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

Abstract

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-tointerference 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 (i) for RZF the optimal regularization parameter, (ii) for ZF the optimal number of users, (iii) for ZF and RZF the optimal power allocation scheme and (iv) the optimal amount of feedback in large FDD/TDD multi-user systems. Numerical simulations suggest that the deterministic approximations are accurate even for small M, K.

Resource Allocation for Energy Efficiency in 5G Wireless Networks

“…With favorable propagation characteristics [47] and deterministic channel behavior [10,54], the low-complexity linear beamforming designs such as conjugate or ZF beamforming are easily performed in massive MIMO [35,56,58]. In our recent work [41], the optimal ZF beamforming for power allocation offers better performance compared to conjugate beamforming, meanwhile, these beamformers maintain the users' QoS under a limited power budget.…”

“…In our recent work [41], the optimal ZF beamforming for power allocation offers better performance compared to conjugate beamforming, meanwhile, these beamformers maintain the users' QoS under a limited power budget. However, in most of previous works [27,31,56,58], massive MIMO is properly applied to serve smaller numbers of users by a large array of low-power transmit antennas under QoS requirement. To support more users, massive MIMO must change its transmission schedule to provide a service-wise for many users.…”

“…Under such an environment [10,47,54], massive MIMO system provides favorable propagation characteristics and deterministic channels' eigenvalue distribution behavior. In the earlier work [31], a lowcomplexity zero-forcing (ZF) beamforming [56,58] is to perform well to serve a smaller number of users with a large array of low-power transmit antennas. In the latter work [42], massive MIMO can schedule its service for serving many users as possible by the fractional time transmission, and thus, a sufficient number of users are served in one of time fractions.…”

A Multi-Cell MMSE Precoder for Massive MIMO Systems and New Large System Analysis

“…Theorem 1 (Theorem 1 in [12]): Let D ∈ C M×M be deterministic and H ∈ C M×B be random with independent 2 The limit superior of a sequence xn is defined by lim sup n xn lim n→∞ (sup {xm : m n}); the limit inferior is defined as lim infnxn lim n→∞ (inf {xm : m n}). …”

“…Theorem 2 (see [12]) Let Θ ∈ C M×M be Hermitian nonnegative definite with uniformly bounded spectral norm (with respect to M ). Under the same conditions for D and H as in Theorem 1,…”