Low Complexity LMMSE Receiver for OTFS

Abstract: Orthogonal time frequency space modulation is a two dimensional (2D) delay-Doppler domain waveform. It uses inverse symplectic Fourier transform (ISFFT) to spread the signal in time-frequency domain. To extract diversity gain from 2D spreaded signal, advanced receivers are required. In this work, we investigate a low complexity linear minimum mean square error receiver which exploits sparsity and quasi-banded structure of matrices involved in the demodulation process which results in a log-linear order of complexity without any performance degradation of BER.

Overview of Low Complexity LMMSE Receiver for OTFS

The paper "Low Complexity LMMSE Receiver for OTFS" presents an innovative solution to the computational challenges associated with implementing a linear minimum mean square error (LMMSE) receiver for Orthogonal Time Frequency Space (OTFS) modulation. OTFS has emerged as a promising waveform for high-mobility scenarios, such as those encountered in 5G New Radio (5G-NR), due to its ability to spread data symbols across the delay-Doppler domain. This modulation technique is inherently resistant to the deleterious effects of time-varying channels, such as inter-symbol and inter-carrier interference (ISI and ICI), but requires advanced receiver architectures to fully exploit its potential for diversity gain.

Problem Statement

High-mobility channels present significant challenges in maintaining communication reliability due to Doppler shifts and delay spreads. Traditional Orthogonal Frequency Division Multiplexing (OFDM) systems, even when augmented with multi-numerology configurations, struggle to efficiently handle these variations without inducing interference. Although OTFS is well-suited for such environments, the design of efficient receivers remains a hurdle, particularly when considering linear receivers like LMMSE, which are simpler than their non-linear counterparts but suffer from computational burdens when processing large-scale systems.

Solution Proposal

The authors propose a low-complexity LMMSE receiver architecture for OTFS that leverages the sparsity and quasi-banded structure of channel matrices to significantly reduce computational requirements. By focusing on LU decomposition techniques adapted for quasi-banded matrices, the authors achieve a reduction in the order of complexity to $O(MN\log_2(N))$, dramatically decreasing the number of complex multiplications needed compared to the naive implementation of LMMSE receivers.

Detailed Contributions

1. LU Factorization Approach: The paper introduces a partitioned structure for the channel matrix, allowing for efficient LU factorization. This partitioning exploits the sparse and quasi-banded nature of the channel matrices inherent in high-mobility vehicular channels, thereby reducing the computational complexity associated with matrix inversion and multiplication.
2. Complexity Optimization: The complexity analysis shows that the proposed approach reduces operations from cubic to near-linear complexity. This significant optimization makes the LMMSE processing feasible for real-world applications where the number of subcarriers ($M$) and time slots ($N$) are large. For instance, the complexity reduction can be up to $10^7$ times in certain 3GPP channel conditions.
3. BER Performance Evaluation: Simulations indicate that the proposed LMMSE receiver does not incur a performance penalty in terms of Bit Error Rate (BER), maintaining parity with direct implementations of traditional approaches while gaining diversity advantages. In particular, OTFS-based receivers outperform OFDM counterparts significantly, despite the streamlined complexity.

Implications and Future Work

The implications of this work are substantial for the deployment of OTFS in 5G and beyond networks, particularly in vehicular ad hoc networks (VANETs) and other high-speed mobility scenarios. The reduction in receiver complexity facilitates practical implementation, making it more viable to deploy OTFS systems in environments characterized by rapid channel variations.

Furthermore, the techniques outlined in this paper open avenues for further research into optimizing linear receiver architectures not only for OTFS but potentially other modulation schemes that could benefit from similar structural analysis of channel matrices. Future work could explore hybrid receiver architectures, incorporate ML-based channel estimation techniques, or extend the application of this complexity reduction strategy to MIMO-OTFS systems.

In summary, while the paper focuses on a specific receiver design approach, the methodologies and insights provided can foster significant advancements in the broader domain of next-generation wireless communication systems, ensuring reliability and efficiency in increasingly complex operating environments.