Efficient Implementation of Mixing Sequence-Based Van der Pol–Duffing System on the Modulated Wideband Converter Compressed Sensing Scheme

In practical systems, the modulated wideband converter (MWC), known as a sub-Nyquist sampling scheme for blind spectrum detection in compressed sensing (CS) theory, is used to reduce the Nyquist frequency for energy efficiency and low-cost computation. In the implementation of the MWC, the Bernoulli random mixing sequence is considered optimal to efficiently recover sparse spectra and is usually at high cost for most current sub-sampling systems. This work firstly exploits a Van der Pol–Duffing (VdPD) nonlinear dynamical system in electric circuits, which is easy to be found in practice with extremely low cost and low energy, to generate a random mixing sequence with a flexible length and then characterizes the efficient implementation of the VdPD mixing sequence on the MWC under the CS conditions. The results show that the VdPD random mixing sequence method for the MWC approaches the optimal Bernoulli method under different practical considerations of mixing sequence length and random power levels of wideband signal and outperforms other existing ones in terms of the correct detection rate and the false alarm rate. These results also show that there exists an optimum ratio of MWC physical channels and mixing sequence length, which is about 30 percent, to maximize the correct detection probability. Compared to any other mixing sequence, the VdPD mixing sequence has an advantage of flexible length with no synchronization error in practice. This indicates the practical and efficient implementation of the random mixing sequence generated by the VdPD system on the MWC scheme.