Uplink Linear Receivers for Multi-cell Multiuser MIMO with Pilot Contamination: Large System Analysis

TL;DR

This paper analyzes uplink multi-user MIMO systems with large antenna arrays, focusing on the impact of pilot contamination on SINR and demonstrating the benefits of MMSE filtering through large system analysis and simulations.

Contribution

It provides a large system analysis of MMSE receivers under pilot contamination, deriving explicit SINR expressions and demonstrating their effectiveness compared to matched filtering.

Findings

MMSE filter achieves significant SINR gains over matched filter.

SINR with MMSE filter is close to that with perfect channel estimates.

Simulation results match large system analysis even with small antenna arrays.

Abstract

Base stations with a large number of transmit antennas have the potential to serve a large number of users at high rates. However, the receiver processing in the uplink relies on channel estimates which are known to suffer from pilot interference. In this work, making use of the similarity of the uplink received signal in CDMA with that of a multi-cell multi-antenna system, we perform a large system analysis when the receiver employs an MMSE filter with a pilot contaminated estimate. We assume a Rayleigh fading channel with different received powers from users. We find the asymptotic Signal to Interference plus Noise Ratio (SINR) as the number of antennas and number of users per base station grow large while maintaining a fixed ratio. Through the SINR expression we explore the scenario where the number of users being served are comparable to the number of antennas at the base station. The SINR explicitly captures the effect of pilot contamination and is found to be the same as that employing a matched filter with a pilot contaminated estimate. We also find the exact expression for the interference suppression obtained using an MMSE filter which is an important factor when there are significant number of users in the system as compared to the number of antennas. In a typical set up, in terms of the five percentile SINR, the MMSE filter is shown to provide significant gains over matched filtering and is within 5 dB of MMSE filter with perfect channel estimate. Simulation results for achievable rates are close to large system limits for even a 10-antenna base station with 3 or more users per cell.