Performance analysis of opportunistic CSMA schemes in cognitive radio networks

Abstract

In this paper, we consider underlay cognitive radio (CR) networks where an amount of interference caused by secondary stations (STAs) has to be kept below a predefined level, which is called interference temperature. We propose opportunistic p-persistent carrier sense multiple access schemes for the CR networks, which opportunistically exploit wireless channel conditions in transmitting data to the secondary access point. We also devise an adaptive interference-level control technique to further improve quality-of-service of a primary network by limiting the excessive interference due to collisions among STAs. The performances of the proposed schemes are mathematically analyzed, and they are validated with extensive computer simulations. The simulation results show that the proposed schemes achieve near optimal throughput of the secondary network while they are backward-compatible to the conventional p-persistent CSMA scheme.

Appendix

1.1 The CDF of the effective channel gain $f_i$

The CDF of $f_i$ is, by definition, given as

$$\begin{aligned} F_F(x)=\, & {} {\text {Pr}}\left\{ {f \le x}\right\} \nonumber \\=\, & {} {\text {Pr}}\left\{ {f \le x,\gamma _i\le Q /\overline{P}}\right\} +{\text {Pr}}\left\{ {f \le x,\gamma _i> Q /\overline{P}}\right\} \nonumber \\=\, & {} {\text {Pr}}\left\{ {\overline{P} \eta _i \le x,\gamma _i\le Q /\overline{P}}\right\} +{\text {Pr}}\left\{ { Q \frac{\eta _i}{\gamma _i} \le x,\gamma _i> Q /\overline{P}}\right\} \nonumber \\=\, & {} {\text {Pr}}\left\{ {\overline{P} \eta _i \le x}\right\} {\text {Pr}}\left\{ {\gamma _i\le Q /\overline{P}}\right\} +{\text {Pr}}\left\{ { Q \frac{\eta _i}{\gamma _i} \le x,\gamma _i> Q /\overline{P}}\right\} \nonumber \\=\, & {} \left( {1-e^{-\frac{x}{\overline{P} \mu _H}}}\right) \left( {1-e^{-\frac{ Q }{\overline{P} \mu _G}}}\right) +{\text {Pr}}\left\{ { Q \frac{\eta _i}{\gamma _i} \le x,\gamma _i> Q /\overline{P}}\right\} . \end{aligned}$$

(30)

${\text {Pr}}\left\{ { Q \frac{\eta _i}{\gamma _i} \le x,\gamma _i> Q /\overline{P}}\right\}$ in (30) can be further derived as follows.

$$\begin{aligned} {\text {Pr}}\left\{ { Q \frac{\eta _i}{\gamma _i} \le x,\gamma _i> Q /\overline{P}}\right\}= & {} \int _{ Q /\overline{P}}^{\infty }{{\text {Pr}}\left\{ { Q \frac{\eta _i}{t} \le x|\gamma _i=t}\right\} f_\varGamma (t) dt}\nonumber \\= & {} \int _{ Q /\overline{P}}^{\infty }{{\text {Pr}}\left\{ { Q \frac{\eta _i}{t} \le x}\right\} \left( {\frac{1}{\mu _G}e^{-\frac{t}{\mu _G}}}\right) dt}\nonumber \\= & {} e^{-\frac{ Q }{\overline{P} \mu _G}}-\left( {\frac{\mu _H Q }{\mu _G x+\mu _H Q }}\right) e^{-\left( {\frac{x}{\overline{P} \mu _H}+\frac{ Q }{\overline{P} \mu _G}}\right) }. \end{aligned}$$

(31)

By substituting (31) into (30), we obtain the CDF of the effective secondary channel gain $f_i$ given as

$$\begin{aligned} \begin{array}{lll} F_F(x)=1-e^{-\frac{x}{\overline{P} \mu _H}}+\left( {\frac{\mu _G x}{\mu _G x+\mu _H Q }}\right) e^{-\left( {\frac{x}{\overline{P} \mu _H}+\frac{ Q }{\overline{P} \mu _G}}\right) }. \end{array} \end{aligned}$$

(32)