Asymptotic Data Rates of Receive-Diversity Systems with MMSE Estimation and Spatially Correlated Interferers

Abstract

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.

Asymptotic data rates of limited-rank transmissions in wireless networks with interferers at correlated locations

“…Then, the second term on the RHS of (8) is small and moreover, it approaches zero as c → ∞. A similar property is shown for single transmit antenna systems in [5]. Thus, if c → ∞ after n, N, R → ∞:…”

“…of the random variables p 1n , p 2n , · · · p nn . Thus, from Theorem 1 of [5] and the subsequent analysis, we note that the upper and lower bounds above asymptotically approach the same limit in probability, respectively as follows…”

“…Such systems are suitable for analysis using the framework we developed here. The proof that this model satisfies our assumptions follows along similar lines as the proof for single-antenna transmissions with random cells from, [5] and is omitted for brevity. Note that since we do not consider the effects of channel estimation and pilot contamination (e.g see [17]) here, our results should be interpreted as upper bounds on achievable spectral efficiencies with practical channel estimation approaches.…”

“…[2], [3]) for which some exact (although not in closed-form) results are available, most authors use asymptotic approximations of some form (e.g. [4], [1], [5]), or approximate user locations as being independent (e.g. [6], [7]).…”

“…[6], [7]). In this work, we consider a wireless network where Siddhartan receivers have a large number of antennas but unlike [5] where single antenna transmitters and linear minimum-mean-squareerror (MMSE) receivers were assumed, we allow for multiple transmit antennas and analyze the mutual information between the received and transmitted signal vectors. We limit the rank of transmit covariance matrices which has been shown to increase the network-wide spectral efficiencies in a wide range of networks with spatially independent transmitters (e.g.…”