Scalable Multivariate Fronthaul Quantization for Cell-Free Massive MIMO

The conventional approach to the fronthaul design for cell-free massive MIMO system follows the compress-and-precode (CP) paradigm. Accordingly, encoded bits and precoding coefficients are shared by the distributed unit (DU) on the fronthaul links, and precoding takes place at the radio units (RUs). Previous theoretical work has shown that CP can be potentially improved by a significant margin by precode-and-compress (PC) methods, in which all baseband processing is carried out at the DU, which compresses the precoded signals for transmission on the fronthaul links. The theoretical performance gain of PC methods are particularly pronounced when the DU implements multivariate quantization (MQ), applying joint quantization across the signals for all the RUs. However, existing solutions for MQ are characterized by a computational complexity that grows exponentially with the sum-fronthaul capacity from the DU to all RUs. In this work, we first present $\alpha$-parallel MQ ($\alpha$-PMQ), a novel MQ scheme whose complexity for quantization is exponential in the fronthaul capacity towards individual RUs. $\alpha$-PMQ tailors MQ to the topology of the network by allowing for parallel local quantization steps for RUs that do not interfere too much with each other. The performance of $\alpha$-PMQ is seen to be close to exact MQ in the regime when both schemes are feasible. We then introduce neural MQ, which replaces the exhaustive search in MQ with gradient-based updates for a neural-network-based decoder, attaining a quantization complexity that grows linearly with the sum-fronthaul capacity. This makes neural-MQ the first truly scalable MQ strategy. Numerical results demonstrate that neural-MQ outperforms CP across all values of the fronthaul capacity regimes.