Robust signal‐to‐noise ratio and noise variance estimation for single carrier frequency domain equalisation ultra‐wideband wireless systems

In block‐mode transmission, single carrier frequency domain equalisation‐based ultra‐wide‐band technique is a promising physical‐layer candidate scheme. Here, the authors address the noise variance estimation problem for signal‐to‐noise ratio estimation in such systems. Our investigations focus on the estimation schemes both robust to the pilot sequence and the channel type. First, the authors, respectively, define the correlated noise samples and the uncorrelated ones, where the difference signals or the sum signals of two adjacent received pilot signals are included. Then, with the help of the Cramer–Rao lower bound (CRLB) theorem, the authors either use the correlated or the uncorrelated samples to estimate the noise variance based on the difference signals and the sum signals, respectively, regardless of the pilot sequences. The corresponding CRLBs are also given and analysed. Finally, under either the correlated or the uncorrelated noise samples, the authors propose to linearly combine the estimator of the difference signals with that of the sum signals where the weight coefficients are optimised. Since the proposed two combined estimators are not only robust to the pilot sequence but also automatically adapt the weights to the channel condition, they can significantly outperform the existing estimators.