Fundamental limits via CRB of semi-blind channel estimation in Massive MIMO systems

TL;DR

This paper analyzes the fundamental limits of semi-blind channel estimation in massive MIMO systems using CRB metrics, revealing conditions under which estimation accuracy can be improved or bounded.

Contribution

It provides new asymptotic expressions for CRB in massive MIMO, highlighting the impact of training length and user count on estimation bounds.

Findings

CRB can be arbitrarily small with increasing block length if training length grows proportionally.

Estimation error remains bounded if training sequences grow proportionally to users.

Semi-blind estimation reduces training requirements compared to traditional methods.

Abstract

This paper investigates the asymptotic behavior of the deterministic and stochastic Cram\'er-Rao Bounds (CRB) for semi-blind channel estimation in massive multiple-input multiple-output (MIMO) systems. We derive and analyze mathematically tractable expressions for both metrics under various asymptotic regimes, which govern the growth rates of the number of antennas, the number of users, the training sequence length, and the transmission block length. Unlike the existing work, our results show that the CRB can be made arbitrarily small as the transmission block length increases, but only when the training sequence length grows at the same rate and the number of users remains fixed. However, if the number of training sequences remains proportional to the number of users, the channel estimation error is always lower-bounded by a non-vanishing constant. Numerical results are presented to support our findings and demonstrate the advantages of semi-blind channel estimation in reducing the required number of training sequences.