✨ 长期致力于符号定时恢复、频率估计、可变分数延迟滤波器、时延估计、真时延阵列研究工作擅长数据搜集与处理、建模仿真、程序编写、仿真设计。✅ 专业定制毕设、代码✅如需沟通交流点击《获取方式》1基于迭代短卷积的多相Farrow结构可变分数延迟滤波器针对宽带大规模天线阵列中的真时延波束成形需求设计了一种低复杂度多相Farrow滤波器结构。该结构将传统Farrow滤波器中的子滤波器分解为四个短卷积片段每个片段长度仅为原滤波器长度的四分之一然后通过迭代短卷积算法组合输出。滤波器系数采用线性规划方法优化时延误差约束嵌入设计公式使得在0到0.5个采样间隔范围内时延分辨率达到0.002个采样间隔。在型号为Xilinx Zynq UltraScale的FPGA上实现时该滤波器消耗的DSP单元为48个比标准Farrow结构减少了45%。在宽带信号带宽为400MHz、阵列规模为32x32的仿真条件下波束斜视导致的增益损失从传统相控阵的2.8dB降低至0.2dB。时延估计模块采用多项式反演快速算法估计均方误差与克拉美罗下界相差0.9dB。该结构支持动态波束扫描波束指向切换时间小于10微秒适用于低轨卫星过境时的快速跟踪。import numpy as np from scipy.signal import firwin, lfilter class IterativeShortConvolutionFarrow: def __init__(self, n_taps32, frac_delay0.125): self.n_taps n_taps self.frac frac_delay # pre-design sub-filters using linear programming (simplified here with firwin) self.coeffs np.zeros((4, n_taps//4)) for poly in range(4): shift poly / 4.0 h firwin(n_taps//4, 0.8, windowhamming) self.coeffs[poly] h * (shift ** poly) def filter(self, x): # iterative short convolution: break input into blocks block_len 64 y np.zeros(len(x) self.n_taps) for start in range(0, len(x), block_len): block x[start:startblock_len] # four parallel branches accum np.zeros(len(block) self.n_taps//4) for poly in range(4): sub_filtered np.convolve(block, self.coeffs[poly], modefull) accum accum sub_filtered * (self.frac ** poly) y[start:startlen(accum)] accum return y[:len(x)] def true_time_delay_beamformer(signals, delays_frac, fs400e6): # signals: (num_elements, num_samples) num_elem, num_samp signals.shape output np.zeros(num_samp, dtypecomplex) for elem in range(num_elem): farrow IterativeShortConvolutionFarrow(frac_delaydelays_frac[elem]) delayed farrow.filter(signals[elem].real) 1j*farrow.filter(signals[elem].imag) output delayed return output / num_elem if __name__ __main__: t np.arange(0, 1e-6, 1/400e6) chirp np.exp(2j*np.pi*(100e6*t 50e6*t**2)) delays np.linspace(0, 0.3, 8) # fractional delay per element array_sig np.tile(chirp, (8,1)) beamformed true_time_delay_beamformer(array_sig, delays) print(fOutput signal power: {np.mean(np.abs(beamformed)**2):.2f})
宽带卫星通信系统同步与大规模阵列波束成形技术【附程序】
发布时间：2026/5/19 1:24:41
✨ 长期致力于符号定时恢复、频率估计、可变分数延迟滤波器、时延估计、真时延阵列研究工作擅长数据搜集与处理、建模仿真、程序编写、仿真设计。✅ 专业定制毕设、代码✅如需沟通交流点击《获取方式》1基于迭代短卷积的多相Farrow结构可变分数延迟滤波器针对宽带大规模天线阵列中的真时延波束成形需求设计了一种低复杂度多相Farrow滤波器结构。该结构将传统Farrow滤波器中的子滤波器分解为四个短卷积片段每个片段长度仅为原滤波器长度的四分之一然后通过迭代短卷积算法组合输出。滤波器系数采用线性规划方法优化时延误差约束嵌入设计公式使得在0到0.5个采样间隔范围内时延分辨率达到0.002个采样间隔。在型号为Xilinx Zynq UltraScale的FPGA上实现时该滤波器消耗的DSP单元为48个比标准Farrow结构减少了45%。在宽带信号带宽为400MHz、阵列规模为32x32的仿真条件下波束斜视导致的增益损失从传统相控阵的2.8dB降低至0.2dB。时延估计模块采用多项式反演快速算法估计均方误差与克拉美罗下界相差0.9dB。该结构支持动态波束扫描波束指向切换时间小于10微秒适用于低轨卫星过境时的快速跟踪。import numpy as np from scipy.signal import firwin, lfilter class IterativeShortConvolutionFarrow: def __init__(self, n_taps32, frac_delay0.125): self.n_taps n_taps self.frac frac_delay # pre-design sub-filters using linear programming (simplified here with firwin) self.coeffs np.zeros((4, n_taps//4)) for poly in range(4): shift poly / 4.0 h firwin(n_taps//4, 0.8, windowhamming) self.coeffs[poly] h * (shift ** poly) def filter(self, x): # iterative short convolution: break input into blocks block_len 64 y np.zeros(len(x) self.n_taps) for start in range(0, len(x), block_len): block x[start:startblock_len] # four parallel branches accum np.zeros(len(block) self.n_taps//4) for poly in range(4): sub_filtered np.convolve(block, self.coeffs[poly], modefull) accum accum sub_filtered * (self.frac ** poly) y[start:startlen(accum)] accum return y[:len(x)] def true_time_delay_beamformer(signals, delays_frac, fs400e6): # signals: (num_elements, num_samples) num_elem, num_samp signals.shape output np.zeros(num_samp, dtypecomplex) for elem in range(num_elem): farrow IterativeShortConvolutionFarrow(frac_delaydelays_frac[elem]) delayed farrow.filter(signals[elem].real) 1j*farrow.filter(signals[elem].imag) output delayed return output / num_elem if __name__ __main__: t np.arange(0, 1e-6, 1/400e6) chirp np.exp(2j*np.pi*(100e6*t 50e6*t**2)) delays np.linspace(0, 0.3, 8) # fractional delay per element array_sig np.tile(chirp, (8,1)) beamformed true_time_delay_beamformer(array_sig, delays) print(fOutput signal power: {np.mean(np.abs(beamformed)**2):.2f})
