Question

Suppose that we are given the following communication system described in Fig. 1 with the channel corrupted by an additive white Gaussian noise z with zero mean and variance 1 where the channel input.x is used for signal transmission to produce the channel output y,i.e., r- x . Then the channel is further passed through a hard limiter, i.e., sign detector described by Q2(r) in Fig.2 decisions 22(r) Figure 1. A channel with the input x and output r corrupted by a Gaussian noise z where Figure 2. Sign detector (a) (5 points) Assume that two signals so1 and s, -1 will be used for transmission with probabilities 1/4 and 3/4. Let the decision costs be deined by Cy is the cost of claiming signal s, when S, is actually transmitted. Construct a binary channel resulting from the sign detector in Fig. 2 for ov) in Fig. 1. Using the binary channel constructed in part (a) without knowing cy and T, find the Neyman-Pearson detector and its ROC curve. - Using the fact that eda-d(x) and O(x)-1-Φ(x) .

Answer 1

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