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N-Point FFT on a standard gaussian noise results in real and imaginary results that are gaussian distributed with variance N/2. This results in the magnitude of the FFT being Rayleigh distributed with mode parameter Binary-FSK signal that shifts between 1000KHz and 1200KHz is detected using non-coherent integration of FFT data #detection #integration #noncoherent #statistics

One oversimplified method to look for a valid signal in a frequency band is to first compute the FFT of the signal in the desired frequency band and then ascertain if any point in FFT is crossing a detection threshold. This can be achieved by computing the ratio of the maximum of the FFT output to that of the sample mean value. There are host of other applications that use detection procedure which is very similar to this max-mean ratio test. My task is to find a closed form

This weekend I talked to my favorite professor about my previous supposedly simple probability problem. He quickly pointed out that this can be solved as a Hitting Time problem defined as where So Hitting Time is our detection time. The probability that this detection time is less than a given time t is given by Since t is assumed to be continuous and at Therefore, However, if So, the simplest way to make this discrete is to do the following simple approximation when The figu

I have a normal random variable that varies with time t as where Detection criterion is when the random variable So what is the probability that detection occurs at time t=i? Since where where But when I did a monte-carlo run of the problem I am having the mismatch between my calculation and monte carlo as in the figure below. Now my question is where did I go wrong in my calculation? -Update: I found the bug. My assumption about the independence of X terms is not correct i.e

So this is the first time I got into a “cart before the horse” situation with regarding to writing technical papers. I have collected extensive data regarding wireless signal strength variation in an indoor environment and I have figured out a method to track a transmitter’s position using Bhattacharyya coefficient. You can see a quick demo of this technique in action here. However, I am unable to figure out the math behind it. Essentially, my method measures signal strength

Recently I came across this method commonly applied in financial statistics for computing joint distributions from marginal distributions and a dependency metric. A recent paper that I submitted to Globecom tries to leverage this technique to create a cost function for localizing a wireless transmitter by measuring its signal strength by multiple wireless receivers placed at known locations in an indoor environment. Signal strength measured by receivers without processing is