Array geometry optimization for direction-of-arrival estimation including subarrays and tapering

This paper focuses on the estimation of the direction-of-arrival (DOA) of signals impinging on a linear sensor array. In contrast to conventional arrays, where the number of channels equals the number of sensors, we use tapered subarray structures. For this type of array, each channel consists of several sensor elements with different amplitude tapering. By this means, a pre-focussing can be achieved for angular regions, where targets are likely to appear. As a consequence, the DOA mean squared error in the corresponding regions is reduced. As the subarrays affect the statistical properties of the baseband signal model, we extend the well known definitions of the Maximum Likelihood DOA estimator and the Crame¿r-Rao bound (CRB). Furthermore, we present an expression for the ambiguity function for a single signal based on the Maximum Likelihood estimator. This function and the CRB are used to optimize the sensor geometry, subarray tapering and subarray configuration. As external conditions such as the range of possible DOA´s, the DOA region of interest and the signal power range are also included in the optimization, the array can be adjusted to external requirements defined by a specific application and function. By this means, optimum (single source) DOA estimation performance for a specific area of application can be achieved. An evolution strategy is used for the optimization. To show the DOA estimation performance of the optimized arrays and to confirm the validity of the extended CRB, simulation results are presented. Compared to conventional arrays, the optimized tapered subarray structures provide a significantly better DOA accuracy.