The transmitter sends one of four equally likely symbols

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For the QPSK communications system of Example 8.13, identify the acceptance sets for the MAP hypothesis test when the symbols are not equally likely. Sketch the acceptance sets when σ = 0.8, E = 1, P[H₀] = 1/2, and P[H₁] = P[H₂] = P[H₃] = 1/6.

Example 8.13

In a quaternary phase shift keying (QPSK) communications system, the transmitter sends one of four equally likely symbols {s₀,s₁,s₂,s₃}. Let Hi denote the hypothesis that the transmitted signal was s_i. When si is transmitted, a QPSK receiver produces the vector X = [X₁ X₂] such that

Where N₁ and N₂ are iid Gaussian (0,σ) random variables that characterize the receiver noise and E is the average energy per symbol. Based on the receiver output X, the receiver must decide which symbol was transmitted. Design a hypothesis test that maximizes the probability of correctly deciding which symbol was sent.

Reference no: EM131083917

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