Multi slot-throughput tradeoff in an improved energy detector based faded cognitive radio network

Abstract

In this paper, the impact of a multi slot based cooperative spectrum sensing (CSS) on the performance of a cognitive radio (CR) network has been investigated. Each CR user, equipped with an improved energy detector (IED), uses a number of mini slots of the sensing time to perform the spectrum sensing. Each CR uses OR logic to combine the sub local decisions generated in each mini slot to obtain a local decision at CR level. Local decisions are sent to fusion centre (FC) over reporting channel. The FC obtains a final decision about the presence of primary user (PU) by combining the local decisions using a fusion rule: Majority or Maximal Ratio Combining. The performance of the CSS is assessed in terms of detection probability and false alarm probability considering both the sensing and reporting channels are Rayleigh faded. Furthermore, the impact of a number of sensing slots and IED parameter on throughput of CR network is also evaluated under the proposed spectrum sensing scenario. Impacts of several sensing parameters such as sensing channel SNR and reporting channel SNR on the performance of CR network are also evaluated. Performances of two fusion rules under study are compared. Effect of sensing error and synchronisation error is indicated. Further the study is extended for independent but non identically distributed (i.n.i.d.) Rayleigh faded channels as well as for a multiple PU scenario also.

Appendix

Proof of (19)

$$\begin{aligned} P_{d,FC}&= P(y_{i, FC}\ge \lambda _{FC}|D_i=1)P(D_i=1|H_1)\nonumber \\ &\quad +\,P(y_{i, FC}\ge \lambda _{FC}|D_i=0)P(D_i=0|H_1) \end{aligned}$$

(35)

where $P(y_{i, FC}\ge \lambda _{FC}|D_i=1)$ and $P(y_{i, FC}\ge \lambda _{FC}|D_i=0)$ are the detection probabilities at FC and can be represented as $P(y_{i, FC}\ge \lambda _{FC}|D_i=1)= P_{d,FC}^{1}$ and $P(y_{i, FC}\ge \lambda _{FC}|D_i=0)= P_{d,FC}^{0}$ respectively as in [25],

$$\begin{aligned} P_{d,FC}^{1,0}&= \int _0^\infty \left[ \int _{\lambda _{FC}}^\infty (y_{i,FC}|_{D_i=1,0})dy_{i,FC}\right] f_{\gamma _r}(x)dx\nonumber \\&= (1/2)\left[ {\mathrm {erfc}}\left( \mp \sqrt{1/2\sigma _w^2}\right) \mp \exp \Bigg (1/\bar{\gamma }_r\right. \nonumber \\&\left. \left. \quad -\,2\sqrt{1/2\sigma _w^2\bar{\gamma }_r}\right) \pm \sqrt{1/2\sigma _w^2} \exp (1/\bar{\gamma }_r)\right. \nonumber \\&\quad \left. \int \nolimits _0^1 t^{-3/2} \exp (-1/2\sigma _w^2t)\exp (-t/\bar{\gamma }_r){\mathrm {d}}t\right] \end{aligned}$$

(36)

whereas $P(D_i=1|H_1)$ and $P(D_i=0|H_1)$ are the detection probabilities at CR level which can be represented as $P(D_i=1|H_1)= P_d^l = (1-[1-P_{d(i,j)}^F]^M)$ and $P(D_i=0|H_1)=1- P_d^l = (P_{d(i,j)}^F)^M$ respectively. Thus (35) can be written as,

$$\begin{aligned} P_{d,FC}&= P\left( y_{i, FC}\ge \lambda _{FC}|D_i=1\right) P\left( D_i=1|H_1\right) \\&\quad +\,P\left( y_{i, FC}\ge \lambda _{FC}|D_i=0\right) P\left( D_i=0|H_1\right) \\&= P_{d,FC}^{1}\left( 1-\left[ 1-P_{d(i,j)}^F\right] ^M\right) +P_{d,FC}^{0}\left( P_{d(i,j)}^F\right) ^M \end{aligned}$$

Proof of (20) :

$$\begin{aligned}P_{f,FC}&= P\left( y_{i, FC}\ge \lambda _{FC}|D_i=1\right) P\left( D_i=1|H_0\right) \nonumber \\&\quad +\,P\left( y_{i, FC}\ge \lambda _{FC}|D_i=0\right) P\left( D_i=0|H_0\right) \end{aligned}$$

(37)

The detection probabilities $P(y_{i, FC}\ge \lambda _{FC}|D_i=1)$ and $P(y_{i, FC}\ge \lambda _{FC}|D_i=0)$ are given in the proof of (19). Whereas $P(D_i=1|H_0)$ and $P(D_i=0|H_0)$ are the false alarm probabilities at CR level can be represented as $P(D_i=1|H_0)= P_f^l = (1-[1-P_{f(i,j)}^F]^M)$ and $P(D_i=0|H_0)=1- P_f^l = (P_{f(i,j)}^F)^M$ respectively. Thus (37) can be written as,

$$\begin{aligned} P_{f,FC}&= P\left( y_{i, FC}\ge \lambda _{FC}|D_i=1\right) P(D_i=1|H_0)\\&\quad +\,P\left( y_{i, FC}\ge \lambda _{FC}|D_i=0\right) P\left( D_i=0|H_0\right) \\&= P_{d,FC}^{1}\left( 1-\left[ 1-P_{f(i,j)}^F\right] ^M\right) +P_{d,FC}^{0}\left( P_{f(i,j)}^F\right) ^M \end{aligned}$$