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Abstract-The spectral efficiency of a representative uplink of a given length, in interference-limited, spatially-distributed wireless networks with hexagonal cells, simple power control, and multiantenna linear Minimum-Mean-Square-Error receivers is found to approach an asymptote as the numbers of base-station antennas N and wireless nodes go to infinity. An approximation for the area-averaged spectral efficiency of a representative link (averaged over the spatial base-station and mobile distributions), for Poisson distributed base stations, is also provided. For large N, in the interference-limited regime, the area-averaged spectral efficiency is primarily a function of the ratio of the product of N and the ratio of base-station to wireless-node densities, indicating that it is possible to scale such networks by linearly increasing the product of the number of base-station antennas and the relative density of base stations to wireless nodes, with wirelessnode density. The results are useful for designers of wireless systems with high inter-cell interference because it provides simple expressions for spectral efficiency as a function of tangible system parameters like base-station and wireless-node densities, and number of antennas. These results were derived combining infinite random matrix theory and stochastic geometry.

We consider a user-centric co-operative cellular network, where base stations (BSs) close to a mobile co-operate to detect its signal using a (joint) linear minimum-mean-square-error receiver. The BSs are at arbitrary positions and mobiles are modeled as a planar Poisson Point Process (PPP). Combining stochastic geometry and infinite-randommatrix theory, we derive a simple expression for the spectral efficiency of this complex system as the number of antennas grows large. This framework is applied to BS locations from PPPs and hexagonal grids, and are validated through Monte Carlo simulations. The results reveal the influence of tangible system parameters such as mobile and base-station densities, number of antennas per BS, and number of co-operating BSs on achievable spectral efficiencies. Among other insights, we find that for a given BS density and a constraint on the total number of cooperating antennas, all co-operating antennas should be located at a single BS. On the other hand, in our asymptotic regime, for the same number of co-operating antennas, if the network is limited by the area density of antennas, then the number of co-operating BSs should be increased with fewer antennas per BS.

An asymptotic technique is presented to characterize the data rate (bits/symbol) achievable on a wireless link in a spatially distributed network with active interferers at correlated positions, N receive diversity branches, and linear Minimum-Mean-Square-Error (MMSE) receivers. This framework is then applied to systems including analogs to Matern type I and type II networks which are useful to model systems with Medium-Access Control (MAC), cellular uplinks with orthogonal transmissions and frequency reuse, and Boolean cluster networks. It is found that for our network models, with moderately large N, the correlation between interferer positions does not significantly influence the rate resulting in simple approximations for the data rates achievable in such networks which are known to be difficult to analyze and for which only a few results are available. These results can help system designers to optimize parameters such as frequency reuse factors in cellular networks and understand the trade off between improved data rates and increased costs associated with increasing diversity orders for wide range of system models.

An asymptotic technique is presented for finding the spectral efficiency of multi-antenna links in wireless networks where transmitters have Channel-State-Information (CSI) corresponding to their target receiver. Transmitters are assumed to transmit independent data streams on a limited number of channel modes which limits the rank of transmit covariance matrices. This technique is applied to spatially distributed networks to derive an approximation for the asymptotic spectral efficiency in the interference-limited regime as a function of link-length, interferer density, number of antennas per receiver and transmitter, number of transmit streams and path-loss exponent. It is found that targeted-receiver CSI, which can be acquired with low overhead in duplex systems with reciprocity, can increase spectral efficiency several fold, particularly when link lengths are large, node density is high or both. Additionally, the per-link spectral efficiency is found to be a function of the ratio of node density to the number of receiver antennas, and that it can often be improved if nodes transmit using fewer streams. These results are validated for finite-sized systems by Monte-Carlo simulation and are asymptotic in the regime where the number of users and antennas per receiver approach infinity.