EM Algorithm for Non-Data-Aided SNR Estimation of Linearly-Modulated Signals over SIMO Channels

In this paper, we address the problem of non-data-aided SNR estimation in wireless SIMO channels. We derive the per-antenna ML SNR estimator using the expectation-maximization (EM) algorithm under constant channels and additive white Gaussian noise (AWGN). The new method is valid for any arbitrary constellation. It is NDA and, therefore, does not impinge on the hole throughput of the system. We obtain two non linear vector equations which are tackled by a less complex approach based on the EM algorithm. The noise components are assumed to be spatially uncorrelated over all the antenna elements and temporally white with equal power. Besides, in order to evaluate our EM-ML SNR estimator, we derive the Cramer-Rao lower bound (CRLB) in the DA case. Monte Carlo simulations show, that our new estimator offers, a substantial performance improvement over the SISO ML SNR estimator due to the optimal usage of the mutual information between the antenna branches, and that it reaches the derived DA CRLBs. To the best of our knowledge, we are the first to derive the ML per-antenna SNR estimators as well as the CRLBs in the NDA and the DA case, respectively, both over SIMO channels.