In this paper, we propose a reconstruction approach for a multiple-sinusoidal signal. The signal reconstruction requires a small number of samples and is based on a sub-Nyquist sampling scheme with dual rate channels. In the proposed sampling scheme, the samples are grouped into multiple cosets. To obtain enough different cosets to reconstruct a signal, the sampling rates of channels are required to be relative coprime. For each coset, the Whittaker–Shannon interpolation formula is employed to construct the relation between the sub-Nyquist samples and the original signal, which is used to construct the measurement matrix. Since the multiple-sinusoidal signal is sparse in the frequency domain, compressed sensing theory can be adopted to reconstruct the signal. Simulation results are reported to demonstrate the feasibility and effectiveness of the proposed approach.
The time-interleaved analog-to-digital converters (TIADCs) technique is an efficient solution to improve the sampling rate of the acquisition system with low-speed ADCs. However, channel mismatches such as gain mismatch, time skew mismatch, and offset mismatch may seriously degrade the performance of TIADC. Furthermore, for high-speed signal acquisition, the gain and time skew mismatches would vary with the signal frequency, and the traditional fixed model does not work any longer. In this paper, a series of sinusoidal signals are adopted to estimate the variable mismatches. First, an autocorrelation-based approach is presented to estimate the gain mismatch. The information about the gain mismatch is extracted from the autocorrelation function of sub-ADC output samples. Then, the time skew mismatch is estimated by utilizing the particle swarm optimization algorithm. The reported simulation results show that the mismatches can be accurately estimated. Finally, a commercial 12.5 GSPS four-channel TIADC system is utilized to verify the performance of the proposed method. The spurious free dynamic range of the system can be improved by about 20 dB, and the effectiveness of the proposed estimation method is demonstrated.
The wideband spectrum estimation is an essential step in the wireless network. In order to avoid employing power-hungry high-rate analog-to-digital converters (ADCs), the CS-based sub-Nyquist sampling approaches are used to estimate the wideband spectrum. In this paper, we propose a sub-Nyquist sampling system based on the analog to information converter (AIC), and the proposed system is constructed by multiple parallel channels with a banks of low pass filters. The system model is constructed in the time domain. To estimate the power spectrum, we define a new power spectrum of samples with a finite length, called the circular power spectrum (CPS), served as the aim we strive to estimate. The defined CPS can clearly reflect the power of the signal varying with frequency and is also with the same length as the equivalent digital samples. The experimental results indicate that the defined CPS can be successfully estimated from samples captured by the proposed sub-Nyquist sampling system whose overall sampling rate is much lower than the Nyquist rate.
Compressive sensing (CS) aims at decreasing sampling rate to reduce the needed number of samples. On the other hand, the one-bit CS is proposed to reduce the quantization bit. In this paper, we proposed a one-bit CS system aiming at acquiring the multiband sparse signal which is a very popular signal model in wireless communication, especially in cognitive radio. This proposed system, called direct one-bit sampler (DOS), is simple in hardware implementation, and it consists of only a comparator working at Nyquist rate. In the stage of signal reconstruction, it can be equivalent to a special multicoset sampler which is a popular scheme in CS. Moreover, we propose an enhanced binary iterative hard thresholding (BIHT), a popular one-bit recovery algorithm, to deal with the multiple measurement vectors in the one-bit CS framework. Both the theoretical model and experimental results demonstrate that the proposed DOS, with the help of the enhanced BIHT, can not only accurately recover the positions of active subbands of the multiband sparse signal but also roughly estimate the power of each active subband.
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