# Location Information-Assisted Robust Beamforming Design for Ultra-Wideband Communication Systems
## 5 Simulation Results  
In this section, the performance of the proposed location information-assisted method is verified by simulation, and the effect of the number of antennas, SINR threshold, and room size on the proposed robust power allocation is analyzed. Assuming that \(J=6\), \(N=5\), \(K=4\), the reflection coefficient \(\Gamma_{\mathrm{R}}=0.7\). The probability of the constraints are set to \(0.05\), i.e., \(\rho_{j}=0.05,\forall j\).  
The SINR generated by 5000 random channels is summarized as a cumulative distribution function (CDF) in Figure 3. It can be seen in Figure 3 that the CDF rate of the non-robust power distribution cannot guarantee the minimum rate requirement, while the proposed robust power distribution satisfies the minimum rate constraint. In the non-robust beamforming method, there is no way to always assign extra power to users to suppress interference from other users; therefore, it is difficult for SINR to maintain at a certain level. However, the robust method proposed can allocate a reasonable amount of power to the users in order to improve the signal-to-noise ratio, thus the SINR value is always greater than the threshold value.  
In order to demonstrate the performance of the proposed robust beamforming method, we compare the performance with the non-robust beamforming method (which ignores the estimation errors) and the worst-case scheme (which is presented in [31]). The variation curve of the average transmit power with the SINR threshold in the robust, non-robust, and worst-case is shown in Figure 4. Compared with the non-robust power allocation, robust power allocation requires more power to maintain the SINR at a stable level. In addition, compared with the worst-case robust beamforming, the proposed method yields less conservative results.  
Figure 5 analyzes the situation in different scene sizes. It can be seen that as the room size becomes larger, the transmit power for both the robust and the non-robust beamforming gradually becomes larger. Since this paper assumes that the BSs are mainly arranged in the four corners of the scene, the measurement distance error between the BSs and the UE inevitably increases as the scene size increases, which leads to both robust beamforming and non-robust beamforming that require more power to cope with the channel error.  
Figure 6 gives the average transmit power versus the transmit antenna number. As the number of antennas increases, the power required for the non-robust, robust, and worst-case scenarios gradually decreases. We can see that the method is more effective than the worst-case method, and therefore the method is less conservative. In addition, form the Equation (21), the CRLB of the user location is inversely proportional to the antenna number. Increasing the antennas number not only improves the accuracy of the user location but also improves the reliability of the reconstructed channel.  
Figure 3: CDF rate of over 5000 random channel realizations.  
Figure 4: Average transmit power versus the SINR \(\gamma\) (dB).  
Figure 5: Average transmit power versus the scene size.  
Figure 6: Average transmit power versus the antenna number.