Analytical upper bound on optimum joint decoding capacity of Wyner GCMAC using hadamard inequality

This paper presents an original analytical expression for an upper bound on the optimum joint decoding capacity of Wyner circular Gaussian cellular multiple access channel (C-GCMAC) for uniformly distributed mobile terminals (MTs) across the cells. This upper bound is referred to as Hadamard upper bound (HUB) and is a novel application of the Hadamard inequality established by exploiting the Hadamard operation between the channel fading and channel path gain matrices. In this context, we employ an approximation approach based on the estimation of probability density function (PDF) of Hadamard product of two matrices. A closed-form expression has been derived to capture the effect of variable user density in adjacent cells on optimal joint decoding capacity. The results of this paper demonstrate that the analytical HUB based on the proposed approximation approach converges to the theoretical results for medium range of signal to noise ratios and shows a comparable tighter bound on optimum joint decoding capacity.