Decentralized Shaping for Pilot Generation and Detection in Opportunistic Communications

The uncoordinated design of pulse shaping filters for opportunistic communications is addressed. We show that under degrees-of-freedom sensing uncertainties the waveform design problem can be cast as a minimum-norm optimization, admitting hence a closed-form expression. Because designed waveforms are adapted to scenario working conditions, proposed design scheme may be considered in pilot reference signals design to achieve orthogonality, regardless the traditionally considered pilot symbols orthogonality. Hence, the effect of interferences such as pilot contamination is diminished. However, a crucial aspect relies on their detectability. Since each node uses only local observations from the wireless network, the sensed degrees-of-freedom may slightly differ from one node to others. In this paper we prove that, thanks to the existence of some invariances, designed waveforms can be detected by neighboring nodes. Even though degrees-of-freedom sensing uncertainties may incur in a performance loss, we propose a least-squares constrained basis pursuit algorithm to reduce the effect of uncertainties by considering only the degrees-of-freedom subspace intersection.