  In this paper, quantizer design for weak-signal detection under arbitrary
binary channel in generalized Gaussian noise is studied. Since the performances
of the generalized likelihood ratio test (GLRT) and Rao test are asymptotically
characterized by the noncentral chi-squared probability density function (PDF),
the threshold design problem can be formulated as a noncentrality parameter
maximization problem. The theoretical property of the noncentrality parameter
with respect to the threshold is investigated, and the optimal threshold is
shown to be found in polynomial time with appropriate numerical algorithm and
proper initializations. In certain cases, the optimal threshold is proved to be
zero. Finally, numerical experiments are conducted to substantiate the
theoretical analysis.
