radar emitter location problem - calculating bounds

Hi all,

I have a project which I have to do in one of the courses in my graduate studdies, and I would be happy to get some advices regarding what books ar articles to look for relevant material, and how to treat the problem theoretically and for simulation (matlab).

Strictly speaking, I don’t have a clue how to even start this. Its actually a project that suppose to involve estimation theory and im not sure how deep I have to know about radar theory in order to solve it.

In addition, If I can use staff that’s already is written and ready for use (and im sure its there, just don’t know where to look and what ecxatly to look for), I would be happy to use it, instead of sitting trying to figure it out only by myself.

So here it is:


A radar transmits a signal (pulses)

U(t) = sum(k=0 to k=K-1)(s(t-kT))

With fourier transform:

U(w) = s(w)*sum(k=0 to k=K-1)(exp(-jwkT)

The radar receive the signal:

Y(t) = alpha*sum(k=0 to k=K-1)(s(t-tao-kT))exp(-jk*phi) + w(t)

(w(t) is probably noise)

Y(w) = alpha*s(w)*exp(-jw*tao)*sum(k=0 to k=K-1)*exp(-jk(wT+phi))

Whereas:

Alpha-may be complex
Tao-time delay
Phi-doppler pahse shift

1.find the Fisher Information Matrix (FIM) and the CRLB (Cramer Rao Lower Bound) dor estimation of phi, alpha, and tao.

2. Find the Barankin Bound for estimation of phi, alpha and tao.

3. Repeat parts 1 and 2 for the the model:

y(t) = alpha * sum(k=0 to k=K-1)(s(t-tao-kT))*exp(-jk*phi)

while assuming that the signals are orthogonal: si orthogonal to sj (where I not equal j)

4. do simulation (matlab) for all the above


note: its possible to sample the signals at nyquist rate, and work with the

samples. You can assume that bandwidth of all signals at part 3 is the

same.



Thanks for any help