On deflection as a performance criterion in detection

The performance of detection systems is usually characterized by the receiver operating characteristics (ROC) curves. Because of the complexity of the calculation of such curves simpler performance criteria are useful. Among these, the deflection criterion, or output signal-to-noise ratio, is one of the most interesting. The advantages and limitations of the deflection are first analyzed. Attention is especially paid to the relation between singular detection and infinite deflection. Maximization of the deflection in the class of linear-quadratic (L-Q) systems is also discussed and it is shown that in order to detect a deterministic signal in some kinds of non-gaussian noise a quadratic term can introduce an almost singular detection. This situation is analyzed by computer simulations and comparisons between results obtained via the deflection or the ROC curves indicate the interest of the deflection in the analysis of the performance of some nonlinear system