501 lines
19 KiB
Python
501 lines
19 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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from matplotlib.patches import Rectangle
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import os
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# ============================================================
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# 0. 全局绘图设置（尽量兼容中文）
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# ============================================================
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plt.rcParams['font.sans-serif'] = [
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'Microsoft YaHei', 'SimHei', 'PingFang SC',
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'Noto Sans CJK SC', 'Arial Unicode MS', 'DejaVu Sans'
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]
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plt.rcParams['axes.unicode_minus'] = False
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# ============================================================
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# 1. 用户参数区（你可以根据论文需要自行调整）
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# ============================================================
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ARRAY_TYPE = 'ULA' # 'ULA' 或 'NULA'
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N_ant = 24 # 阵元数
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N_RF = 4 # 射频链数
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d_lambda = 0.5 # 阵元间距（单位：波长），ULA 用
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target_angle = 5.0 # 目标角度
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clutter_angle = -15.0 # 强杂波角度
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sector_min = 0.0 # TSC-OMP 扇区下界
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sector_max = 10.0 # TSC-OMP 扇区上界
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clutter_band_half = 2.0 # 杂波邻域半宽（用于统计“杂波误选率”）
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noise_power = 1.0
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SNR_dB = -15.0 # 故意设置得较低，便于显现伪峰
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INR_dB = 35.0 # 强干扰
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L_snapshots = 48 # 快拍数，故意设置得不高，便于显现伪峰
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diag_loading_ratio = 0.01 # 对角加载比例
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MC = 400 # Monte Carlo 次数
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# 字典设置
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full_grid = np.arange(-90.0, 90.0 + 0.5, 0.5) # 传统OMP：全空间字典
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tsc_grid = np.arange(sector_min, sector_max + 0.1, 0.1) # TSC-OMP：局部字典
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# 宽波束先验
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broad_step = 0.5
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# 输出文件夹
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save_dir = 'pseudo_peak_results'
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os.makedirs(save_dir, exist_ok=True)
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# ============================================================
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# 2. 阵列位置定义
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# ============================================================
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def get_array_positions(array_type='ULA', N=24, d=0.5):
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"""
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返回阵列位置（单位：波长）
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"""
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if array_type.upper() == 'ULA':
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pos = np.arange(-(N - 1) / 2, (N - 1) / 2 + 1) * d
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return pos.astype(float)
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elif array_type.upper() == 'NULA':
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# 一个示例性的 NULA 阵列位置（非均匀、递增排序、近似关于0分布）
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# 你也可以改成与你论文代码完全一致的 NULA 位置
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pos = np.array([
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-5.75, -5.10, -4.40, -3.85, -3.15, -2.60,
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-2.05, -1.45, -0.95, -0.35, 0.20, 0.75,
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1.25, 1.85, 2.45, 3.05, 3.70, 4.30,
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4.95, 5.65, 6.35, 7.05, 7.85, 8.70
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])
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pos = pos - np.mean(pos)
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return pos.astype(float)
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else:
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raise ValueError("ARRAY_TYPE 只能是 'ULA' 或 'NULA'")
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array_pos = get_array_positions(ARRAY_TYPE, N_ant, d_lambda)
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# ============================================================
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# 3. 基本函数
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# ============================================================
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def steering_vector(theta_deg, array_pos):
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"""
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阵列导向矢量 a(theta)
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theta_deg : 角度（度）
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array_pos : 阵元位置（单位：波长）
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"""
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theta_rad = np.deg2rad(theta_deg)
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phase = 2 * np.pi * array_pos * np.sin(theta_rad)
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a = np.exp(1j * phase).reshape(-1, 1)
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return a
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def build_dictionary(angle_grid, array_pos, normalize=True):
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"""
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构造字典矩阵 A = [a(theta1), a(theta2), ...]
