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Symbol Detection for Coarsely Quantized OTFS

Junwei He, Haochuan Zhang, Chao Dong, Huimin Zhu

TL;DR

This work tackles symbol detection for OTFS systems with coarse receiver quantization, showing that quantization yields an imbalanced, non-isotropic effective channel that breaks the delay-Doppler circular shift and degrades detection. It adopts a generalized linear model and compares GAMP and GEC-SR, finding that GEC-SR is more robust to the nonlinearity but computationally expensive. The authors then introduce a low-complexity variant of GEC-SR that uses fast inversion of quasi-banded matrices by approximating the covariance with a scaled identity, enabling efficient block-inversion-based computation and reducing cost while preserving performance. Simulation results demonstrate near-GEC-SR performance across path counts and show that 3-bit quantization incurs only modest loss, indicating practical cost/power savings for OTFS in quantized receiver implementations.

Abstract

This paper explicitly models a coarse and noisy quantization in a communication system empowered by orthogonal time frequency space (OTFS) for cost and power efficiency. We first point out, with coarse quantization, the effective channel is imbalanced and thus no longer able to circularly shift the transmitted symbols along the delay-Doppler domain. Meanwhile, the effective channel is non-isotropic, which imposes a significant loss to symbol detection algorithms like the original approximate message passing (AMP). Although the algorithm of generalized expectation consistent for signal recovery (GEC-SR) can mitigate this loss, the complexity in computation is prohibitively high, mainly due to an dramatic increase in the matrix size of OTFS. In this context, we propose a low-complexity algorithm that incorporates into the GEC-SR a quick inversion of quasi-banded matrices, reducing the complexity from a cubic order to a linear order while keeping the performance at the same level.

Symbol Detection for Coarsely Quantized OTFS

TL;DR

This work tackles symbol detection for OTFS systems with coarse receiver quantization, showing that quantization yields an imbalanced, non-isotropic effective channel that breaks the delay-Doppler circular shift and degrades detection. It adopts a generalized linear model and compares GAMP and GEC-SR, finding that GEC-SR is more robust to the nonlinearity but computationally expensive. The authors then introduce a low-complexity variant of GEC-SR that uses fast inversion of quasi-banded matrices by approximating the covariance with a scaled identity, enabling efficient block-inversion-based computation and reducing cost while preserving performance. Simulation results demonstrate near-GEC-SR performance across path counts and show that 3-bit quantization incurs only modest loss, indicating practical cost/power savings for OTFS in quantized receiver implementations.

Abstract

This paper explicitly models a coarse and noisy quantization in a communication system empowered by orthogonal time frequency space (OTFS) for cost and power efficiency. We first point out, with coarse quantization, the effective channel is imbalanced and thus no longer able to circularly shift the transmitted symbols along the delay-Doppler domain. Meanwhile, the effective channel is non-isotropic, which imposes a significant loss to symbol detection algorithms like the original approximate message passing (AMP). Although the algorithm of generalized expectation consistent for signal recovery (GEC-SR) can mitigate this loss, the complexity in computation is prohibitively high, mainly due to an dramatic increase in the matrix size of OTFS. In this context, we propose a low-complexity algorithm that incorporates into the GEC-SR a quick inversion of quasi-banded matrices, reducing the complexity from a cubic order to a linear order while keeping the performance at the same level.
Paper Structure (5 sections, 9 equations, 6 figures, 1 table)

This paper contains 5 sections, 9 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model for OTFS Coarsely Quantized
  3. The Proposed Algorithm
  4. Simulation Results
  5. Conclusion

Figures (6)

  • Figure 1: An example on communication via OTFS with finite-precision ADC at the receiver, where $M = 8$, $N = 2$, $P = 2$, $k_{\max} = 8$ and $l_{\max} = 2$.
  • Figure 2: MSE performance of state-of-the-art competitors (with $P=16$): (a) Original EP shan2022orthogonalyuan2021iterativeminka2001familywu2021vector outperforms original AMP raviteja2018interferencedonoho2009message in the case without quantization; (b) Their generalized versions can handle the coarse quantization effectively, with GEC-SR he2017generalized being the best of the four.
  • Figure 3: Lower upper decomposition on $\bf{T}$ reduces the overall complexity of inverting $\bf{\Psi}$.
  • Figure 4: The proposed algorithm is robust to the change of propagation path: (a) $P = 6$, (b) $P = 14$.
  • Figure 5: The proposed algorithm performs equally good as the $\mathcal{O}(M^3 N^3)$-complexity GEC-SR at only the cost of $\mathcal{O}(MN)$ multiplications per iteration: (a) $P = 14$, $\infty$-bit, and $\text{SNR} = 12 \, \text{dB}$; (b) $P = 6$.
  • ...and 1 more figures