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】

✨ 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
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（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_taps=32, frac_delay=0.125): 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, window='hamming') 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:start+block_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], mode='full') accum = accum + sub_filtered * (self.frac ** poly) y[start:start+len(accum)] += accum return y[:len(x)] def true_time_delay_beamformer(signals, delays_frac, fs=400e6): # signals: (num_elements, num_samples) num_elem, num_samp = signals.shape output = np.zeros(num_samp, dtype=complex) for elem in range(num_elem): farrow = IterativeShortConvolutionFarrow(frac_delay=delays_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(f'Output signal power: {np.mean(np.abs(beamformed)**2):.2f}')