This paper exploits the parallelism between Discrete Gabor Transform (DGT) and Generalized Frequency-Division Multiplexing (GFDM) that exists when the synthesis function, i.e. the pulse shaping filter, and the analysis function, i.e. the receiving filter, satisfy the Wexler–Raz identity. Choosing functions that satisfy the Wexler–Raz condition allows optimal symbol-by-symbol detection for a DGT-based GFDM receiver in case of transmission over an additive white Gaussian noise channel. However, multipath fading is the major problem of the wireless communication channel, hence, when transmission takes place over frequency selective channel, symbol-by-symbol detection is no longer optimal due to interference generated among the transmitted symbols. In this work, we deal with the design of linear and non-linear receivers for DGT-based GFDM transmission over a frequency selective channel that allows a good trade-off between complexity and performance. Different equalization schemes to mitigate distortions, such as Maximum Likelihood, Zero-Forcing and Minimum Mean-Squared Error, are developed and analyzed. Monte Carlo simulations are used to evaluate the error rate performance achieved with the considered design. A comparison is done with other works in the literature.

本文利用了离散伽柏变换（DGT）与广义频分复用（GFDM）之间的并行性，当合成函数（即脉冲整形滤波器）和分析函数（即接收滤波器）满足Wexler–Raz身份时，存在。选择满足Wexler–Raz条件的功能，可以在基于加性高斯白噪声信道传输的情况下，对基于DGT的GFDM接收机进行逐个符号的最佳检测。然而，多径衰落是无线通信信道的主要问题，因此，当在频率选择信道上进行传输时，由于在所传输的符号之间产生的干扰，逐个符号的检测不再是最优的。在这项工作中 我们处理在频率选择通道上基于DGT的GFDM传输的线性和非线性接收器的设计，该设计允许在复杂性和性能之间进行良好的权衡。开发并分析了不同的减轻失真的均衡方案，例如最大似然，迫零和最小均方误差。蒙特卡洛模拟用于评估通过考虑的设计实现的错误率性能。与文献中的其他作品进行了比较。蒙特卡洛仿真用于评估通过考虑的设计实现的错误率性能。与文献中的其他作品进行了比较。蒙特卡洛模拟用于评估通过考虑的设计实现的错误率性能。与文献中的其他作品进行了比较。