We perform Monte Carlo simulations to compare the theoretical results with the sim- ulation. The results for energy based spectrum sensing under various fading channels are described in this section based on varying fading channels and their properties. Firstly, the simulation results are verified by comparing them with the theoretical re- sults for AWGN, Rayleigh and Rice (for Rice the theory only exists for Ns= 2) channels,
and only then, the simulations are extended to show the energy detector’s performance under Rice fading channel by varying Ns, the LAP eNodeB altitude, ρ and K. The fol-
lowing transmission parameters were fixed in our simulations; fc= 2.6GHz, transmit
power Pt= 13dBm, α = 2.4, and Pn= −105dBm. The terrestrial terminal is considered
to be directly below the LAP or in other words the distance d between the transmitting terrestrial terminal and the sensing LAP base station is the same as the LAP altitude without loss of generality. Furthermore, the received signal power in dBm is given by Ps= Pt− L(d).
Figure3.2shows the C-ROC curves for the AWGN and the Rayleigh fading chan- nels under different values of ρ and Ns. From the figure, it is clearly seen the degrada-
tion in the detection performance for the Rayleigh fading case compared to the AWGN case, and furthermore, verification of the simulation and the theoretical results match- ing is conducted for the AWGN and the Rayleigh channels. Figure 3.3 depicts the C-ROC curves for the Rice fading channel (specifically for Ns = 2) for different values
of ρ and K. From the figure, it is observed that the detection performance under the Rice channel approaches the detection performance of the AWGN channel as expected. Thus, it can be observed that the simulation and theoretical results match well with each other verifying our simulation model for the Rice channel as well.
10−3 10−2 10−1 100
10−3 10−2 10−1 100
Prob of False Alarm
Prob of Miss Detection
Theory Simulation Rayleigh: ρ = −5dB, N s = 4 Rayleigh: ρ = 5dB, N s = 4 AWGN: ρ = 5dB, N s = 4 AWGN: ρ = 5dB, N s = 16
FIGURE 3.2: Complementary ROC for the AWGN and Rayleigh enve- lope fading channels, theory versus simulation comparisons.
10−3 10−2 10−1 100 10−3
10−2 10−1 100
Prob of False Alarm
Prob of Miss Detection
Rice Theory (N s=2) Rice Simulations K = 4dB, ρ = 4dB K = −10dB, ρ = 10dB K = 4dB, ρ = 10dB AWGN Theory: ρ = 10dB
FIGURE3.3: Complementary ROC curves for the Rice envelope fading channel, with Ns= 2, comparing theory versus simulations.
After verification from the simulation model with theoretical analysis from Figure
3.2and Figure3.3, we further conduct simulations to study the detection performance of the aerial base station under the Rice fading channel. One should note that as men- tioned before theoretical results do not exist in literature for energy detection under Rice channel for Ns> 2, and therefore we present simulation results here. Such simu-
lation results can be used to identify how many samples are required to perform energy based sensing in order to maintain a prescribed detection probability to be set by the regulatory body, as an example let us set the required minimum detection probability for the operation is PD = 0.9or alternatively PM = 0.1. Figure3.3depicts the C-ROC
curves under the Rice channel for various values Ns, as expected increasing the num-
ber of samples for the energy estimate improves the detection performance and the results shown in Figure3.4quantifies the detection performance in terms of the C-ROC curves.
10−3 10−2 10−1 100 10−3
10−2 10−1 100
Prob of False Alarm
Prob of Miss Detection
Decreasing N
s = [32, 16, 8 , 4, 2]
ρ = 5.26dB, K =−10dB, LAP Altitude = 1000m
FIGURE3.4: Complementary ROC curves for Rice envelope fading chan- nel with varying Ns.
The detection performance was analysed for various LAP altitudes under the Rice fading channel and the corresponding results are presented in Figure3.5. The results clearly indicate that the detection performance degrades with increasing LAP altitudes mainly due to the drop in the mean received signal to noise ratio resulting from the increased path-loss between the LAP and the terrestrial terminal. It is clearly identified that even with Ns = 20the detection performance can only be met with a high value
of false alarm probability. Therefore, it is desired to increase Nsto meet the required
10−3 10−2 10−1 100 10−3
10−2 10−1 100
Prob of False Alarm
Prob of Miss Detection
LAP Altitude = 1000m N s = 20, K = 0dB, ρ = 5.6dB LAP Altitude = 2500m N s = 20, K = 0dB, ρ = −4.3dB LAP Altitude = 1500m N s = 20, K = 0dB, ρ = 1dB
FIGURE3.5: Complementary ROC curves for Rice envelope fading chan- nel with varying LAP altitudes.
Figure3.6on the other hand, depicts the detection performance under various Rice factor values K for Ns = 10. Again, it is observed that when K decreases the desired
detection performance cannot be achieved without sacrificing on the false alarm prob- ability. Therefore, using the simulation results one is able to decide on the required number of samples Nsfor the Rice channel for varying channel conditions.
10−3 10−2 10−1 100
10−3 10−2 10−1 100
Prob of False Alarm
Prob of Miss Detection
LAP Altitude = 1000m, N
s = 10, ρ = 5.26dB
Decreasing values of K(dB) = [40, 20, 10, 0 −10]
FIGURE3.6: Complementary ROC curves for Rice envelope fading chan- nel with varying Rice factor K.