Asymptotically optimum quantization with time invariant breakpoints for signal detection
Abstract
The nonlinear equations whose solution determines the locally optimum detection quantizer design are derived for a general parametric detection problem where the breakpoints are constrained to be time invariant. These quantizers maximize the efficacy of a test based on quantized data. Some specific optimum detection quantizer problems for the case of timeinvariant breakpoints have been solved in the past, but only for the special case when the locally optimum nonlinearity factors in a certain way. Examples of observation models that do not satisfy these conditions are given. It is demonstrated that the locally optimum quantizer design for the timeinvariant breakpoint constraint is the same as that quantizer design that minimizes the timeaverage meansquare difference between the quantizer and the locally optimum timevarying nonlinearity. A specific result shows that the optimum quantizer is not symmetric for the quadratic detector for random signal in Gaussian noise.
 Publication:

IEEE Transactions on Information Theory
 Pub Date:
 March 1991
 Bibcode:
 1991ITIT...37..402B
 Keywords:

 Asymptotic Methods;
 Optimization;
 Random Noise;
 Random Signals;
 Signal Detection;
 Data Reduction;
 Invariance;
 Signal Distortion;
 Communications and Radar