Covariance Matrix Estimation for Massive MIMO

Abstract

We propose a novel pilot structure for covariance matrix estimation in massive multiple-input multiple-output (MIMO) systems in which each user transmits two pilot sequences, with the second pilot sequence multiplied by a random phase-shift. The covariance matrix of a particular user is obtained by computing the sample cross-correlation of the channel estimates obtained from the two pilot sequences. This approach relaxes the requirement that all the users transmit their uplink pilots over the same set of symbols. We derive expressions for the achievable rate and the mean-squared error of the covariance matrix estimate when the proposed method is used with staggered pilots. The performance of the proposed method is compared with existing methods through simulations.

On Achievable Rates for Massive Mimo System with Imperfect Channel Covariance Information

“…Both ChEst pilots and CovEst pilots are assumed to be of length P symbols. The spatial covariance matrices are assumed to be constant over a considerably longer timeinterval and bandwidth than a single coherence block [16]- [19]. Specifically, we assume that Each of the τ s coherence blocks contain ChEst pilots for channel estimation, whereas only N R out of the τ s coherence blocks contain CovEst pilots in addition to the ChEst pilots (as can be seen in Fig.…”

“…However, among these methods, only the estimators in [18] and [19] are in closed-form and consequently, lend themselves to analysis. Moreover, since [19] is seen to outperform [18], we select the estimator in [19] for performance analysis when the estimate is used for both LMMSE-type and element-wise LMMSE-type channel estimation.…”

“…For (20), we expand E{|tr(X −1 A)| 2 } using (19) Using (19), the above equation can be further simplified to (21).…”

“…Work [18] presents two methods which avoid contamination in the covariance matrices by utilizing dedicated orthogonal pilots for each user for estimating its individual spatial covariance matrix. In [19], a new pilot structure and a covariance matrix estimation method are developed that offer higher throughput and lower mean squared error (MSE) of the channel estimates than earlier methods. Although [19] requires additional pilots for estimating the individual covariance matrices of each user, it does not assume any additional structures on the covariance matrices of the users, and it does not require backhaul communication between the neighboring cells, unlike [16] and [17], respectively.…”

Large-System Analysis of Massive MIMO with Optimal M-MMSE Processing

“…The covariance/correlation matrix R jli ∈ C M×M accounts for the large-scale fading, including pathloss and spatial correlation [4]. These matrices are assumed to be known, but practical estimation methods are found in [14]- [16].…”