Low-Rank Covariance-Assisted Downlink Training and Channel Estimation for FDD Massive MIMO Systems

Abstract

Abstract-We consider the problem of downlink training and channel estimation in frequency division duplex (FDD) massive MIMO systems, where the base station (BS) equipped with a large number of antennas serves a number of single-antenna users simultaneously. To obtain the channel state information (CSI) at the BS in FDD systems, the downlink channel has to be estimated by users via downlink training and then fed back to the BS. For FDD large-scale MIMO systems, the overhead for downlink training and CSI uplink feedback could be prohibitively high, which presents a significant challenge. In this paper, we study the behavior of the minimum mean-squared error (MMSE) estimator when the channel covariance matrix has a low-rank or an approximate low-rank structure. Our theoretical analysis reveals that the amount of training overhead can be substantially reduced by exploiting the low-rank property of the channel covariance matrix. In particular, we show that the MMSE estimator is able to achieve exact channel recovery in the asymptotic low-noise regime, provided that the number of pilot symbols in time is no less than the rank of the channel covariance matrix. We also present an optimal pilot design for the single-user case, and an asymptotic optimal pilot design for the multi-user scenario. Lastly, we develop a simple model-based scheme to estimate the channel covariance matrix, based on which the MMSE estimator can be employed to estimate the channel. The proposed scheme does not need any additional training overhead. Simulation results are provided to verify our theoretical results and illustrate the effectiveness of the proposed estimated covariance-assisted MMSE estimator.Index Terms-Massive MIMO systems, downlink training and channel estimation, channel covariance matrix, low rank structure, MMSE estimator.

On the Ergodic Rate Lower Bounds With Applications to Massive MIMO

“…These settings include, for example, the case of sparse support of the channel angular scattering function, yielding highly correlated channel vectors, and the case of cell-free massive MIMO [10], where antennas are spatially distributed over a large area and only a relatively small number of antennas have significant large-scale channel strength with respect to any given user. The case of highly correlated channel vectors received a lot of attention motivated by propagation models for mm-waves and by the opportunity of exploiting the channel sparsity in order to use compressed sensing techniques for channel estimation with reduced pilot overhead (e.g., see [11]- [16]). Also, during the revision of this paper, the bounding technique in Lemma 3, taken from our ArXiv preprint [17], was used in [18] to provide a more accurate performance analysis of cell-free massive MIMO.…”

Security Vulnerability of FDD Massive MIMO Systems in Downlink Training Phase

“…The BS can design the pilot signal matrix in different ways but two extreme cases are important here. In the first case, the BS uses the optimal pilots in (8). In the second case which is the worst case scenario, the BS uses the complementary of these pilots.…”

FDD Massive MIMO via UL/DL Channel Covariance Extrapolation and Active Channel Sparsification

“…where the additional constraint (26b) turns all the terms of the type [A] m,k z m,k in (25) to z m,k in (26), the constraint (26c) results from the combination of the constraints (25b) and (25d), and (26d) results from the combination of (25c) with (25e). The formulation in (26) can be seen as a modified maximum cardinality bipartite matching with selective vertices, in which the vertices with x m = 1 and y k = 1 are selected to participate in the maximum cardinality matching. The eventual mixed integer linear program is given as in (14).…”