#### 5.2. Decentralized Wireless Network Performance in Shared Channels

This subsection presents results of the performance of SU’s network under different channel sensing conditions (i.e., for different path loss coefficients and levels of fading uncertainty). The results include the average number of received packets (${E}_{\mathrm{r}}$) given ${n}^{\mathrm{SU}}$ transmitters, and the conditional throughput of the secondary network.

We considered the MPR scenario where the SU

${}_{\mathrm{rx}}$ can receive multiple packets simultaneously whenever the outcome of the spectrum sensing indicates the channel as being idle. We have considered the scenario illustrated in

Figure 1, a SU receiver circled by SUs and PUs. Regarding the secondary network, we considered

${n}^{\mathrm{SU}}$ SUs transmitters located in the area

${A}_{in}$$=\pi {R}_{G}^{2}$, which were distributed according to the PDF in (

2). The nodes from the primary network were distributed according to a 2D Poisson point process. Assuming that the SU

${}_{\mathrm{rx}}$ senses the channel as vacant, it will receive

${n}^{\mathrm{SU}}$ transmissions plus the total number of transmissions from the PUs located outside the sensing region (i.e.,

${A}_{out}=\pi ({{R}_{E}}^{2}-{{R}_{G}}^{2})$). Different noise (

${N}_{0}$) and fading (

${\mathsf{\Psi}}_{k}$) realizations were used on each trial, being the receiving condition (

26) observed for each SU transmitter

j. The expected number of received packets,

${E}_{\mathrm{r}}$ was computed from the simulations’ data. The simulations were parameterized according to the data presented in

Table 1. Regarding the computation of

${\mathrm{P}}_{S}$ in (

32) we have adopted the FFT algorithm with domain

x set to

$[-500,500]$ and a step of

$3\times {10}^{-4}$.

Figure 3 illustrates the average number of received packets given

${n}^{\mathrm{SU}}$ transmitters, for different values of path loss coefficients and two levels of fading uncertainty (i.e., with and without fading). The curves identified as “Simul.” represent the data obtained through simulation, while the ones identified as “Teor.” were obtained by numerically computing (

34). The curves identified as “Teor. without sensing” were obtained by numerically computing (

38) and represents the scenario where the SU

${}_{\mathrm{rx}}$ does not perform spectrum sensing, and as consequence, the SUs are allowed to transmit, even when the PUs are located within the sensing region transmit (i.e.,

${A}_{in}=\pi {R}_{G}^{2}$). In the latter scenario, the receiving condition (

26) takes into account transmissions from the PUs located outside and inside of the sensing region. The SPR case is highlighted in

Figure 3 with the rectangle “SPR:

${n}^{\mathrm{SU}}=1$”.

From

Figure 3 we observe that the numerical values of

${E}_{\mathrm{r}}$ closely follow the results obtained by simulation. The figure shows the maximum point of operation of the MPR-based PHY layer. After that point

${E}_{\mathrm{r}}$ decreases as

$\alpha $ increases. The decrease is because with the increase of

$\alpha $ the power propagation losses increase with the distance, meaning that the SUs further away from the SU

${}_{\mathrm{rx}}$ receiver will experience a lower probability of successful transmission. Finally, by comparing the results of the average number of received packets for the cases with and without the spectrum sensing, we observe that the average number of received packets increases when spectrum sensing is adopted. By using spectrum sensing the SU

${}_{\mathrm{rx}}$ achieves a better performance regarding the MPR communication, because the interference caused by the PUs’ transmissions located in the sensing region is avoided.

Figure 4 and

Figure 5 represent the conditional throughput by computing (

37) against different values of

${n}^{\mathrm{SU}}$ and different parameterization of

${P}_{D}$. In both figures we consider two scenarios of propagation effects: path loss (

$\alpha =2$) without fading; and path loss (

$\alpha =2$) with fading (

${\sigma}_{\xi}=0.7$). The

${S}^{\mathrm{SU}}$ without sensing was computed according to (

38).

Figure 4 represents the conditional throughput,

${S}^{\mathrm{SU}}$, for different values of

${P}_{D}$ and considering

${n}^{\mathrm{SU}}$ equal to 1, 10 and 20 nodes. Note that

${n}^{\mathrm{SU}}$ equal to 1 node represents an SPR scenario in which the probability of successful reception only depends on the SNR. As in

Figure 3, in

Figure 5 the SPR scenario is represented when

${n}^{\mathrm{SU}}$ is equal to 1, which is highlighted by the rectangle “SPR:

${n}^{\mathrm{SU}}=1$”.

From

Figure 4 and considering the SPR scenario (i.e.,

${n}^{\mathrm{SU}}=1$), the conditional throughput of the scenarios with and without sensing are very close for both values of

$\alpha $. Although results of conditional throughput do not show a huge advantage by performing a sensing technique at the receiver, it should be noticed that when using sensing a certain level of protection to the PUs is guaranteed. Regarding the MPR scenario, as can be seen for

$\alpha $ equal to 2 and without fading the conditional throughput is higher when sensing is performed. On the other hand, for worst propagation conditions (i.e.,

$\alpha =3$ and

${\sigma}_{\xi}=0.7$), the conditional throughput for both cases (i.e., with and without sensing) is very similar when

${P}_{D}$ is between

$0.85$ and

$0.93$. For values of

${P}_{D}$ lower than

$0.85$ the conditional throughput decrease with

${P}_{D}$ due to the fact that the used energy threshold criterion sets a higher probability of

${P}_{FA}$ as

${P}_{D}$ decreases. For values of

${P}_{D}$ close to 1 the performance of the SUs’ network is degraded since the number of samples required to guarantee the level of protection to the PUs increases with

${P}_{D}$.

Figure 5 illustrates the conditional throughput given

${n}^{\mathrm{SU}}$ and for two levels of protection to the PUs’ network (i.e.,

${P}_{D}$ equal to

$97.0\%$ and

$99.9\%$).

From

Figure 5 we observe that the channel propagation condition greatly influences

${S}^{\mathrm{SU}}$. Different from the results in

Figure 3, where the scenario with sensing achieves higher

${E}_{\mathrm{r}}$ than the scenario without sensing,

Figure 5 shows that

${S}^{\mathrm{SU}}$ in the worst propagation conditions (i.e.,

$\alpha =3$ and

${\sigma}_{\xi}=0.7$) decreases, since the number of samples needed to sense the channel increases.

In

Figure 6 and

Figure 7 we illustrate the surface of the SUs’ network conditional throughput for different values of

${n}^{\mathrm{SU}}$ and

${P}_{D}$.

Figure 6 and

Figure 7 represent, respectively, the scenarios with best (i.e.,

$\alpha =2$ and without fading) and worst (i.e.,

$\alpha =3$ and

${\sigma}_{\xi}=0.7$) propagation conditions from

Figure 3.

As already observed in the previous figures, from

Figure 6 and

Figure 7 we observe that the conditional throughput achieved by the SUs’ network is lower under more severe channel propagation conditions. The conditional throughput decreases due to two reasons: the sensing period that guarantees an optimal operation of the EBS technique (i.e.,

${P}_{FA}\approx 0$ and

${P}_{D}\approx 1$) increases with

$\alpha $; and the maximum number of successful received packets given the number of simultaneous transmitters decreases as

$\alpha $ and

${\sigma}_{\xi}$ increase.

Based on the results of

Figure 6 and

Figure 7, we conclude that the maximum SU network throughput is achieved by properly adjusting the number of simultaneous transmissions performed by the SUs and the detection probability. However, the maximum throughput does not assures full protection to the PUs network in scenarios for worst channel propagation conditions.