Joint Constellation Shaping Using Gradient Descent Approach for MU-MIMO Broadcast Channel
Maxime Vaillant, Alix Jeannerot, Jean-Marie Gorce
TL;DR
The paper tackles the non-degraded MU-MIMO downlink by moving beyond linear precoding to a learned joint constellation design that directly optimizes the minimum mutual information across users. It introduces a MAX-MIN encoder and a cross-entropy-based loss, enabling a stochastic gradient descent with projection to enforce power constraints. Through Adam-based projected SGD, the method yields joint constellations that outperform standard MU-LP (including MMSE and ZF baselines) in both real and complex channel scenarios, sometimes approaching or surpassing equal-rate benchmarks. The work demonstrates notable gains in fairness and minimum-user performance, highlighting the potential of non-linear constellation design for MU-MIMO, while acknowledging scalability and adaptability challenges for larger $K$ and changing channels.
Abstract
We introduce a learning-based approach to optimize a joint constellation for a multi-user MIMO broadcast channel ($T$ Tx antennas, $K$ users, each with $R$ Rx antennas), with perfect channel knowledge. The aim of the optimizer (MAX-MIN) is to maximize the minimum mutual information between the transmitter and each receiver, under a sum-power constraint. The proposed optimization method do neither impose the transmitter to use superposition coding (SC) or any other linear precoding, nor to use successive interference cancellation (SIC) at the receiver. Instead, the approach designs a joint constellation, optimized such that its projection into the subspace of each receiver $k$, maximizes the minimum mutual information $I(W_k;Y_k)$ between each transmitted binary input $W_k$ and the output signal at the intended receiver $Y_k$. The rates obtained by our method are compared to those achieved with linear precoders.