An antipodal binary signal si(t) is a +A-V or -A-V pulse during the in- terval (0,T). Determine
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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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First lets find the optimum detection threshold using the formula rt A2 PH1 P... View the full answer
Related Book For
Elementary Statistics A Step By Step Approach
ISBN: 9780077665807
9th Edition
Authors: Allan G. Bluman
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