Probability and Statistics MATLAB project

ECE 352: MATLAB Final Project

Due: Thursday 12/7

Simulate a radar detection system that has additive Gaussian(0,1) noise in the received signal. In addition, assume the internal circuitry of the receiver introduces a “squared distortion” non-linearity in the received signal such that the signal (measured in volts) is given by the following values:

2

2

TargetAbsent

TargetPresent( )

N dN X

v N d v N

   

  

Write a MATLAB program to simulate this system to answer the following questions:

1) Simulate and plot PFA and PMISS as a function of the receiver threshold voltage x0, where -2 ≤ x0 ≤ 6 for two transmit voltages, v = {1, 2}, and three square distortion values, d = {0, 0.2, 0.4}. Do the two error probability curves, PFA and PMISS, change much due to the distortion? Comment about the effect and give strong reasoning to support your observation.

2) Plot the ROC for both transmit voltages and the three square distortion values in the previous problem. Does the ROC change much due to the distortion? Comment about the effect and give strong reasoning to support your observation.

3) In this binary hypothesis test, P[H0] is the probability that the target is absent and P[H1] is the probability that the target is present. Suppose we know that P[H0] = 0.8. Use the Maximum A Posteriori Probability (MAP) Test to compute the probability of error, PERR, and plot it versus threshold voltage for both transmit voltages and the three square distortion values in the previous problem. Also use MATLAB to find the threshold voltage that minimizes PERR for each operating point. Comment on the effect of the square distortion on PERR for both voltages.

4) Considering that this is a radar system, the cost of a false alarm is much less than the cost of a miss. Suppose the cost of a false alarm, C10, is 1 and the cost of a miss, C01, is 5. Use MATLAB to compute the expected cost, E[C], of test errors by evaluating the minimum cost test equation for both transmit voltages and the three square distortion values in the previous problem. Also use MATLAB to find the threshold voltage that minimizes the cost for each operating point. Do the curves of E[C] differ much from PERR? Comment about the effect and give strong reasoning to support your observation.

Write a report documenting your results and conclusions. Include your MATLAB program(s), with comments that explain your operations and your methodology. You may choose one other person to work with on this project – please email the instructor information on who you will work with by Tuesday 11/9.