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Low Complexity Turbo SIC-MMSE Detection for Orthogonal Time Frequency Space Modulation

Qi Li, Jinhong Yuan, Min Qiu, Shuangyang Li, Yixuan Xie

TL;DR

This work tackles reliable detection for ZP-OTFS in doubly selective channels by introducing a low-complexity iterative SIC-MMSE detector and a turbo receiver. The core idea is cross-domain processing with time-domain MMSE filters applied per symbol layer, enabling interference cancellation and iterative refinement; a soft variant further exploits constellation information. An approximate SIC-MMSE is then proposed to dramatically reduce complexity by recycling MMSE weights over nearby sub-channels and exploiting Doppler-induced phase relations, with complexity scaling as $\mathcal{O}\big(\frac{(M-l_{max}) N l_{max}^3}{\Delta m}\big)$. State-evolution-based analysis and simulations show close-to-optimal MSE performance and significant BER gains over MRC for 4QAM and 16QAM OTFS, including turbo gains with LDPC decoders. The methods are applicable to ZP-OTFS and extendable to CP-OTFS, offering practical low-complexity, high-performance detection for high-mobility wireless systems.

Abstract

Recently, orthogonal time frequency space (OTFS) modulation has garnered considerable attention due to its robustness against doubly-selective wireless channels. In this paper, we propose a low-complexity iterative successive interference cancellation based minimum mean squared error (SIC-MMSE) detection algorithm for zero-padded OTFS (ZP-OTFS) modulation. In the proposed algorithm, signals are detected based on layers processed by multiple SIC-MMSE linear filters for each sub-channel, with interference on the targeted signal layer being successively canceled either by hard or soft information. To reduce the complexity of computing individual layer filter coefficients, we also propose a novel filter coefficients recycling approach in place of generating the exact form of MMSE filter weights. Moreover, we design a joint detection and decoding algorithm for ZP-OTFS to enhance error performance. Compared to the conventional SIC-MMSE detection, our proposed algorithms outperform other linear detectors, e.g., maximal ratio combining (MRC), for ZP-OTFS with up to 3 dB gain while maintaining comparable computation complexity.

Low Complexity Turbo SIC-MMSE Detection for Orthogonal Time Frequency Space Modulation

TL;DR

This work tackles reliable detection for ZP-OTFS in doubly selective channels by introducing a low-complexity iterative SIC-MMSE detector and a turbo receiver. The core idea is cross-domain processing with time-domain MMSE filters applied per symbol layer, enabling interference cancellation and iterative refinement; a soft variant further exploits constellation information. An approximate SIC-MMSE is then proposed to dramatically reduce complexity by recycling MMSE weights over nearby sub-channels and exploiting Doppler-induced phase relations, with complexity scaling as . State-evolution-based analysis and simulations show close-to-optimal MSE performance and significant BER gains over MRC for 4QAM and 16QAM OTFS, including turbo gains with LDPC decoders. The methods are applicable to ZP-OTFS and extendable to CP-OTFS, offering practical low-complexity, high-performance detection for high-mobility wireless systems.

Abstract

Recently, orthogonal time frequency space (OTFS) modulation has garnered considerable attention due to its robustness against doubly-selective wireless channels. In this paper, we propose a low-complexity iterative successive interference cancellation based minimum mean squared error (SIC-MMSE) detection algorithm for zero-padded OTFS (ZP-OTFS) modulation. In the proposed algorithm, signals are detected based on layers processed by multiple SIC-MMSE linear filters for each sub-channel, with interference on the targeted signal layer being successively canceled either by hard or soft information. To reduce the complexity of computing individual layer filter coefficients, we also propose a novel filter coefficients recycling approach in place of generating the exact form of MMSE filter weights. Moreover, we design a joint detection and decoding algorithm for ZP-OTFS to enhance error performance. Compared to the conventional SIC-MMSE detection, our proposed algorithms outperform other linear detectors, e.g., maximal ratio combining (MRC), for ZP-OTFS with up to 3 dB gain while maintaining comparable computation complexity.
Paper Structure (21 sections, 1 theorem, 59 equations, 13 figures, 1 table, 1 algorithm)

This paper contains 21 sections, 1 theorem, 59 equations, 13 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. OTFS System Models
  3. Transmitter
  4. Channel
  5. Receiver
  6. Input-Output Relations for ZP-OTFS in Time Domain
  7. Iterative SIC-MMSE with Hard and Soft Estimates
  8. SIC-MMSE Detection in the Time Domain with Hard Interference Cancellation
  9. Soft Interference Cancellation
  10. Low complexity approximate SIC-MMSE
  11. Approximate SIC-MMSE
  12. SINR Analysis for Approximate SIC-MMSE
  13. Complexity Analysis for Approximate SIC-MMSE Per Iteration
  14. Performance Analysis
  15. SISO Iterative Decoding and Detection
  16. ...and 6 more sections

Key Result

Proposition 1

The number of approximated signal layer $\Delta m$ is a function of $\nu_{max}$ and $\Delta \beta$, and it is given by where $a$ and $\theta$ are the magnitude and phase of $\mu_{n,m} = {\bf w}^{*}_{n,m}{\bf H}_{n,m}[:,l']$, respectively.

Figures (13)

  • Figure 1: Time domain input-output relation for all symbols with $N=8,M=8,l_{max}=3$.
  • Figure 2: Time domain input-output relation for the $n$-th block with $l_{max}=3$.
  • Figure 3: Relation between the number of approximated sub-channels $\Delta m$ and the given MSE tolerance $\Delta \beta$, when maximum Doppler index is $\nu_{max}=3.79, 4.79, 5.79$ which correspond to Doppler shift of 888Hz, 1122Hz, and 1357Hz, respectively.
  • Figure 4: Relation between the number of approximated sub-channels $\Delta m$ and the maximum Doppler index $\nu_{max}$, when MSE tolerance $\Delta \beta=0.005, 0.01, 0.02$.
  • Figure 5: SINR for each symbol after SIC-MMSE and the approximate SIC-MMSE filtering for 16QAM OTFS with $M=512, N=128$.
  • ...and 8 more figures

Theorems & Definitions (3)

  • Remark 1
  • Proposition 1
  • proof