An Mary quadrature amplitude modulation (QAM) communications system can be viewed as a generalization of the QPSK system described in Example 11.13. In the QAM system, one of M equally likely symbols s0,...,sm-1 is transmitted every unit of time. When symbol si is transmitted, the receiver produces the two-dimensional vector output

X = si + N,

where N has iid Gaussian (0, σ2) components. Based on the output X, the receiver must decide which symbol was transmitted. Design a hypothesis test that maximizes the probability of correctly deciding what symbol was sent.

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Sil Si 812 T2