Thomas Feys

Thomas Feys, Xavier Mestre, François Rottenberg

Massive multiple input multiple output (MIMO) systems are typically designed under the assumption of linear power amplifiers (PAs). However, PAs are typically most energy-efficient when operating close to their saturation point, where they cause non-linear distortion. Moreover, when using conventional precoders, this distortion coherently combines at the user locations, limiting performance. As such, when designing an energy-efficient massive MIMO system, this distortion has to be managed. In this work, we propose the use of a neural network (NN) to learn the mapping between the channel matrix and the precoding matrix, which maximizes the sum rate in the presence of this non-linear distortion. This is done for a third-order polynomial PA model for both the single and multi-user case. By learning this mapping a significant increase in energy efficiency is achieved as compared to conventional precoders and even as compared to perfect digital pre-distortion (DPD), in the saturation regime.

Thomas Feys, Liesbet Van der Perre, François Rottenberg

Massive MIMO systems are typically designed assuming linear power amplifiers (PAs). However, PAs are most energy efficient close to saturation, where non-linear distortion arises. For conventional precoders, this distortion can coherently combine at user locations, limiting performance. We propose a graph neural network (GNN) to learn a mapping between channel and precoding matrices, which maximizes the sum rate affected by non-linear distortion, using a high-order polynomial PA model. In the distortion-limited regime, this GNN-based precoder outperforms zero forcing (ZF), ZF plus digital pre-distortion (DPD) and the distortion-aware beamforming (DAB) precoder from the state-of-the-art. At an input back-off of -3 dB the proposed precoder compared to ZF increases the sum rate by 8.60 and 8.84 bits/channel use for two and four users respectively. Radiation patterns show that these gains are achieved by transmitting the non-linear distortion in non-user directions. In the four user-case, for a fixed sum rate, the total consumed power (PA and processing) of the GNN precoder is 3.24 and 1.44 times lower compared to ZF and ZF plus DPD respectively. A complexity analysis shows six orders of magnitude reduction compared to DAB precoding. This opens perspectives to operate PAs closer to saturation, which drastically increases their energy efficiency.

Thomas Feys, Liesbet Van der Perre, François Rottenberg

Massive MIMO systems are moving toward increased numbers of radio frequency chains, higher carrier frequencies and larger bandwidths. As such, digital-to-analog converters (DACs) are becoming a bottleneck in terms of hardware complexity and power consumption. In this work, non-linear precoding for coarsely quantized downlink massive MIMO is studied. Given the NP-hard nature of this problem, a graph neural network (GNN) is proposed that directly outputs the precoded quantized vector based on the channel matrix and the intended transmit symbols. The model is trained in a self-supervised manner, by directly maximizing the achievable rate. To overcome the non-differentiability of the objective function, introduced due to the non-differentiable DAC functions, a straight-through Gumbel-softmax estimation of the gradient is proposed. The proposed method achieves a significant increase in achievable sum rate under coarse quantization. For instance, in the single-user case, the proposed method can achieve the same sum rate as maximum ratio transmission (MRT) by using one-bit DAC's as compared to 3 bits for MRT. This reduces the DAC's power consumption by a factor 4-7 and 3 for baseband and RF DACs respectively. This, however, comes at the cost of increased digital signal processing power consumption. When accounting for this, the reduction in overall power consumption holds for a system bandwidth up to 3.5 MHz for baseband DACs, while the RF DACs can maintain a power reduction of 2.9 for higher bandwidths. Notably, indirect effects, which further reduce the power consumption, such as a reduced fronthaul consumption and reduction in other components, are not considered in this analysis.