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MCMC method can achieve the maximal channel capacity.
Calculate W = 1 m + 1 ∑ i = 0 m W i and maximal channel capacity Cmax (optimize transmit power, distance and allocation time at scheme 1).
However, with small alpha, MCMC method optimizes the transmit power, the distance, the allocation time simultaneously and achieves the maximal channel capacity in any channel model.
Step 3: If end-to-end channel capacity of scheme 2 is close to maximal channel capacity C max - C C max ≤ α, the algorithm is finished.
When the end-to-end channel capacity (C = min(C i )) is approximate to the maximal channel capacity (Cmax), we have C ̄ ≈ C max and | max C i - C ̄ | ≈ | min C i - C ̄ |.
The MCMC method is constructed to find the optimal state of transmit power, distance and allocation time that has the end-to-end channel capacity close to the maximal channel capacity.
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As shown in Figure 10, there are the optimal numbers of relays in the sense of maximal end-to-end channel capacity of each number of phases.
There is the optimum number of relays for each access control on the MAC layer that achieves the maximal end-to-end channel capacity.
In other words, the optimized distance, transmit power and allocation time at scheme 1 is one of the optimal solutions for maximal end-to-end channel capacity of any channel model.
Additionally, the maximal end-to-end channel capacity and the optimal number of relays are changed, depending on the transmit power of TX, the total transmit power of RS, the transmission environment (W), and so on.
The channel capacity maximization problem is now changed to the choice of the maximal number of real, non-negative values γ i - 1 i k subject to the power constraint ∑ k = 1 M γ i - 1 i k = snr i.
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