HW3Solutions

# HW3Solutions - ECEN 661 Modulation Theory Homework#3...

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ECEN 661 - Modulation Theory Homework #3 Solutions 1. (a) Phase Trellis Diagram Phase State Diagram ( ) (b) Phase Trellis 2 π 3 2 π 3 0 p t () e j 2 π 3 tT = 2 π 3 2 π 3 0 +1 / pt -1 / p * t +1 / e j 2 π 3 e j –2 π 3 1 / p * t 1 / p * t e j 2 π 3 π /4 /4 −π/4 −3π/4 T s 2 T s 3 T s 4 T s

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The behavior of the phase trellis is time variant and cyclic (with a cycle of ). Hence, the behavior of the phase depends on not only the starting phase during a bit interval but also whether it is an even or an odd numbered bit interval. Hence, we will need to have 8 states in the state dia- gram to represent the four possible starting phases and the even/odd time interval. 2. For 16-QAM, the PSD is proportional to . For the three pulse shapes given we have: (i) Square: , (ii) Half-sinusoid: , (iii) Full-cosine: . The table below shows the relavent bandwidths which were measured from the plot given Table 1: Bandwidth of Various Pulses Pulse BW(3dB)/Rb BW(null)/Rb BW(30dB)/Rb Square 0.221 0.5 4.80 Half-Sinusoid 0.297 0.75 2.28 Full-Cosine 0.360 1.0 1.85 2 T s θπ 4 = even –4 = even θ 3 π 4 = even θ 3 π = even 4 = odd = odd θ 3 π 4 = odd θ 3 π = odd Gf () 2 2 sinc 2 fT s 2 sinc s 12 sinc s + + [] 2 2 sinc s 1 2sinc s sinc s 1 + ++ 2
3.

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## This note was uploaded on 02/21/2012 for the course ECEN 611 taught by Professor Miller during the Spring '08 term at Texas A&M.

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HW3Solutions - ECEN 661 Modulation Theory Homework#3...

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