# Gyre Precoding and T-Transformation-Based GFDM System for UAV-Aided mMTC Network
## 3 Numerical Results and Relative Discussion  
This section presents the numerical outcomes for the secured mmWave cooperative UAV-aided CP-less GFDM system. The considered simulation parameters are presented in Table 1. Based on the noise power of \(-80\) dBm, which corresponds to \(1\times 10^{-11}\) W, the Additive white Gaussian noise (AWGN) component is introduced at different receive antennas of the main UAV [36]. In this scenario, there is a ground BS, one main and two cooperative UAVs, which are connected in an integrated UAV-terrestrial network to serve eight massive machine-type communications (mMTC) users, which are 1.5 m above the ground surface. The heights of the main and cooperative two UAVs are 120 m, 100 m, and 100 m, respectively. The transmitting antenna height of the ground BS is 50 m, and the 3D transmission distances from the ground BS to the main UAV, first cooperative UAV, and second cooperative UAV are 157.80 m, 122.47 m, and 187.0829 m, respectively, and from the main UAV to eight mMTC users are 131.31 m, 128.62 m, 123.66 m, 121.28 m, 124.77 m, 127.64 m, 133.22 m, and 122.41 m, respectively. The 3D transmission distance from the main UAV to the two cooperative UAVs is identical and is of 53.85 m. Considering the heights of the buildings and ground base station, the cooperative UAV's trajectory path is preferably being considered as circular and not random. Thus, the chance of any conflict with existing infrastructure is absolutely minimal. Three-dimensional Brownian perturbation model-based [30] trajectory planning combines the randomness with directed motion, and thus, the role of UAVs in successful signal transmission is being observed. The energy consumption of each UAV associates both communication-related energy consumption and propulsion energy consumption. Here, a single UAV controlling ground node (GN) based energy-efficient rotary-wing UAV communications is considered, and a 3D-based Brownian perturbation mobility model is applied, which controls UAV speed /deviation from the UAV target position, which, in turn, reduces propulsion energy consumption [37]. Basically, the proposed scheme can importantly balance the additional consumption of power of UAVs. The transmitting UAVs and ground mMTC users have different channel state information (CSI). In such case, MIMO flat-fading channels are estimated utilizing the probabilistic path loss model cited in [32]. In this study, the implementation of the PLS technique is based on the utilization of [PERSON]'s hyperchaos mapping system presented in Figure 3. Chaotic systems have been extensively used in physical layer encryption because of their high initial sensitivity and good randomness. In chaotic encryption schemes, sharing of the initial value between the transmitter and receiver is an important factor of system security, which makes it difficult for illegal users to steal information through malicious attacks. To achieve higher security performance, [PERSON]'s hyperchaos mapping system is considered by introducing new state variables in the encryption. Figure 3 shows that the behavior of the system is fully dependent on the considered parameter values. In Figure 4, a 3D plot of various keys assigned to individual mMTC user is shown, which confirms that assigned keys are different for different mMTC users. In Figure 5, the cumulative distribution function (CDF) of the 3D positioning errors for both the main and two cooperative UAVs have been presented in a static scene. It can be seen from the CDF that the error at 95% confidence is 0.08 m in vertical \(Z\) direction and average 0.06 m in both horizontal X and Y directions for the main UAV. In the case of the cooperative UAV #1 with identical confidence level, the positional error is 0.06 m in vertical \(Z\) direction and 0.12 m in horizontal X direction and 0.05 m in horizontal Y direction. In the case of cooperative UAV #2, the positional error is 0.06 m in