Abstract
In this paper, we analyze the performance of cognitive multi-hop networks employing the two most common cooperation protocols, decode-and-forward (DF) and amplify-and-forward (AF). In order to provide the primary quality of service, strict limits on the transmit powers of the secondary nodes are imposed. Considering transmissions over independent but not necessarily identically distributed (i.n.i.d.) Rayleigh fading channels, an exact closed-form expression for the outage probability (OP) of the secondary transmission is derived for cognitive DF relay networks under the constraint of satisfying a required OP of the primary transmission. In addition, for the cognitive AF relay networks, a lower bound for the OP and an upper bound for the symbol error probability of the secondary transmission under considering constraint on the received-interference at the primary destination is obtained. For additional insights, the diversity order for both cases is also provided .
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Appendices
Proof of Proposition 1
Notice that the RVs \(x = {\left| {{h_{\text{{PT}},\text{{PD}}}}} \right| ^2}\) and \(y = {\left| {{h_{\ell ,\text{{PD}}}}} \right| ^2}\) follow the exponential distribution with parameters \(\frac{1}{{\sigma _{\text{{PT}},\text{{PD}}}^2}}\) and \(\frac{1}{{\sigma _{\ell ,\text{{PD}}}^2}}\), respectively. Thus, by using the joint probability density function of RVs \(x\) and \(y\), and considering (1) we have
where \(\text{{R}} = {\gamma _{\text{{PT}}}}x - {\gamma _\ell }y\varTheta < \varTheta \).
Proof of Proposition 4
In order to evaluate the SOP, we need to obtain the CDF of RV \(U = \frac{X}{{YZ}}\), where RVs \(X\), \(Y\), and \(Z\) follow the exponential distribution with parameters \(\frac{1}{{\sigma _X^2}}\), \(\frac{1}{{\sigma _Y^2}}\) and \(\frac{1}{{\sigma _Z^2}}\), respectively. The CDF of the RV \(U\) is obtained from [8] as
where \(\varGamma \left( {.,.} \right) \) is the incomplete Gamma function [12], Eq. (8.350.2)]. So, \(\Pr \left( {{\gamma _{\ell + 1}} < \gamma } \right) \) can be obtained from (27) by substituting \(X = \bar{\gamma } {\left| {{h_{\ell ,\ell + 1}}} \right| ^2}\), \(Y = {\left| {{h_{\text{{PT}},\ell + 1}}} \right| ^2}\) and \(Z = {{\bar{\gamma } }_I}{\left| {{h_{\ell ,\text{{PD}}}}} \right| ^2}\). Therefore, the CDF of the upper bounded SIR, \({\gamma _{A{F_{up}}}}\), is given by
where \({x_\ell } = \frac{{\bar{\gamma }\sigma _{\ell ,\ell + 1}^2}}{{\sigma _{PT,\ell + 1}^2{{\bar{\gamma } }_I}\sigma _{\ell ,PD}^2\gamma }}\).
Hence, according to the preceding equation, the lower bound for the SOP can be given by
where \({\gamma _{\text{{th}}}}\) is an outage threshold.
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Najafi, M., Ardebilipour, M., Soleimani-Nasab, E. et al. Multi-Hop Cooperative Communication Technique for Cognitive DF and AF Relay Networks. Wireless Pers Commun 83, 3209–3221 (2015). https://doi.org/10.1007/s11277-015-2590-0
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DOI: https://doi.org/10.1007/s11277-015-2590-0