ULAs with different array apertures and different numbers of array elements through Monte Carlo simulations. The results show that minimum linear array apertures of

This work was supported in part by the National University of Singapore (NUS) under the Grant no. R-263-000-469-112 and in part by the US ONR research fund under the Project no. 09PR03332-01.