Information-Preserving Spatial Filtering for Direction-of-Arrival Estimation

This work investigates the problem of directionof-arrival estimation with a large number of antennas. As in practice the number of antennas M is limited by power and hardware constraints, here the possibility to compress the receive signal, prior to the estimation task, to K < 2M real-valued outputs is discussed. Under a Bayesian perspective, we state the problem of finding a linear spatial filter (2M inputs, K outputs) which preserves the information about the directionof-arrival parameter in an optimum way. In order to attain the lowest possible mean squared error with the compressed data, the filter is designed such that the Bayesian Cramér-Rao bound is minimized. An iterative gradient-based filter solution is proposed and the potential estimation performance is investigated for different setups. Simulations of the maximum a posteriori (MAP) estimator show that the accuracy predicted by theory can be attained in practice at low computational cost.