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Low-Complexity Polynomial Channel Estimation in Large-Scale MIMO with Arbitrary Statistics (1401.5703v2)

Published 22 Jan 2014 in cs.IT and math.IT

Abstract: This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as massive MIMO, where there are hundreds of antennas at one side of the link. Motivated by the fact that computational complexity is one of the main challenges in such systems, a set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced for arbitrary channel and interference statistics. While the conventional minimum mean square error (MMSE) estimator has cubic complexity in the dimension of the covariance matrices, due to an inversion operation, our proposed estimators significantly reduce this to square complexity by approximating the inverse by a L-degree matrix polynomial. The coefficients of the polynomial are optimized to minimize the mean square error (MSE) of the estimate. We show numerically that near-optimal MSEs are achieved with low polynomial degrees. We also derive the exact computational complexity of the proposed estimators, in terms of the floating-point operations (FLOPs), by which we prove that the proposed estimators outperform the conventional estimators in large-scale MIMO systems of practical dimensions while providing a reasonable MSEs. Moreover, we show that L needs not scale with the system dimensions to maintain a certain normalized MSE. By analyzing different interference scenarios, we observe that the relative MSE loss of using the low-complexity PEACH estimators is smaller in realistic scenarios with pilot contamination. On the other hand, PEACH estimators are not well suited for noise-limited scenarios with high pilot power; therefore, we also introduce the low-complexity diagonalized estimator that performs well in this regime. Finally, we ...

Citations (160)

Summary

  • The paper introduces Polynomial ExpAnsion CHannel (PEACH) estimators that reduce the computational complexity of channel estimation in large-scale MIMO from cubic to square scaling by approximating matrix inversions.
  • PEACH estimators achieve near-optimal performance even with low polynomial degrees and exhibit efficacy under challenging conditions like pilot contamination.
  • The proposed estimators demonstrate robustness to statistical mismatches and offer practical implications for enabling real-time, adaptive implementations in future high-density wireless networks.

Low-Complexity Polynomial Channel Estimation in Large-Scale MIMO

The paper presents a novel approach to channel estimation within large-scale MIMO systems, introducing a set of estimators named Polynomial ExpAnsion CHannel (PEACH) estimators. Conventional minimum mean square error (MMSE) estimators, although powerful, are computationally intensive in these systems due to their cubic complexity. The authors propose PEACH estimators to significantly reduce this burden, offering estimations with complexity scaling with the square of matrix dimensions instead of the cube. This reduction is achieved by approximating the inversion operation required in MMSE estimation with matrix polynomials whose coefficients are optimized to minimize mean square error (MSE).

Key Contributions and Findings

The paper underscores several significant contributions and findings:

  1. Complexity Reduction: The paper addresses the computational complexity challenges in large-scale MIMO systems, reducing it from cubic to square complexity using polynomial expansions for Bayesian estimation and theoretical bounds on the MSE achieved with these low-degree expansions.
  2. PEACH Estimators Performance: The paper examines the performance of PEACH estimators against conventional estimators, revealing that PEACH estimators achieve near-optimal performance with low polynomial degrees. This aspect is notably observed under pilot contamination scenarios, showing efficacy even in challenging interference conditions.
  3. Optimization of Polynomial Coefficients: The optimization of coefficients is crucial for achieving minimal MSE with PEACH estimators. These optimizations ensure performance improvements and mitigate the deleterious effects of interference relative to the norms seen in the context of large-dimensional matrix inversions.
  4. Robustness to Statistical Mismatches: There is an exploration of robustness in verifying performance when statistical knowledge is imperfect. The estimators demonstrated high adaptability under significant statistical variability, suggesting practical viability even when precise channel statistics aren't available.
  5. Diagonized Estimator Variant: While the PEACH estimators are primarily suited for scenarios with significant pilot contamination, the paper introduces an alternative diagonalized estimator. This estimator has lower complexity and performs well under noise-limited scenarios with high SNR, thus broadening the applicative scope of estimation strategies.

Practical and Theoretical Implications

The practical implications of the research include its potential role in enhancing spectral efficiency for future communication systems characterized by dense antenna arrays. The reduced computational complexity also facilitates real-time adaptive implementations in these systems, providing viable enhancements for wireless system design.

Theoretically, the paper extends the understanding of Bayesian channel estimation by leveraging polynomial approximations effectively, thereby fostering a pathway for integrating optimal estimations in scenarios previously dominated by prohibitive complexity constraints. Future developments could leverage these foundations towards refining low-complexity estimations in other domains like precoding and error correction in expansive MIMO configurations.

Conclusion

The research contributes substantially to the domain of large-scale MIMO systems, mitigating computational complexity while maintaining robust estimation performance amid arbitrary channel statistics and interference conditions. The findings offer scalable insights applicable across future high-density wireless networks, alleviating significant processor burdens prevalent in real-time system implementations. The optimizations introduced for polynomial expansions in the estimation processes mark a significant forward step in the theoretical treatments and practical applications of channel estimation in complex network environments.