00:01
Okay, so since some of the symbols or numbers are not readable, i'll give you a general guidance as to how to solve this problem.
00:09
Problem.
00:09
So to design a detector for deciding whether a signal is present, which is h1, or absent, which is hnu, in each of the n equals 1000 realizations of a random vector y, with each realization having m of 16 elements, you can follow these steps.
00:34
So the signal signal model is hν, y equals z for signal absent, and h1, y equals as plus z for signal present, where z represents circularly symmetric complex gaussian noise, a is a real -valued positive constant amplitude, and s is a signal vector defined with phase phi.
01:10
So the first thing you want to do is to load the data from the mdt24 .mat file containing the realization of y.
01:24
And second thing you do is to define the signal vector s.
01:30
So, given phi equals 2 pi d over lambda sine of theta, where theta is equal to 20 degrees, and d equals lambda over 2, we'll calculate phi and construct the signal vector s as s equals 1e to negative j phi e to negative j to phi all the way up to e to negative j m minus 1 phi transpose.
02:12
Now, for step 3, the noise z is circularly symmetric complex complex gaussian with variance of...
02:23
So z is a circularly symmetric complex gaussian with variance sigma z1 squared of 1.
02:48
Now this means each element of z has independent zero mean gaussian real and imaginary parts with variance sigma squared z1 over 2.
02:59
So the next thing you do is to design the detector.
03:19
So the detector needs to differentiate between h0 or hν and h1...