Structured Channel Covariance Estimation from Limited Samples in Massive MIMO

Obtaining channel covariance knowledge is of great importance in various Multiple-Input Multiple-Output MIMO communication applications, including channel estimation and covariance-based user grouping. In a massive MIMO system, covariance estimation proves to be challenging due to the large number of antennas ($M\gg 1$) employed in the base station and hence, a high signal dimension. In this case, the number of pilot transmissions $N$ becomes comparable to the number of antennas and standard estimators, such as the sample covariance, yield a poor estimate of the true covariance and are undesirable. In this paper, we propose a Maximum-Likelihood (ML) massive MIMO covariance estimator, based on a parametric representation of the channel angular spread function (ASF). The parametric representation emerges from super-resolving discrete ASF components via the well-known MUltiple SIgnal Classification (MUSIC) method plus approximating its continuous component using suitable limited-support density function. We maximize the likelihood function using a concave-convex procedure, which is initialized via a non-negative least-squares optimization problem. Our simulation results show that the proposed method outperforms the state of the art in various estimation quality metrics and for different sample size to signal dimension ($N/M$) ratios.Comment: 27 pages, 9 figure

New challenges in covariance estimation: multiple structures and coarse quantization

In this self-contained chapter, we revisit a fundamental problem of multivariate statistics: estimating covariance matrices from finitely many independent samples. Based on massive Multiple-Input Multiple-Output (MIMO) systems we illustrate the necessity of leveraging structure and considering quantization of samples when estimating covariance matrices in practice. We then provide a selective survey of theoretical advances of the last decade focusing on the estimation of structured covariance matrices. This review is spiced up by some yet unpublished insights on how to benefit from combined structural constraints. Finally, we summarize the findings of our recently published preprint "Covariance estimation under one-bit quantization" to show how guaranteed covariance estimation is possible even under coarse quantization of the samples