This paper considers the problem of detecting the presence/absence of signals in low SN R 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. If we have no knowledge of the modulation scheme of the signal we are trying to detect, then there exists an absolute "SN R 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 SN R 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 SN R wall. This is an open problem, but we compute this tradeoff for some simple detectors.

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Abstract-Cognitive Radios have been advanced as a technology for the opportunistic use of under-utilized spectrum since they are able to sense the spectrum and use frequency bands if no Primary user is detected. However, the required sensitivity is very demanding since any individual Radio might face a deep fade. We propose light-weight cooperation in sensing based on hard decisions to mitigate the sensitivity requirements on individual radios.We show that the "link budget" that system designers have to reserve for fading is a significant function of the required probability of detection. Even a few cooperating users (∼10-20) facing independent fades are enough to achieve practical threshold levels by drastically reducing the individual detection requirements. Hard decisions perform almost as well as soft decisions in achieving these gains. Shadowing correlation limits these gains and hence a few independent users perform better than many correlated users.Unfortunately, cooperative gain is very sensitive to adversarial/failing Cognitive Radios. Radios that fail in a known way (always report the presence/absence of a Primary user) can be compensated for by censoring them. On the other hand, radios that fail in unknown ways or may be malicious, introduce a bound on achievable sensitivity reductions. As a rule of thumb, if we believe that

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We review how Shannon's classical notion of capacity is not enough to characterize a noisy communication channel if the channel is intended to be used as part of a feedback loop to stabilize an unstable scalar linear system. While classical capacity is not enough, another sense of capacity (parametrized by reliability) called "anytime capacity" is shown to be necessary for the stabilization of an unstable process. The required rate is given by the log of the unstable system gain and the required reliability comes from the sense of stability desired. A consequence of this necessity result is a sequential generalization of the Schalkwijk/Kailath scheme for communication over the AWGN channel with feedback.In cases of sufficiently rich information patterns between the encoder and decoder, adequate anytime capacity is also shown to be sufficient for there to exist a stabilizing controller. These sufficiency results are then generalized to cases with noisy observations, delayed control actions, and without any explicit feedback between the observer and the controller. Both necessary and sufficient conditions are extended to continuous time systems as well. We close with comments discussing a hierarchy of difficulty for communication problems and how these results establish where stabilization problems sit in that hierarchy.