Multi-Band Covariance Interpolation with Applications in Massive MIMO

Abstract

In this paper, we study the problem of multiband (frequency-variant) covariance interpolation with a particular emphasis towards massive MIMO applications. In massive MIMO, the communication between each Base Station (BS) with $M$ » 1 antennas and each single-antenna user occurs through a collection of scatterers in the environment, where the channel vector of each user at BS antennas consists in a weighted linear combination of the array responses of the scatterers, where each scatterer has its own angle of arrival (AoA) and complex channel gain. The array response at a given AoA depends on the wavelength of the incoming planar wave and is naturally frequency dependent. While in typical wireless communication applications the signal bandwidth is narrow enough, such that the channel second-order statistics (notably, the channel covariance matrix) can be considered frequency independent, in many other applications such as Frequency Division Duplexing (FDD) the uplink (UL) and the downlink (DL) channels are separated by a large frequency interval, such that the dependence of the channel covariance on frequency cannot be ignored. In this paper, we show that although this dependence is generally negligible for a small number of antennas M, it results in a considerable distortion of the covariance matrix when M →∞. Moreover, we prove that this frequency-dependent distortion can be fully compensated by a suitable covariance interpolation in frequency. We analyze the covariance interpolation problem mathematically and prove its stability under a very mild reciprocity condition on the angular power spread function (PSF) of the users. We also investigate the validity of our results using numerical simulations.