A technique to improve the fixed-sphere decoding algorithm for Spectrally Efficient Frequency Division Multiplexing systems - Liu, Boyi; Yang, Liu; Li, Mengyan; Zhang, Lifu; Zhang, Tao; Luo, Fengguang; Hu, Yongming (Optics communications, 2025)
Spectral Efficient Frequency Division Multiplexing (SEFDM) enhances spectral efficiency by narrowing subcarrier bandwidth, however it introduces severe inter-carrier interference (ICI). Currently, the most effective solution is the Fixed Sphere Detection (FSD) algorithm. In previous studies, we found that in order to better reduce the computational complexity of FSD, it is always through adding preprocessing and other pre-algorithms. Although this approach can effectively fix the search radius g in FSD, the complexity of the FSD algorithm itself has not been reduced. Since FSD determines the exploration path by fixing the tree width (Tw), and the selection of exploration paths can directly affect the final search for the optimal candidate values. In this paper we analyze the traditional algorithm from three angles - computational path, ICI generation, and computational complexity, and propose an Optimization Fixed Sphere Detection (OFSD) algorithm. It reduces the number of calculations required when initially selecting exploration paths by narrowing the search range. This allows us to avoid most unnecessary calculations during path selection. In this way, we can greatly reduce the computational complexity. Based on the simulation results, the proposed algorithm in the paper achieves a significant reduction in computational complexity compared to the FSD algorithm (up to 25% at maximum), while the performance drops by at most 0.12 dB when BCF is 0.8 and drops by at most 0.09 dB when BCF is 0.9. Due to the bandwidth compression technique, Spectrally Efficient Frequency Division Multiplexing (SEFDM) improves spectral efficiency at the cost of severe inter-carrier interference (ICI), and fixed sphere detection (FSD) algorithm plays a key role in mitigating ICI. Although the traditional FSD algorithm has good performance, its complexity is still high. Based on the shortcomings of previous studies, the main innovations of our work are as follows:1.We conducted a detailed analysis of the FSD algorithm, focusing on the computation path and complexity.2.We propose an optimized FSD (OFSD) algorithm by reducing the search range to lower the complexity significantly while maintaining acceptable performance.3.Simulation results show that the proposed OFSD algorithm can reduce the computation complexity by up to 25% compared with FSD, while the performance degradation is within 0.12 dB for a bandwidth compression factor of 0.8.4.The OFSD algorithm strikes a good balance between complexity and performance, providing an efficient solution for practical implementation of SEFDM systems.