Orthogonal circulant structure and chaotic phase modulation based analog to information conversion

- A novel orthogonal circulant structure and chaotic phase modulation based modulated wideband converter (OCSCPM-MWC) is proposed. In order to realize spectrum-blind sub-Nyquist sampling of sparse multiband analog signal, we are inspired to spread the input signal to the whole spectrum by taking advantage of chaos phase modulation. The motivation is that chaos is easily implemented in hardware circuit and performs with sharp autocorrelation function and wideband power spectrum property.
- A thorough theoretical analysis to our proposed OCSCPM-MWC method is conducted, which yielding some useful theoretical guarantees. The analysis consists of three parts: (i) We demonstrate that the number of measurements required for both uniform and non-uniform recovery are optimal. (ii) Moreover, we derive the theoretical condition that guarantees OCSCPM-MWC to satisfy expected restricted isometry property (ExRIP). Compared with the conservative conditions of RIP, ExRIP could provide practical and reasonable theoretical guarantees for signal recovery in MWC. (iii) We analyze the impact of both measurement noise and signal noise which exists in the signal before acquisition in OCSCPM-MWC system, respectively.
- Sufficient computer simulations are carried out under different situations and they confirm the effectiveness of the proposed approach.

Modulated wideband converter (MWC) is used to implement analog to information conversion (AIC) to realize sub-Nyquist sampling of sparse multiband analog signal. In this paper, we combine orthogonal circulant matrix with chaos to develop an orthogonal circulant structure and chaotic phase modulation based modulated wideband converter (OCSCPM-MWC). Firstly, random waveforms of different channels in the system correspond to the row vectors of measurement matrix. We use the frequency-domain approach to construct orthogonal circulant matrix. The waveforms of different channels can be generated by various cyclic shifts of the same original waveform and orthogonal to each other. This can greatly reduce the degrees of freedom of the random waveforms, and a superior recovery performance can be obtained. Secondly, we construct chaotic phases of generating elements of orthogonal circulant matrix. The input signal is modulated according to the power spectrum of chaos. We derive the theoretical condition for the orthogonal circulant measurement matrix to satisfy expected restricted isometry property (ExRIP). In addition, we analyze the impact of measurement noise and signal noise on the OCSCPM-MWC system, respectively. Computer simulations are carried out under different situations and they confirm the effectiveness of the proposed approach.