Asymptotically Tight Capacity Bounds for a Class of Memoryless Nonlinear AWGN Channels

Abstract:
Capacity upper and lower bounds are proposed for a class of time-discrete, memoryless nonlinear communication channels subject to additive white Gaussian noise in this paper. The channel nonlinearity is described by the complex-valued power function f(X) = X(exp n) with n 2 N. The complex-valued channel input X is subject to an average power constraint. For the capacity analysis, first the nonlinear channels are transformed into equivalent linear channels, which incorporate the nonlinearity in the input constraints. Next, capacity lower bounds are derived by assessing the differential entropy of the channel output by means of the differential entropy of the channel input. Based on these results, a dual expression for the capacity will be evaluated which yields the capacity upper bounds. As an outcome, simple expressions for the capacity bounds are derived in closed form. The bounds are asymptotically tight for high signal to noise ratios so that the approximation error vanishes if the signal-to-noise ratio tends to infinity.