## 5 Numerical Results and Analysis
### Secrecy Performance Analysis  
In the next experiments, we analyze the secrecy performance of our proposed scheme and compare it with the conventional AN-DM schemes. In a practical case, the Eves would be located as close to LU as possible (even in the same locations as LUs) to eavesdrop messages. We consider that there are four Eves whose locations are closed to LUs, even same as the LUs, and they cooperate with each other. The locations of Eves are set as \((r_{e_{1}},\,\theta_{e_{1}})=(1600\) m, \(30^{\circ})\) close to LU 1, \((r_{e_{2}},\,\theta_{l_{e_{2}}})=(2000\) m, \(-50^{\circ})\) same to LU 2, and \((r_{e_{3}},\,\theta_{e_{3}})=(2500\) m, \(55^{\circ})\) close to LU 3, \((r_{e_{4}},\,\theta_{e_{4}})=(3050\) m, \(-35^{\circ})\) close to LU 4. In order to show the effective reception of independent LU and verify the superiority of the SM with cooperative LUs, we first analyze BER performance of each LU (without cooperation) under different scenarios, and then simulate the SER performance of cooperative LUs.  
Figure 7 illustrates the BER performance of LU and Eve versus the desired received power to noise ratio under different scenarios, where the baseband modulation modes of each LU is BPSK. From Figure 7a, we can observe that (1) our optimal method ensures the effective reception of LU 1; (2) the desired received power to noise ratio requested for the proposed scheme is less than the AN-DM schemes (approximately \(1\) dB when BER \(\approx 10^{-2}\)); (3) the BERs at Eve 1 are almost equal to  
Figure 5: The spatial power distribution of confidential messages in range dimension.  
Figure 6: The signal to interference-plus-noise ratio (SINR) spatial distribution versus (**a**) angle-range, (**b**) angle dimension, and (**c**) range dimension.  
\(10^{-5}\) in Figure 7a, which means that an Eve close to a LU is difficult to receive meaningful message in proposed scheme and AN-DM schemes, respectively. LU 3 and LU 4 have a similar BER performance to LU 1. From Figure 7b, we can see that (1) LU 2 also has satisfactory BER performance; (2) even when the Eve's location is the same as the location of LU 2, the Eve still cannot intercept the message transmitted to LU 2 with the proposed scheme, whereas the Eve successfully wiretaps the confidential message with AN-DM schemes; (3) in a worst case where MP-WFRFT parameters are perfectly leaked to Eves, our proposed scheme also cannot ensure secure transmission between transmitter station and LU 2.  
Next, Figure 8 shows the SER performance of cooperative LUs versus the desired received power to noise ratio, where the number of active LU is \(L=2\). From Figure 8, we can observe that (1) the SER of Eves is low with all of desired received power to noise ratio, which shows that Eves cannot retrieve the confidential messages without/with the leakage of WFRFT parameters based on the proposed scheme. When MP-WFRFT parameters are leaked to Eves, the SER of Eves is only little better than the case without leakage; (2) the desired received power to noise ratio is less than the AN-DM schemes.  
In general, the proposed scheme can ensure the valid reception for each LU. Moreover, with the SM and MP-WFRFT technology based on cooperative LUs, the eavesdropping capability of Eves is degraded, and thus we can ensure wireless communication security even in the worst case, in which one or some (but not all) independent messages and MP-WFRFT parameters are leaked to Eves. Furthermore, the WFRFT technique overcomes the low-power-efficiency drawback of the conventional  
Figure 8: The SER performance of cooperative LUs versus the desired received power to noise ratio.  
Figure 7: The bit error rate (BER) performance with independent LU versus the desired received power to noise ratio: (**a**) LU 1 and (**b**) LU 2.  
AN-DM schemes, and the SM technology improves the capacity of communication system due to the use of indices information.