Maximum Likelihood SNR Estimation of Hyper Cubic Signals Over Gaussian Channel

In this letter, we address the problem of closed-form data aided (DA) and non-data aided (NDA) maximum likelihood (ML) signal-to-noise ratio (SNR) estimation for hyper-cubic modulated signals over Gaussian channel. The requirement of high SNR is exploited to derive closed-form expression of unbiased NDA ML SNR estimator. Exact expressions for the DA and NDA Cramer-Rao lower bound (CRLB) on the variance of these estimators are also determined analytically. The Monte Carlo simulation method is used to compute the normalized mean squared error (NMSE) of the estimators, and the results show that the NMSEs approach the respective normalized CRLBs.