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Low Complexity Precoding and Detection in Multi-user Massive MIMO OTFS Downlink

Brijesh Chander Pandey, Saif Khan Mohammed, P. Raviteja, Yi Hong, Emanuele Viterbo

TL;DR

This paper proposes a novel OTFS based multi-user precoder at the base station and a corresponding low complexity detector (LCD) at the user terminals (UTs), which allows for separate demodulation of each DD domain information symbol at the UT.

Abstract

We consider the problem of degradation in performance of multi-carrier multi-user massive MIMO systems when channel induced Doppler spread is high. Recently, Orthogonal Time Frequency Space (OTFS) modulation has been shown to be robust to channel induced Doppler spread. In OTFS based systems, information symbols are embedded in the delay-Doppler (DD) domain where they are jointly modulated to generate the time-domain transmit signal. Due to the multi-path delay and Doppler shifts, the DD domain information symbols need to be jointly demodulated at the receiver. For multi-carrier based communication (e.g., Orthogonal Frequency Division Multiplexing (OFDM)), massive MIMO systems have been shown to achieve high spectral and energy efficiency with low complexity multi-user precoding in the downlink. Extending the same to OTFS based downlink multi-user massive MIMO systems is challenging due to the requirement for joint demodulation of all information symbols at the user terminal (UT). In this paper, we solve this problem by proposing a novel OTFS based multi-user precoder at the base station (BS) and a corresponding low complexity detector (LCD) at the user terminals (UTs), which allows for separate demodulation of each DD domain information symbol at the UT. The complexity of the proposed precoder increases only linearly with increasing number BS antennas Q and the number of UTs. We show, through analysis, that as Q increases (with total transmitted power decreased linearly with Q), the proposed low complexity detector achieves a sum SE close to that achieved with optimal joint demodulation at each UT. Numerical simulations confirm our analysis and also show that the SE and error rate performance of the proposed OTFS based massive MIMO precoder and LCD detector is significantly more robust to channel induced Doppler spread when compared to OFDM based multi-user massive MIMO systems.

Low Complexity Precoding and Detection in Multi-user Massive MIMO OTFS Downlink

TL;DR

This paper proposes a novel OTFS based multi-user precoder at the base station and a corresponding low complexity detector (LCD) at the user terminals (UTs), which allows for separate demodulation of each DD domain information symbol at the UT.

Abstract

We consider the problem of degradation in performance of multi-carrier multi-user massive MIMO systems when channel induced Doppler spread is high. Recently, Orthogonal Time Frequency Space (OTFS) modulation has been shown to be robust to channel induced Doppler spread. In OTFS based systems, information symbols are embedded in the delay-Doppler (DD) domain where they are jointly modulated to generate the time-domain transmit signal. Due to the multi-path delay and Doppler shifts, the DD domain information symbols need to be jointly demodulated at the receiver. For multi-carrier based communication (e.g., Orthogonal Frequency Division Multiplexing (OFDM)), massive MIMO systems have been shown to achieve high spectral and energy efficiency with low complexity multi-user precoding in the downlink. Extending the same to OTFS based downlink multi-user massive MIMO systems is challenging due to the requirement for joint demodulation of all information symbols at the user terminal (UT). In this paper, we solve this problem by proposing a novel OTFS based multi-user precoder at the base station (BS) and a corresponding low complexity detector (LCD) at the user terminals (UTs), which allows for separate demodulation of each DD domain information symbol at the UT. The complexity of the proposed precoder increases only linearly with increasing number BS antennas Q and the number of UTs. We show, through analysis, that as Q increases (with total transmitted power decreased linearly with Q), the proposed low complexity detector achieves a sum SE close to that achieved with optimal joint demodulation at each UT. Numerical simulations confirm our analysis and also show that the SE and error rate performance of the proposed OTFS based massive MIMO precoder and LCD detector is significantly more robust to channel induced Doppler spread when compared to OFDM based multi-user massive MIMO systems.

Paper Structure

This paper contains 14 sections, 3 theorems, 77 equations, 13 figures, 2 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. OTFS Modulation and Demodulation
  4. Proposed Multi-user Downlink Precoding in DD Domain
  5. Low Complexity Detection of Received Multi-user OTFS Signal
  6. Numerical Simulations
  7. Coded Error Rate Performance Comparison between OTFS and OFDM Massive MIMO Systems with Imperfect CSI
  8. Conclusion
  9. Derivation of (\ref{['eqn10']}) and (\ref{['eq_channel']})
  10. Expression for $\gamma_{s,s',r,p}/Q \,\,\,\, (s \ne s')$
  11. Expression for ${\gamma_{s,s,r,r}}/{Q}$
  12. Expression for $\gamma_{s,s,r,p}/Q \,\,\,\, (r \ne p)$
  13. Proof of Theorem \ref{['thm34']}
  14. OTFS Channel Estimation

Key Result

Theorem 1

For a given set of channel parameters ${\mathcal{P}} = \left\{ \{L_s\}_{s=1}^K, \{ \theta_{s,i}, \phi_{s,i}, \tau_{s,i}, \nu_{s,i}, g_{s,i} \}_{s=1, i=1}^{K, L_s} \right\}$, the SE achieved by the $s$-th UT with the proposed LCD detector is given by

Figures (13)

  • Figure 1: A multi-user massive MIMO downlink system.
  • Figure 2: Block diagram of the BS downlink transmitter with the proposed OTFS Multi-user Massive MIMO Precoder.
  • Figure 3: Block diagram of the receiver at the $s$-th UT with the proposed LCD detector.
  • Figure 4: Sum SE (bits/s/Hz) versus number of BS antennas $Q$ (constant $\rho \, Q = 0.1$).
  • Figure 5: Sum SE (bits/s/Hz) versus maximum Doppler shift $\nu_{max}$ (Hz).
  • ...and 8 more figures

Theorems & Definitions (3)

  • Theorem 1
  • Corollary 1
  • Theorem 2