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Traditional parallel multi-coset sampling (MCS), which has several sub-Analog-to-Digital-Converters (sub-ADCs) working parallelly, is an attractive sub-Nyquist sampling technique for wideband sparse signals. However, the mismatch among sub-ADCs in traditional parallel MCS, such as bias, gain, and timing skew mismatch, degrades the signal acquisition performance greatly. In this paper, a serial MCS scheme based on clocking single ADC with nonuniform clock is proposed. The nonuniform sampling clock is generated by a pseudo-random binary sequence generator. An additional Sample/Hold (S/H) is used to improve the analog bandwidth of the serial MCS. Moreover, universal sampling pattern is designed for the proposed serial MCS. The sampling pattern design should not only maximize the Kruskal rank of compressed sensing matrix but also take the ADC’s sub-Nyquist sampling rate into consideration. Numeral experiments are presented demonstrating that the mismatch among sub-ADCs in traditional parallel MCS degrades the reconstruction performance greatly, and the proposed serial MCS can avoid the mismatch tactfully.

Wideband sparse signal is also called a multiband signal. Its frequency support concentrates on several continuous intervals and is distributed over a wide spectrum [

The joint sparsity of multiband signal can be utilized to reduce the sampling rate requirement. Several sub-Nyquist sampling techniques have been proposed to acquire multiband signal at a sub-Nyquist rate [

In this paper, a serial multi-coset sampling scheme based on clocking single ADC with nonuniform clock is proposed. The nonuniform clock is generated by the pseudo-random binary sequence generator. An additional Sample/Hold (S/H) is used to improve the analog bandwidth of the proposed serial MCS. Moreover, universal sampling pattern is designed for the proposed serial MCS. The sampling pattern design should not only maximize the Kruskal rank of compressed sensing matrix but also take the ADC’s sub-Nyquist sampling rate into consideration. Although the sampling rate requirement of the ADC based on the proposed serial MCS is higher than that of the traditional parallel MCS, the proposed MCS does not exist channel mismatch problem and its size is smaller. Numeral experiments are presented demonstrating the proposed serial MCS has a better reconstruction performance than the traditional parallel MCS.

Let

The frequency support of

Typical wideband sparse signal.

We wish to design a sampling system and it should have the following properties: first, sampling rate requirement should be as low as possible; second, the position of active subbands is not available beforehand for both the sampling and reconstruction stage; third, the proposed sampling system is supposed to only use currently available integrated circuits.

Let

Figure

Block diagram of the traditional parallel MCS.

An overview of the proposed serial MCS is shown in Figure

Block diagram of the proposed serial MCS.

Sampling process of the proposed serial MCS.

Let

For practical application consideration, the nonuniform sampling clock is provided by a pseudo-random binary sequence generator. The current state-of-the-art PRBS generator can reach alteration rate of 80GHz [

The output voltage of S/H drifts slowly when it is in the hold mode. The drift is caused by the current leakage of the hold capacitor of the S/H, and the output voltage of S/H decays as the hold time increases. According to the datasheet of S/H (HMC760LC4B), the drift consists of two parts. One part is fixed, and the other part has a linear relationship with the hold voltage. The total drift can be approximated by

The proposed serial MCS has a higher sampling rate requirement for the ADC than the traditional parallel MCS. The sampling rate requirement for ADC is

The connection between the continuous time Fourier transform of input signal

The frequency support of

A sampling pattern

From the above description, the selection of

Let the sampling pattern

Matrix

The performance of the proposed serial MCS is evaluated with the following signal:

In the first experiment, we test the feasibility of the proposed serial MCS. Reconstruction result is compared with the traditional parallel MCS. The mismatch parameters are set as follows: the timing skew mismatch is 2% of the Nyquist sampling interval; the bias and gain mismatch are both 2% of the maximal signal amplitude. Original signal spectrum is shown in Figure

Original spectrum.

Reconstructed spectrum by proposed serial MCS.

Reconstructed spectrum by traditional parallel MCS.

In the second experiment, we investigate the reconstruction performance with respect to each kind of mismatch separately. 200 trials are performed for each experiment. Figures

Reconstruction performance (only bias mismatch).

Reconstruction performance (only gain mismatch).

Reconstruction performance (only timing skew mismatch).

In the third experiment, we investigate the reconstruction performance with respect to different input SNR over the range

Reconstruction performance with respect to input SNR.

In the fourth experiment, in order to demonstrate the validity of the proposed MCS for other signal, Quadrature Phase-Shift Keying (QPSK) signal is used as the test signal. It is generated by the following model:

It is shown in Figure

Reconstruction performance with respect to input SNR.

A serial MCS is proposed based on clocking single ADC with nonuniform clock for acquiring wideband sparse signal. The design of universal sampling pattern is also included for the proposed serial MCS. Compared with the traditional parallel MCS, the proposed serial MCS does not exist the mismatch among sub-ADCs, so higher dynamic range can be obtained. Simulation results show that the proposed serial MCS has a better reconstruction performance than the traditional parallel MCS.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.