Low Complexity Polynomial Expansion Detector with Deterministic Equivalents of the Moments of Channel Gram Matrix for Massive MIMO Uplink


We consider a low complexity polynomial expansion (PE) detector in a massive multiple-input multiple-output (MIMO) uplink channel. In contrast to most massive MIMO systems in the literature, where single antenna user equipments (UEs) are assumed, multiple antenna UEs are employed in this paper. Moreover, the channel between a base station (BS) and a UE is a jointly correlated Rician fading channel. The PE detector reduces the computational complexity of the minimum mean square error (MMSE) detector by replacing the matrix inversion with an approximate matrix polynomial. The coefficients of the approximate matrix polynomial are computed from the deterministic equivalents of the moments of the channel Gram matrix. We use operator-valued free probability, which is a more general version of free probability, to derive the deterministic equivalents. In particular, we use the operator-valued moment-cumulant formula. The proposed low complexity PE detector is easy to compute. Simulation results show that the proposed detector can achieve performance close to the MMSE detector.


Electrical and Computer Engineering


National Natural Science Foundation (China)
Ministry of Science and Technology of the People's Republic of China. 863 Program
National Science and Technology Major Project of China
Huawei Cooperation Project
National Science Foundation (U.S.)


The work of A. A. Lu and X. Q. Gao was supported in part by National Natural Science Foundation of China under Grants 61320106003, 61471113, and 61401095, the China High-Tech 863 Plan under Grants 2015AA01A701 and 2014AA01A704, National Science and Technology Major Project of China under Grant 2014ZX03003006-003, and the Huawei Cooperation Project. The work of Y. R. Zheng and C. Xiao was supported in part by USA National Science Foundation under Grants ECCS-1231848, ECCS-1408316, and ECCS-1539316

Keywords and Phrases

Antennas; Expansion; Fading channels; Matrix algebra; Mean square error; MIMO systems; Probability; Complexity polynomial; Correlated Rician fading channels; Deterministic equivalents; Free probabilities; Matrix polynomials; Minimum mean square error detectors; Multi-input multi-output; Polynomial expansion; Polynomials; Massive multiinput multi-output (MIMO); Operator-valued free probability; Polynomial expansion (PE) detector

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Article - Journal

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© 2016 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Feb 2016