Spectral Efficiency Scaling Laws in Dense Random Wireless Networks With Multiple Receive Antennas

This paper considers large random wireless networks, where transmit-and-receive node pairs communicate within a certain range while sharing a common spectrum. By modeling the spatial locations of nodes as a Poisson point process, analytical expressions for the ergodic spectral efficiency of a typical node pair are derived as a function of the channel state information available at a receiver (CSIR) in terms of relevant system parameters: the density of communication links, the number of receive antennas, the path loss exponent, and the operating signal-to-noise ratio. One key finding is that when the receiver only exploits CSIR for the direct link, the sum spectral efficiency increases linearly with the density, provided the number of receive antennas increases as a certain superlinear function of the density. When each receiver exploits CSIR for a set of dominant interfering links in addition to that of the direct link, the sum spectral efficiency increases linearly with both the density and the path loss exponent if the number of antennas is a linear function of the density. This observation demonstrates that having CSIR for dominant interfering links provides an order gain in the scaling law. It is also shown that this linear scaling holds for direct CSIR when incorporating the effect of the receive antenna correlation, provided that the rank of the spatial correlation matrix scales superlinearly with the density. These scaling laws are derived from integral representations of the distribution of the signal to interference and noise ratio, which are of independent interest and which in turn derived from stochastic geometry and more precisely from the theory of shot noise fields. Simulation results back the scaling laws and the integral representations.