  The exact closed-form expressions for outage probability and bit error rate
of spectrum sharing-based multi-hop decodeand- 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 cognitivemulti-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. All the analytical expressions are verified by Monte-Carlo
simulations confirming the advantage ofmultihop DF relaying networks in
cognitive environments.
