Universal decoding for frequency-selective fading channels

We address the problem of universal decoding in unknown frequency-selective fading channels, using an orthogonal frequency-division multiplexing (OFDM) signaling scheme. A block-fading model is adopted, where the bands´ fading coefficients are unknown yet assumed constant throughout the block. Given a codebook, we seek a decoder independent of the channel parameters whose worst case performance relative to a maximum-likelihood (ML) decoder that knows the channel is optimal. Specifically, the decoder is selected from a family of quadratic decoders, and the optimal decoder is referred to as a quadratic minimax (QMM) decoder for that family. As the QMM decoder is generally difficult to find, a suboptimal QMM decoder is derived instead. Despite its suboptimality, the proposed decoder is shown to outperform the generalized likelihood ratio test (GLRT), which is commonly used when the channel is unknown, while maintaining a comparable complexity. The QMM decoder is also derived for the practical case where the fading coefficients are not entirely independent but rather satisfy some general constraints. Simulations verify the superiority of the proposed QMM decoder over the GLRT and over the practically used training sequence approach.