For an optimal receiver design for a binary communication sy

For an optimal receiver design for a binary communication system with AWGN For this problem, where channel noise NOT AWGN, the conditional probability density functions are Area of Trapezoid = average of two base lengths times the altitude ((6 + 2)/2) Times altitude = 4 Times altitude From the geometry - if we call the altitude (or, height) -- \'h\' -- the two trapeziods cross at x = 0 at 0.50 h ((6 + 2)/2) Times h = 4h The altitude of the trapezoids was not given, but the area of each conditional probability density function equal to one (1) If so, 4h = 1 -- h = 1/4 At x = 0 1/2 h = 1/8 Area A_0 = A_1 = (1/2)* (1)* (1/8) Area A_0 = A_1 = 1/16 If transmission of 0 or 1 is equally likely, what are the optimal decision thresholds? If transmission of 0 or 1 is equally likely, what is the corresponding error probability? If the probability of transmitting a 0 is 0.40 and the probability of transmitting a 1 is 0.60 compute the optimal threshold.

Solution

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to obatain optical bit error rate for the receved signal it is important to take 0/1 decisions bases on optimum setting of the decision thereshold.this decision making sometimes referred as slising depend on impairement of optical signal has expirence during the propagation. over the fiber