A Theoretical Framework for Optimizing Multicarrier Systems Under Time and/or Frequency-Selective Channels

Abstract

A highly relevant case of wireless transmission over time-selective channel (TSC) and/or frequency-selective channel (FSC) is when the channel-state information is only known at the receiver. Under these scenarios, this letter aims to derive the necessary conditions for a unitary transmitter matrix to maximize the coded modulation (CM) capacity. We approach the problem by considering the CM capacity upper bound (UB) instead of the general one due to simplification of the problem and tightness at high signal-to-noise ratio regions. The theoretical analysis reveals that the optimal waveforms spread the symbols over the domain of selectivity of the channel. To demonstrate this result, we evaluate orthogonal frequency-division multiplex- ing (OFDM), single carrier (SC), and orthogonal chirp-division multiplexing (OCDM), where we have that: 1) OCDM and SC are optimal for FSCs and 2) OCDM and OFDM are optimal for TSCs. Finally, we show that the UB has the same performance order as the real CM capacity, providing evidence that the UB criteria are meaningful for the optimization of a communication system.