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The purpose of this paper is to present a compressed sensing (CS)-based sampling system for ultra-wide-band (UWB) signal. By exploiting the sparsity of signal, this new sampling system can sub-Nyquist sample a multiband UWB signal, whose unknown frequency support occupies only a small portion of a wide spectrum.

A random Rademacher sequence is used to sense the signal in the frequency domain, and a matrix constructed by Hadamard basis is used to compress the signal. The probability of reconstruction is proved mathematically, and the reconstruction matrix is developed in the frequency domain.

Simulation results indicate that, with an ultra-low sampling rate, the proposed system can capture and reconstruct sparse multiband UWB signals with high probability. For sparse multiband UWB signals, the proposed system has potential to break through the Shannon theorem.

Different from the traditional sub-Nyquist techniques, the proposed sampling system not only breaks through the limitation of Shannon theorem but also avoids the barrier of input bandwidth of analog-to-digital converters (ADCs).

The purpose of this paper is to present a model calibration technique for modulated wideband converter (MWC) with non-ideal lowpass filter. Without making any change to the system architecture, at the cost of a moderate oversampling, the calibrated system can perform as the system with ideal lowpass filter.

A known test sparse signal is used to approximate the finite impulse response (FIR) of the practical non-ideal lowpass filter. Based on the approximated FIR filter, a digital compensation filter is designed to calibrate the practical filter. The calibrated filter can meet the perfect reconstruction condition. The non-ideal sub-Nyquist samples are filtered by a compensation filter.

Experimental results indicate that, by calibrating the MWC with the proposed algorithm, the impaction of non-ideal lowpass filter could be avoided. The performance of signal reconstruction could be improved significantly.

Without making any change to the MWC architecture, the proposed algorithm can calibrated the non-ideal lowpass filter. By filtering the non-ideal sub-Nyquist samples with the designed compensation filter, the original signal could be reconstructed with high accuracy.