Compressive sensing with sub-Nyquist clocks using frequency division multiplexed random sequences

Compressive sensing is a newly emerging theory that provides the means to recover a signal from samples obtained at a sub-Nyquist rate. This in turn leads to tremendous reduction in power consumption of receivers because of the direct correlations between the sampling rate and power consumption of analog-to-digital converters, which constitutes a considerable amount of the receiver´s power consumption. In this paper, we propose an architecture for the random demodulator, which is a compressive sensing based receiver, that requires a sub-Nyquist digital clock rather than a Nyquist rate clock. In a conventional random demodulator, the input signal is mixed with a pseudo random sequence, running at the signal´s Nyquist rate and then integrated and sampled. In order to overcome this constraint, we propose the use of frequency division multiplexing, in the analog domain, of many digitally generated random sequences running at a sub-Nyquist rate to generate an effective random sequence. The major gain in this approach is that the restricting requirement of having a fast clock is levitated, thus allowing to extend the capabilities of the random demodulator beyond the restrictions imposed by the digital technology.