Optimization of Augmented Coprime Array for a Specific number of Sensors

In this paper, optimization is carried out for the augmented coprime array (ACA) for a specific number of sensors to achieve maximum consecutive degrees-of-freedom (DOF). We know that ACA is a very popular configuration for direction-of-arrival (DOA) estimation for its advantage of less mutual coupling. ACA consists of two subarrays where both of them share the first sensor. The number of elements in each of the subarrays is 2M and $N$ where $M$ and $N$ are coprime. The number of consecutive DOF an ACA achieves with $N$ + 2M – 1 sensors is 2M N + 2M – 1. Here, we optimize the ACA structure for a given number of sensors and find out the values of $M$ and $N$ so that the array can achieve maximum DOF. We also give closed-form expressions of the DOF for a specific number of sensors. For DOA estimation, the spatial smoothing MUltiple SIgnal Classification (MUSIC) algorithm is used. In the simulation part, we estimate the spatial spectrum of this array, analyze the DOF versus the number of sensors and also look into the root mean square error (RMSE) performance of the array.