APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

SECOND SEMESTER M.TECH DEGREE EXAMINATION, MAY 20 1 7
Electronics and Communication Engineering

01 EC6302Estimation and Detection Theory
Max. Marks:60 Duration: 3 Hours
Answer any two questions from each PART
PART A

1. Consider the binary hypothesis problem with received conditional probabilities as shown
below. The hypotheses Ho and Hi are equally likely. Calculate the minimum probability

of error.
1 7+ )= ree [
5 1८1 =
(४ | 4०) ‏و-ہخے-‎ for Ill n and 2 2
‏(ا-2)1-6‎
‎(9 Marks)
2. Write a short note on Generalized LikelihoodRatio Test. (9 Marks)
3. a) Derive Bayes risk factor.
b) Derive Chernoff bound. (9 Marks)

PART B

− r fi =0 ∙ ⋅

∆⋅∣∱∠∣⊓⊢∧≁↭∣⊓∣∘↾⊓≯↿⋅∙⋅∙⇅⋅∣∩⋀⋔∈∣∽∈⋀∣≤∂⊓⋃∩∣≺∩∘⋁∨⋂ parameter, r is a known

constant, and w(n) 15 zero mean white noise with variance 0 °, find the BLUE of A and
the minimum variance. Does the minimum variance approach zero as N *00?

(9 Marks)

5. Prove that, ifGaussian prior PDF is assumed for an unknown parameter, MMSE and MAP
estimator will give same estimate values for that parameter.
(9 Marks)

6. Let x denote the vector composed of three zero mean random variables with a
covariance matrix, Cxx= ‏م 1 م‎ .If y = Ax, determine the matrix A, so that the

covariance matrix ofy is | or equivalently, so that the random variables {yl, y2, y3} are
uncorrelated and have unit variance also find the relation between A and csx.
(9 Marks)