Large System Analysis of Linear Precoding in Correlated MISO Broadcast Channels Under Limited Feedback

By Sebastian Wagner, Romain Couillet, Merouane Debbah, Dirk T. M. Slock. IEEE Transactions on Information Theory, 2009

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In this paper, we study the sum rate performance of zero-forcing (ZF) and regularized ZF (RZF) precoding in large MISO broadcast systems under the assumptions of imperfect channel state information at the transmitter and per-user channel transmit correlation. Our analysis assumes that the number of transmit antennas M and the number of single-antenna users K are large while their ratio remains bounded. We derive deterministic approximations of the empirical signal-to-interference plus noise ratio (SINR) at the receivers, which are tight as M, K → ∞. In the course of this derivation, the per-user channel correlation model requires the development of a novel deterministic equivalent of the empirical Stieltjes transform of large dimensional random matrices with generalized variance profile. The deterministic SINR approximations enable us to solve various practical optimization problems. Under sum rate maximization, we derive 1) for RZF the optimal regularization parameter; 2) for ZF the optimal number of users; 3) for ZF and RZF the optimal power allocation scheme; and 4) the optimal amount of feedback in large FDD/TDD multiuser systems. Numerical simulations suggest that the deterministic approximations are accurate even for small M, K.

Subfields: Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/9b7d4d6f6f8a8f555a719edd89292d8d246b7dc2

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Citations in the corpus

Complex diffusion-weighted image estimation via matrix recovery under general noise models (2018, neutral): “Although analogous fixed point equations (Wagner et al., 2012) and eigenvalue confinement guarantees (Kammoun and Alouini, 2016) are available for more general noise models such as those of non stationary encodings in (11), we do not know of any numerical tool developed for general random interactio”
Energy-Efficient Design of MIMO Heterogeneous Networks With Wireless Backhaul (2015, methodology): “By conditioning on the interference Im+ Is, and by using a similar approach as the one in the proof of Lemma 2, whenKb,Mm → ∞ with βb = KbMs/Mm < 1, the SINR in (72) satisfies [52]”
Reconfigurable Intelligent Surfaces for Energy Efficiency in Wireless Communication (2018, background): “, 2 b >> 1 ; and ii ) all involved channels are perfectly known at BS that employs Zero-Forcing (ZF) transmission, which is known to be optimal in the high-SINR regime 1 [45], [46].”
Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need? (2013, background): “Theorem 2 ([20], see also [19]): Let Θ ∈ CN×N be Hermitian nonnegative definite with uniformly bounded spectral norm (with respect to N ).”
Asymptotic Max-Min SINR Analysis of Reconfigurable Intelligent Surface Assisted MISO Systems (2019, background): “Note that these deterministic equivalents are tight for moderate system dimensions as well [20], [29]–[31], [34], [35].”
Massive Connectivity With Massive MIMO—Part I: Device Activity Detection and Channel Estimation (2017, background): “We emphasize that while massive MIMO system has been extensively studied in the literature [20]–[24], conventional analysis focuses on the regime of small number of users as compared to the number of BS antennas.”
Energy Efficient Multi-User MISO Communication Using Low Resolution Large Intelligent Surfaces (2018, background): “To make the targeted problem more tractable, we assume that all involved channels are perfectly known at BS that employs Zero-Forcing (ZF) transmission, which is known to be optimal in the high-SINR regime [25].”
Massive MIMO Systems With Non-Ideal Hardware: Energy Efficiency, Estimation, and Capacity Limits (2013, background): “We refer to [34], [35], [37], and [38] for some relevant works in the case of ideal hardware.”
Joint Spatial Division and Multiplexing: Opportunistic Beamforming, User Grouping and Simplified Downlink Scheduling (2014, methodology): “In order to calculate the limiting values we use the technique of deterministic equivalent approximation pioneered in [37], and applied to the JSDM setting in [11].”