Universal decoding over Gaussian fading channels - metric calculation and performance evaluation

In a previous work, a universal decoder in a competitive minimax sense was developed for unknown block fading linear white Gaussian channels. For a given codebook (with finite blocklength), a high SNR optimal metric for the decoder was found, whose direct calculation requires solving a non-convex optimization problem and may be formidable. In this paper, the metric calculation problem is facilitated by semidefinite programming, which leads to a low-complexity approximation for the metric. The competitive minimax performance of the optimal decoder (i.e., its worst case power loss compared to the maximum likelihood decoder, which has full knowledge of the channel) is evaluated, and upper lower bounds are derived for the performance evaluation of non-optimal decoders - the training sequence and the generalized likelihood test decoders.