Abstract

We present an analytical framework for the channel estimation and the data detection in massive multiple-input multiple-output uplink systems with 1-bit analog-to-digital converters (ADCs) and i.i.d. Rayleigh fading. First, we provide closed-form expressions of the mean squared error (MSE) of the channel estimation considering the state-of-the-art linear minimum MSE estimator and the class of scaled least-squares estimators. For the data detection, we provide closed-form expressions of the expected value and the variance of the estimated symbols when maximum ratio combining is adopted, which can be exploited to efficiently implement minimum distance detection and, potentially, to design the set of transmit symbols. Our analytical findings explicitly depend on key system parameters such as the signal-to-noise ratio (SNR), the number of user equipments, and the pilot length, thus enabling a precise characterization of the performance of the channel estimation and the data detection with 1-bit ADCs. The proposed analysis highlights a fundamental SNR trade-off, according to which operating at the right noise level significantly enhances the system performance.

Highlights

  • The migration of operating frequencies from first- to fourthgeneration wireless systems, i.e., from 800 MHz to the sub3 GHz range, did not bring major changes in terms of signal propagation

  • Rayleigh fading channels among the user equipments (UEs), the Bussgang linear MMSE (BLM) estimator can be simplified as a scaled LS estimator with UE-specific scaling factors and that using a common optimized scaling factor for all the UEs entails a negligible performance loss

  • We focus on the performance evaluation of the data detection with 1-bit analog-to-digital converters (ADCs) with respect to the different parameters using the analytical results presented in Sections IV-A and IV-B

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Summary

INTRODUCTION

The migration of operating frequencies from first- to fourthgeneration wireless systems, i.e., from 800 MHz to the sub GHz range, did not bring major changes in terms of signal propagation. The current fifth generation (5G) features a more pronounced transition in this respect by operating at sub GHz frequencies and, eventually, up to 30 GHz with the objective of boosting the data rates. Following this trend, beyond-5G systems will exploit the large amount of bandwidth available in the mmWave band (i.e., 30 GHz–300 GHz) and raise the operating frequencies up to 1 THz [2]. As in the system model illustrated, each base station (BS) antenna is generally equipped with a dedicated radiofrequency (RF) chain that includes complex, power-hungry analog-to-digital/digital-to-analog converters (ADCs/DACs) [4]. While the transmit power can be made inversely proportional to the number of antennas, the power consumed

ADC RF
Contribution
SYSTEM MODEL
Channel Estimation
Uplink Data Transmission
CHANNEL ESTIMATION WITH 1-BIT ADCS
MSE of the Channel Estimation
Tractable Upper Bounds
Numerical Results and Discussion
DATA DETECTION WITH 1-BIT ADCS AND MRC
Expected Value and Variance of the Estimated Symbols
Findings
CONCLUSIONS
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