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Transient Interference Suppression Algorithm Based on Time Frequency Sparse Prior for Skywave OTHR
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摘要: 针对瞬态干扰严重影响天波超视距雷达(OTHR)目标检测性能的问题，提出了一种基于时频稀疏先验(TFSP)的瞬态干扰抑制算法。TFSP同时利用了瞬态干扰在慢时域的稀疏先验以及海杂波和目标在多普勒频域的稀疏先验构造目标函数，通过交替方向乘子法(ADMM)进行最优化以实现瞬态干扰抑制。不同于现有算法“干扰定位—剔除—数据恢复”的处理步骤，TFSP能够直接分离瞬态干扰分量并恢复无干扰频谱。最后，通过OTHR实测数据实验验证了TFSP在对海和对空模式下均能得到良好的瞬态干扰抑制结果，相比于多数现有方法，TFSP具有更高的输出信噪比(SNR)以及更高的运算效率，其输出SNR增加了3～5 dB，运算复杂度仅为线性对数阶。Abstract: The target detection performance of skywave Over-the-Horizon Radar (OTHR) often struggles with transient interference. To address this issue, we have developed a transient interference suppression algorithm that uses Time Frequency Sparsity Prior (TFSP). TFSP uses the sparse nature of transient interference in the slow-time domain along with the sparse prior of sea clutter and targets in the Doppler frequency domain to construct an objective function, that is optimized using the Alternating Direction Method of Multipliers (ADMM) to effectively suppress transient interference. Unlike traditional methods that focus on locating and eliminating interference before recovering data, TFSP can directly separate transient interference components and restore an interference-free Doppler spectrum. Experimental results from OTHR data confirm that TFSP effectively suppresses transient interference in sea and air modes. TFSP offers a higher output Signal-to-Noise Ratio (SNR) and higher computational efficiency than most existing methods. In particular, it increases the output SNR by approximately 3～5 dB while maintaining computational complexity at a linear logarithmic order.
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图 2 CS瞬态干扰抑制方法示意图
Figure 2. Schematic diagram of CS transient interference suppression method
图 3 TFSP瞬态干扰抑制方法示意图
Figure 3. Schematic diagram of TFSP transient interference suppression method
图 4 两种探测模式下改变$ {\gamma _1} $与$ \gamma $的NMSE
Figure 4. NMSE when changing $ {\gamma _1} $ and $ \gamma $ in two detection modes
图 5 对海模式下慢时域TFSP瞬态干扰抑制结果
Figure 5. Sea mode TFSP interference suppression result in slow time domain
图 6 对海模式下各算法RD域瞬态干扰抑制结果
Figure 6. Sea mode transient interference suppression results of each algorithm in RD domain
图 7 对海模式下各算法多普勒域瞬态干扰抑制结果
Figure 7. Sea mode transient interference suppression results of each algorithm in Doppler domain
图 8 对空模式下慢时域TFSP瞬态干扰抑制结果
Figure 8. Air mode TFSP interference suppression result in slow time domain
图 9 对空模式下各算法RD域瞬态干扰抑制结果
Figure 9. Air mode transient interference suppression results of each algorithm in RD domain
图 10 对空模式下各算法多普勒域瞬态干扰抑制结果
Figure 10. Air mode transient interference suppression results of each algorithm in Doppler domain
图 11 乘法次数随向量维度变化的曲线
Figure 11. The curve of multiplication times changing with vector dimension
1 TFSP算法
1. TFSP algorithm
输入：受瞬态干扰的慢时域信号y、参数$\gamma $, ${\gamma _1}$, $\rho = 0.1$，最大
迭代次数$K = 100$；输出：慢时域瞬态干扰分量o、纯净频谱x； 初始化：初始向量$ {\boldsymbol{o}} = {\bf{0}} $, $ {\boldsymbol{x}} = {\bf{0}} $, $ {\boldsymbol{n}} = {\bf{0}} $, $ {\boldsymbol{b}} = {\bf{0}} $，中间变量
$ {\boldsymbol{u}} = {\bf{0}} $，初始化迭代次数$k = 1$；执行迭代$k = 1,2, \cdots ,K$ 计算梯度$ \nabla {g^k}\left( {\boldsymbol{o}} \right) = {{\boldsymbol{o}}^k} - {\boldsymbol{y}} + \sqrt M {\mathrm{IFFT}}\left( {{{\boldsymbol{x}}^k} + {{\boldsymbol{n}}^k} - {{\boldsymbol{b}}^k}/\rho } \right) $； 通过式(18)更新$ {{\boldsymbol{o}}^{k + 1}} $； 更新中间变量$ {{\boldsymbol{u}}^{k + 1}} = {\mathrm{FFT}}\left( {{\boldsymbol{y}} - {{\boldsymbol{o}}^{k + 1}}} \right)/\sqrt M $ 更新$ {{\boldsymbol{x}}^{k + 1}} = {\mathcal{P}_{\left( {{\gamma _1}/\rho } \right){\ell _1}}}\left( {{{\boldsymbol{u}}^{k + 1}} - {{\boldsymbol{n}}^k} + {{\boldsymbol{b}}^k}/\rho } \right) $； 更新$ {{\boldsymbol{n}}^{k + 1}} = \left( {{{\boldsymbol{b}}^k} + \rho \left( {{{\boldsymbol{u}}^{k + 1}} - {{\boldsymbol{x}}^{k + 1}}} \right)} \right)/\left( {\rho + 1} \right) $； 更新$ {{\boldsymbol{b}}^{k + 1}} = {{\boldsymbol{b}}^k} + \tau \rho \left( {{{\boldsymbol{u}}^{k + 1}} - {{\boldsymbol{x}}^{k + 1}} - {\boldsymbol{{n}}^{k + 1}}} \right) $； 更新迭代次数$k = k + 1$； 当满足$k > K$或$\left\| {{{\boldsymbol{x}}^{k + 1}} - {{\boldsymbol{x}}^k}} \right\|_2^2/\left\| {{{\boldsymbol{x}}^k}} \right\|_2^2 < {10^{ - 6}}$时； 停止迭代 
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表 1 各算法的运行时间(s)
Table 1. Running time of each algorithm (s)
算法 对海模式的运行时间 对空模式的运行时间 FFT(对比) 0.021 0.007 AR模型 0.13 0.05 鲁棒平滑 572.51 3.27 PRCA-SVT 3252.78 42.03 IALM 15521.43 73.24 FACAMP 17.51 0.87 TFSP 3.42 0.72
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