在带限数字通信系统中，平方根奈奎斯特（square-root Nyquist,SR-NYQ）滤波器通常同时应用于系统的发送端和接收端，可以有效减少符号间干扰（inter symbol interference,ISI）。本文提出了一种基于遗传算法（genetic algorithm,GA）的线性相位SR-NYQ滤波器设计方法，其中滤波器ISI、通带和阻带波纹被融合构造为适应度函数。得益于GA强大的全局优化能力，该方法设计的原型滤波器在更加接近奈奎斯特条件的同时，提供了优于传统根升余弦滤波器的设计灵活性。此外，本文设计的SR-NYQ滤波器在正交频分复用系统中作为匹配和成型滤波器进行测试，并与传统的根升余弦滤波器进行对比。仿真对比结果表明，本文所设计的SR-NYQ滤波器具有更好的频率响应，可以显著降低符号错误率。
In band-limited digital communications, square-root Nyquist (SR-NYQ) filters are commonly applied at both the transmitter and receiver to effectively mitigate sampling inter symbol interference (ISI). This paper proposes a novel design method for linear-phase SR-NYQ filters based on genetic algorithms (GA), in which the fitness function consists of key performance metrics including ISI, passband ripple and stopband ripple. Due to the excellent global optimization capability of GA, the proposed method enables a closer approximation to the ideal Nyquist condition while providing additional design flexibility. To evaluate performance, the proposed SR-NYQ filter is compared with the conventional root raised cosine filter within an orthogonal frequency division multiplexing (OFDM) system. Simulation results demonstrate that the SR-NYQ filter designed using the proposed method achieves a superior frequency response and significantly reduces the symbol error rate (SER).
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