Asymptotic Behavior of Zero-Forcing Precoding based on Imperfect Channel Knowledge for Massive MISO FDD Systems

TL;DR

This paper analyzes the asymptotic behavior of zero-forcing precoding in massive MISO FDD systems with imperfect channel knowledge, revealing surprising interference elimination properties and limitations of LMMSE estimates.

Contribution

It provides a novel asymptotic analysis of zero-forcing precoding with LS and LMMSE channel estimates in massive MISO FDD systems, highlighting unexpected interference behavior.

Findings

Zero-forcing with LS estimates becomes interference-free asymptotically.

LMMSE estimates do not eliminate interference under contaminated observations.

Numerical simulations confirm analytical results.

Abstract

In this work, we study the asymptotic behavior of the zero-forcing precoder based on the least squares (LS) and the linear minimum mean-square error (LMMSE) channel estimates for the downlink (DL) of a frequency-division-duplex (FDD) massive multiple-input-single-output (MISO) system. We show analytically the rather surprising result that zero-forcing precoding based on the LS estimate leads asymptotically to an interference-free transmission, even if the number of pilots used for DL channel training is less than the number of antennas available at the base station (BS). Although the LMMSE channel estimate exhibits a better quality in terms of the MSE due to the exploitation of the channel statistics, we show that in the case of contaminated channel observations, zero-forcing based on the LMMSE is unable to eliminate the inter-user interference in the asymptotic limit of high DL transmit powers. In order for the results to hold, mild conditions on the channel probing phase are assumed. The validity of our analytical results is demonstrated through numerical simulations for different scenarios.