Universal decoding for linear Gaussian fading channels in the competitive minimax sense

We address the problem of communicating over an unknown linear fading channel with additive white Gaussian noise, in the high SNR regime. A block fading model is adopted where the channel fading vector is unknown, yet assumed constant during the block. For a given codebook, a competitive minimax criterion is used to find a decoder ignorant of the specific channel fading prevailing, yet its performance, relative to the Maximum Likelihood decoder, has the best worst case. For a codebook with two codewords, the decoder is found explicitly, and a numerical method is described to find its performance.