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The exact closed-form expressions for outage probability and bit error rateof spectrum sharing-based multi-hop decodeand- forward (DF) relay networks innon-identical Rayleigh fading channels are derived. We also provide theapproximate closed-form expression for the system ergodic capacity. Utilizingthese tractable analytical formulas, we can study the impact of key networkparameters on the performance of cognitivemulti-hop relay networks underinterference constraints. Using a linear network model, we derive an optimumrelay position scheme by numerically solving an optimization problem ofbalancing average signal-to-noise ratio (SNR) of each hop. The numericalresults show that the optimal scheme leads to SNR performance gains of morethan 1 dB. All the analytical expressions are verified by Monte-Carlosimulations confirming the advantage ofmultihop DF relaying networks incognitive environments.

Spectrum Sharing-based Multi-hop Decode-and-Forward Relay Networks under  Interference Constraints: Performance Analysis and Relay Position  Optimization