Cramer-Rao Bound for SNR Estimation of Hyper-Cubic Signals Over Gaussian Channel

In this contribution we derive analytical expression for the Cramer-Rao lower bound (CRLB) on the variance of unbiased non-data-aided (NDA) signal to noise ratio (SNR) estimates of the hyper-cubic modulated signals. Underlying channel is assumed to be additive white Gaussian noise (AWGN) channel. Asymptote of the CRLB for higher SNR case is also derived in closed form. It has been shown that in low SNR region the CRLB changes significantly for different dimensions of hyper-cubic constellation (HCC) and observations. For higher dimensions corresponding CRLB is large but it gets reduced considerably as number of observations is increased. However at high SNR the behavior is reversed. The asymptote of published DA-CRLB for multi-order square-QAM is compared with the asymptote of NDA-CRLB for the HCC, and it is shown that at high SNR both depict same behavior.