MMSE Channel Estimation in Large-Scale MIMO: Improved Robustness with Reduced Complexity

TL;DR

This paper introduces reduced-complexity channel estimation methods that achieve the performance of MMSE in terms of estimation accuracy and uplink spectral efficiency while demonstrating improved robustness in practical scenarios where channel statistics must be estimated.

Abstract

Large-scale MIMO systems with a massive number N of individually controlled antennas pose significant challenges for minimum mean square error (MMSE) channel estimation, based on uplink pilots. The major ones arise from the computational complexity, which scales with $N^3$, and from the need for accurate knowledge of the channel statistics. This paper aims to address both challenges by introducing reduced-complexity channel estimation methods that achieve the performance of MMSE in terms of estimation accuracy and uplink spectral efficiency while demonstrating improved robustness in practical scenarios where channel statistics must be estimated. This is achieved by exploiting the inherent structure of the spatial correlation matrix induced by the array geometry. Specifically, we use a Kronecker decomposition for uniform planar arrays and a well-suited circulant approximation for uniform linear arrays. By doing so, a significantly lower computational complexity is achieved, scaling as $N\sqrt{N}$ and $N\log N$ for squared planar arrays and linear arrays, respectively.

Figures (11)

• Figure 1: Diagram of the UPA located in the $yz$-plane, with a planar wave impinging with elevation $\theta$ and azimuth $\varphi$.
• Figure 2: NSAE of the correlation matrix as a function of the elevation angular spread for KBA and NKP. We consider a UPA with $N_\mathsf{H}=N_\mathsf{V}=16$ elements, using $\Delta_\mathsf{H}=\Delta_\mathsf{V}=\lambda/2$ at $3\,\mathrm{GHz}$. The azimuth angle is $\overline{\varphi}=0^\circ$ with angular spread $\sigma_\varphi=10^\circ$. Both azimuth and elevation angles follow a Gaussian distribution.
• Figure 3: NMSE for a square UPA with $N_\mathsf{H}=N_\mathsf{V}=\sqrt{N}$. The UPA parameters are reported in Table \ref{['tab:UPA']}. The simulation parameters are those of Table \ref{['tab:system']}.
• Figure 4: Average NMSE as a function of the angular spread $\sigma_\theta$ of the elevation angle for the UPA with parameters reported in Table \ref{['tab:UPA']} and $N_\mathsf{H}=N_\mathsf{V}=16$. The simulation parameters are those of Table \ref{['tab:system']}.
• Figure 5: NMSE as a function of the ULA size $N$.