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.