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"""
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A = np.hstack([steering_vector(ang, array_pos) for ang in angle_grid])
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if normalize:
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A = A / np.sqrt(A.shape[0])
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return A
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def omp_trace(w_opt, A_dic, angle_grid, N_RF):
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"""
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传统 OMP / TSC-OMP 的公共实现：只是在字典上不同
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返回：
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F_RF : 最终模拟矩阵
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chosen_ang : 每一步选中的角度
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proj_hist : 每一步投影谱 |A^H r|
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"""
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res = w_opt.copy()
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F_RF = np.zeros((A_dic.shape[0], 0), dtype=np.complex128)
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chosen_ang = []
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proj_hist = []
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for _ in range(N_RF):
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proj = np.abs(A_dic.conj().T @ res).flatten()
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proj_hist.append(proj.copy())
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idx = np.argmax(proj)
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chosen_ang.append(float(angle_grid[idx]))
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atom = A_dic[:, idx:idx+1]
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F_RF = np.hstack((F_RF, atom))
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coeff = np.linalg.pinv(F_RF) @ w_opt
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res = w_opt - F_RF @ coeff
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return F_RF, np.array(chosen_ang), proj_hist
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def build_broad_prior_vector(array_pos, sector_min, sector_max, step=0.5):
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"""
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宽波束先验导向向量：对目标扇区做叠加
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"""
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a_broad = np.zeros((len(array_pos), 1), dtype=np.complex128)
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for th in np.arange(sector_min, sector_max + 1e-12, step):
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a_broad += steering_vector(th, array_pos)
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a_broad /= np.linalg.norm(a_broad)
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return a_broad
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def build_sample_prior(array_pos,
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target_angle,
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clutter_angle,
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SNR_dB,
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INR_dB,
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noise_power,
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L_snapshots,
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diag_loading_ratio,
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sector_min,
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sector_max,
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broad_step=0.5):
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"""
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构造有限快拍样本协方差下的先验数字权值 w_prior
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这是让传统 OMP 更容易显现伪峰风险的关键
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"""
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N_ant = len(array_pos)
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sig_p = 10 ** (SNR_dB / 10.0)
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INR_linear = 10 ** (INR_dB / 10.0)
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a_t = steering_vector(target_angle, array_pos)
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a_c = steering_vector(clutter_angle, array_pos)
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s_t = np.sqrt(sig_p / 2) * (
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np.random.randn(1, L_snapshots) + 1j * np.random.randn(1, L_snapshots)
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)
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s_c = np.sqrt(INR_linear / 2) * (
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np.random.randn(1, L_snapshots) + 1j * np.random.randn(1, L_snapshots)
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)
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n_t = np.sqrt(noise_power / 2) * (
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np.random.randn(N_ant, L_snapshots) + 1j * np.random.randn(N_ant, L_snapshots)
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)
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X = a_t @ s_t + a_c @ s_c + n_t
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R_hat = (X @ X.conj().T) / L_snapshots
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dl = diag_loading_ratio * np.real(np.trace(R_hat)) / N_ant
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R_hat = R_hat + dl * np.eye(N_ant)
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a_broad = build_broad_prior_vector(array_pos, sector_min, sector_max, broad_step)
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# 用低快拍样本协方差构造“先验数字权值”
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w_prior = np.linalg.solve(R_hat, a_broad)
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w_prior /= np.linalg.norm(w_prior)
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return w_prior
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def count_stats(chosen_angles, sector_min, sector_max, clutter_angle, clutter_band_half):
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"""
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统计：
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P_hit : 目标扇区命中率
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P_clutter : 杂波误选率
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P_out : 扇区外误选率
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"""
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chosen_angles = np.array(chosen_angles)
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hit = np.sum((chosen_angles >= sector_min) & (chosen_angles <= sector_max))
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clutter = np.sum((chosen_angles >= clutter_angle - clutter_band_half) &
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(chosen_angles <= clutter_angle + clutter_band_half))
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out = np.sum((chosen_angles < sector_min) | (chosen_angles > sector_max))
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return hit, clutter, out
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def compute_badness_score(proj, angle_grid, sector_min, sector_max, clutter_angle, clutter_band_half):
