A Successive Optimization Approach to Pilot Design for Multi-Cell Massive MIMO Systems

Hayder Al-Salihi,Trinh Van Chien,Mohammad Reza Nakhai,Tuan Anh Le

doi:10.1109/lcomm.2018.2812891

Hayder Al-Salihi, Trinh Van Chien + Show 2 more

Open Access

https://doi.org/10.1109/lcomm.2018.2812891

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Abstract

In this letter, we introduce a novel pilot design approach that minimizes the total mean square errors of the minimum mean square error estimators of all base stations (BSs) subject to the transmit power constraints of individual users in the network, while tackling the pilot contamination in multi-cell massive MIMO systems. First, we decompose the original non-convex problem into distributed optimization sub-problems at individual BSs, where each BS can optimize its own pilot signals given the knowledge of pilot signals from the remaining BSs. We then introduce a successive optimization approach to transform each optimization sub-problem into a linear matrix inequality form, which is convex and can be solved by available optimization packages. Simulation results confirm the fast convergence of the proposed approach and prevails a benchmark scheme in terms of providing higher accuracy.

Highlights

In multi-cell Massive MIMO systems, each base station (BS) requires accurate knowledge of the channel state information (CSI) obtained during the pilot training phase
In this letter, we introduce a novel pilot design approach that minimizes the total mean square errors of the minimum mean square error estimators of all base stations (BSs) subject to the transmit power constraints of individual users in the network, while tackling the pilot contamination in multicell Massive MIMO systems
Pilot signals need to be reused over cells, causing spatially correlated interference, known as pilot contamination that degrades the performance of a Massive MIMO system [1]

Summary

Introduction

In multi-cell Massive MIMO systems, each base station (BS) requires accurate knowledge of the channel state information (CSI) obtained during the pilot training phase. To attain accurate channel estimates, perfectly orthogonal pilot allocations to users are required. This requirement is impractical, since the pilot overhead has to be proportional to the number of users in the entire system. In order to address the pilot contamination problem, the authors of [2] proposed a superimposed channel estimation approach by adding a low power pilot signal to the data signal at the transmitter. Formulate an optimization problem to find optimal pilot signals that minimize the total derived MSE of the MMSE estimators of all BSs in the network subject to a transmit power constraint at each user. Notation: Bold lower/upper case letters are used for vectors/matrices; · F and · stand for the Frobenius norm and the Euclidean norm; (·)T and (·)H is the regular and complex conjugate transpose operator, respectively; Tr (·) is the trace of a matrix; X 0 is the positive semidefinite condition; Ia is an a × a identity matrix; diag{x} is a diagonal matrix which the diagonal entries are elements of the vector x; CN(·, ·) is a circularly symmetric complex Gaussian distribution; E[·] is the expectation of a random variable; O(·) is the big-O notation

System Model

A Successive Optimization Pilot Design

1: Inputs

Simulation Results