# 2008 Research Summary

## Fundamental Limits on Robust Spectrum Sensing for Cognitive Radios

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Rahul Tandra and Anant Sahai

This project considers the problem of detecting the presence/absence of signals in low SNR environments. The context is cognitive radios trying to opportunistically share spectrum along with potential primary users that must be detected in order to avoid causing harmful interference. Small modeling uncertainties are unavoidable in any practical system and so robustness to modeling uncertainties is a fundamentally important performance metric.

We propose simple mathematical models for these uncertainties and establish two main results [1-3]. If we have no knowledge of the modulation scheme of the signal we are trying to detect, then there exists an absolute "SNR wall" below which every detector will fail to be robust, no matter how long the detector can observe the channel. Upper and lower bounds are computed that show any detector is essentially as non-robust as the radiometer. Given knowledge of the signal, we prove that both coherent and cyclostationary feature detectors are also non-robust to model uncertainties when channel coherence times are finite. The scaling of the SNR wall with coherence time is worse than for cyclostationary detectors as compared to coherent detectors. These results strongly suggest that all detectors are non-robust.

This has implications for wireless spectrum regulators. We argue that the tension between primary and secondary users is captured by the technical question of computing the optimal tradeoff between capacity and robustness as quantified by the SNR wall. This is an open problem and is the topic of future research.

- [1]
- R. Tandra and A. Sahai, "SNR Walls for Signal Detection,"
*IEEE Journal on Selected Topics in Signal Processing,*April 2007 (submitted). - [2]
- R. Tandra and A. Sahai, "SNR Walls for Feature Detectors,"
*Proceedings of the IEEE Dynamic Spectrum Access Networks,*April 2007. - [3]
- R. Tandra and A. Sahai, "Fundamental Limits on Detection in Low SNR," master's thesis, UC Berkeley, 2005.