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Beyond MMSE: Rank-1 Subspace Channel Estimator for Massive MIMO Systems

Bin Li, Ziping Wei, Shaoshi Yang, Yang Zhang, Jun Zhang, Chenglin Zhao, Sheng Chen

TL;DR

The paper tackles the problem of acquiring accurate channel state information in massive MIMO without prohibitive computational cost. It introduces a two-stage rank-1 subspace estimator that first extracts high-resolution AoA information via a space-embedding Hankel matrix and a MUSIC-like approach, then performs ML-based gain estimation using post-reception beamforming. Theoretical results show CRLB gains of order $\mathcal{O}(1/M)$, with an extra $\mathcal{O}(\log_{10} M)$ gain over linear MMSE, and a fast low-rank implementation reducing complexity to $\mathcal{O}(K (P^2+NP) M)$. Numerical simulations across full-rank and low-rank channels demonstrate substantial NMSE improvements, near-ML BER performance, and near-ML spectral efficiency with dramatically lower complexity than MMSE. Overall, the method significantly extends the accuracy-complexity region for CSI in massive MIMO and holds promise for next-generation wireless systems.

Abstract

To glean the benefits offered by massive multi-input multi-output (MIMO) systems, channel state information must be accurately acquired. Despite the high accuracy, the computational complexity of classical linear minimum mean squared error (MMSE) estimator becomes prohibitively high in the context of massive MIMO, while the other low-complexity methods degrade the estimation accuracy seriously. In this paper, we develop a novel rank-1 subspace channel estimator to approximate the maximum likelihood (ML) estimator, which outperforms the linear MMSE estimator, but incurs a surprisingly low computational complexity. Our method first acquires the highly accurate angle-of-arrival (AoA) information via a constructed space-embedding matrix and the rank-1 subspace method. Then, it adopts the post-reception beamforming to acquire the unbiased estimate of channel gains. Furthermore, a fast method is designed to implement our new estimator. Theoretical analysis shows that the extra gain achieved by our method over the linear MMSE estimator grows according to the rule of O($\log_{10}M$), while its computational complexity is linearly scalable to the number of antennas $M$. Numerical simulations also validate the theoretical results. Our new method substantially extends the accuracy-complexity region and constitutes a promising channel estimation solution to the emerging massive MIMO communications.

Beyond MMSE: Rank-1 Subspace Channel Estimator for Massive MIMO Systems

TL;DR

The paper tackles the problem of acquiring accurate channel state information in massive MIMO without prohibitive computational cost. It introduces a two-stage rank-1 subspace estimator that first extracts high-resolution AoA information via a space-embedding Hankel matrix and a MUSIC-like approach, then performs ML-based gain estimation using post-reception beamforming. Theoretical results show CRLB gains of order , with an extra gain over linear MMSE, and a fast low-rank implementation reducing complexity to . Numerical simulations across full-rank and low-rank channels demonstrate substantial NMSE improvements, near-ML BER performance, and near-ML spectral efficiency with dramatically lower complexity than MMSE. Overall, the method significantly extends the accuracy-complexity region for CSI in massive MIMO and holds promise for next-generation wireless systems.

Abstract

To glean the benefits offered by massive multi-input multi-output (MIMO) systems, channel state information must be accurately acquired. Despite the high accuracy, the computational complexity of classical linear minimum mean squared error (MMSE) estimator becomes prohibitively high in the context of massive MIMO, while the other low-complexity methods degrade the estimation accuracy seriously. In this paper, we develop a novel rank-1 subspace channel estimator to approximate the maximum likelihood (ML) estimator, which outperforms the linear MMSE estimator, but incurs a surprisingly low computational complexity. Our method first acquires the highly accurate angle-of-arrival (AoA) information via a constructed space-embedding matrix and the rank-1 subspace method. Then, it adopts the post-reception beamforming to acquire the unbiased estimate of channel gains. Furthermore, a fast method is designed to implement our new estimator. Theoretical analysis shows that the extra gain achieved by our method over the linear MMSE estimator grows according to the rule of O(), while its computational complexity is linearly scalable to the number of antennas . Numerical simulations also validate the theoretical results. Our new method substantially extends the accuracy-complexity region and constitutes a promising channel estimation solution to the emerging massive MIMO communications.
Paper Structure (30 sections, 6 theorems, 54 equations, 12 figures, 1 table)

This paper contains 30 sections, 6 theorems, 54 equations, 12 figures, 1 table.

Table of Contents

  1. Introduction
  2. Channel Estimation Aided With AoA
  3. Rank-1 Subspace Channel Estimator
  4. Single-User Uplink Channel Estimation
  5. Multiple-User Uplink Channel Estimation
  6. Complexity Analysis
  7. Theoretical Performance Analysis
  8. Error of Estimated Channel AoAs
  9. Error of Estimated Channel Gains
  10. Error of Estimated Channel Vector
  11. Gain Over Linear MMSE Estimator
  12. Fast Rank-1 Subspace Estimator
  13. Randomized Low-rank Approximation
  14. Complexity Analysis
  15. Theoretical Analysis on Approximated Pseudo-spectrum
  16. ...and 15 more sections

Key Result

Theorem 1

When the uplink AoAs of a single-antenna UE are exactly known, i.e., $\widehat{\theta}_p=\theta_p$ for $0\le p\le P-1$, and the number of BS antennas $M$ is large, the channel gains estimated by using the post-reception beamforming (eq5) are unbiased, i.e., $\mathsf{E}[\hat{\alpha}_p]=\alpha_p$, wit

Figures (12)

  • Figure 1: Normalized MSE performance of our rank-1 subspace estimator and the linear MMSE estimator as functions of SNR for the full-rank, sparse and uncorrelated channel, given $M=128$, $K=40$, $B=2K$ and $L=M/2$.
  • Figure 2: SNR gain of our rank-1 subspace method over the classical linear MMSE estimator as function of $M$ for the full-rank sparse channel of Fig. \ref{['fig:1']}, with $K=40$, $B=2K$ and $L=M/2$.
  • Figure 3: Normalized MSE performance of five channel estimators as functions of SNR for the full-rank, sparse and uncorrelated channel, given $M=256$, $K=40$, $B=2K$ and $L=M/2$.
  • Figure 4: Time complexity of four channel estimators for the full-rank sparse channel of Fig. \ref{['fig:3']}: (a) as functions of $K$, given $M=256$, $B=2K$ and $L=M/2$, and (b) as functions of $M$, given $K=40$, $B=2K$ and $L=M/2$.
  • Figure 5: Normalized MSE performance of various channel estimator for the low-rank, sparse and correlated channel, given $\text{rank}(\bm{H})=20$, $M=256$, $K=40$, $L=M/2$, and $B=K$.
  • ...and 7 more figures

Theorems & Definitions (14)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Lemma 1
  • Theorem 3
  • proof
  • Theorem 4
  • Remark 1
  • Theorem 5
  • ...and 4 more