Optimal linear detectors for additive noise channels

We describe procedures for designing optimal and suboptimal linear detectors (discrete-time case) for additive white noise channels. We rst describe a technique for designing linear detectors based on the Wiener theory of nonlinear systems. Next, exact expressions for optimal linear detector are found when the noise amplitude's probability distribution is stable. We then describe how to computationally design the optimal linear detector when the noise is Laplacian. Considering all the linear detectors thus derived, the ad hoc Wiener approach is shown to be suboptimal, and no general form for the optimal linear detector's unit-sample response is apparent. Performance analyses and simulations indicate substantial performance losses occur when linear detectors are used instead of optimal (likelihood ratio) ones. Permission to publish abstract separately granted.