Active Spectrum Sensing with Sub-Nyquist sampling

At high carriers, enabling low power wireless devices to use opportunistically the available spectrum requires an analog front-end that can sweep different bands quickly, since Nyquist sampling is prohibitively expensive. In this paper we propose a new framework that allows to optimize a sub-Nyquist sampling front-end to combine the benefits of optimum sequential sensing with those of compressive spectrum sensing. The sensing strategy we propose is formulated as an optimization problem whose objective of maximizing a utility decreasing linearly with the number of measurement and increasing monotonically with the components found empty. The optimization designs the optimum measurement selecting the best linear combinations of sub-bands to mix to accrue the maximum utility. The structure of the utility represents the trade-off between exploration, exploitation and risk of making an error that is characteristic of the spectrum sensing problem. We characterize the optimal policy under constraints on the sensing matrix and derive the approximation factor of the greedy approach. Second, we present the analog front-end architecture and map the measurement model into the abstract optimization problem proposed and analyzed in the first part of the paper. Numerical simulations corroborate our claims and show the benefits of combining opportunistic spectrum sensing with sub-Nyquist sampling.