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Global and Local Optimization Algorithms for Optimal Signal Set Design

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ABSTRACT

The problem of choosing an optimal signal set for non-Gaussian detection was reduced to a smooth inequality constrained mini-max nonlinear programming problem by Gockenbach and Kearsley. Here we consider the application of several optimization algorithms, both global and local, to this problem. The most promising results are obtained when special-purpose sequential quadratic programming (SQP) algorithms are embedded into stochastic global algorithms.

No MeSH data available.


Optimal constellation for Hyperbolic Secant noise, M = 16, sine-cosine basis.
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f8-j62kea: Optimal constellation for Hyperbolic Secant noise, M = 16, sine-cosine basis.

Mentions: We ran Algorithm MLSL for 20 different problem instances. The algorithm was stopped after it appeared that no better local minimizers would be found (i.e., the estimate of the global minimum remained constant for several MLSL iterations). In Tables 4 and 5 we list our computed minimum values for instances of (SS) with M = 8 and M = 16, respectively. Note that our solutions respectively. Note that our solutions agree with those reported in Ref. [7]. In all cases, execution was terminated after no more than 10 to 15 minutes. In Figs. 3 through 8 we show the optimal signal constellations for several of the instances of (SS) corresponding to the optimal values listed in Tables 4 and 5.


Global and Local Optimization Algorithms for Optimal Signal Set Design
Optimal constellation for Hyperbolic Secant noise, M = 16, sine-cosine basis.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4862810&req=5

f8-j62kea: Optimal constellation for Hyperbolic Secant noise, M = 16, sine-cosine basis.
Mentions: We ran Algorithm MLSL for 20 different problem instances. The algorithm was stopped after it appeared that no better local minimizers would be found (i.e., the estimate of the global minimum remained constant for several MLSL iterations). In Tables 4 and 5 we list our computed minimum values for instances of (SS) with M = 8 and M = 16, respectively. Note that our solutions respectively. Note that our solutions agree with those reported in Ref. [7]. In all cases, execution was terminated after no more than 10 to 15 minutes. In Figs. 3 through 8 we show the optimal signal constellations for several of the instances of (SS) corresponding to the optimal values listed in Tables 4 and 5.

View Article: PubMed Central - PubMed

ABSTRACT

The problem of choosing an optimal signal set for non-Gaussian detection was reduced to a smooth inequality constrained mini-max nonlinear programming problem by Gockenbach and Kearsley. Here we consider the application of several optimization algorithms, both global and local, to this problem. The most promising results are obtained when special-purpose sequential quadratic programming (SQP) algorithms are embedded into stochastic global algorithms.

No MeSH data available.