### What is the probability of error with equal gain combining

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##### Reference no: EM13247411

Three independent diversity branches are used to transmit a BPSK modulated data over a channel described by: y= sqrt(p)*h*x+n. where y is the recieved signal, x is the transmitted signal (+or-1 with equal probabilities). Assume that h is a random variable with PDF. Pn(h)=0.1*d(h-1)+0.9d(h-3). n is a zero mean white gaussian noise with variance 0.5. Assume that the channel state info is available at the reciever for each of the three branches.

(a) what is the optimal decision rule at the reciever?

(b) What is the probability of error with equal gain combining?

(c) What is the probability of error with MRC?

(d) What is the probability of error with SC?

(e) What is the probability of error if we make hard-decision on each branch and then use majority-logic combining to make the final decision?

(f) What is the probability of error if we select the "best" two branches, and then use MRC with these two branches?

(g) Order the schemes of (b) through (f) from best to worst in terms of performance for large SNRs.

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