# Spatial Coding Based on Minimum BER in 1-Bit Massive MIMO Systems

## TL;DR

This paper introduces a spatial coding method based on minimum BER for 1-bit massive MIMO systems, significantly improving error performance by reducing the input set and mitigating quantization errors.

## Contribution

The paper proposes a novel spatial coding technique that reduces input set size using minimum BER criterion combined with non-linear precoding in 1-bit massive MIMO systems.

## Key findings

- Significant BER improvement with spatial coding
- Removal of error floor caused by coarse quantization
- Enhanced system performance in massive MIMO settings

## Abstract

We consider a downlink 1-bit quantized multiuser (MU) multiple-input-multiple-output (MIMO) system, where 1-bit digital-to-analog (DACs) and analog-to-digital converters (ADCs) are used at the transmitter and the receiver for economical and computational efficiency. We end up with a discrete memoryless channel with input and output vectors belonging to the QPSK constellation. In the context of massive (MIMO) systems the number of base station (BS) antennas is much larger than the number of receive antennas. This leads to high input cardinality of the channel. In this work we introduce a method to reduce the input set based on the mimimum bit-error-ratio (BER) criterion combined with a non-linear precoding technique. This method is denoted as spatial coding. Simulations show that this spatial coding improves the BER behavior significantly removing the error floor due to coarse quantization.