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Single-user coded 16-APSK transmission is studied from the perspective of achievable information rate and channel simulation, in the context of DVB-S2 over a nonlinear satellite channel. Achievable information rates are calculated as a function of downlink SNR and input backoff for the nonlinear amplifier, for both a memoryless end-to-end model and for a model with memory-order two. These provide benchmarks for real decoder simulations, and it is shown that achievable rate calculations are highly-predictive of actual performance and of proper IBO. We also show modification to the constellation ring ratio can provide significant savings in SNR, at least for the adopted nonlinear Saleh model. Finally, a two-pass decoding that employs hard-decision feedback from the LDPC decoder is able to gain another 0.4 dB in performance without significant complexity increase. This gain is predicted by our achievable rate analysis.

Two-way amplify-and-forward relaying between earth terminals with both users sharing the same bandwidth offers an improvement in spectral efficiency of 100%, relative to traditional frequency-multiplexing, without increase in downlink resources. This co-existence is possible due to the side-information retained in each receiver about its own 'echo' signal. While this has been widely studied in the context of linear relaying, two-way amplify/forward on a nonlinear satellite channel raises additional questions, dealing with synchronization to allow mitigation of self-interference; the achievable information rates and optimal amplifier backoff; and the performance of a 'real' two-way system in the context of DVB-S2 coding and modulation.

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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,