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

This paper presents the derivation of an analytical expression for the Cramer-Rao Lower Bound (CRLB) on the variance of unbiased, non-data-aided (NDA) signal-to-noise ratio (SNR) estimators for hyper-cubic modulated signals. The analysis assumes Gamma noise (GN) channel model. It is demonstrated that, in the low-SNR regime, the CRLB varies significantly based on the hyper-cubic constellation (HCC) dimensionality and the number of observations. For higher-dimensional constellations, the CRLB is initially large but decreases substantially with an increasing number of observations. Conversely, in the high-SNR region, this behavior is reversed. Analysis of the data-assisted (DA) CRLB and NDA-CRLB for square quadrature amplitude modulation at more than one level and HCC respectively, reveals that their estimation variance characteristics converge toward comparable behaviour under high-SNR conditions.