TY - JOUR

T1 - Sufficient condition on hypothesis statistics for suboptimality of the identical-quantizer parallel distributed detection system

AU - Yang, Yi Hong

AU - Wang, Peng Hua

AU - Chen, Po-Ning

PY - 2018/2/17

Y1 - 2018/2/17

N2 - A challenge in designing an optimal parallel distributed detection system is its exponentially increasing number of possible combinations of local quantization rules with respect to n local sensors. Instead, one may focus on a much easier task of finding the best identical-quantizer system (IQS). This raises an important query about when the simple best IQS is globally optimal in Bayes detection error, particularly under a finite number of sensors. We consider this issue by asking the different but relevant question of when the best IQS is only suboptimal. By numerical experiments over the simplest system setting with ternary local observations and binary local quantizers, we find and prove that for every even n ≥ 2, if the output statistics of a local quantizer are symmetric with respective to the two hypotheses, the corresponding IQS design can never be optimal in the sense of minimizing the Bayes detection error subject to equal prior probabilities. Our analysis also indicates that asymptotically, one can almost halve the detection error of an IQS by replacing one of the identical local quantizers with a different one when the two hypothesis distributions place most of their probability masses, respectively, on two different local observation outcomes.

AB - A challenge in designing an optimal parallel distributed detection system is its exponentially increasing number of possible combinations of local quantization rules with respect to n local sensors. Instead, one may focus on a much easier task of finding the best identical-quantizer system (IQS). This raises an important query about when the simple best IQS is globally optimal in Bayes detection error, particularly under a finite number of sensors. We consider this issue by asking the different but relevant question of when the best IQS is only suboptimal. By numerical experiments over the simplest system setting with ternary local observations and binary local quantizers, we find and prove that for every even n ≥ 2, if the output statistics of a local quantizer are symmetric with respective to the two hypotheses, the corresponding IQS design can never be optimal in the sense of minimizing the Bayes detection error subject to equal prior probabilities. Our analysis also indicates that asymptotically, one can almost halve the detection error of an IQS by replacing one of the identical local quantizers with a different one when the two hypothesis distributions place most of their probability masses, respectively, on two different local observation outcomes.

KW - Identical-quantizer system

KW - hypothesis statistics

KW - distributed detection

KW - DESIGN

KW - MIMO

UR - http://www.scopus.com/inward/record.url?scp=85042911729&partnerID=8YFLogxK

U2 - 10.1080/02533839.2018.1437361

DO - 10.1080/02533839.2018.1437361

M3 - Article

AN - SCOPUS:85042911729

SN - 0253-3839

VL - 41

SP - 98

EP - 111

JO - Journal of the Chinese Institute of Engineers, Transactions of the Chinese Institute of Engineers,Series A/Chung-kuo Kung Ch'eng Hsuch K'an

JF - Journal of the Chinese Institute of Engineers, Transactions of the Chinese Institute of Engineers,Series A/Chung-kuo Kung Ch'eng Hsuch K'an

IS - 2

ER -