適用於抗都卜勒AFDM系統之低複雜度期望傳播檢測器設計

Abstract

在第六代行動通訊系統（6G）中，高速移動環境所引發之都卜勒效應對傳統正交分頻多工（Orthogonal Frequency Division Multiplexing, OFDM）系統造成嚴重干擾，導致其性能大幅衰退。仿射分頻多工（Affine Frequency Division Multiplexing, AFDM）因具備高頻譜效率及優異的抗都卜勒特性，近年來被視為極具潛力的替代方案。然而，為充分發揮AFDM潛藏的全多樣性增益，仍須仰賴高效率且精確的符號檢測機制。 本研究因應此挑戰，導入期望傳播（Expectation Propagation, EP）作為AFDM系統之檢測框架，藉由估計傳送符號的聯合後驗機率分佈以強化解碼性能。儘管EP 展現出優異的檢測效果，其演算法本身須反覆執行矩陣逆運算，造成運算複雜度相當高。雖然紐曼級數近似（Neumann-Series Approximation, NSA）於部分文獻中被採用以降低逆運算之成本，但在本研究所考量之AFDM系統中，由於通道矩陣條件數偏高，使得NSA的效果不彰。 為解決此一問題，本研究提出消息傳遞初始化之近似變異期望傳播演算法（Message Passing-Initialized Approximated-Variance EP, MPI-AVEP）。該方法充分利用AFDM通道矩陣所呈現之準帶狀結構（Quasi-banded structure），以實現低複雜度的LDL分解，進而將整體運算複雜度自傳統立方級顯著降低至與子載波數成線性關係，並在性能上達到接近原始EP之水準。然而，此基於LDL分解之MPI-AVEP 演算法僅於整數都卜勒偏移（Integer Doppler shift）之稀疏通道環境下有效；若處於非整數都卜勒偏移（Fractional Doppler shift）環境，則通道稀疏性將不復存在，導致此基於LDL方法於位元錯誤率（BER）表現上明顯劣化。 為克服此限制，本研究進一步提出基於預處理共軛梯度法（Preconditioned Conjugate Gradient, PCG）之 MPI-AVEP 演算法，專為非整數都卜勒場景設計。透過搭配有效的預處理器，該方法在維持穩健檢測效能的同時，仍具備良好的運算效率，進一步拓展AFDM於高速移動通訊環境中的實際應用潛力。

High-mobility communications in 6G systems face challenges due to Doppler effects, which severely degrade the performance of traditional orthogonal frequency division multiplexing (OFDM). Affine frequency division multiplexing (AFDM) has emerged as a promising alternative, offering high spectral efficiency and inherent robustness to Doppler shifts. However, to fully exploit its diversity gain, efficient symbol detection algorithms are essential for optimal performance. To this end, we introduce expectation propagation (EP) as an effective detection framework for AFDM systems, which enhances detection performance by jointly estimating the posterior distribution of transmitted symbols. Despite its effectiveness, EP suffers from high computational complexity due to repeated matrix inversions. Although the Neumann Series Approximation (NSA) is commonly used to alleviate this burden, it proves ineffective in AFDM systems due to the ill-conditioning of their channel matrices. To address this challenge, we propose the Message Passing-initialized approximated variance EP (MPI-AVEP) algorithm, which exploits the quasi-banded structure of AFDM channel matrices to enable a low-complexity LDL decomposition. This method reduces the computational complexity from cubic to linear in the number of subcarriers, while maintaining performance comparable to that of standard EP. However, the LDLT-based MPI-AVEP is primarily effective in integer Doppler scenarios, where channel sparsity is preserved. In fractional Doppler scenarios, the loss of sparsity causes the LDLT-based method to break down, leading to a deterioration in bit error rate (BER) performance. To overcome this limitation, we propose a Preconditioned Conjugate Gradient (PCG) based MPI-AVEP algorithm, specifically designed for fractional Doppler scenarios. By incorporating an effective preconditioner, this approach not only ensures robust detection performance but also maintains computational efficiency, thereby extending the practical applicability of AFDM to challenging high-mobility environments.