Cascaded Compensation of Filter Phase Imperfections in Random Demodulation

Analog-to-information converter (AIC) is an architecture that implements the compressive sensing (CS) theory and it is capable to generate compressed and digitized output directly from an analog input. Unfortunately, the hardware implementation of AIC inevitably faces the impact of non-ideal factors in the devices. The calibration link is crucial and can have a significant impact on the quality of the signal reconstruction at the back end of the AIC. Random Demodulation (RD) is one of the AICs with a simple structure, and its own structure and calibration link are relatively easy to implement. Low-pass filtering plays an important role in the RD analog acquisition process. In the back-end of the AIC, the impulse response of the low-pass filter in the time domain is constructed as part of the measurement matrix, which directly affects the accuracy of the signal reconstruction in the digital part of the AIC. Existing calibrations mostly focus on amplitude calibration, while the phase distortion of the low-pass filter reduces the accuracy of signal recovery in the RD, which is hardly considered in the calibrations of low-pass filters. To tackle this problem, a Cascaded compensation method of filter phase imperfections is designed, in which a specific all-pass filter is cascaded with the original phase distortion filter so that the phase of the cascaded filters is linear. Comparative simulation experiments were obtained for input signals with different sparsity. The results show that the Signal-to-Noise Ratio (SNR) is significantly improved by using the cascaded phase compensation method, which demonstrates that the proposed method is effective.