Moment-Based Estimation of the Signal-to-Noise Ratio for Oversampled Narrowband Signals

Assuming the symbol timing to be established, blind estimation of the signal-to-noise ratio (SNR), based on second-and fourth-order moments of the envelope such that the knowledge of the carrier phase becomes obsolete, is well documented in the technical literature. However, to the best of the authors´ knowledge, nothing is reported in this respect if the symbol timing is not available or reliable enough, as it might easily happen in practice. Motivated by this background, a moment-based SNR estimator is developed when both timing and carrier phase are unknown. Applied to narrowband signals as they are accessible at the output of the matched receiver filter, the derivation of the algorithm turns out to be fairly intricate from the analytical point of view although the final result is surprisingly simple, i. e., apart from some constants depending on modulation scheme and pulse shape, it is formally not much different from the relationship with perfect symbol timing recovery.