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"""
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用于自动挑选一个“传统OMP伪峰最明显”的代表性实验样本
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"""
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proj = np.array(proj).flatten()
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target_mask = (angle_grid >= sector_min) & (angle_grid <= sector_max)
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clutter_mask = (angle_grid >= clutter_angle - clutter_band_half) & (angle_grid <= clutter_angle + clutter_band_half)
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out_mask = ~target_mask
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target_peak = np.max(proj[target_mask]) if np.any(target_mask) else 1e-12
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clutter_peak = np.max(proj[clutter_mask]) if np.any(clutter_mask) else 0.0
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out_peak = np.max(proj[out_mask]) if np.any(out_mask) else 0.0
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score = max(clutter_peak / (target_peak + 1e-12),
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out_peak / (target_peak + 1e-12))
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return score
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# ============================================================
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# 4. 构造字典
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# ============================================================
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A_dic_full = build_dictionary(full_grid, array_pos, normalize=True)
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A_dic_tsc = build_dictionary(tsc_grid, array_pos, normalize=True)
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# ============================================================
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# 5. Monte Carlo 验证
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# ============================================================
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all_angles_full = []
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all_angles_tsc = []
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full_hit_total = 0
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full_clutter_total = 0
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full_out_total = 0
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tsc_hit_total = 0
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tsc_clutter_total = 0
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tsc_out_total = 0
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# 保存一个“代表性最差样本”，用于画第一步投影谱
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best_bad_score = -1.0
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rep_full_proj0 = None
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rep_tsc_proj0 = None
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rep_full_chosen = None
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rep_tsc_chosen = None
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for mc in range(MC):
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w_prior = build_sample_prior(
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array_pos=array_pos,
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target_angle=target_angle,
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clutter_angle=clutter_angle,
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SNR_dB=SNR_dB,
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INR_dB=INR_dB,
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noise_power=noise_power,
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L_snapshots=L_snapshots,
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diag_loading_ratio=diag_loading_ratio,
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sector_min=sector_min,
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sector_max=sector_max,
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broad_step=broad_step
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)
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# 传统OMP（全空间字典）
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_, chosen_full, proj_hist_full = omp_trace(w_prior, A_dic_full, full_grid, N_RF)
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# TSC-OMP（目标扇区局部字典）
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_, chosen_tsc, proj_hist_tsc = omp_trace(w_prior, A_dic_tsc, tsc_grid, N_RF)
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all_angles_full.extend(chosen_full.tolist())
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all_angles_tsc.extend(chosen_tsc.tolist())
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h, c, o = count_stats(chosen_full, sector_min, sector_max, clutter_angle, clutter_band_half)
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full_hit_total += h
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full_clutter_total += c
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full_out_total += o
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h, c, o = count_stats(chosen_tsc, sector_min, sector_max, clutter_angle, clutter_band_half)
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tsc_hit_total += h
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tsc_clutter_total += c
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tsc_out_total += o
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# 选一个“传统OMP最容易看到伪峰”的样本
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cur_score = compute_badness_score(proj_hist_full[0], full_grid,
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sector_min, sector_max,
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clutter_angle, clutter_band_half)
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# 优先考虑“传统OMP至少有一个原子落在扇区外或杂波邻域”的样本
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bad_event = np.any((chosen_full < sector_min) | (chosen_full > sector_max)) or \
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np.any((chosen_full >= clutter_angle - clutter_band_half) &
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(chosen_full <= clutter_angle + clutter_band_half))
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if bad_event and cur_score > best_bad_score:
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best_bad_score = cur_score
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rep_full_proj0 = proj_hist_full[0]
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rep_tsc_proj0 = proj_hist_tsc[0]
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rep_full_chosen = chosen_full.copy()
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rep_tsc_chosen = chosen_tsc.copy()
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# 如果一个“明确坏样本”都没抓到，就退而选投影谱最坏的那一个
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if rep_full_proj0 is None:
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# 再跑一遍，抓 score 最高的
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best_bad_score = -1.0
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for mc in range(MC):
