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Effective throughput maximization for in-band sensing and transmission in cognitive radio networks

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Abstract

In cognitive radio networks, a secondary user is expected to utilize idle periods in a spectrum band but avoid interfering with busy periods occupied by primary users in the same band. To achieve the above goal, usually a secondary user periodically senses a spectrum band, and once an idle period is detected, the secondary user sends data in a transmission time. Due to (i) miss-detection of busy periods or (ii) unpredictable arrivals of busy periods, a secondary user may send data in busy periods, which causes useless data transmission. A secondary user usually cares about effective throughput which excludes the useless transmitted data. In order to alleviate the useless data transmission and enhance effective throughput, we consider dividing one long data transmission into two or more smaller data transmissions. Analyses, which are verified by simulations, are developed in this paper to calculate effective throughput in a periodic sensing structure with sensing errors. We use the analyses to select a set of parameters of sensing and transmission such that effective throughput is maximized at a certain load while the interference is below a pre-determined level. Besides, we study two policies, namely, fixed parameter policy and dynamic parameter policy, to maximize effective throughput in a spectrum band with variable loads; the former policy selects and applies one fixed set of parameters to different loads, but the latter policy uses different sets of parameters in different loads respectively. Numerical results show that the dynamic parameter policy outperforms the fixed parameter policy.

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Notes

  1. The channel environment, in which an energy detector is applied, is usually assumed to be an environment with additive white Gaussian noise.

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Acknowledgments

This research was partially supported by the National Science Council, Taiwan, R.O.C. under grant NSC99-2221-E-017-008-.

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Correspondence to Show-Shiow Tzeng.

Appendix: Derivation of the threshold γ

Appendix: Derivation of the threshold γ

Using the definition of a standard Gaussian complementary cumulative distribution function, we re-write Eq. 2 as follows:

$$ P_f = {\frac{1}{\sqrt{2 \pi}}} \int\limits_{\left({\frac{\gamma}{n_d B}}-1\right) \sqrt{N}}^{\infty} e^{-t^2/2} dt. $$
(39)

Let \(s={\frac{n_dB}{\sqrt N}}t+n_dB\), then \(t=\left({\frac{s}{n_dB}}-1\right) \sqrt N\) and \(dt={\frac{\sqrt N}{n_dB}}ds\); then, Eq. 39 is re-written as follows:

$$ \begin{aligned} P_f&= \int\limits_{\gamma}^{\infty} {\frac{\sqrt N}{\sqrt{2 \pi} n_dB}} \exp\left[ -{\frac{1}{2}} \left(\left({\frac{s}{n_dB}}-1\right) \sqrt{N}\right)^2 \right] ds\\ &= \int\limits_{\gamma}^{\infty} {\frac{1}{\sqrt{2 \pi}(n_dB/\sqrt{N})}} \exp\left[-{\frac{(s-n_dB)^2}{2(n_dB/\sqrt{N})^2}}\right] ds\\ &= \int\limits_{\gamma}^{\infty} f_a(s) ds, \hbox{where}\;f_a\, \hbox{is\,a\,normal\,distribution\,with\, mean}\, n_dB\,\hbox{and\;variance} (n_dB)^2/N. \end{aligned} $$
(40)

Similar to the above derivation, the miss-detection probability P m can be also re-written as follows:

$$ \begin{aligned} P_m&=\int\limits_{-\infty}^{\gamma} {\frac{\sqrt N}{\sqrt{2 \pi} (n_dB+s_p)}} \exp\left[-{\frac{1}{2}} \left(\left({\frac{s}{n_dB+s_p}}-1\right) \sqrt{N}\right)^2 \right] ds\\ &= \int\limits_{-\infty}^{\gamma} f_m(s) ds, \,\hbox{where}\;f_m\; \hbox{is\;a\;normal\;distribution\;with\;mean}\;n_dB+s_p\; \hbox{and\;variance}\, (n_dB+s_p)^2/N. \end{aligned} $$
(41)

We would like to find γ to minimize the \(P_{on}P_m+P_{off}P_f\); that is,

$$ {\frac{\partial({P_{on}P_m + P_{off}P_f })}{\partial{\gamma}}}=0 $$
(42)
$$ \Rightarrow P_{on}f_m(s) - P_{off}f_a(s)=0 $$
(43)

After expanding f m (s) and f a (s), we rearrange Eq. 43 as follows:

$$ \gamma^2\left({\frac{N}{2(n_dB)^2}} - {\frac{N}{2(n_dB+s_p)^2}}\right) +\gamma\left({\frac{N}{n_dB+s_p}} - {\frac{N}{n_dB}}\right)-\ln\left({\frac{P_{off} (n_dB+s_p)}{P_{on}n_dB }}\right)=0 $$
(44)

Solving Eq. 44, we obtain the value of threshold γ.

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Tzeng, SS., Huang, CW. Effective throughput maximization for in-band sensing and transmission in cognitive radio networks. Wireless Netw 17, 1015–1029 (2011). https://doi.org/10.1007/s11276-011-0331-1

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