Optimal choice of signal compensation in coaxial cable: Modified non-negative Tikhonov regularization method within Bayesian frame

Abstract

As a key medium for signal transmission, coaxial cable is widely used in various fields such as television broadcast, communication and radar system. With the increase of signal frequency, bandwidth and transmission distance, the distortion problem brought by the coaxial cable becomes serious and cannot be ignored. Specifically, the coaxial cable often encounters accidental extrusion, stretching or folding, and becomes deformed during use, which will cause more serious distortion to the transmitted signal. Inspired by the inverse analysis approach, we propose a modified signal compensation method on the basis of the non-negative Tikhonov regularization method with Bayesian inference. The modified method doesn’t have non-negative constraint to the input signal. The modified method is firstly employed for the compensation of double exponential pulse, whose waveform is identical to that of high-altitude nuclear electromagnetic pulse signal, transmitted in a 10-m coaxial cable. The compensated signal is almost the same to the input signal, the relative error (RE) in between the compensated signal and input signal is only 0.6%, which is much smaller than that of output signal and input signal (10.1%). Moreover, the modified method is utilized to compensate other three types of signals, and the compensated signals match well with the input signals. Furthermore, the compensation results for these four types of signals of the modified method are compared with those by using one of the most commonly used de-convolution method, i.e., inverse filtering method, which considers both the amplitude and phase response. The REs vary from 5.0% to 8.4% for the inverse filtering method. In contrast, the maximum RE for the modified method is below 1.1%, demonstrating a significantly improved performance in the signal compensation.