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Q.1 (40p) Wireless Channel and Diversity
A wireless channel observes two fading amplitudes, \( a_{1}=0.2 \) and \( a_{2}=1.4 ???????

Q.1 (40p) Wireless Channel and Diversity A wireless channel observes two fading amplitudes, \( a_{1}=0.2 \) and \( a_{2}=1.4 \) with equal probabilities. (a) What is probability of error for binary phase shift keying (BPSK) system if the average SNR \( \left(E_{b} / N_{0}\right) \) is \( 10 \mathrm{~dB} \) ? (b) If the channel does not observe fading, what would be the average SNR to achieve bit error rate that you calculated in part A? (c) Suppose receiver is modified and number of antennas is increased from 1 to 3, and all three antennas observe the fading independently. A device measures the fading amplitudes (SNRs) of each antenna and utilizes signal coming from antenna whose fading amplitude (SNR) is the highest (also called Selective Combining). In that case, what would be the probability of error if SNR is \( 20 \mathrm{~dB} \) ?


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(a) To calculate the probability of error for a BPSK system with an average SNR of 10 dB, we can use the Q function, which is defined as Q(x) = (1/sqr
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