Optimal Adaptive Array and Angle Tracking for Multiple Targets - A Re-examination of Optimal Array Processing

The optimal array for detecting the signal from a desired direction but contaminated by receiver noise and strong interference from different sources with unknown arriving-angles is re-examined. The well-known optimal array is obtained by inverting the covariance matrix of interference and noise to maximize the signal to interference and noise ratio (SINR). In practice, the covariance matrix is unknown and has to be estimated by a sample covariance matrix. The optimal array is thus estimated by inverting the sample covariance matrix. This procedure has been employed in optimal array research without challenge. However, it is shown in this paper that the estimated optimal array fails to yield the highest SINR in the case of unknown arriving-angles. Instead the highest SINR can be achieved by optimally estimating the arriving-angles of interference followed by a constrained matched filter, which maximizes the signal to noise ratio subject to canceling the interference from the estimated arriving-angles. In order to reduce the computational burden, an angle-tracking system for multiple targets is adopted to achieve the optimal estimation of arriving-angles. The resulting system of angle-tracking adaptive array offers the highest SINR at a computational burden only on 2 the order of N middot M² multiplications within a radar range-cellDeltatau, rather than N³ multiplications in the well-known but questionable estimated optimal array. Here N is the number of sensors in the array and M the number of interference sources. Typically, N = 1,000 in a planar radar array, M = 2-10 and Deltatau = 1 mus. Numerical simulations confirm the theoretical results