The effect of parameters on the signal compensation performance in the modified non-negative Tikhonov regularization method within a Bayesian frame

Abstract

Recently, a modified non-negative Tikhonov regularization method within the Bayesian frame is successfully proposed, and has been demonstrated to have excellent compensation performance towards the signal distortion induced by the long-distance transmission in coaxial cable. However, how the parameters of this modified method affecting the compensation performance has not yet been investigated and analyzed, which may in turn bring some obstacles in the practical utilizations of this modified method. Herein, we carried out a systematic study on the effect of parameters on the signal compensation performance of this modified method. The bias constant D has almost no influence on the compensation performance if the unknown input signal satisfies the non-negative constraint. When the signal-to-noise ratio (SNR) is less than 40 dB, the compensation performance is continuously improved as the SNR increases. Once the SNR attains ~40 dB, the compensated signal is nearly identical to the input signal. Further increment of SNR cannot give rise to an improved compensation performance, the relative error (RE) in between the compensated signal and input signal nearly keeps unchanged. The sampling frequency interval ∆f of S21 should satisfy the restriction of ∆f=Fs/n, with Fs and n representing the sampling frequency of digital oscilloscope and number of points of the output signal, respectively. The compensation performance maintains excellent initially, whereas it rapidly deteriorates as ∆f exceeds a certain value that is highly related to the length of impulse response function. This study can provide a beneficial reference for the application of the modified signal compensation method.