Low-Complexity Channel Estimation in Large-Scale MIMO using Polynomial Expansion

TL;DR

This paper introduces low-complexity polynomial expansion methods for channel estimation in large-scale MIMO systems, significantly reducing computational costs while maintaining near-optimal accuracy, especially under pilot contamination conditions.

Contribution

It proposes Polynomial Expansion CHannel (PEACH) estimators that approximate matrix inversion with low-order polynomials, reducing complexity in massive MIMO channel estimation.

Findings

PEACH estimators achieve near-optimal MSE with low polynomial orders

Polynomial order L balances complexity and estimation accuracy

Pilot contamination can improve estimator performance by allowing smaller L

Abstract

This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as "massive MIMO". Unlike previous works on this topic, which mainly considered the impact of inter-cell disturbance due to pilot reuse (so-called pilot contamination), we are concerned with the computational complexity. The conventional minimum mean square error (MMSE) and minimum variance unbiased (MVU) channel estimators rely on inverting covariance matrices, which has cubic complexity in the multiplication of number of antennas at each side. Since this is extremely expensive when there are hundreds of antennas, we propose to approximate the inversion by an L-order matrix polynomial. A set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced. The coefficients of the polynomials are optimized to yield small mean square error (MSE). We show numerically that near-optimal performance is achieved with low polynomial orders. In practice, the order L can be selected to balance between complexity and MSE. Interestingly, pilot contamination is beneficial to the PEACH estimators in the sense that smaller L can be used to achieve near-optimal MSEs.