在廣義空間調變系統中，為了克服天線間訊號干擾及多重路徑所產生之符元間干擾，使用最大概似偵測器來處理。然而其雖為最佳之偵測器，其複雜度隨星座點數呈現指數上升。而樹狀搜尋之M演算法可解決此問題，使複雜度大幅下降，但仍有可接受的錯誤率。在其他論文中，FDF-M演算法利用通道循環的特性，配合M演算法，成功地使用頻域前置濾波器達成良好的效能。然而，在傳送端天線數量大於接收端數量(稱之為秩虧系統)的情況下，FDF-M演算法之錯誤率表現不佳。本篇論文著重於頻域前置濾波器，提出MFDF-M演算法，其利用多頻帶之頻域前置濾波器，並限制每個頻帶之通道長度，讓系統在受到多頻帶之前置濾波器處理後仍能使用樹狀搜尋。經由這樣的設計可以使得系統之均方誤差在秩虧時達到可接受的程度，並使得錯誤率在秩虧系統的情況下將能夠降低。由於 MFDF-M 之位元錯誤率較不理想，因此透過MFDF-M 前置濾波器之特徵去修改FDF-M演算法(修改後之演算法稱為FDF-M-R)，使其系統誤差之共變異數矩陣之對角線方塊矩陣為單位矩陣，寬鬆了FDF-M的目標響應之對角線區塊限制，使FDF-M-R系統能夠在秩虧的情況下使用。在秩虧或非秩虧系統下，FDF-M-R皆擁有比FDF-M更好之錯誤率，與更低之複雜度。

In generalized spatial modulation system, maximum likelihood detector is the optimal detector to overcome the signal interference between different antennas and inter-symbol interference caused by multipath propagation. But its complexity increases exponentially with the number of generalized spatial modulation constellation points. M-algorithm can be used to mitigate the problem because it reduces the complexity significantly with an acceptable error rate. FDF-M algorithm, by exploiting cyclic nature of the channel and in combination with M-algorithm, successfully uses the frequency-domain prefilter to achieve better performance. However, in rank-deficient scenarios, the error rate performance of the FDF-M algorithm is unsatisfactory. This paper focuses on the design of the frequency-domain prefilter and proposes MFDF-M algorithm. By using the multi-band frequency-domain prefilter and limiting the channel length of each band, the algorithm allows the system to use tree-search detection after the received signal is processed by the multi-band prefilter. This design ensures that, in rank-deficient scenarios, MFDF-M algorithm's mean square error remains acceptable, and the bit error rate can be reduced. To further enhance the bit error rate of MFDF-M algorithm, we modify FDF-M algorithm based on the characteristics of MFDF-M algorithm’s prefilter, resulting in the FDF-M-R algorithm. This modified algorithm ensures that the diagonal block matrices of covariance matrix of the system error are identity matrices. The method relaxes the diagonal block constraint of the target response in FDF-M algorithm, allowing FDF-M-R system to be used in the case of rank-deficient channels. Compared to FDF-M, FDF-M-R shows better error rate and lower complexity in both rank-deficient and non-rank-deficient systems.

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