How Much Training is Needed in One-Bit Massive MIMO Systems at Low SNR?

TL;DR

This paper analyzes the training requirements for one-bit massive MIMO systems at low SNR, deriving optimal training length and power strategies to maximize spectral efficiency, highlighting differences from conventional systems.

Contribution

It provides a closed-form approximation for uplink rate and investigates optimal training length and power allocation in one-bit massive MIMO systems at low SNR.

Findings

Optimal training length exceeds the number of users.

Training and data power optimization offers limited spectral efficiency gains.

Optimal training length depends on coherence interval and transmit power.

Abstract

This paper considers training-based transmissions in massive multi-input multi-output (MIMO) systems with one-bit analog-to-digital converters (ADCs). We assume that each coherent transmission block consists of a pilot training stage and a data transmission stage. The base station (BS) first employs the linear minimum mean-square-error (LMMSE) method to estimate the channel and then uses the maximum-ratio combining (MRC) receiver to detect the data symbols. We first obtain an approximate closed-form expression for the uplink achievable rate in the low SNR region. Then based on the result, we investigate the optimal training length that maximizes the sum spectral efficiency for two cases: i) The training power and the data transmission power are both optimized; ii) The training power and the data transmission power are equal. Numerical results show that, in contrast to conventional massive MIMO systems, the optimal training length in one-bit massive MIMO systems is greater than the number of users and depends on various parameters such as the coherence interval and the average transmit power. Also, unlike conventional systems, it is observed that in terms of sum spectral efficiency, there is relatively little benefit to separately optimizing the training and data power.