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w_prior = build_sample_prior(
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array_pos=array_pos,
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target_angle=target_angle,
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clutter_angle=clutter_angle,
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SNR_dB=SNR_dB,
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INR_dB=INR_dB,
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noise_power=noise_power,
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L_snapshots=L_snapshots,
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diag_loading_ratio=diag_loading_ratio,
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sector_min=sector_min,
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sector_max=sector_max,
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broad_step=broad_step
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)
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_, chosen_full, proj_hist_full = omp_trace(w_prior, A_dic_full, full_grid, N_RF)
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_, chosen_tsc, proj_hist_tsc = omp_trace(w_prior, A_dic_tsc, tsc_grid, N_RF)
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cur_score = compute_badness_score(proj_hist_full[0], full_grid,
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sector_min, sector_max,
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clutter_angle, clutter_band_half)
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if cur_score > best_bad_score:
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best_bad_score = cur_score
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rep_full_proj0 = proj_hist_full[0]
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rep_tsc_proj0 = proj_hist_tsc[0]
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rep_full_chosen = chosen_full.copy()
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rep_tsc_chosen = chosen_tsc.copy()
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# ============================================================
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# 6. 统计量计算
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# ============================================================
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total_selections = MC * N_RF
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P_hit_full = full_hit_total / total_selections
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P_clutter_full = full_clutter_total / total_selections
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P_out_full = full_out_total / total_selections
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P_hit_tsc = tsc_hit_total / total_selections
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P_clutter_tsc = tsc_clutter_total / total_selections
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P_out_tsc = tsc_out_total / total_selections
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print("==================================================")
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print(f"阵列类型: {ARRAY_TYPE}")
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print(f"SNR = {SNR_dB:.1f} dB, INR = {INR_dB:.1f} dB, 快拍数 = {L_snapshots}, MC = {MC}")
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print("--------------------------------------------------")
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print("传统 OMP（全空间字典）:")
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print(f"目标扇区命中率 P_hit = {P_hit_full:.4f}")
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print(f"杂波误选率 P_clutter = {P_clutter_full:.4f}")
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print(f"扇区外误选率 P_out = {P_out_full:.4f}")
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print("--------------------------------------------------")
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print("TSC-OMP（目标扇区约束字典）:")
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print(f"目标扇区命中率 P_hit = {P_hit_tsc:.4f}")
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print(f"杂波误选率 P_clutter = {P_clutter_tsc:.4f}")
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print(f"扇区外误选率 P_out = {P_out_tsc:.4f}")
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print("==================================================")
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# 保存统计结果到 txt
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with open(os.path.join(save_dir, 'pseudo_peak_statistics.txt'), 'w', encoding='utf-8') as f:
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f.write(f"阵列类型: {ARRAY_TYPE}\n")
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f.write(f"SNR = {SNR_dB:.1f} dB, INR = {INR_dB:.1f} dB, 快拍数 = {L_snapshots}, MC = {MC}\n\n")
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f.write("传统 OMP（全空间字典）:\n")
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f.write(f"P_hit = {P_hit_full:.6f}\n")
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f.write(f"P_clutter = {P_clutter_full:.6f}\n")
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f.write(f"P_out = {P_out_full:.6f}\n\n")
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f.write("TSC-OMP（目标扇区约束字典）:\n")
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f.write(f"P_hit = {P_hit_tsc:.6f}\n")
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f.write(f"P_clutter = {P_clutter_tsc:.6f}\n")
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f.write(f"P_out = {P_out_tsc:.6f}\n")
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# ============================================================
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# 7. 画图1：第一步投影谱对比（最适合论文说明“伪峰”）
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# ============================================================
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fig1, axes = plt.subplots(2, 1, figsize=(10, 9))
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# 上图：传统OMP第一步投影谱
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ax = axes[0]
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ax.plot(full_grid, rep_full_proj0, 'b-', linewidth=1.8, label='传统OMP第一步投影谱')
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ax.axvline(target_angle, color='g', linestyle='--', linewidth=1.5, label=f'目标 {target_angle:.2f}°')
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ax.axvline(clutter_angle, color='r', linestyle='--', linewidth=1.5, label=f'杂波 {clutter_angle:.2f}°')
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# 标出目标扇区
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ymax = 1.05 * np.max(rep_full_proj0)
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rect = Rectangle((sector_min, 0), sector_max - sector_min, ymax,
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facecolor='green', alpha=0.10, edgecolor=None)
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ax.add_patch(rect)
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ax.text((sector_min + sector_max) / 2, 0.93 * ymax, '目标扇区', color='green',
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ha='center', va='top', fontsize=11)
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# 标出杂波邻域
