Cramer-Rao Lower Bounds of NDA SNR estimation for BPSK modulated signals over MISO with STBC channels

Abstract

In this paper, the Cramer-Rao Lower Bounds (CRLB) for the estimation of Non Data Aided (NDA) Signal to Noise Ratio (SNR) estimation of Binary Phase Shift keying (BPSK) modulated signals over Multiple Input Single Output (MISO) with Space Time Block Codes (STBC) channels is derived. The Alamouti transmit diversity model is used in this paper. Our assumption is that the received signal is corrupted by additive white Gaussian noise (AWGN) with unknown variance, and scaled by fixed unknown complex channel gain. The lower bounds were derived for non-data aided estimation when the transmitted symbols are unknown to the receiver. The NDA bound is then compared to the Data Aided (DA) estimation where the transmitted symbols are known to the receiver. Numerical integration is being used to find the Fisher Information Matrix (FIM) elements in order to calculate the CRLB in the NDA case. It is shown that there is a significant improvement when compared to the Single Input Single Output (SISO) CRLB. In addition, the difference between the NDA and DA CRLBs become smaller at low SNR when diversity is used.