Optimality of the Bussgang Linear MMSE Channel Estimator for MIMO Systems with 1-Bit ADCs
Ding, Minghua; Atzeni, Italo; Tölli, Antti; Swindlehurst, A. Lee (2024-10-07)
IEEE
07.10.2024
M. Ding, I. Atzeni, A. Tölli and A. L. Swindlehurst, "Optimality of the Bussgang Linear MMSE Channel Estimator for MIMO Systems with 1-Bit ADCs," 2024 IEEE 25th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Lucca, Italy, 2024, pp. 411-415, doi: 10.1109/SPAWC60668.2024.10694302.
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© 2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
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Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202410156304
https://urn.fi/URN:NBN:fi:oulu-202410156304
Tiivistelmä
Abstract
In this paper, we study the optimality of the Bussgang linear minimum mean squared error (BLMMSE) channel estimator for multiple-input multiple-output systems with 1-bit analog-to-digital converters. We compare the BLMMSE with the optimal minimum mean squared error (MMSE) channel estimator, which is generally non-linear, and we develop a novel framework based on the orthant probability of a multivariate normal distribution to compute the MMSE channel estimate. Then, we analyze the equivalence of the MMSE and BLMMSE channel estimators under specific assumptions on the channel correlation or pilot symbols. Interestingly, the BLMMSE channel estimator turns out to be optimal in several specific cases. Our study culminates with the presentation of a necessary and sufficient condition for the BLMMSE channel estimator to be optimal.
In this paper, we study the optimality of the Bussgang linear minimum mean squared error (BLMMSE) channel estimator for multiple-input multiple-output systems with 1-bit analog-to-digital converters. We compare the BLMMSE with the optimal minimum mean squared error (MMSE) channel estimator, which is generally non-linear, and we develop a novel framework based on the orthant probability of a multivariate normal distribution to compute the MMSE channel estimate. Then, we analyze the equivalence of the MMSE and BLMMSE channel estimators under specific assumptions on the channel correlation or pilot symbols. Interestingly, the BLMMSE channel estimator turns out to be optimal in several specific cases. Our study culminates with the presentation of a necessary and sufficient condition for the BLMMSE channel estimator to be optimal.
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