1. Consider a baseband digital signal given by: x(t) = k=-Xkp(t-kTs), (Equation 1.1) where p(t) is...

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1. Consider a baseband digital signal given by: x(t) = Σk=-Xkp(t-kTs), (Equation 1.1) where p(t) is a unit-energy square pulse with duration T5, Ts is the symbol period and k is an integer. It is assumed that the sequence of symbols {X} is independent. It is also assumed that the symbols X, are drawn from an alphabet A = {-7A, -5A, -3A, -A, A, 3A, 5A, 7A) of equal probability for 8-ary Pulse Amplitude Modulation (8-PAM) transmission. (b) Assume that the 8-PAM signal is received using an ideal detector with the received signal y(t) related to the transmitted signal x(t) by: y(t) = x(t) + n(t) (Equation 1.2) where n(t) is additive white Gaussian noise. The symbols are equiprobable, and the energy per symbol-to-noise ratio, S/N, = 13 dB. (i) Using either Q-function or complementary error function (erfc(-)) expressions for symbol error rate for polar baseband signals, find the symbol error rate. [7 marks] (ii) Explain how the 3-bit codes can be assigned to the PAM levels to ensure that the bit error rate is not significantly greater than the symbol error rate. [2 marks] 1. Consider a baseband digital signal given by: x(t) = Σk=-Xkp(t-kTs), (Equation 1.1) where p(t) is a unit-energy square pulse with duration T5, Ts is the symbol period and k is an integer. It is assumed that the sequence of symbols {X} is independent. It is also assumed that the symbols X, are drawn from an alphabet A = {-7A, -5A, -3A, -A, A, 3A, 5A, 7A) of equal probability for 8-ary Pulse Amplitude Modulation (8-PAM) transmission. (b) Assume that the 8-PAM signal is received using an ideal detector with the received signal y(t) related to the transmitted signal x(t) by: y(t) = x(t) + n(t) (Equation 1.2) where n(t) is additive white Gaussian noise. The symbols are equiprobable, and the energy per symbol-to-noise ratio, S/N, = 13 dB. (i) Using either Q-function or complementary error function (erfc(-)) expressions for symbol error rate for polar baseband signals, find the symbol error rate. [7 marks] (ii) Explain how the 3-bit codes can be assigned to the PAM levels to ensure that the bit error rate is not significantly greater than the symbol error rate. [2 marks]

Answer rating: 100% (QA)

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