Signal Compensation of Coaxial Cable Based on Modified Non-negative Tikhonov Regularization Method within Bayesian Inference
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摘要: 随着信号频率、带宽及传输距离的增大，信号在同轴电缆传输过程中的畸变问题变得越来越严重。特别地，如果同轴电缆在使用过程中还意外地遭受了挤压、拉伸或折叠，信号畸变问题将会变得更加严重。该文基于贝叶斯推理的非负Tikhonov正则化方法，提出一种改进的信号补偿方法。该方法可有效规避逆分析中的病态矩阵问题，利用同轴电缆的冲击响应函数，并结合输出端口的测量信号，即可实现输入信号的重构。并以长度15 m的受挤压同轴电缆为对象，采用此方法对3种不同样式的脉冲信号(双指数脉冲信号、调制方波信号、双极脉冲信号)进行了传输畸变补偿。结果表明：该方法均能实现优异的补偿效果，补偿后信号与输入信号间偏差远远低于传统的衰减补偿法。并且，该方法具有较强的鲁棒性，当信噪比大于30 dB时，即可保持好的稳定性。
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关键词:
- 信号补偿 /
- 改进的非负Tikhonov正则化方法 /
- 同轴电缆
Abstract: With the increase of signal frequency, bandwidth and transmission distance, the signal distortion problem brought by the coaxial cable becomes serious and can not be ignored. Specifically, if the coaxial cable is accidentally squeezed, stretched or folded during use, the signal distortion problem will become more serious. Herein, a modified signal compensation method is proposed based on the non-negative Tikhonov regularization method with Bayesian inference. This method can effectively avoid the ill-conditioned matrix problem in the inverse analysis. The input signal can be reconstructed by using impulse response function of coaxial cable and measured output signal. Three different types of pulse signals, i.e., double exponential pulse signal, modulated square wave signal, and bipolar pulse signal, transmitted in a 15 m extruded coaxial cable are compensated. The results show that this method can achieve excellent compensation effect, and the deviation between the compensated signal and the input signal is far lower than that of typical attenuation compensation method. Moreover, the modified method exhibits strong robustness. When the signal-to-noise ratio is larger than 30 dB, it can maintain good stability. -
表 1 输出信号、采用改进补偿方法补偿后信号与输入信号间相对偏差(%)
信号样式 输出与输入信号偏差 补偿与输入信号偏差 双指数脉冲信号 16.5 1.5 调制方波信号 24.4 2.4 双极脉冲信号 25.3 2.3 
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表 3 不同信噪比下改进补偿方法补偿后信号与输入信号间相对偏差(%)
信号样式 45 dB 40 dB 35 dB 30 dB 25 dB 20 dB 双指数脉冲信号 1.5 1.5 1.7 3.4 11.1 17.0 调制方波信号 2.4 2.5 2.8 6.3 19.1 33.1 双极脉冲信号 2.3 2.5 3.0 6.5 18.6 28.3
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表 4 不同信噪比下衰减补偿法补偿后信号与输入信号间相对偏差(%)
信号样式 45 dB 40 dB 35 dB 30 dB 25 dB 20 dB 双指数脉冲信号 9.0 9.3 12.0 17.2 22.0 31.0 调制方波信号 10.5 11.1 15.5 22.5 27.5 35.5 双极脉冲信号 13.3 13.7 16.3 24.3 29.3 36.3
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