An antipodal binary signal si(t) is a +A-V or -A-V pulse during the in- terval (0,T). Determine the optimum detection threshold if the a-priory probabilities are

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An antipodal binary signal s;(t) is a +A-V or -A-V pulse during the in- terval (0,T). Determine the optimum detection threshold a* if the a-priory probabilities are P(S1) = 0.5 P(S₁) = 0.7 Find the probability of error Pe when P(8₁) = P(8₂) = 0.5, A= 10 mV, the bit rate of the data is 10¹ b/s, and = 10-9 W/Hz (A Table of Q-functions is included in the formula booklet) If the bit rate is increased to 105 b/s, what value of A is need to attain the same Pe in (c) Z 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 4.00 4.25 4.75 5.20 5.60 Q (z) 0.5000 0.4801 0.4602 0.4404 0.4207 0.4013 0.3821 0.3632 0.3446 0.3264 0.3085 0.2912 0.2743 0.2578 0.2420 0.2266 0.2169 0.1977 0.1841 0.1711 0.00003 10-5 10-6 10-7 10-8 Z 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 Q (2) z 0.1587 2.00 0.1469 2.05 0.1357 2.10 0.1251 2.15 0.1151 2.20 0.1056 2.25 0.0968 2.30 0.0885 2.35 0.0808 2.40 0.0735 2.45 0.0668 2.50 0.0606 2.55 0.0548 2.60 0.0495 2.65 0.0446 2.70 0.0401 2.75 0.0359 2.80 0.0322 2.85 0.0287 2.90 0.0256 2.95 Q (z) 0.0228 0.0202 0.0179 0.0158 0.0139 0.0122 0.0107 0.0094 0.0082 0.0071 0.0062 0.0054 0.0047 0.0040 0.0035 0.0030 0.0026 0.0022 0.0019 0.0016 z 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 Q (2) 0.00135 0.00114 0.00097 0.00082 0.00069 0.00058 0.00048 0.00040 0.00034 0.00028 0.00023 0.00019 0.00016 0.00013 0.00011 0.00009 0.00007 0.00006 0.00005 0.00004 An antipodal binary signal s;(t) is a +A-V or -A-V pulse during the in- terval (0,T). Determine the optimum detection threshold a* if the a-priory probabilities are P(S1) = 0.5 P(S₁) = 0.7 Find the probability of error Pe when P(8₁) = P(8₂) = 0.5, A= 10 mV, the bit rate of the data is 10¹ b/s, and = 10-9 W/Hz (A Table of Q-functions is included in the formula booklet) If the bit rate is increased to 105 b/s, what value of A is need to attain the same Pe in (c) Z 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 4.00 4.25 4.75 5.20 5.60 Q (z) 0.5000 0.4801 0.4602 0.4404 0.4207 0.4013 0.3821 0.3632 0.3446 0.3264 0.3085 0.2912 0.2743 0.2578 0.2420 0.2266 0.2169 0.1977 0.1841 0.1711 0.00003 10-5 10-6 10-7 10-8 Z 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 Q (2) z 0.1587 2.00 0.1469 2.05 0.1357 2.10 0.1251 2.15 0.1151 2.20 0.1056 2.25 0.0968 2.30 0.0885 2.35 0.0808 2.40 0.0735 2.45 0.0668 2.50 0.0606 2.55 0.0548 2.60 0.0495 2.65 0.0446 2.70 0.0401 2.75 0.0359 2.80 0.0322 2.85 0.0287 2.90 0.0256 2.95 Q (z) 0.0228 0.0202 0.0179 0.0158 0.0139 0.0122 0.0107 0.0094 0.0082 0.0071 0.0062 0.0054 0.0047 0.0040 0.0035 0.0030 0.0026 0.0022 0.0019 0.0016 z 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 Q (2) 0.00135 0.00114 0.00097 0.00082 0.00069 0.00058 0.00048 0.00040 0.00034 0.00028 0.00023 0.00019 0.00016 0.00013 0.00011 0.00009 0.00007 0.00006 0.00005 0.00004

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Firstly we need to find the optimum detection threshold alpha given the apriori probabilities Let Ps1 be the probability that signal s1 is sent Ps1 05 ... View the full answer