Hw5Soln - ECE 5670 Digital Communications ECE department Cornell University Spring 2011 Homework 5 Solutions Instructor Salman Avestimehr Office

Info iconThis preview shows pages 1–3. 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 5 Solutions Instructor: Salman Avestimehr Office 325 Rhodes Hall 1. The channel has bandwidth W = 4 kHz (i.e. bandwidth is between [- 2 kHz, 2 kHz ] ) and we are using raised cosine pulse shape with β = 0 . 5 . Therefore the symbol rate should satisfy 1 T (1 + β ) = W (1) Therefore 1 T = W 1 + β = 4000 1 . 5 = 2667 symbols/sec (2) (a) Since 1 bit/symbol is transmitted in BPSK, the bit rate is 2667 bits/sec. (b) We send 4 bits/symbol in a 16-PAM. Therefore, the bit rate is 4 × 2667 = 10668 bits/sec. 2. The bandwidth of the channel is W = 4 kHz . Hence, the rate of transmission should be less or equal to 4000 symbols/sec. If an M-PAM constellation is employed, then the required symbol rate is 1 T = 9600 log M symbols/sec (3) If a signal pulse with raised cosine spectrum with roll-off factor β is used for shaping, then we should have 1 T (1 + β ) ≤ 4000 (4) Therefore we should have 9600 log M (1 + β ) ≤ 4000 (5) Therefore log M ≥ 9600(1 + β ) 4000 (6) And since we want to have β ≥ . 5 we need to set log M such that log M ≥ 9600(1 + β ) 4000 ( β ≥ . 5) ≥ 9600 × 1 . 5 4000 = 3 . 6 (7) So we set M = 16 and β = 0 . 66 so that (5) is satisfied with equality. Therefore the symbol rate is 1 T = 9600 log M = 2400 symbols/sec (8) Now in the error probability of M-PAM is P M = 2( M- 1) M Q s 3 p average ( M 2- 1) σ 2 ! (9) Therefore since M = 16 and σ 2 = N 2 W = 4 × 10- 7 we should have 10- 6 = 30 16 Q r 3 p average 1 . 02 × 10- 4 !...
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 / 4

Hw5Soln - ECE 5670 Digital Communications ECE department Cornell University Spring 2011 Homework 5 Solutions Instructor Salman Avestimehr Office

This preview shows document pages 1 - 3. Sign up to view the full document.

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