Cognitive radio is a smart wireless communication concept that is able to promote the efficiency of the spectrum usage by exploiting its free frequency bands, namely spectrum
holes. Detection of spectrum holes is one of the first steps of implementing a cognitive radio system. Another step towards the feasibility and a real implementation of a cognitive radio network is the problem of location awareness. This problem arises when we do consider a realistic scenario in hybrid overlay/underlay systems, when these spectrum opportunities permit cognitive radios to transmit below the primary users tolerance threshold. In this case, the cognitive radio, have to estimate robustly the primary users locations in the network in order to adjust its transmission power function of the estimated location in the network. Adding to this the fact that in wideband radio one may not be able to acquire signals at the Nyquist sampling rate due to the current limitations in Analog-to-Digital Converter (ADC) technology, we end up with a system that should, at a sub-Nyquist rate, properly recover the bands over which the primary users transmit and estimate their location in the network. In this paper 1, we proposed to analyze all these arisen problems. During the problem formulation and when analyzing more deeply the equations related to each question apart, we will make the link between the formulation of spectrum sensing, location awareness and the hardware limitation by describing those problems in a unique compressed sensing formalism. Via
the proposed framework, we made it possible to overcame a challenging postulate of fixed frequency spectrum allocation by also estimating the spectrum usage boundaries in a blind way.
