Scalable Multivariate Fronthaul Quantization for Cell-Free Massive MIMO

Abstract

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. This work sets out to design scalable MQ strategies for PC-based cell-free massive MIMO systems. For the low-fronthaul capacity regime, we present alpha-parallel MQ (alpha-PMQ), whose complexity is exponential only in the fronthaul capacity towards an individual RU, while performing close to full MQ. 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. For the high-fronthaul capacity regime, we then introduce neural MQ, which replaces the exhaustive search in MQ with gradient-based updates for a neural-network-based decoder, attaining a complexity that grows linearly with the sum-fronthaul capacity. Numerical results demonstrate that the proposed scalable MQ strategies outperform CP for both the low and high-fronthaul capacity regimes at the cost of increased computational complexity at the DU (but not at the RUs).

Figures (9)

• Figure 1: Cell-free massive MIMO architecture considered in this project, consisting of $N$ multi-antenna UEs, $M$ multi-antenna RUs, and a DU. All baseband processing is done at the DU, which carries out compression of the baseband signals for transmission over capacity-limited fronthaul links.
• Figure 2: (Left) In the conventional compress-and-precode (CP) scheme, the DU transmits information bits to all RUs, as well as the corresponding compressed precoding matrix to each RU. (Right) In the precode-and-compress (PC) scheme, the DU transmits the respective precoded and compressed baseband vector to each RU. This paper studies novel multivariate compression strategies for PC.
• Figure 3: Previous work on reduced complexity MQ introduced SMQ, which applies sequential local quantization (for a number of iterations equal to the number of RUs) lee2016multivariate. The proposed $\alpha$-parallel multivariate quantization ($\alpha$-PMQ) scheme allows for the signals of multiple RUs to be updated using local quantization in parallel. To determine the local quantization schedule, depending on the hyperparameter $\alpha$, an interference graph with RUs as nodes is constructed. At each iteration (square box), for all RUs in an independent set of the interference graph, the DU carries out local quantization in parallel. An edge between RUs is included in the interference graph if the level of interference between RUs is larger then a threshold determined by $\alpha$.
• Figure 4: Illustration of neural codebook $f(b_m|\theta_m)$for RU $m$: the input is the binary message $b_m \in \{0,1\}^{B_m}$ of size $B_m$; the output is the transmitted symbol vector $\hat{x}_m \in \mathbbm{R}^{2 N_m^\text{tx}}$ of size $2N_m^\text{tx}$ with first $N_m^\text{tx}$ elements used for the real part of $\hat{x}_m$ while the remaining $N_m^\text{tx}$ elements for the imaginary part of $\hat{x}_m$. The number $K_m$ of hidden layers and the corresponding number $D_m$ of hidden neurons can be freely chosen, and we set by default $K_m=1$ and $D_m=B_m$.
• Figure 5: Spectral efficiency as a function of the computational complexity normalized with respect to the computational complexity required by VQ. We assume $M=8$ RUs equipped with $N_m^\text{tx}=2$ antennas under fronthaul capacity $B_m=2$ and $N=3$ UEs equipped with $N_n^\text{rx}=2$ antennas that wish to receive $L_n=1$ data stream. The positions of the RUs are fixed, while UE positions are randomly distributed for each channel realization. The channel is generated by following 3GPP urban micro (UMi) models 3gpp.