Homework #6

EE510WS ( Introduction to Radar Systems

Instructions:
You can either stop by my office and submit a hard copy of your work, or use email/fax to submit your solutions (email submission is preferred).
Only one submission is required, containing solutions to all problems.
For email submission, you can either type your solutions using a word processor, or scan your handwritten solutions into an electronic format. If you have multiple pages, please combine them into a single file in Word or PDF format, and send it to my regular email address (Hongbin.Li@stevens.edu). Do not use myWebCT email account. Please avoid sending files of excessive size (>10 Mb), since my campus email may get full and your submission will get lost.
For fax submission, you can fax it to me at 201-216-8246. Include a cover page with my name so that your submittal will not get lost. Also indicate the total # of pages in your fax.
You may solve the problems according to the following schedules:
After Lecture #11: Problem 1-3
After Lecture #12: Problem 4-5
After Lecture #13: Problem 6-8

Consider detection of a real-valued constant in zero-mean real-valued Gaussian noise. Let the noise variance ??2 = 2, the number of samples N = 1, and the constant m = 4. What is the SNR for this case? Sketch approximately the distributions p(y|H0) and p(y|H1); be sure to label appropriate numerical values on your axes. Write the likelihood ratio and log-likelihood ratio for this problem. Simplify your expressions.
Continuing with the same parameters given in problem #1, suppose we want to have PFA = 0.01 (1%). What is the required value of the threshold T? What is the resulting value of PD? You can use lookup tables or MATLAB to calculate the values of functions such as erf(), errc(), erf-1(), or erfc-1() that you may need.
Consider detection of a constant in complex Gaussian noise. Let the total noise variance ??2 = 2, the number of samples N = 1, and the…