Massive MIMO Systems with Hardware-Constrained Base Stations Emil Björnson ‡*, Michail Matthaiou ‡§, and Mérouane Debbah ‡ ‡ Alcatel-Lucent Chair on Flexible Radio, Supélec, France * Dept. Signal Processing, KTH, and Linköping University, Sweden § ECIT, Queen’s University Belfast, U.K., and S2, Chalmers, Sweden Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)1

A Conjecture for Massive MIMO ”Massive MIMO can be built with inexpensive, low-power components.” “Massive MIMO reduces the constraints on accuracy and linearity of each individual amplifier and RF chain.” [5] “Massive MIMO for next generation wireless systems,” by E. G. Larsson, O. Edfors, F. Tufvesson and T. L. Marzetta, in IEEE Communications Magazine, Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)2 Is this true? There are some indicative results in the literature [9]-[11] In this paper we provide a more comprehensive answer! Is this true? There are some indicative results in the literature [9]-[11] In this paper we provide a more comprehensive answer!

Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)3 Introduction

Introduction: Massive MIMO Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)4

What is New with Massive MIMO? Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)5 3 sectors, 4 vertical arrays/sector, 20 antennas/array Image source: gigaom.com On Each Uplink Receiver Chain Different Filters Low-Noise Amplifier (LNA) Mixer, Local Oscillator (LO) Analog-to-Digital Converter (ADC) On Each Uplink Receiver Chain Different Filters Low-Noise Amplifier (LNA) Mixer, Local Oscillator (LO) Analog-to-Digital Converter (ADC)

Hardware-Constrained Base Stations Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)6 Partial answer given in this paper Noise amplification Quantization noise Phase noise Modeling of Imperfections Essential to understand the impact of low- quality components! Modeling of Imperfections Essential to understand the impact of low- quality components!

Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)7 System Model

Basic Assumptions Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)8

Conventional and New Uplink Model Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)9 Phase Drift Rotates phases by Wiener process: Phase Drift Rotates phases by Wiener process: Distortion Noise Proportional to received signal: Distortion Noise Proportional to received signal: Receiver Noise

Characterization: Hardware Imperfections Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)10

Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)11 Overview of Analytic Contributions

Channel Estimator and Predictor Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)12 Need new estimator/ predictor

Achievable User Rates Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)13 Receiver Noise Signal Power Distortion NoiseInter-User Interference Theorem 2 Closed form expressions for all expectations for (maximum ratio combining (MRC)) Theorem 2 Closed form expressions for all expectations for (maximum ratio combining (MRC))

Asymptotic Limit and Scaling Law Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)14 Corollary 1 (Rates with MRC) Inner product of pilot sequences

Interpretation of Scaling Law Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)15 Additive distortions Multiplicative distortions Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)15

Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)16 Numerical Example

Simulation Scenario Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)17

Area Sum Rates Three Cases -Ideal Hardware -Fixed imperfect hardware: -Variable Imperfect hardware: As in Corollary Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)18 Observations Manageable impact if scaling law is fulfilled Otherwise: Drastic reduction Observations Manageable impact if scaling law is fulfilled Otherwise: Drastic reduction MMSE Receiver Higher performance Suffers more from imperfections MMSE Receiver Higher performance Suffers more from imperfections

Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)19 Conclusions

Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)20 Important Conclusions for Massive MIMO Conjecture from [5] is true! Can be deployed with inexpensive and imperfect hardware! Hardware cost increases slower than linear! Important Conclusions for Massive MIMO Conjecture from [5] is true! Can be deployed with inexpensive and imperfect hardware! Hardware cost increases slower than linear!

Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH) Thank You for Listening! Questions? Also check out: E. Björnson, M. Matthaiou, M. Debbah, “Circuit-Aware Design of Energy-Efficient Massive MIMO Systems,” Proceedings of ISCCSP, Athens, Greece, May 2014.