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

We obtain Shannon-theoretic limits for a very simple cellular multiple-access system. In our model the received signal at a given cell site is the sum of the signals transmitted from within that cell plus a factor α (0⩽α⩽1) times the sum of the signals transmitted from the adjacent cells plus ambient Gaussian noise. Although this simple model is scarcely realistic, it nevertheless has enough meat so that the results yield considerable insight into the workings of real systems. We consider both a one dimensional linear cellular array and the familiar two-dimensional hexagonal cellular pattern. The discrete-time channel is memoryless. We assume that N contiguous cells have active transmitters in the one-dimensional case, and that N² contiguous cells have active transmitters in the two-dimensional case. There are K transmitters per cell. Most of our results are obtained for the limiting case as N→∞. The results include the following. (1) We define C_N,Cˆ_N as the largest achievable rate per transmitter in the usual Shannon-theoretic sense in the one- and two-dimensional cases, respectively (assuming that all signals are jointly decoded). We find expressions for limN→∞C_N and limN→∞Cˆ_N. (2) As the interference parameter α increases from 0, C_N and Cˆ_N increase or decrease according to whether the signal-to-noise ratio is less than or greater than unity. (3) Optimal performance is attainable using TDMA within the cell, but using TDMA for adjacent cells is distinctly suboptimal. (4) We suggest a scheme which does not require joint decoding of all the users, and is, in many cases, close to optimal