# An Improved Signal Reconstruction of Modulated Wideband Converter Using a Sensing Matrix Built upon Synchronized Modulated Signals

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## Abstract

Modulated wideband converter is a multi-branch compressed sampling structure in which each branch aliases the sparse input spectrum into a narrow band by mixing a pseudo-random local oscillator (LO) bit sequence. Based on the low-pass sampling sequences of the narrow bands and the sensing matrix which defines the weights of aliasing, the input signal can be recovered by compressed sensing reconstructing algorithms. Because the distortion in the hardware implementation is ignored, the calculated sensing matrix, which is obtained by directly expanding the Fourier values of the LO sequences, cannot lead a satisfactory signal reconstruction. To solve this problem, this paper proposed the concept of relative sensing matrix and considered these distortions as a part of the sensing matrix. To measure the relative sensing matrix, this paper also designs a triggering-based measurement system excited by wideband modulated signals. The system is synchronized by the trigger which controls the restart of input signals, LO sequences, and ADCs. Compared with the classical sinusoidal signals measurement system, the wideband modulated signals are more accessible to be synchronized by the trigger for their identifiable envelope header. A dual-carrier 5 MHz signal is injected to the receiver at a signal noise ratio of 37 dB, with the measured sensing matrix; the two baseband signals are reconstructed with the normalized mean-squared error (NMSE) reaching − 21.05 dB and − 19.72 dB, respectively. This result is much better than the baseband signals reconstructed by the calculated sensing matrix which only have the NMSE of − 7.47 dB and − 6.70 dB.

## Keywords

Modulated wideband converter Compressed sensing Hardware implementation Calibration Sensing matrix## Notes

### Funding

Funding was provided by National Natural Science Foundation of China (Grant No. 61571080).

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