Performance of MMSE multi-antenna receiver under hierarchical Poisson random fields of interferences

Abstract

The cumulative distribution function (CDF) of the signal-to-interference-plus-noise-ratio (SINR) for minimum mean-sQuare-error (MMSE) receivers is studied in this paper. It is discovered that, in the presence of multiple Poisson fields of interferers and independent Rayleigh fading between antennas, the CDF exhibits linear superposition property for multiple Poisson fields. This superposition property is used to generalize known results for a single homogenous Poisson field to multiple Poisson fields, non-homogenous Poisson fields and hierarchical clustered Poisson fields of interferers.

Performance of Multiantenna Linear MMSE Receivers in Doubly Stochastic Networks

“…The parameters used are rT = 10, L = 10, α = 4, σ 2 = 10 −12 , and 100, 000 Monte-Carlo trials.Given Lemma 2, if we set q = 2π 2 ρ α csc π ǫ+2 α ξ (ǫ+2)/α , then F ξ (ξ) approaches a step at adeterministic value 2π 2 ρ α csc π ǫ+2 α −α/(ǫ+2)as L → ∞. This implies that for large number ofantennas L, SIR ≈ 2π 2 ρ αL csc π ǫ+2 α −α/(ǫ+2) r −α Twhich is consistent with the findings in[19].To validate(20), we conducted Monte Carlo simulations which indicate a close agreement between the simulations and the theoretical prediction as illustrated inFig. 3 which shows PDFs of the SINR for the intensity function Λ(r, θ) = 0.023 √ r .…”

“…In a recent, independent parallel work [20] (which appeared after our conference paper that forms the basis of the results in this work [21]) the CDF of the SINR was derived for hierarchical Poisson networks which is used to analyze Poisson cluster networks. In [20] the authors assume that the representative transmitter whose SINR is analyzed, is located at a deterministic point which is not part of a cluster, even though all other transmitters in the network belong to clusters.…”

“…In a recent, independent parallel work [20] (which appeared after our conference paper that forms the basis of the results in this work [21]) the CDF of the SINR was derived for hierarchical…”

Spatial multiplexing in heterogeneous networks with MMSE receiver

“…Now by using the independence of Φ p and Φ m and substituting (11) and (12) into (8), and then unconditioning the probability we will obtain the final result.…”

“…This line of work has been extended to determine the capacity and coverage of HetNets in [8] [10]. In [11], the performance of MMSE receivers with single-antenna transmission is analyzed in a Poisson field of interference. The PPP model was used in [5], [12] to analyze SM with MMSE receivers in ad hoc networks.…”