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rect2 = Rectangle((clutter_angle - clutter_band_half, 0), 2 * clutter_band_half, ymax,
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facecolor='red', alpha=0.10, edgecolor=None)
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ax.add_patch(rect2)
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ax.text(clutter_angle, 0.80 * ymax, '杂波邻域', color='red',
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ha='center', va='top', fontsize=11)
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# 标出传统OMP选中的角度
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for idx, ang in enumerate(rep_full_chosen):
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val = rep_full_proj0[np.argmin(np.abs(full_grid - ang))]
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ax.plot(ang, val, 'ko')
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ax.text(ang, val + 0.02 * ymax, f'{idx+1}:{ang:.1f}°', fontsize=9, ha='center')
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ax.set_title('传统OMP第一步投影谱', fontsize=13, fontweight='bold')
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ax.set_xlabel('角度 (°)')
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ax.set_ylabel(r'$|a^H(\theta)r^{(0)}|$')
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ax.grid(True, linestyle='--', alpha=0.5)
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ax.set_xlim([-90, 90])
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ax.legend(loc='upper right', fontsize=10)
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# 下图：TSC-OMP第一步投影谱
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ax = axes[1]
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ax.plot(tsc_grid, rep_tsc_proj0, 'm-', linewidth=1.8, label='TSC-OMP第一步投影谱')
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ax.axvline(target_angle, color='g', linestyle='--', linewidth=1.5, label=f'目标 {target_angle:.2f}°')
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for idx, ang in enumerate(rep_tsc_chosen):
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val = rep_tsc_proj0[np.argmin(np.abs(tsc_grid - ang))]
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ax.plot(ang, val, 'ko')
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ax.text(ang, val + 0.02 * np.max(rep_tsc_proj0), f'{idx+1}:{ang:.1f}°', fontsize=9, ha='center')
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ax.set_title('TSC-OMP第一步投影谱', fontsize=13, fontweight='bold')
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ax.set_xlabel('角度 (°)')
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ax.set_ylabel(r'$|a^H(\theta)r^{(0)}|$')
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ax.grid(True, linestyle='--', alpha=0.5)
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ax.set_xlim([sector_min, sector_max])
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ax.legend(loc='upper right', fontsize=10)
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plt.tight_layout()
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fig1.savefig(os.path.join(save_dir, f'Fig1_projection_compare_{ARRAY_TYPE}.png'), dpi=300, bbox_inches='tight')
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# ============================================================
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# 8. 画图2：被选原子角度分布直方图
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# ============================================================
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fig2, axes = plt.subplots(2, 1, figsize=(10, 8), sharex=False)
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|
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# 传统OMP
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ax = axes[0]
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bins_full = np.arange(-90, 90 + 1, 1.0)
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ax.hist(all_angles_full, bins=bins_full, color='steelblue', edgecolor='black', alpha=0.85)
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ax.axvline(target_angle, color='g', linestyle='--', linewidth=1.5, label='目标')
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ax.axvline(clutter_angle, color='r', linestyle='--', linewidth=1.5, label='杂波')
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ax.axvspan(sector_min, sector_max, color='green', alpha=0.10, label='目标扇区')
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ax.set_title('传统OMP所选原子角度分布', fontsize=13, fontweight='bold')
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ax.set_xlabel('被选原子角度 (°)')
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ax.set_ylabel('出现次数')
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ax.grid(True, linestyle='--', alpha=0.5)
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ax.legend(fontsize=10)
|
|
|
|
# TSC-OMP
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ax = axes[1]
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bins_tsc = np.arange(sector_min, sector_max + 0.2, 0.2)
|
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ax.hist(all_angles_tsc, bins=bins_tsc, color='orchid', edgecolor='black', alpha=0.85)
|
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ax.axvline(target_angle, color='g', linestyle='--', linewidth=1.5, label='目标')
|
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ax.axvspan(sector_min, sector_max, color='green', alpha=0.10, label='目标扇区')
|
|
ax.set_title('TSC-OMP所选原子角度分布', fontsize=13, fontweight='bold')
|
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ax.set_xlabel('被选原子角度 (°)')
|
|
ax.set_ylabel('出现次数')
|
|
ax.grid(True, linestyle='--', alpha=0.5)
|
|
ax.legend(fontsize=10)
|
|
|
|
plt.tight_layout()
|
|
fig2.savefig(os.path.join(save_dir, f'Fig2_hist_compare_{ARRAY_TYPE}.png'), dpi=300, bbox_inches='tight')
|
|
|
|
# ============================================================
|
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# 9. 画图3：伪峰统计指标柱状图
|
|
# ============================================================
|
|
fig3, ax = plt.subplots(figsize=(9, 6))
|
|
|
|
metrics = ['目标扇区命中率', '杂波误选率', '扇区外误选率']
|
|
omp_values = [P_hit_full, P_clutter_full, P_out_full]
|
|
tsc_values = [P_hit_tsc, P_clutter_tsc, P_out_tsc]
|
|
|
|
x = np.arange(len(metrics))
|
|
width = 0.34
|
|
|
|
bars1 = ax.bar(x - width/2, omp_values, width, label='传统OMP', color='steelblue')
|
|
bars2 = ax.bar(x + width/2, tsc_values, width, label='TSC-OMP', color='orchid')
|
|
|
|
for bars in [bars1, bars2]:
|
|
for b in bars:
|
|
h = b.get_height()
|
|
ax.text(b.get_x() + b.get_width()/2, h + 0.01, f'{h:.3f}',
|
|
ha='center', va='bottom', fontsize=10)
|
|
|
|
ax.set_xticks(x)
|
|
ax.set_xticklabels(metrics, fontsize=11)
|
|
ax.set_ylim([0, 1.08])
|
|
ax.set_ylabel('概率 / 比例', fontsize=12)
|
|
ax.set_title('传统OMP与TSC-OMP伪峰统计指标对比', fontsize=13, fontweight='bold')
|
|
ax.grid(True, axis='y', linestyle='--', alpha=0.5)
|
|
ax.legend(fontsize=11)
|
|
|
|
plt.tight_layout()
|
|
fig3.savefig(os.path.join(save_dir, f'Fig3_stat_compare_{ARRAY_TYPE}.png'), dpi=300, bbox_inches='tight')
|
|
|
|
# ============================================================
|
|
# 10. 显示图像
|
|
# ============================================================
|
|
plt.show() |