  In this paper, we tackle for the first time the problem of maximum likelihood
(ML) estimation of the signal-to-noise ratio (SNR) parameter over time-varying
single-input multiple-output (SIMO) channels. Both the data-aided (DA) and the
non-data-aided (NDA) schemes are investigated. Unlike classical techniques
where the channel is assumed to be slowly time-varying and, therefore,
considered as constant over the entire observation period, we address the more
challenging problem of instantaneous (i.e., short-term or local) SNR estimation
over fast time-varying channels. The channel variations are tracked locally
using a polynomial-in-time expansion. First, we derive in closed-form
expressions the DA ML estimator and its bias. The latter is subsequently
subtracted in order to obtain a new unbiased DA estimator whose variance and
the corresponding Cram\'er-Rao lower bound (CRLB) are also derived in closed
form. Due to the extreme nonlinearity of the log-likelihood function (LLF) in
the NDA case, we resort to the expectation-maximization (EM) technique to
iteratively obtain the exact NDA ML SNR estimates within very few iterations.
Most remarkably, the new EM-based NDA estimator is applicable to any
linearly-modulated signal and provides sufficiently accurate soft estimates
(i.e., soft detection) for each of the unknown transmitted symbols. Therefore,
hard detection can be easily embedded in the iteration loop in order to improve
its performance at low to moderate SNR levels. We show by extensive computer
simulations that the new estimators are able to accurately estimate the
instantaneous per-antenna SNRs as they coincide with the DA CRLB over a wide
range of practical SNRs.
