Abstract
Abstract. This paper focuses on the estimation of the direction-of-arrival (DOA) of signals impinging on a sensor array. A novel method of array geometry optimization is presented that improves the DOA estimation performance compared to the standard uniform linear array (ULA) with half wavelength element spacing. Typically, array optimization only affects the beam pattern of a specific steering direction. In this work, the proposed objective function incorporates, on the one hand, a priori knowledge about the signal's DOA in terms of a probability density function. By this means, the array can be adjusted to external conditions. On the other hand, a modified beam pattern expression that is valid for all possible signal directions is taken into account. By controlling the side lobe level and the beam width of this new function, DOA ambiguities, which lead to large DOA estimation errors, can be avoided. In addition, the DOA fine error variance is minimized. Using a globally convergent evolution strategy, the geometry optimization provides array geometries that significantly outperform the standard ULA with respect to DOA estimation performance. To show the quality of the algorithm, four optimum geometries are presented. Their DOA mean squared error is evaluated using the well known deterministic Maximum Likelihood estimator and compared to the standard ULA and theoretical lower bounds.
Highlights
This paper deals with the problem of estimating the direction-of-arrival (DOA) of signals impinging on an array of spatially distributed sensors
A novel method of array geometry optimization is presented that improves the DOA estimation performance compared to the standard uniform linear array (ULA) with half wavelength element spacing
We focus on the deterministic Maximum Likelihood (DML) DOA estimator, which is asymptotically consistent and statistically efficient under certain regularity conditions (Stoica and Nehorai, 1989)
Summary
This paper deals with the problem of estimating the direction-of-arrival (DOA) of signals impinging on an array of spatially distributed sensors. A narrow beam width increases the possibility of angular signal separability in the multiple signal case It is well known in DOA estimation, that the mean squared error (MSE) departs from the Cramer-Rao lower bound when the signal-to-noise (SNR) ratio (or the sample size) falls below a specific limit. All attempts of array geometry optimization that aim at DOA performance improvement have to take this MSE characteristic, which is based on a trade-off between SLL and beam width of the beam pattern, into account. To take “real world” external conditions into account, we further incorporate a probability density function (PDF), defined for all valid steering directions It is affected, for instance, by the angular a priori distribution of the target’s DOA, the element factor of the sensors, the transmit beam pattern and the effect of blinds or radomes. Some examples for optimum array geometries are presented and their DOA estimation performance is compared to the standard ULA using Monte Carlo simulations and the Cramer-Rao lower bound
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