# HW7S - ECE 402 Communications Engineering Homework 7...

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ECE 402: Communications Engineering Homework 7 Solutions (Fall 2009) 1. (a) As noted in class, for the sinc pulse the null bandwidth is W null = 1 /T and the data rate is R = k/T , so η = R/W null = k = 6 bps/Hz. (b) For M = 64, we want 10 - 8 = P b 4 log 2 M ± 1 - 1 M Q ˆs 3 PT ( M - 1) N 0 ! = Q ˆ s 3 PT 63 N 0 ! = 1 . 714 × 10 - 8 . In MATLAB, we ﬁnd qfuncinv(1.7140e-008)=5.518 , so the required SNR is s 3 PT 63 N 0 = 5 . 518 = PT N 0 = 63 × (5 . 518) 2 3 = 639 . 4 . We conclude that E b /N 0 = PT/kN 0 = 106 . 6 or in decibels, 20 . 28 dB. (c) The spectral eﬃciency of this system is η = 6 bps/Hz. By Shannon’s Formula, the best possible tradeoﬀ between power and bandwidth eﬃciency is E b /N 0 (2 η - 1) . The best power eﬃciency is therefore E b /N 0 (2 6 - 1) / 6 = 10 . 5 or in decibels, 10.21 dB, which is much smaller than in part (b)! 2. (a) Since antenna absorption and scattering losses are ignored, η T = η R = 1. The wavelength is λ = c/f = 0 . 15 m and the diameter of the transmit and receive antennas is D T = D R = 1 . 22 m.

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HW7S - ECE 402 Communications Engineering Homework 7...

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