# Gyre Precoding and T-Transformation-Based GFDM System for UAV-Aided mMTC Network
## 3 Numerical Results and Relative Discussion
In Figure 8b, it is observable that the estimated achievable ergodic rates for different mMTC users are very much improved with the application of gyre decoding and T-transformation scheme than in the absence of them, as shown in Figure 8a. It is also noticeable from the figure that the achievable ergodic rate values decrease when the UAV transmission power is varied. By analyzing all the estimated achievable ergodic rates for mMTC user 1 through mMTC user 8, the maximum and minimum average achievable ergodic rate is found to have values 9.856 bps/Hz and 6.553 bps/Hz, respectively. Considering Brownian motion, it is observable that for the \(x,y,z\) coordinate variation of 0.2 m relative to UAV's fixed positions, the mean error in estimated achievable ergodic rates at different \(E_{b}/N_{0}\) values is found to be of 0.26 bps/Hz. On the other hand, in the case of \(x,y,z\) coordinate variation of \(-0.2\) m relative to UAV's fixed positions, the mean error in estimated achievable ergodic rates is of \(-0.83\) bps/Hz. In Figure 9, the estimated achievable ergodic rate values for ground mMTC users confined within a circular region of a 50 m radius are presented. In such case, ground BS transmit power (46 dBm = 39.81 W) and UAV base station transmit power (30 dBm = 1 W) from Table 10.3 of [5] has been considered. From the 3D displayed achievable ergodic rate of Figure 9 with identical heights of all the UAVs at 100 m, 200 m, and 300 m, it is seen that with increase in UAV height, the estimated achievable ergodic rate values decrease. The maximum estimated achievable ergodic rate in the case of UAV heights of 100 m, 200 m, and 300 m are found to have values of 14.26 bps/Hz, 13.19 bps/Hz, and 12.21 bps/Hz. In Figure 10, estimated maximum achievable ergodic rate values at different normalized signal-to-noise ratios (\(E_{b}/N_{0}\)) are compared with the similar works of different authors from [38; 39; 40]. It is quite clear from the figure that the proposed system outperforms all the other similar works utilizing different systems. Performance in terms of achievable ergodic rate is even better with gyre decoding and T-transformation scheme utilized in tandem than merely with gyre decoding. An acceptable out-of-band (OOB) power reductions of 318.77 dB, 317.31 dB, 319.25 dB, 321.71 dB, 320.93 dB, 321.22 dB, 320.73 dB, and 319.97 dB are attained for the case of mMTC user 1 through mMTC user 8, respectively. The result illustrated in Figure 11 is a typical case of OOB power reduction performance of mMTC user 1. Figure 8: Estimated achievable ergodic rate when both gyre decoding and inverse T-transformation schemes are (**a**) absent and (**b**) present. Figure 11: Power spectral density of the proposed system for typically chosen case of mMTC user 1. Figure 10: Comparative analysis of achievable ergodic rates between the proposed system and other similar communication systems. Figure 4:0 Estimation of achievable ergodic rate of randomly distributed mMTC users within a circular region of a 50 m radius and all UAVs at heights: (**a**) 100 m, (**b**) 200 m, and (**c**) 300 m.  
of the proposed system implementing (3,2) single parity check (SPC) and repeat and accumulate (RA) concatenated channel-coding scheme is better than other two concatenated channel-coding schemes tested in this system. Figure 4:1 BER analysis of the proposed system adopting (3,2) SPC and RA concatenated channel-coding technique. Figure 4:2 BER analysis of the proposed system adopting LDPC and (3,2) SPC concatenated channel-coding technique. Figure 4:3 BER analysis of the proposed system adopting LDPC and RA concatenated channel-coding technique. It is seen from Figure 12 that the BER varies from 33.30% to 29.40% for a typically assumed \(E_{b}/N_{0}\) value of 10 dB with the system utilizing low density parity check (LDPC) and (3,2) SPC concatenated channel-coding technique. Overall, BER performance is not quite satisfactory for any of the mMTC users. In SNR region of 11 dB to 21 dB, some mMTC users are getting their signals with almost identical BER.