Reliable communication for the noncoherent additive white Gaussian channel

Abstract

The development of simple coding and decoding schemes for the Phase Ambiguous Additive White Gaussian Channel is considered in this dissertation. By phase ambiguous we mean that a narrowband signal transmitted over the Additive White Gaussian ( AWG ) Channel is shifted in phase by a random variable that remains fixed for the duration of the signal. When the phase ambiguity is modeled as an uniformly distributed random variable, the channel is referred to as the Noncoherent Additive White Gaussian ( NAWG ) Channel. When the first stage of the decoder is a phase locked loop, the phase ambiguity can be modeled by a discrete random variable that takes values corresponding to the phase angles of the signal set underlying the constellation used by the encoder. This channel is termed the Acoherent Additive White Gaussian ( AAWG ) Channel. Even when the encoder is a finite state machine, the optimum decoder for the NAWG channel cannot be implemented. We examine a suboptimum decoding scheme for the NAWG Channel. The primary component of the suboptimum decoder is a set of p identical decoders for the AWG Channel. When a finite state machine is used as the encoder, the suboptimum decoders we propose are implementable, We study the performance of our suboptimum decoder in relation to that of the optimum decoder for the NAWG channel and that of the optimum decoder for the AWG channel. We show that the suboptimum decoder, for values of p equal to 4 and 8 performs close to optimum in a variety of situations. Reliable communication for the AAWG channel is achieved by using rotationally invariant (RI) codes. We demonstrate that the decoders used in RI schemes are suboptimum. We develop a performance measure for our decoder when used on the AAWG channel. We construct alternative codes, which, when used with our suboptimum decoders, perform as well and in some cases even better, than RI codes. Finally we simulate the performance of the scheme we propose, and demonstrate its reliability for communication over the AAWG and NAWG channels.