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The exact closed-form expressions for outage probability and bit error rate of spectrum sharing-based multi-hop decode-and-forward (DF) relay networks in non-identical Rayleigh fading channels are derived. We also provide the approximate closed-form expression for the system ergodic capacity. Utilizing these tractable analytical formulas, we can study the impact of key network parameters on the performance of cognitive multi-hop relay networks under interference constraints. Using a linear network model, we derive an optimum relay position scheme by numerically solving an optimization problem of balancing average signal-to-noise ratio (SNR) of each hop. The numerical results show that the optimal scheme leads to SNR performance gains of more than 1 dB. AU the analytical expressions are verified by Monte-Carlo simulations confirming the advantage of multihop DF relaying networks in cognitive environments.