TY - GEN

T1 - Asymptotic expansions for sample size in signal detection

AU - Burnashev, Marat V.

AU - Poor, H. Vincent

PY - 1993/1/1

Y1 - 1993/1/1

N2 - The number of samples required for signal detection is considered as a function of the error probabilities. This problem is treated in the context of detecting a constant signal in additive, independent and identically distributed noise. Detectors that base their decisions on the comparison with a threshold of accumulated, nonlinearly transformed observations are treated. Asymptotic expressions are derived for the relationship between sample size and error probabilities for this model in two situations: that in which the nonlinearity has a partially absolutely continuous output distribution; and that in which it has a lattice output distribution. Traditional analyses of such problems have involved only the lowest-order terms of such relationships (i.e., central limit results), leading to performance indices such as the Pitman asymptotic relative efficiency (ARE). Such indices are known to be of limited accuracy in predicting performance for more moderate sample sizes. Here, the behavior of sample size as a function of error probabilities is considered in more detail, leading to more accurate indices of relative efficiencies for such detection problems. Several specific examples are examined in detail, and numerical results are included to illustrate the significantly improved performance estimation afforded thereby for even small sample sizes.

AB - The number of samples required for signal detection is considered as a function of the error probabilities. This problem is treated in the context of detecting a constant signal in additive, independent and identically distributed noise. Detectors that base their decisions on the comparison with a threshold of accumulated, nonlinearly transformed observations are treated. Asymptotic expressions are derived for the relationship between sample size and error probabilities for this model in two situations: that in which the nonlinearity has a partially absolutely continuous output distribution; and that in which it has a lattice output distribution. Traditional analyses of such problems have involved only the lowest-order terms of such relationships (i.e., central limit results), leading to performance indices such as the Pitman asymptotic relative efficiency (ARE). Such indices are known to be of limited accuracy in predicting performance for more moderate sample sizes. Here, the behavior of sample size as a function of error probabilities is considered in more detail, leading to more accurate indices of relative efficiencies for such detection problems. Several specific examples are examined in detail, and numerical results are included to illustrate the significantly improved performance estimation afforded thereby for even small sample sizes.

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M3 - Conference contribution

AN - SCOPUS:0027262028

SN - 0780308786

T3 - Proceedings of the 1993 IEEE International Symposium on Information Theory

BT - Proceedings of the 1993 IEEE International Symposium on Information Theory

PB - Publ by IEEE

T2 - Proceedings of the 1993 IEEE International Symposium on Information Theory

Y2 - 17 January 1993 through 22 January 1993

ER -