HW6Solutions

# HW6Solutions - ECEN 661 Modulation Theory Homework#6...

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ECEN 661 - Modulation Theory Homework #6 Solutions 1. Let the two FSK waveforms be written as so that the signals are separated in frequency by . Then the correlation coefficient between the two is Neglecting the first term assuming produces . The square Euclidean distance between the two waveforms is . In the case of FSK the two signals are equal energy so that and hence . The error probability is then . Clearly the error probability will be minimized when is minimized. The minimum value of the sinc function occurs when its argument is 1.43 (this must be determined numerically). The optim frequency spacing is then . 2. Somehow this problem inadvertantly slipped into two consecutive homeworks. See HW5 solu- tions for detailed solution. s 0 t () A 2 π f c f 2 ---- +   t θ + cos = s 1 t A 2 π f c f 2 t θ + cos = f ρ 12 , s 0 t s 1 t t d 0 T E 1 E 2 ---------------------------------- 2 T -- 2 π f c f 2 + t θ + cos 2 π f c f 2 t θ + cos t d 0 T == 1 T 4 π f c t 2 θ + cos t d 0 T 1 T 2 π f t cos t d 0 T + = f c 1 T » ρ , 2 π f

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HW6Solutions - ECEN 661 Modulation Theory Homework#6...

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