SNR Estimation Over SIMO Channels From Linearly Modulated Signals

In this paper, we address the problem of data-aided (DA) and nondata-aided (NDA) per-antenna signal-to-noise ratio (SNR) estimation over wireless single-input multiple-output (SIMO) channels from linearly modulated signals. Under constant channels and additive white Gaussian noise (AWGN), we first derive the DA maximum-likelihood (ML) SNR estimator in closed-form expression. The performance of the DA ML estimator is analytically carried out by deriving the closed-form expression of its bias and variance. Besides, in order to compare its performance with the fundamental limit, we derive the DA Cramér-Rao lower bound (CRLB) in closed-form expression. In the NDA case, the expectation-maximization (EM) algorithm is derived to iteratively maximize the log-likelihood function. The performance of the NDA ML estimator is empirically assessed using Monte Carlo simulations. Moreover, we introduce an efficient algorithm, which applies to any one/two-dimensional
M
-ary constellation, to numerically compute the NDA CRLBs. In this paper, the noise components are assumed to be spatially uncorrelated over all the antenna elements and temporally white. In both cases, we show that our new inphase and quadrature I/Q-based estimators offer substantial performance improvements over the single-input single-output (SISO) ML SNR estimator due to the optimal usage of the statistical dependence between the antenna branches, and that it reaches the corresponding CRLB over a wide SNR range. We also show that the use of the I/Q-based ML estimators can lead to remarkable performance improvements over the moment-based estimators for the same antenna-array size. Moreover, it is shown that SIMO configurations can contribute to decreasing the required number of iterations of the EM algorithm.