Shannon-theoretic approach to a Gaussian cellular multiple-access channel with fading

Shannon-theoretic limits on the achievable throughput for a simple infinite cellular multiple-access channel (MAC) model (Wyner 1994) in the presence of fading are presented. In this model, which is modified to account for flat fading, the received signal, at a given cell-site´s antenna, is the sum of the faded signals transmitted from all users within that cell plus an attenuation factor α∈[0,1] times the sum of the faded signals received from the adjacent cells, accompanied by Gaussian additive noise. This model serves as a tractable model providing considerable insight into complex and analytically intractable real-world cellular communications. Both linear and planar cellular arrays are considered with exactly K active users in each cell. We assume a hyper-receiver, jointly decoding all of the users, incorporating the received signals from all of the active cell-sites. The hyper-receiver is assumed to be aware of the codebooks and realizations of the fading processes of all the users in the system. In this work we consider the intracell time-division multiple-access (TDMA) and the wideband (WB) protocols. We focus on the maximum reliably transmitted equal rate. Bounds to this rate are found for the intracell TDMA protocol by incorporating information-theoretic inequalities and the Chebyshev-Markov moment theory as applied to the limiting distribution of the eigenvalues of a quadratic form of tridiagonal random matrices. We demonstrate our results for the special case where the amplitudes of the fading coefficients are drawn from a Rayleigh distribution, i.e., Rayleigh fading. For this special case, we observe the rather surprising result that fading may increase the maximum equal rate, for a certain range of α as compared to the nonfaded case. In this setting, the WB strategy, which achieves the maximum reliable equal rate of the model, is proved to be superior to the TDMA scheme. An upper bound to the maximum equal rate of the WB scheme is also obtained. This bound is asymptotically tight when the number of users is large (K≫1). The asymptotic bound shows that the maximum equal rate of the WB scheme in the presence of fading is higher than the rate which corresponds to the nonfaded case for any intercell interference factor α∈[0,1] signal-to-noise ratio (SNR) values. This result is found to be independent of the statistics of the fading coefficients