Capacity Analysis of Interference Alignment With Bounded CSI Uncertainty

Abstract

Interference alignment (IA) has been demonstrated to achieve the degree-of-freedom (DoF) of an interference channel given perfect global channel state information (CSI). In this letter, we consider the case of imperfect CSI with bounded errors and derive a capacity lower bound of the channel using IA. We show that this lower bound is within 1 bps/Hz of the capacity of the perfect CSI case up to a certain signal-to-noise ratio (SNR) which we refer to it as the saturating SNR. Further, we introduce a new metric called modified DoF (mDoF) in order to characterize the multiplexing performance of IA with imperfect CSI at finite SNR. Simulation results for the 3-user case are provided to illustrate the region within which the actual capacity of IA falls.

Interference Alignment in Two-Tier Randomly Distributed Heterogeneous Wireless Networks Using Stochastic Geometry Approach

“…IA is a promising approach to increase the degrees-offreedom (DoF) of HetNets by aligning the interference from different transmitters into the same lower-dimensional interference subspace at each receiver [15]- [18]. IA concept originated from an elegant coding scheme for 2-user MIMO X channel [15].…”

“…[16] and [17] studied the performance of wireless networks with Poisson clustered process (PCP) based on the probability generating function (PGF) where perfect intra-cluster channel state information (CSI) was available and the intra-cluster interference was completely eliminated by using the IA approach. Moreover, the case of imperfect CSI with bounded errors was considered in [18], and a capacity lower bound of the channel by using IA was derived. These traditional methods to implement IA may not be optimal to achieve the highest spectrum efficiency in the presence of the path-loss effect.…”

On Analytical Achievable Rate for MIMO Linear Interference Alignment with Imperfect CSI

“…It is thus indispensable to directly investigate the achievable rate of various IA schemes. The achievable rate of IA under imperfect CSI are investigated [11][12][13][14][15][16]. In [11], the impact of channel error on the achievable rate of IA was first investigated and closed-form lower and upper bounds of the sum mutual information of IA are derived.…”

“…It is found that the loss in sum rate is bounded by a constant if the error variance is proportional to the inverse the SNR, and thus the full DoF is achievable. Paper [13] studied the performance of IA with bound CSI errors, and tight lower bound was derived, but the upper bound was not considered. The work in [14] considered the scenario where the main channel CSI is perfect but the crosstalk CSI is in errors, and obtained a closed-form rate through analyzing the statistical distribution of the saturating SNR.…”

“…Inspired by the work of [11][12][13][14][15][16][17][18], and motivated by (1) Practical communication systems have to design IA precoders and interference suppressing filters based on imperfect CSI; (2) As an analytical metric, achievable rate suits the practical communication systems better than DoF, since masses of practical systems operate in the low and medium SNR regime. We expect to further investigate the impact of channel uncertainty on the achievable rate of IA network and provide general analytical closed-form expressions to offer a more convenient metric for practical IA systems design.…”