Covariance Shaping for Massive MIMO Systems

Abstract

The low-rank behavior of massive multiple-input multiple-output (MIMO) channel covariance matrices and its exploitation for pilot decontamination and statistical beamforming are well documented. Existing algorithms, however, rely on signal subspace separation among user equipments (UEs) and, as such, they tend to fail when the distance between UEs becomes small. This paper proposes a solution to this problem via covariance shaping at the UE-side in the case where the UEs are equipped with (a small number of) multiple antennas. The key resides in: i) exploiting general non-Kronecker MIMO channel structures that allow the transmitter to suitably alter the channel statistics perceived by the base station, and ii) sacrificing some spatial degrees of freedom at each UE so as to improve the statistical orthogonality between closely spaced UEs. Numerical results illustrate the sum-rate performance gains of the proposed covariance shaping method with respect to existing ones.

Recent Advances in Acquiring Channel State Information in Cellular MIMO Systems

“…The number of such components depends on several factors, including the frequency band and the radio scattering environment, which are in general beyond the designer's control. Nevertheless, when multi-antenna UEs are deployed, statistical beamforming at the UE side can be exploited to let the UEs excite a suitable channel subspace, with the aim to further reduce the number of relevant components to be estimated [38], [39].…”

On the Performance of Covariance Shaping in Massive MIMO Systems

“…The previos condition occurs when the covariance matrices are rank deficient and share the same eigenbasis. However, such property is rarely satisfied in practice and, in this respect, covariance shaping was proposed in [9] as a means to enforce statistical orthogonality by acting at the UEside. By preemptively applying statistical beamforming, the UEs aim at reducing interference by separating their channel statistics.…”

“…To cope with this issue, our prior work [9] proposes to exploit the inherent spatial selectivity properties at modern UEs, which are equipped with a small-to-moderate number of antennas, towards a suitable shaping of the channel covariance matrix performed at the UE-side. This approach, referred to as covariance shaping, is obtained by means of a statistical beamforming that effectively allows the UEs to excite a suitable subset of all the possible propagation directions towards the BS with the aim of reducing their spatial correlation.…”

“…This approach, referred to as covariance shaping, is obtained by means of a statistical beamforming that effectively allows the UEs to excite a suitable subset of all the possible propagation directions towards the BS with the aim of reducing their spatial correlation. In particular, covariance shaping was shown in [9] to successfully enforce partial or full orthogonality between the signal subspaces of two UEs placed close to each other in the context of pilot-contaminated channel estimation [10], outperforming the scenario where the antennas at the UEs are directly used for spatial multiplexing.…”

“…In this paper, we analyze in depth the performance of such covariance shaping method in a massive MIMO system. To do so, we firstly extend the work in [9], which focused on the case of two UEs, to a more general multi-user setting. Then, we explore the behavior of such approach in different realistic scenarios, pointing out its effectiveness in separating the channel statistics of different UEs.…”