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 time-invariant 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 time-invariant breakpoint constraint is the same as that quantizer design that minimizes the time-average mean-square difference between the quantizer and the locally optimum time-varying 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:
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- Asymptotic Methods;
- Optimization;
- Random Noise;
- Random Signals;
- Signal Detection;
- Data Reduction;
- Invariance;
- Signal Distortion;
- Communications and Radar