A binary communication system transmits the same information on two diversity channels. The two received signals...

 

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A binary communication system transmits the same information on two diversity channels. The two received signals after matched filters and sampling are = where E{n} => E{n} = 0, E{n}} = 0, E{n} = o, and n and n are uncorrelated Gaussian variables. The detector bases its decision on the linear combination of r and r2; i.e., r = 11+k+2 1. Determine the value of k that minimizes the probability of error. 2. Plot the probability of error for = 1 and 3 and either k = 1 or k is the optimum value found in (1). Compare the results. A binary communication system transmits the same information on two diversity channels. The two received signals after matched filters and sampling are = where E{n} => E{n} = 0, E{n}} = 0, E{n} = o, and n and n are uncorrelated Gaussian variables. The detector bases its decision on the linear combination of r and r2; i.e., r = 11+k+2 1. Determine the value of k that minimizes the probability of error. 2. Plot the probability of error for = 1 and 3 and either k = 1 or k is the optimum value found in (1). Compare the results.