2. (a) An NRZ binary signal is present the input of a decision circuit in a...

 

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2. (a) An NRZ binary signal is present the input of a decision circuit in a baseband data receiver. The signal is in the presence of white Gaussian noise with an RMS level of a volts. The data signal can assume a level of either A volts or 0 volts corresponding to a logic 1 level and logic 0 level respectively. Show that the receiver error probability (P.) is defined by: P P. =-=-erfec(202) [20 marks] (b) If the binary levels are of equal probability, determine the average signal to noise ratio (in dB) to achieve an error probability of 0.004. An excerpt from the Complementary Error Functions Table is shown in Table Q2.1 below. X erfc(x) X 1.8 0.010909 1.81 0.010475 1.82 0.010057 1.83 0.009653 1.84 0.009264 Table Q2.1 erfc(x) 1.85 0.008889 1.86 0.008528 1.87 0.008179 1.88 0.007844 1.89 0.007521 2. (a) An NRZ binary signal is present the input of a decision circuit in a baseband data receiver. The signal is in the presence of white Gaussian noise with an RMS level of a volts. The data signal can assume a level of either A volts or 0 volts corresponding to a logic 1 level and logic 0 level respectively. Show that the receiver error probability (P.) is defined by: P P. =-=-erfec(202) [20 marks] (b) If the binary levels are of equal probability, determine the average signal to noise ratio (in dB) to achieve an error probability of 0.004. An excerpt from the Complementary Error Functions Table is shown in Table Q2.1 below. X erfc(x) X 1.8 0.010909 1.81 0.010475 1.82 0.010057 1.83 0.009653 1.84 0.009264 Table Q2.1 erfc(x) 1.85 0.008889 1.86 0.008528 1.87 0.008179 1.88 0.007844 1.89 0.007521