A minimax optimal decoder for OFDM over unknown frequency-selective fading channels

We address the problem of decoding in unknown frequency selective fading channels, using an OFDM signaling scheme and adopting a block fading model. For a given codebook, we seek a decoder independent of the channel fading, 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. The intuitively appealing QMM decoding procedure is derived for the case where the fading is unknown, and also for the case where the fading coefficients satisfy some general constraints. The QMM decoder is also shown to outperform the generalized likelihood ratio test (GLRT), while maintaining a comparable complexity. Simulations verify the superiority of the proposed decoder over the GLRT and over the practically used training sequence approach.