Evaluation of the Q Function

Author

Shnidman, David A.

Author_Institution

Massachusetts Institute of Technology,Lexington,Mass

Volume

Issue

fYear

1974

fDate

3/1/1974 12:00:00 AM

Firstpage

342

Lastpage

346

Abstract

A convenient method of evaluating the $Q$ function over the parameter space quarter plane is presented. The $Q$ function is first expressed as an infinite series. The $N$ term truncated series $Q_{N}(a, b)$ is used to approximate $Q(a, b)$ for $a^{2} + b^{2} \\leq R$ where the choice of $N$ depends on the accuracy desired and $R$ is determined by considerations such as computer bit capacity, computational time, and accuracy. For $a^{2} + b^{2} > R$ , alternate expressions are used. When $b - a \\geq d$ , we approximate $Q$ by 0, and when $b - a \\leq d$ , we approximate $Q$ by 1. The accuracy is dependent on the choice of the constant $d$ . In the reniainder of the quarter plane, $a^{2} + b^{2} > R$ and $| b - a < d$ , and an efficient expression is used, but it is of limited accuracy (from 10^-5to 10^-9) near the line $a = b$ .

Keywords

DPSK signal detection; Digital signal detection; FSK signal detection; PAM signal detection; Q function; Contracts; Convergence; Equations; Jacobian matrices; Parameter estimation; Testing;

fLanguage

English

Journal_Title

Communications, IEEE Transactions on

Publisher

ieee

ISSN

0090-6778

Type

jour

DOI

10.1109/TCOM.1974.1092184

Filename

1092184

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1239299