problem set4

problem set4 - ELEC 531: STATISTICAL SIGNAL PROCESSING...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ELEC 531: STATISTICAL SIGNAL PROCESSING Department of Electrical and Computer Engineering Rice University Fall 2007 Problem Set 4 Due: September 27, 2008 Problem 4.1 Let the observations be of the form Y = H θ + N where θ and N are statistically independent Gaussian random vectors. θ ∼ N ( 0 ,K θ ) N ∼ N ( 0 , K n ) The vector θ has dimension M ; the vectors Y and N have dimension L . (a) Derive b θ MMSE , the minimum mean-squared error estimator of θ . (b) Show that this estimator and the optimum linear estimator b θ LMMSE are equal. (c) Find an expression for the mean-squared error for these estimators. Problem 4.2 Consider the communication system shown below. The message X is a N (0 2 X ) random variable. The transmitter output is hX , and the receiver input is Y = hX + N, where N in an N (0 2 N ) random variable that is statistically independent of Y . RCVR XMTR + X N hX Y X Figure 1: Suppose the transmitter is subject to intermittent failure, i.e. h is a random variable
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

problem set4 - ELEC 531: STATISTICAL SIGNAL PROCESSING...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online