Calculating the Performance of a Soft-Information-Based Best Linear Unbiased Estimator of Amplitude and Carrier Phase Offset

This paper analytically calculates the expectation and the variance of a soft-information-based best linear unbiased estimator of amplitude and carrier phase offset. Long data frames are considered. The calculation includes the impact on the performance of the presence of training symbols as well as non-Gaussianity of the log-likelihood ratios (LLRs) fed to the estimator input. It is also analyzed how the properties of the estimator are affected when the ratio between the mean and variance of the LLRs is not equal to 1/2