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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-offreedom 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 degreesof-freedom subspace intersection.

The waveform optimization problem for opportunistic communications is addressed, based on sensing the secondorder statistics of the existing transmissions. We propose a minimum-norm waveform optimization that exhibits robustness to the worst-case subspace mismatch, minimizes the spectral overlapping with the existing transmissions, is rotationally invariant, and has maximally white spectrum. The derived solution can be seen as a different kind of signal dimension-based spreading. In addition, the effects of the residual interference caused to the existing transmissions are studied. Numerical results are provided to assess the performance of the proposed solution in the frequency domain for the asymptotic case. The level of induced interference is compared to traditional null space techniques.

The statistical side information of interference channels is exploited in this paper to derive a novel uncoordinated on-line pilot design strategy for opportunistic communications. Assuming a time division duplex (TDD), or frequency division duplex (FDD) with feedback, wireless network and reciprocity, we prove that the space-frequency pilot design technique in terms of minimum cross-interference to external-network users reduces to a classical minimum-norm problem. The advantages of this novel methodology are time-domain invariance to noise-subspace rotations, a maximally flat angle-frequency response, and robustness in front of frequency calibration errors. Simulation results are reported to assess the performance of the proposed strategy and the advantages of its low-resolution quantization in low signal-tonoise ratio (low-SNR) regimes. Index Terms-Opportunistic communications, pilot and waveform design, multi-antenna systems, distributed networks, wideband regime.