HW5Solutions

HW5Solutions - ECEN 661 - Modulation Theory Homework #5...

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ECEN 661 - Modulation Theory Homework #5 Solutions 1. For any binary signalling format, the probability of error for the ML coherent detector is . In this case the two signals are: , . The distance squared for these two signals is: . These integrals work out to be , . Hence, , . The error probability will be minimized by choosing so that is minimized. This occurs when and the resulting error probability is . The asymptotic gain (relative to orthogonal FSK) is . 2. (a) The inner circle has radius . The outer circle must have radius . (b) The circle must have radius of . P e Q d 2 2 N o ---------   = s 1 t () A ω c t cos = s 2 t A ω c ω + t cos = d 2 s 1 t s 2 t [] 2 t d 0 T s 1 t 2 t d 0 T s 2 t 2 t d 0 T 2 s 1 t s 2 t t d 0 T + == s 1 t 2 t d 0 T A 2 T 2 E b s 2 t 2 t d 0 T A 2 T 2 E b s 1 t s 2 t t d 0 T A 2 2 ω ---------- ω T sin E b sinc 2 f T d 2 2 E b 2 E b sinc 2 f T = P e Q E b N o ------ 1 s i n c –2 f T  = f sinc 2 f T f 0.715 T = P e Q 1.2172 E b N o ----- = 1.2172 0.8536dB = a A 2 ------ = bA 13 + 2 ---------------- = r A 2 π 8 sin ------------------------- =
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This note was uploaded on 02/21/2012 for the course ECEN 661 taught by Professor Miller during the Spring '11 term at Texas A&M.

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HW5Solutions - ECEN 661 - Modulation Theory Homework #5...

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