The calculation of the probability of detection and the generalized Marcum <e1>Q</e1>-function

by: DA Shnidman

Information Theory, IEEE Transactions on, Vol. 35, No. 2. (1989), pp. 389-400.

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Abstract

A highly reliable, accurate, and efficient method of calculating the probability of detection, <e1>P</e1>N(<e1>X</e1>,<e1>Y </e1>), for <e1>N</e1> incoherently integrated samples, where <e1>X</e1> is the constant received signal-to-noise ratio of a single pulse and <e1>Y</e1> is the normalized threshold level, is presented. The useful range of parameters easily exceeds most needs. On a VAX/11 computer with double precision calculations, better than 13-place absolute accuracy is normally achieved. There is a gradual loss of accuracy with increasing parameter values. For example, for <e1>N</e1>=109, and with both <e1>NX</e1> and <e1>Y</e1> near 107, the accuracy can drop to ten places. The function <e1>P</e1>N(<e1>X</e1>,<e1>Y </e1>) can be equated to the generalized Marcum <e1>Q</e1>-function, <e1>Q</e1>m(α,β). The corresponding limits on α and β are roughly 4500 for the 13-place accuracy and 60000 for ultimate (INTEGER×4) limit

@article{citeulike:2802234, abstract = {A highly reliable, accurate, and efficient method of calculating the probability of detection, <e1>P</e1>N(<e1>X</e1>,<e1>Y </e1>), for <e1>N</e1> incoherently integrated samples, where <e1>X</e1> is the constant received signal-to-noise ratio of a single pulse and <e1>Y</e1> is the normalized threshold level, is presented. The useful range of parameters easily exceeds most needs. On a VAX/11 computer with double precision calculations, better than 13-place absolute accuracy is normally achieved. There is a gradual loss of accuracy with increasing parameter values. For example, for <e1>N</e1>=109, and with both <e1>NX</e1> and <e1>Y</e1> near 107, the accuracy can drop to ten places. The function <e1>P</e1>N(<e1>X</e1>,<e1>Y </e1>) can be equated to the generalized Marcum <e1>Q</e1>-function, <e1>Q</e1>m(\α,\β). The corresponding limits on \α and \β are roughly 4500 for the 13-place accuracy and 60000 for ultimate (INTEGER\×4) limit}, author = {Shnidman, D. A. }, booktitle = {Information Theory, IEEE Transactions on}, citeulike-article-id = {2802234}, doi = {10.1109/18.32133}, journal = {Information Theory, IEEE Transactions on}, keywords = {acquisition, detection, probability}, number = {2}, pages = {389--400}, posted-at = {2008-05-15 18:55:44}, priority = {2}, title = {The calculation of the probability of detection and the generalized Marcum <e1>Q</e1>-function}, url = {http://dx.doi.org/10.1109/18.32133}, volume = {35}, year = {1989} }

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TY - JOUR ID - citeulike:2802234 L3 - citeulike-article-id:2802234 TI - The calculation of the probability of detection and the generalized Marcum <e1>Q</e1>-function T2 - Information Theory, IEEE Transactions on JF - Information Theory, IEEE Transactions on VL - 35 IS - 2 SP - 389 EP - 400 N2 - A highly reliable, accurate, and efficient method of calculating the probability of detection, <e1>P</e1>N(<e1>X</e1>,<e1>Y </e1>), for <e1>N</e1> incoherently integrated samples, where <e1>X</e1> is the constant received signal-to-noise ratio of a single pulse and <e1>Y</e1> is the normalized threshold level, is presented. The useful range of parameters easily exceeds most needs. On a VAX/11 computer with double precision calculations, better than 13-place absolute accuracy is normally achieved. There is a gradual loss of accuracy with increasing parameter values. For example, for <e1>N</e1>=109, and with both <e1>NX</e1> and <e1>Y</e1> near 107, the accuracy can drop to ten places. The function <e1>P</e1>N(<e1>X</e1>,<e1>Y </e1>) can be equated to the generalized Marcum <e1>Q</e1>-function, <e1>Q</e1>m(α,β). The corresponding limits on α and β are roughly 4500 for the 13-place accuracy and 60000 for ultimate (INTEGER×4) limit KW - acquisition KW - detection KW - probability AU - Shnidman, DA PY - 1989/// UR - http://dx.doi.org/10.1109/18.32133 ER -

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