Performance limits for filtered multitone modulation in fading channels

In this paper, we investigate the best attainable performance for filtered multitone modulation (FMT) in time-variant frequency-selective fading channels when optimal maximum-likelihood (ML) detection is deployed. FMT generalizes the popular orthogonal frequency division multiplexing (OFDM) scheme through the deployment of subchannel shaping filters. The performance limits are derived by extending to this multichannel context the matched filter bounding technique. We first conduct an exact calculation for the average and the distribution of the matched filter error rate bound. Then, we follow a numerical procedure that overcomes the problems of accuracy and ill conditioning in the implementation of the exact method. This study allows for an analytical treatment of the diversity effect on performance as a function of the time/frequency selectivity of the channel. It is found that FMT is a diversity transform that is capable of yielding coding gains and time/frequency diversity gains as a function of the subcarrier spacing and the subchannel filter shape.