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Unformatted text preview: EE132A, Spring 2009 Communication Systems Prof. John Villasenor Handout# 19 TAs: Pooya Monajemi and Erica Han Homework 6 Solutions 1. (a) The time domain expression for the signal space is given by: 2 ( ) cos 2 ( 1) 1 8 4 i c E s t f t i t T i T π π = − − , ≤ ≤ , = , , L Or equivalently, 2 ( ) cos ( 1) cos2 sin ( 1) sin 2 4 4 1 8 i c c E s t i f t i f t T t T i π π π π = − + − , ≤ ≤ , = , , L (b) Considering the nearest neighbors only, the distance between any two adjacent symbols is given by 2 sin 8 d E π = as shown in Figure 1. Figure 1. Distance between symbols for 8-PSK signal constellation Then the probability of symbol error is erfc 2 erfc sin 8 2 2 sin 8 E d P N E N E Q N π π ≈ = = For 8-PSK constellations, each symbol consists of 3 bits. Then, For 8-PSK constellations, each symbol consists of 3 bits....
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- Spring '09
- Sin, bit error probability, Baseband, Eb sin, PE erfc sin, Eb sinc