Is probability of detection (average) better than 50% possible when there is no apriori distribution knowledge and SNR is less than (minus)-5dB ? I would appreciate if you could you suggest papers dealing with this limiting problem. Papers outside the range of IEEEXPLORE are especially welcomed.
My earliest results show that it could be possible. I am interested in (radar) target detection and assume that the two distributions for and are both continuous and have decaying tails along both sides of a single peak. Distributions could be asymmetrical. I could cite to similar work for comparative results.
It is possible (even at SNR much lower than -5dB) when there is NOT noise uncertainty. However, to detect in low SNR needs more sensing time (more samples), so that distribution under H0 and H1 get well separated .
Dear Sharma, thank you for the input. I appreciate it.
But if I may I promote my question further;
Is probability of detection (average) better than 50% possible when (all together)
ONLY GIVEN: Ho and H1 distributions have tails extending to infinity and both has single peak value for the PDF;
- there is NO apriori distribution knowledge,
- NO information on noise,
- samples are limited to say 50 or less and
- SNR is less than (minus) -5dB ?
I would appreciate if you could you suggest papers dealing with this limiting problem. Papers outside the range of IEEEXPLORE are especially welcomed.
My initial results for; no information on the distribution and statistical parameters of noise,very few observed samples as low as 20, are as follows.
I had now completed the first trials of my study, and observed that with no apriori information, using independent 20 observed samples for H1 (given 20 samples of Ho), SNR = 1 is sufficient and roughly Pd=0.9, Pfa=0.5 is possible.
I need to restate that SNRdB could not be negative when there is no info on noise, 0 db is the impossible case and my best is 1 and it is very small.
I will appreciate any comment.
-GokhunT.
Please check my publications for detailed analysis. If further comments, thank you in advance for you interest. GokhunT.
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