Hw6Soln_1 - ECE 5670 : Digital Communications ECE...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: ECE 5670 : Digital Communications ECE department, Cornell University, Spring 2011 Homework 6 Solutions Instructor: Salman Avestimehr Office 325 Rhodes Hall 1. (a) We know from Lecture 14 that the mean of the squared error in the estimate of the th channel coefficient is E [ | h | 2 ] 1 + E [ | h | 2 ] SNR . (1) For large enough SNR, this means that the mean of the squared error decreases as 1 SNR . (2) So, if we increase the SNR by a factor of two, the mean of the squared error decreases by a factor of a half. (b) i. We simply use of a pulse of amplitude E at every L time instances and nothing else: x [ iL ] = E, x [ iL + j ] = 0 , i k- 1 and 1 j L- 1 (3) ii. Since this is just a repetition code, the optimal estimator for h l just is just h l = c l k- 1 i =0 y [ iL + l ] k , l = 0 ,...,L- 1 (4) where c l is chosen to minimize the estimation error E [( h l- h l ) 2 ] . Note that we can write E [( h l- h l ) 2 ] = E [( h l- c l k k- 1 X i =0 ( Eh l + n [ iL + l ])) 2 ] (5) = E [( h l- c l Eh l- c l k k- 1 X i =0 n [ iL + l ]) 2 ] (6) = (1- c l E ) E [ h 2 l ] + c 2 l k 2 k- 1 X i =0 var ( n [ iL + l ])...
View Full Document

This note was uploaded on 10/02/2011 for the course ECE 5670 taught by Professor Scaglione during the Spring '11 term at Cornell University (Engineering School).

Page1 / 5

Hw6Soln_1 - ECE 5670 : Digital Communications ECE...

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