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As in nonturbulent case, since the input distribution that maximizes the mutual information is nonuniform, numerical maximization of the capacity bound in (11) and mutual information over the input distribution for the gamma-gamma atmospheric turbulent channel are shown in Figure 4(a) when and a rectangular pulse shape with are used.
Since the input distribution that maximizes the mutual information varies with the SNR, numerical maximization of the capacity bound in (15) and mutual information over the input distribution for the nonturbulent channel are shown in Figure 2(a) when a rectangular pulse shape with duty cycle of, that is,, and are adopted.
Given a value of s, we can compute the likelihood of the observations, so we could just find the value of s that maximizes this likelihood, either by searching or by standard numerical maximization techniques.
(2) Numerical maximization function of the object optimization.
We use a quasi-Newton method (e.g., Fletcher and Powell, 1963) for the numerical maximization.
The pulses are designed by numerical maximization of BS sequence sensitivity, subject to constraints that ensure low on-resonance excitation.
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In Fig. 2, we show the result of the numerical SINR maximization (51) and BER minimization (52), and compare them with the derived theoretical bounds (47) and (50), considering a frequency-selective relay-destination channel and SNR d =10,12 ,…,30dB.
In our study, Count's numerical likelihood maximization procedure converged for all models for the original data set and for all bootstrap replicates.
The numerical results of heuristics maximization are included in Tables 1, 2, and 3 for both traditional and referential approaches.
As numerical examples, the resonance frequency maximization problem of a cantilever beam, bandwidth maximization of a clamped end beam and the bandwidth minimization problem of a plasmonic grating coupler are presented to demonstrate the validity of the proposed method.
Numerical examples demonstrate that revenue maximization and environment protection policies of the government significantly affect the production ESS of competitive power plants.
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