Channel Covariance Estimation in Multiuser Massive Mimo Systems with an Approach Based on Infinite Dimensional Hilbert Spaces

Abstract

We propose a novel algorithm to estimate the channel covariance matrix of a desired user in multiuser massive MIMO systems. The algorithm uses only knowledge of the array response and rough knowledge of the angular support of the incoming signals, which are assumed to be separated in a well-defined sense. To derive the algorithm, we study interference patterns with realistic models that treat signals as continuous functions in infinite dimensional Hilbert spaces. By doing so, we can avoid common and unnatural simplifications such as the presence of discrete signals, ideal isotropic antennas, and infinitely large antenna arrays. An additional advantage of the proposed algorithm is its computational simplicity: it only requires a single matrix-vector multiplication. In some scenarios, simulations show that the estimates obtained with the proposed algorithm are close to those obtained with standard estimation techniques operating in interference-free and noiseless systems.

Hybrid data and model driven algorithms for angular power spectrum estimation

“…Before we proceed, we discretized all signals and operators to avoid unnecessary technical digressions. However, we emphasize that the results in this study can be straightforwardly extended to the infinite dimensional case described above with the tools in [1]- [4].…”

“…, respectively, the pilot symbol and the channel of the user; and n[k] ∈ C N is a sample from the distribution N C (0, σ 2 I). As common in the literature [5], [14], we assume that 1 Furthermore, pilot symbols and noise are mutually independent, and their distributions do not change with the index k in a sufficiently large time window. Therefore, hereafter we assume that…”

“…nonnegative functions. As shown in [1]- [4], a common feature of realistic massive MIMO models is that the stacked version…”

“…Estimating the angular power spectrum (APS) of a signal impinging on an antenna array from the measured channel covariance matrix is an ill-posed problem with important applications in massive MIMO systems, including pilot decontamination [1], channel covariance matrix estimation in frequency division duplex (FDD) systems [2]- [7], and localization [8], among others. Current approaches for APS estimation can be divided into two main groups: model based methods [2]- [4], [7] and data driven methods [9].…”

“…Model-based methods are able to produce reliable estimates with little side information, no training, and potentially low computational complexity [1]- [4]. However, they do not exploit any information from datasets to improve the estimates or to gain robustness against measurement errors or model uncertainty, or both.…”