This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ECE 562 Fall 2011 December 6, 2011 HOMEWORK ASSIGNMENT 7 SOLUTIONS 1. True or False. Determine if the following statements are True or False. You need to provide a brief justification for your answer to get credit. (a) If the mobile speed is 72 km/hr, the carrier frequency is 900 MHz, and symbol rate for communication is 10 symbols a second, then the mobile experiences slow fading. False: f max = 60 Hz, and T c = 0 . 1 /f max . 1 = T s . (b) In wireless communication, if the speed of the mobile is doubled the delay spread is also doubled. False: The mobile speed has little effect on the delay spread. It is the Doppler speed that gets doubled. (c) A wireless channel with ds = 10 4 seconds and f max = 100 Hz operating with a bandwidth of 1 . 25 MHz is a flat fading channel. False: W ds (d) For a fixed b , P b for binary DPSK signaling over a slow flat fading channel is always larger than P b without fading, irrespective of the distribution of the fading. True: By Jensens inequality since exp is convex. 2. Useful Result. Show that Z Q ( x ) e x/ dx = 1 2 1 r 2 + . Hint: Start with: Z x =0 Q ( x ) e x/ dx = Z x =0 Z t = x e t 2 / 2 2 e x/ dt dx = Z t =0 Z t 2 x =0 e t 2 / 2 2 e x/ dx dt and use the fact that the Gaussian pdf integrates to 1 to conclude the result. Ans: Starting with the hint, Z x =0 Q ( x ) e x/ dx = Z 1 2 e 1 2 t 2 1 2 e 1 2 ( +2 ) t 2 dt = 1 2 Z 1 2 e 1 2 ( +2 ) t 2 dt = 1 2 r 2 + Z 1 r 2 2+...
View Full
Document
 Fall '09

Click to edit the document details