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--- cognitivehistory:codebook_constellation_knowledge 2008/09/15 17:30
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+===== Usefulness of Constellation/Codebook Knowledge in Sensing =====
+==== Idea Description ====
+ Consider the problem of detecting the presence/absence of the primary signal in noise. Assume that the signal does not have any features like pilot tones, cyclostationary features etc. For example, samples drawn independently and identically from a given zero-mean signal constellation satisfy this assumption. On possible metric to measure the performance of a detector is its sample complexity, defined as the number of samples required to attain a given probability of false-alarm (Pfa) and probability of missed-detection (Pmd) as a function of the SNR.
+ For this problem, it is shown that the sample complexity of the energy detector is asymptotically optimal, i.e., the sample complexity of the energy detector and the sample complexity of the optimal Neyman-Pearson detector are identical in the order sense, as the SNR decreases to zero. This suggests that the optimal detector (which requires the exact constellation knowledge) performs as poorly as the energy detector (which does not need the constellation knowledge). So, at low SNRs, knowledge of the constellation/codebook is useless from a sensing point of view.
+==== 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 ====
+==== Related work outside the CR Community ====
+==== Reading Material ====