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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+...
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