Many applications, current and emerging, are faced with a relatively new and interesting channel model. Systems which transmit data through a nonlinear relay, such as a satellite, must deal with a composite channel that can be separated into two distinct channels - the uplink channel between the user and the relay, and the downlink channel between the relay and the final destination. If the system has a strict power limitation and high data rate demands, such as a small satellite transmitting through NASA's TDRSS Network, the dominant noise is present on the uplink rather than the downlink channel. Such a system is deemed to be uplink-noise limited and presents the designer with a number of problems not encountered in a more typical downlink-noise limited channel.
Whereas the transmitted signal constellation can be pre-distorted to take into account the effect of the nonlinearity in the down-link limited channel, no amount of pre-distortion will solve the problems encountered when the majority of the noise is present before the nonlinearity. Instead, the receiver must be modified to reflect the non- Gaussian noise due to the operation of the nonlinearity on Gaussian noise.
Under three assumptions - there is no downlink-noise present, the downlink channel is wideband relative to the data, and the filter proceeding the nonlinearity meets both matched filter and Nyquist requirements - such modifications can be made based on the nature of the nonlinearity. By mapping the ideal decision region through the nonlinearity, performance almost identical to that of a linear-wideband AWGN channel can be achieved. This paper will develop the theoretical performance of the receiver described for a nonlinearity typical of a satellite channel. Performance curves will be presented for QPSK, SPSK, 16PSK and 16QAM modulation schemes.