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The authors presented a cognitive OFDM-based relay spectrum pooling system, and considered the problem of optimum reassignment of subcarriers in the spectrum pools by the relay. They showed that the capacity of the system is maximized when the subcarrier SNRs in the spectrum pools corresponding to the source-relay and relay-destination are similarly ordered. They further characterized a larger class of cost functions - functions that are a composition of an increasing, Schur convex function with a monotonic, super-modular function, for which this reassignment scheme is optimum.
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