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

Recently, a modified non-negative Tikhonov regularization method within the Bayesian frame has been successfully proposed, and demonstrated to have excellent compensation performance towards the signal distortion induced by long-distance transmission in coaxial cable. However, how the parameters of this modified method affect compensation performance has not yet been investigated and analyzed, which may in turn bring some obstacles in the practical utilization 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 does not give rise to an improved compensation performance and the relative error between the compensated signal and input signal remains nearly unchanged. The sampling frequency interval Δf of S21 should satisfy the restriction of Δf=Fs/n , with Fs and n representing the sampling frequency of the digital oscilloscope and number of points of the output signal, respectively. The compensation performance is excellent initially, whereas it rapidly deteriorates once Δf exceeds a certain value that is highly related to the length of the impulse response function. This study provides a beneficial reference for application of the modified signal compensation method.