On the lower performance bounds for DOA estimators from linearly-modulated signals

In this paper, the problem of direction of arrival (DOA) estimation from linearly-modulated signals over AWGN channels is considered. We derive closed-form expressions for the inphase/quadrature Cramér-Rao lower bounds of the data-aided (DA) DOA estimates from any linearly-modulated signal corrupted by additive white circular complex Gaussian noise (AWCCGN). We consider the case of single-source signals impinging on multiple receiving antenna elements, commonly known as single input multiple output (SIMO) configurations. An analytical approach is conducted to compare the achievable performance in coherent estimation against noncoherent estimation over uniform linear array (ULA) and uniform circular array (UCA) configurations. It will be shown that the CRLBs that can be achieved over a ULA are lower than those that can be achievable over a UCA up to a given angular aperture whose expression is also derived in this paper. It will be shown also that ULAs exhibit lower CRLBs in coherent estimation than in noncoherent estimation and that the CRLBs hold, however, the same for UCAs in both estimation schemes.