This shows you the differences between the selected revision and the current version of the page.
| cognitivehistory:snr_walls_using_worst-case_uncertainty 2008/09/15 13:34 | cognitivehistory:snr_walls_using_worst-case_uncertainty 2008/09/15 17:06 current | ||
|---|---|---|---|
| Line 1: | Line 1: | ||
| + | ===== SNR Walls using Worst-case Uncertainty ===== | ||
| + | ==== Idea Description ==== | ||
| + | Consider the problem of [[Robust detection|robustly detecting]] the presence/absence of a signal in the presence of noise. In any real system modeling uncertainties are unavoidable. So, we assume that the distribution of the noise process is uncertain and that it lies within a given bounded uncertainty set. We measure the performance of a detection algorithm by the worst-case probability of false-alarm and worst-case probability of mis-detection, where the worst case is taken over the uncertainty set. Under this model, an SNR wall for a detector is the maximum threshold such that the detector can not robustly detect the signal if the SNR is less than the threshold. | ||
| + | |||
| + | |||
| + | |||
| + | ==== Papers that introduced the idea to the CR community ==== | ||
| + | |||
| + | - Anant Sahai, Niels Hoven, and Rahul Tandra, ``Some fundamental limits on cognitive radios'', in the proceedings of Allerton Conference on Communication, Control, and Computing, October 2004. | ||
| + | |||
| + | |||
| + | ==== Experimental Validation or Invalidation ==== | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | |||
| + | ==== Subsequent Idea Developments ==== | ||
| + | |||
| + | In the context of cognitive radios sensing primary bands, the existence of SNR walls were first shown for the energy detector. This non-robustness result for the energy (2nd moment) detector was extended to show the existence of SNR walls for all higher moment detectors if the signal is `white' and zero-mean. For such signals it was shown that every possible detection algorithm suffers from SNR wall limitations if we impose a [[SNR walls for detectors with finite dynamic range constraints|finite dynamic range constraint]] on the receiver. Subsequently, the existence of [[Absolute SNR walls|absolute SNR walls]] for zero-mean white signals were shown, even for detectors without any finite dynamic range constraints. | ||
| + | |||
| + | This showed that signals without any structure are highly non-robust to uncertainties, irrespective of the actual detection algorithm used. However, for signals with known structure it is possible to get robustness gains by designing detection algorithms that take advantage of the known signal structure. For example, for signals with known narrowband pilots, it was shown that coherent processing gives robustness gains. However, uncertainty in the channel fading process limits the gains from coherent processing and leads to [[SNR walls for Pilot detectors|SNR walls for pilot detectors]]. Similarly, it was shown that signals with cyclostationary features are also non-robust to uncertain frequency selective channel fading, and [[SNR walls for feature detection|SNR walls for cyclostationary feature detectors]] were derived. | ||
| + | |||
| + | Subsequently, [[Noise calibration|run-time noise calibration]] was shown to be a fundamental signal processing technique to give robustness gains. It was shown that noise calibration is feasible for signals with features, where the signal feature occupies a fraction of the degrees of freedom as compared to noise. For instance, for signals with narrowband pilot tones it was shown that noise calibration in the frequency domain makes the signal completely robust to white noise uncertainties. However, colored noise uncertainty bring back the SNR wall even with noise calibration. Similarly, for cyclostationary signal features it was shown that noise calibration is feasible in the time domain. Noise calibration makes these signal robust to white noise uncertainties, while colored noise uncertainties bring back the SNR wall. | ||
| + | |||
| + | The robustness results for various signal structures lead to the natural question of the tradeoff between the data rate achieved by the signaling scheme and its robustness to uncertainties. This tradeoff was called the [[Capacity-Robustness tradeoff| capacity-robustness tradeoff]], and the tradeoff curve for some example signal, detector pairs were derived. This lead to the obvious question of whether it is possible to derive signals such that they are completely robust to uncertainty in the noise and fading process. Recent result show that signal with [[Macroscale feature for overcoming SNR walls|macroscale features]] can overcome SNR walls even under arbitrarily varying noise and fading processes. | ||
| + | |||
| + | |||
| + | |||
| + | [[http://dx.doi.org/10.1109/DYSPAN.2007.79|SNR walls for feature detectors]] respectively. | ||
| + | |||
| + | ==== Related work outside the CR Community ==== | ||
| + | |||
| + | - A. Sonnenschein and P. M. Fishman, [[http://dx.doi.org/10.1109/7.256287|Radiometric detection of spread-spectrum signals in noise of uncertain power]], IEEE Transactions on Aerospace and Electronic Systems, July 1992. | ||
| + | |||
| + | |||
| + | ==== Reading Material ==== | ||
| + | |||
| + | The single best reference to start with is: | ||
| + | |||
| + | - R. Tandra and A. Sahai, [[http://dx.doi.org/10.1109/JSTSP.2007.914879|SNR Walls for Signal Detection]], IEEE Journal on Selected Topics in Signal Processing, Feb 2008. | ||