Minimum distance between points in signal constellation

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Qusetion: Suppose that more than two dimensions are available for our alphabet. Consider an alphabet where the symbols are vertices of an M dimensional hypercube, shown for M = 3 in the following figure

1031_Alphabet.png

Assume that all the symbols are equally likely and the noise in each dimension is independent with variance σ2.

(a) What are the decision regions?

(b) What is the probability of error as a function of M and the minimum distance d between points in the signal constellation.

Reference no: EM131770360

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