[Paper Review] Sum Rate Maximization for MU-MISO with Partial CSIT using Joint Multicasting and Broadcasting

Hamdi Joudeh, Bruno Clerckx|arXiv (Cornell University)|Feb 12, 2015

Advanced MIMO Systems Optimization10 references4 citations

TL;DR

This paper proposes a joint multicasting and broadcasting (JMB) transmission scheme for MU-MISO systems with partial CSIT to maximize the average sum rate (ASR). By formulating the ASR problem as an augmented average weighted sum mean square error (AWSMSE) optimization and solving it via alternating optimization, the method achieves significant rate gains—especially at high SNR—by exploiting a common multicast symbol that enhances degrees of freedom and sum rate performance beyond conventional beamforming.

ABSTRACT

In this paper, we consider a MU-MISO system where users have highly accurate Channel State Information (CSI), while the Base Station (BS) has partial CSI consisting of an imperfect channel estimate and statistical knowledge of the CSI error. With the objective of maximizing the Average Sum Rate (ASR) subject to a power constraint, a special transmission scheme is considered where the BS transmits a common symbol in a multicast fashion, in addition to the conventional private symbols. This scheme is termed Joint Multicasting and Broadcasting (JMB). The ASR problem is transformed into an augmented Average Weighted Sum Mean Square Error (AWSMSE) problem which is solved using Alternating Optimization (AO). The enhanced rate performance accompanied with the incorporation of the multicast part is demonstrated through simulations.

Motivation & Objective

• To address the challenge of sum rate maximization in MU-MISO systems where the base station has only partial CSI, including imperfect estimates and statistical error knowledge.
• To investigate whether joint multicasting and broadcasting (JMB) can improve sum rate performance under partial CSIT, especially in the finite SNR regime.
• To develop a robust precoder design that maximizes the average sum rate (ASR) under power constraints and CSI uncertainty.
• To demonstrate that DoF gains from JMB translate into tangible sum rate improvements at finite SNR, not just asymptotically.
• To show that the proposed scheme reduces to conventional MU-MISO transmission when the common symbol is inactive, e.g., at low SNR.

Proposed method

• Formulates the ASR maximization problem under partial CSIT as an augmented AWSMSE problem, enabling convex relaxation and iterative optimization.
• Uses alternating optimization (AO) to jointly optimize the precoders for the common symbol and private symbols, converging to a stationary point.
• Introduces a stochastic channel model where the true channel is modeled as an estimate plus a zero-mean error with known covariance.
• Applies a weighted sum MSE minimization framework to transform the non-convex ASR problem into a tractable optimization form.
• Employs a power allocation strategy motivated by DoF analysis to initialize the precoders, improving convergence and performance.
• Uses Monte Carlo averaging over channel realizations to compute the ergodic sum rate (ESR), enabling performance evaluation across multiple channel states.

Experimental results

Research questions

• RQ1 Can joint multicasting and broadcasting (JMB) improve the average sum rate (ASR) in MU-MISO systems with partial CSIT?
• RQ2 Does the asymptotic DoF gain from JMB translate into measurable sum rate gains at finite SNR?
• RQ3 How does the performance of the proposed JMB scheme compare to conventional MU-MISO beamforming and DoF-motivated designs?
• RQ4 What is the impact of precoder initialization and power allocation on convergence and performance in the JMB framework?
• RQ5 Under what conditions does the common multicast symbol become beneficial, and when does it reduce to conventional private transmission?

Key findings

• The proposed JMB-AWSMSE scheme achieves higher ergodic sum rates than conventional MU-MISO beamforming and DoF-motivated designs, especially at high SNR.
• At high SNR, the JMB-AWSMSE scheme achieves a sum rate gain exceeding 4 dB over conventional ZF-BF and DoF-motivated schemes when CSIT quality is moderate (α = 0.6).
• The JMB scheme converges to conventional MU transmission at low SNR, where the common symbol is inactive, confirming its adaptability to SNR regimes.
• The algorithm converges to a stationary point regardless of initialization, but convergence speed and final performance depend on initialization, with SVD-based precoder initialization yielding better results at high SNR.
• The DoF-motivated power allocation strategy improves convergence and performance, particularly when combined with SVD-based precoder initialization.
• The ESR performance of JMB-AWSMSE matches the DoF gain (slope at high SNR) of the DoF-motivated scheme but achieves a higher absolute rate, demonstrating practical gains beyond asymptotic analysis.