## 4 Performance Analysis and Simulation Results
### Performance Evaluation and Discussion  
In this subsection, the performance of the both ITXP and RPC schemes is evaluated, and the decision criterion for the schemes is discussed. For better understanding of this section, we present the channel hardening in Figure 3. The \(x\)-axis of the figure represents the ordered eigenvalue of \({\bf{H}}{\bf{H}}^{H}\), which converges to \(N_{t}\), and \(y\)-axis represents the cumulative distribution function (CDF). Figure 3 shows the case in which the number of users is fixed to \(K=4\), and the number of TX antennas increases as \(N_{t}=4\), \(40\), and \(400\). As \(N_{t}\) increases, the randomness of the channel reduces. Figure 3: Channel hardening effect, when \(N_{t}=4,40,400\) and \(K=4\). Then, we should consider the occupancy ratio of \(P_{PA}\) over \(P_{tot}\). When \(P_{PA}\) takes a greater portion than \(P_{R}\) in the \(P_{tot}\), a greater improvement in EE can be obviously achieved by using the IXTP/RPC schemes. The \(PA\) is the most power hungry device, and takes 50-80% of the total power consumption, as we mentioned in Section 1. However, when the proposed schemes are applied in the LS-MIMO-OFDM, it is easily expected that the occupancy ratio of the \(P_{PA}\) could be significantly reduced, because the LS-MIMO system uses a large amount of TX antennas, and a beamforming effect can occur which allows a small radiation power and/or power consumption. A discussion of the case with each scheme is followed by simulation and analytical results in Figure 4. Figure 4a shows the performance of the relative EE in terms of the PAPR reduction, when the PA power consumption takes 80% of the total power consumption, i.e., \(P_{PA}\):\(P_{R}\) = 80:20. Since the RPC is independent of the precoding method, only one curve is shown for the RPC, while there are two curves for the ITXP, ZF and MF because the relative EE of the ITXP depends on the precoding method. In the figure, solid lines represent the results of the analysis of a previous subsection (Equations (19) and (20)), and the red/blue marks of '+'s indicate the results of the simulations. For the simulation, we use the i.i.d. Rayleigh fading channel with static/nomadic users based on Equation (16). For the analytical results, we use the derived closed-form equations, (17) and (18). Since the operating point of the system is in the LS-MIMO region (\(N_{t}\geq 10\) K), due to the channel hardening effect, the analytical results are well-matched with the results of the simulations. Figure 4: Relative EE versus PAPR reduction (dB), when \(N_{t}=400\), \(K=40\); (**a**) \(P_{PA}\):\(P_{R}\) = 80:20; (**b**) \(P_{PA}\):\(P_{R}\) = 20:80; (**c**) \(P_{PA}\):\(P_{R}\) = 90:10–10:90. Solid lines represent the results of analysis (Equations (19) and (20)), and red/blue marks of ‘+’s indicate the results of simulations. In the case of the MF, the ITXP scheme gives only a slight improvement because the increase in \(P_{tx}\) also causes an increase in interference. Although the ZF is superior to the MF in the ITXP scheme, the RPC scheme outperforms the ITXP scheme for both precoding methods. However, this is not always true, as shown in Figure 4b. When the power consumption of the PA takes a much smaller portion, i.e., \(P_{PA}\):\(P_{R}\) = 20:80, as shown in the figure, the ITXP scheme with ZF precoding outperforms the RPC scheme. We should keep in mind that the LS-MIMO system requires only a small TX power and this could induce a small \(P_{PA}\) and/or very large \(P_{R}\) because the RF components must be applied in each antenna which means that as the number of TX antennas increases, \(P_{R}\) can increase. Therefore, for the LS-MIMO systems, we should consider both the ITXP and RPC schemes. Figure 4c shows the performance of relative EE in terms of the PAPR reduction when the ratio varies as follows: \(P_{PA}\):\(P_{R}\) = 90:10-10:90. It is obvious that when \(P_{PA}\) takes a larger portion, we can get a greater EE gain.