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HW9solution - Problem 1(Count as 2 problems Satellite TV...

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Problem 1 (Count as 2 problems) Satellite TV Transmission A signal is transmitted at 10 GHz ( meter 03 . 0 = λ ) from an orbit 30,000 km above the earth. The transmitter gain is 20 dB. In bad weather, the signal may suffer an absorption loss of 2 dB per km through thunderstorm rain 3 km depth. The receiver dish is 0.4 m in diameter. Account for the following losses and gains Distance loss = L s | dB = 20log(4π d / λ) = 20log(4π x 3e7 / 0.03) = 201.9842(dB) Transmitter gain plus receiver gain = Assume η =0.5 G R = 10log[ η(πD / λ) 2 ]=10log[0.5 x (π x 0.4 / 0.03) 2 ] = 29.4315(dB) G T +G R = 49.4315(dB) Absorption loss by rain = 2(dB/km) x 3(km) = 6(dB) Net loss = 201.9842(dB) + 6(dB) = 207.9842(dB) Assume thermal noise Hz W N / 10 4 21 0 - × = . We transmit HDTV at 10 Mbps at 100 W power. Calculate Received power ( W ) = P R | dB = P T | dB + G T +G R = 10log(100)+49.4315(dB) - 207.9842(dB) = -138.5527 (dB) or P R = 1.3955e-14(W) The energy per bit = ε b = P R / R b = 1.3955e-14 / 1e7 = 1.3955e-21 (J/bit) The subsequent 0 / N E b = 1.3955e-21 / 4e-21 = 0.3489 or -4.5730(dB) If we need dB N E b 10 / 0 , is the above 0 / N E b satisfactory? Suppose we use a rate ½ Hamming distance = 14 convolutional encoder. Calculate the coding gain. Is the result satisfactory now?
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