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SJSU EE 160 - Homework # 6

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EE160. Spring 2003. San Jos´e State UniversityHomework # 6 Due: May 13, 2003Problem 1 (textbook 7.34).Binary PSK is used for data transmission over an AWGN channel with power spectraldensity N0/2=10−10W/Hz. The transmitted signal energy is Eb= A2T/2, where Tis the bit duration and A is the signal amplitude. Determine the value of A needed toachieve an error probability of 10−6, if the data rate is:(a) 10 Kbit/s(b) 100 Kbit/s(c) 1 Mbit/sProblem 2 (textbook 7.44).The 16-QAM signal constellation shown in the figure below is an international standardfor (analog) telephone-line modems known as V.29. Determine the decision boundariesfor the detector, assuming equiprobable signals and high SNR so that errors only occurbetween adjacent points.513-113-1-5 -3 5-3-5Problem 3 (textbook 7.47.)A digital communication system transmits data using QAM signaling over a voice-bandtelephone channel at a rate 2400 symbols/s (baud). The additive noise is assumed tobe white and Gaussian. You are asked to determine the energy-per-bit-to-noise ratioEb/N0required to achieve an error probability of 10−5for a bit rate equal to:(a) 4800 bits/s(b) 9600 bits/s(c) 19200 bits/s(d) 31200 bits/s(e) What conclusions can you draw from parts (a) to (d)?(Hint: Use the following expression for the error probability of an M-ary QAM system:PM≈ 4 Q3Eb(M − 1)N0 ,where M =2and  is the number of bits per symbol. Also, if needed, use the followingapproximation of the Gaussian Q-function:Q(x)


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