Cramer-Rao Bound for NDA DOA Estimates of Square QAM-Modulated Signals

This paper addresses the stochastic Cramer-Rao lower bound (CRLB) for the non-data-aided (NDA) direction of arrival (DOA) estimation of square quadrature amplitude (QAM)-modulated signals when the transmitted symbols are supposed to be completely unknown to the receiver. These signals are assumed to be corrupted by additive white circular complex Gaussian noise (AWCCGN). The channel is supposed to be slowly time-varying so that it can be assumed constant over the observation interval. The main contribution of this paper consists in deriving an explicit expression for the Fisher information matrix (FIM) in the case of a single square QAM modulated waveform and an analytical expression for the stochastic CRLB of the NDA DOA estimates. It will be shown that the achievable performance on the DOA estimates hold almost the same irrespectively of the modulation order.