# Reliable Positioning and mmWave Communication via Multi-Point Connectivity +
## 4 Simulation Results
### Achievable Throughput  
Figures 7 and 8 show the spectral efficiency, assuming exact location of each user is perfectly known, as a function of increasing transmit power and link blockage probability, respectively. As expected, spectral efficiency is monotonically increasing with the increase in uplink transmit power \(P_{t}\), shown in the Figure 7. It can be seen, when all LoS links are available, i.e., link blockage probability \(P_{b}=0\), both single-BS and multi-point reception provide comparable performance and converges only at very high transmit power. In other words, reduced analog beamforming gain because of the compromise receive beam \(\bar{\mathbf{\Psi}}_{b}\)\(\forall b\) is recovered with joint reception and efficient interference management to other users. However, for all other cases, coordinated multi-point reception performs significantly better and further this performance gap is also increasing with the increase in link blockage probability \(P_{b}\). This behavior is also expected, with the higher \(P_{b}\), it is more likely that the dominant LoS link to the connected BS is not available in the single-BS method. However, joint-reception not only provides additional links because of the compromise superposition beam but can also implement efficient interference management to other active users, thus higher user-rate, as shown in Figure 8.  
Figure 5: Average positioning accuracy as a function of increasing link blockage probability \(P_{b}\) with the uplink transmit power \(P_{t}=15\) dBm.  
Figure 6: Empirical CDF of average positioning accuracy with different link blocking probabilities \(P_{b}\) and uplink transmit power \(P_{t}=15\) dBm for multi-point reception (solid line) and BS selection method (dashed line).  
In the Figures 9 and 10, we show achievable spectral efficiency with exact and estimated user's location, which is related through the analog beam selection \(\mathbf{w}_{b}^{(k)}\) between a BS-user pair \((b,k)\). As shown in Figure 4, multi-point reception provides relatively better localization accuracy, thus better estimates of the user's position with respect to the exact location, which leads to better spectral efficiency, illustrated in Figures 9 and 10. With the coordinated multi-point reception, estimated position accuracy is in the order of sub-meter level. Thus, the difference between exact and estimated position is relatively small. Therefore, we can choose the exact receive beam at each coordinating BS and hence the performance is comparable to the case when user's location is perfectly known. In contrast, for the BS selection method, the performance gap is because of poor estimate of user location. The performance gain obtained with the joint reception can be clearly seen from the empirical CDF, shown in Figure 11.  
Figure 8: Achievable spectral efficiency assuming exact user location as a function of increasing link blockage probability \(P_{b}\) for the uplink transmit power \(P_{t}\) of \(P_{t}=5\) dBm (dashed line) and \(P_{t}=15\) dBm (solid line).  
Figure 7: Achievable spectral efficiency assuming exact user location as a function of increasing uplink transmit power \(P_{t}\) for the link blocking probability \(P_{b}\) of \(P_{b}=0\) (solid line), \(P_{b}=0.4\) (dotted line) and \(P_{b}=0.8\) (dash-dotted line).  
Figure 11: Empirical CDF of achievable spectral efficiency with link blocking probability \(P_{b}=0.8\) and uplink transmit power \(P_{t}=15\) dBm for exact user location (solid line) and estimated user location (dashed line).  
Figure 10: Achievable spectral efficiency as a function of increasing link blockage probability \(P_{b}\) with the uplink transmit power \(P_{t}=15\) dBm for multi-point reception (solid line) and BS selection method (dashed line).  
Figure 9: Achievable spectral efficiency with as a function of increasing uplink transmit power \(P_{t}\) with the link blocking probability \(P_{b}=0.4\) for multi-point reception (solid line) and BS selection method (dashed line).