Consider the simplest complex constellations of 8PSK and 16PSK which sends symbols along both the I...
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Consider the simplest complex constellations of 8PSK and 16PSK which sends symbols along both the I and Q components, as shown in Fig. 1. Let E denote the average transmit power, and 2 the variance of each of the real and imaginary parts of the additive white Gaussian noise at a receiver. 110 0110 0111 4 0010 . 0101 0011 . . 0001 101 100 001 0100 . JE Admin 22 1100 000 41 1101 . 111 011 010 1201 . 1110 1011 1010 . 27 1424 " 64 43 " 13 84 " " 0000 1000 . a) Derive the error probability of each of the constellations in a singleinputsingleoutput (SISO) Rayleigh fading channel. Give the results in terms of the Qfunction. For analytical tractability, we only take into account the errors between adjacent constellation points. (10 marks) b) Given the signaltonoise ratio (SNR), i.e., . find the rates of errorfree uncoded transmissions using the two constellations. (10 marks) c) Identify the SNR condition under which one constellation can outperform the other. (5 marks) Consider the simplest complex constellations of 8PSK and 16PSK which sends symbols along both the I and Q components, as shown in Fig. 1. Let E denote the average transmit power, and 2 the variance of each of the real and imaginary parts of the additive white Gaussian noise at a receiver. 110 0110 0111 4 0010 . 0101 0011 . . 0001 101 100 001 0100 . JE Admin 22 1100 000 41 1101 . 111 011 010 1201 . 1110 1011 1010 . 27 1424 " 64 43 " 13 84 " " 0000 1000 . a) Derive the error probability of each of the constellations in a singleinputsingleoutput (SISO) Rayleigh fading channel. Give the results in terms of the Qfunction. For analytical tractability, we only take into account the errors between adjacent constellation points. (10 marks) b) Given the signaltonoise ratio (SNR), i.e., . find the rates of errorfree uncoded transmissions using the two constellations. (10 marks) c) Identify the SNR condition under which one constellation can outperform the other. (5 marks)
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Operations Management
ISBN: 9780071091428
4th Canadian edition
Authors: William J Stevenson, Mehran Hojati
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