# Gyre Precoding and T-Transformation-Based GFDM System for UAV-Aided mMTC Network
## 3 Numerical Results and Relative Discussion
\begin{table}
\begin{tabular}{l l} \hline \hline
**Description** & **Value** \\ \hline No. of bits & 2048 \\ No. of subcarriers & 256 \\ No. of sub-symbols in each GFDM block & 10 \\ Time of each sub-symbol & 66.67 \\ No. of GFDM blocks & 6 \\ Carrier spacing (KHz) & 15 \\ GFDM signal bandwidth (MHz) & 3.84 \\ UAV transmission power & 1–10 W \\ Signal-to-noise ratio, \(E_{b}/N_{0}\) (dB) & 0–30 \\ Noise power (dBm) & \(-80\) \\ Average transmission power/channel & 35.68 dBm (3.70 W) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameters. vertical \(Z\) direction and 0.02 m in horizontal X direction and 0.04 m in horizontal Y direction. In all cases, the 3D positional errors of the UAVs are reasonably acceptable in the context of state-of-the-art. The impact of both gyre decoding and the T-transformation scheme on the received signal-to-noise ratio (SNR), received SINR, and achievable ergodic rate with the variation in UAV transmission  
Figure 4: Generated keys for using [PERSON]’s hyperchaos mapping system for different mMTC users. Figure 5: Empirical CDFs \(x\), \(y\), \(z\) values relative to the UAV target position. Figure 3: Three-dimensional reconstructed attractor of [PERSON]’s hyperchaos mapping system in the (\(x\), \(y\), \(z\))-plane. power for eight mMTC users have been illustrated through Figures 6-8. In Figure 6a, the estimated average received SNR values for eight mMTC users without the application of gyre decoding and inverse T-transformation schemes are presented. From Figure 6a, it is seen by analyzing all the estimated SNR values for mMTC user 1 through mMTC user 8, the maximum average SNR value is approximately 30.533 dB, and the minimum average SNR value is approximately 20.529 dB. In Figure 6b, the estimated average SNR values for eight mMTC users with the implementation of both gyre decoding and inverse T-transformation schemes at the receiver are presented. There is no significant difference observed while comparing with the SNR values in the absence of gyre decoding and T-transformation schemes, as shown in Figure 6a. It is seen from Figure 6b by estimating all SNR values for mMTC user 1 through mMTC user 8 that the maximum average SNR value is approximately 29.663 dB, and the minimum average SNR value is approximately 19.659 dB. In Figure 7a, it is quite clear that due to the presence of interfering signals, the effective received SINR values for each mMTC user are reduced. The estimated SINR values of each mMTC user are almost constant in spite of the variation of UAV transmission power. The estimated SINR values for mMTC user 1 through mMTC user 8 are almost \(-4.8310\) dB, \(-9.0268\) dB, \(-6.9553\) dB, \(-6.4912\) dB, \(-10.2783\) dB, \(-9.8867\) dB, \(-12.7168\) dB, and \(-11.8770\) dB, respectively. Figure 7b shows that due to the simultaneous implementation of both gyre decoding and inverse T-transformation schemes based orthogonal spreading codes, the interfering signal power is totally nullified, causing improved SINR performance as compared to the results presented in Figure 7a. The estimated SINR values for mMTC user 1 through mMTC user 8 are identical to SNR values presented in Figure 6b. Figure 6: Estimated average received signal-to-noise ratio (SNR) when both gyre decoding and inverse T-transformation schemes are (**a**) absent and (**b**) present. Figure 7: Estimated average received signal to interference noise ratio (SINR) when both gyre decoding and inverse T-transformation schemes are (**a**) absent and (**b**) present. In Figure 8a, it is observable that even when the UAV transmission power is varied, the estimated achievable ergodic rate for different mMTC users is comparatively low and almost constant. The estimated achievable ergodic rate for mMTC user 1 through mMTC user 8 are 1.2345 bps/Hz, 0.5120 bps/Hz, 0.7976 bps/Hz, 0.8790 bps/Hz, 0.3894 bps/Hz, 0.4243 bps/Hz, 0.2263 bps/Hz, and 0.2731 bps/Hz, respectively.