Massive MIMO Channel Subspace Estimation From Low-Dimensional Projections

Abstract

Massive MIMO is a variant of multiuser MIMO where the number of base-station antennas M is very large (typically ≈ 100), and generally much larger than the number of spatially multiplexed data streams (typically ≈ 10). The benefits of such approach have been intensively investigated in the past few years, and all-digital experimental implementations have also been demonstrated. Unfortunately, the front-end A/D conversion necessary to drive hundreds of antennas, with a signal bandwidth of the order of 10 to 100 MHz, requires very large sampling bitrate and power consumption.In order to reduce such implementation requirements, Hybrid Digital-Analog architectures have been proposed. In particular, our work in this paper is motivated by one of such schemes named Joint Spatial Division and Multiplexing (JSDM), where the downlink precoder (resp., uplink linear receiver) is split into the product of a baseband linear projection (digital) and an RF reconfigurable beamforming network (analog), such that only a reduced number m M of A/D converters and RF modulation/demodulation chains is needed. In JSDM, users are grouped according to similarity of their channel dominant subspaces, and these groups are separated by the analog beamforming stage, where multiplexing gain in each group is achieved using the digital precoder. Therefore, it is apparent that extracting the channel subspace information of the M -dim channel vectors from snapshots of m-dim projections, with m M , plays a fundamental role in JSDM implementation.In this paper, we develop novel efficient algorithms that require sampling only m = O(2 √ M ) specific array elements according to a coprime sampling scheme, and for a given p M , return a p-dim beamformer that has a performance comparable with the best p-dim beamformer that can be designed from the full knowledge of the exact channel covariance matrix. We assess the performance of our proposed estimators both analytically and empirically via numerical simulations. We also demonstrate by simulation that the proposed subspace estimation methods provide near-ideal performance for a massive MIMO JSDM system, by comparing with the case where the user channel covariances are perfectly known.

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“…The BS-LIM channel matrix H is assumed to have a lowrank structure, i.e., rank(H) = R min{N, M }. Similar low-rank properties have been previously exploited in modeling massive MIMO channels under far-field and limited-scattering assumptions [15], [16]. Meanwhile, we assume that the channel matrix G between the LIM and the user is full rank.…”

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“…Here R h andR h are the true covariance and the estimated covariance matrix, respectively, while, U R h and UR h are the matrices containing the singular vectors corresponding to the singular values of the true covariance and estimated covariance matrices, respectively. Intuitively, 1 − η denotes the fraction of signal power lost due to the mismatch between the optimal beamformer and its estimate [19]. Thus, higher the η, better are the obtained estimates.…”

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