We study achievable information rates for nonlinear channels with memory, in the context of satellite communication with QAM modulation. The complete channel model can be described by a Volterra expansion, but large alphabet size and/or large channel memory length may prohibit optimal softoutput demodulator processing, say with the BCJR algorithm. Thus we focus on reduced-state receivers and their achievable information rates as a function of state complexity, amplifier backoff, and receiver input sampling rate. These achievable rates for mismatched receivers are known to be attainable with powerful error control codes and optimal decoding.
I. INTRODUCTIONWe consider transmission of QAM signals via a nonlinear satellite relay, with particular interest in achievable information rates obtainable as a function of downlink SNR, uplink power backoff, and complexity of a reduced-state decoder for the nonlinear channel with memory. More specifically, we investigate the transmission of 16-APSK modulated signals as typical in DVB-S2 systems that are distorted at the transmitter by a traveling wave tube amplifier represented by a memoryless Saleh model [1]. Figure 1 shows this configuration, where h(t) represents transmitter pulse shaping for spectrum control, g() represents the nonlinear amplifier, and h OMUX (t) is the output multiplexing filter. The reciever implements a trellis-based soft intput soft output (SISO) detector. Our model assumes strong uplink signals, so uplink noise due to the satellite amplifiers is ignored, and only downlink noise is considered.In the absence of nonlinear distortion, QAM signals can be optimally detected by the use of a single matched filter, which preserves sufficient statistics. However this no longer is the case when there is a nonlinear element in the transmit chain.It has been recognized that a matched filter (or correlator) bank is able to provide the sufficient statistics for an optimal trellis-based detector for this scenario, see [2]. However the complexity of the optimal detector (either SISO module or sequence decoder) grows as M L , where M is the modulator alphabet size, and L is the channel memory order. Our interest is in producing soft outputs, or symbol likelihoods,