Passive Eavesdroppers Sample Clauses
Passive Eavesdroppers. We study the impact of the number of small-cell BS transmit and receive antennas on the small-cell network DL and UL PHYLS performance under a Poisson field of passive EDs in Fig. 3.1. It can be observed that in all cases, the ergodic secrecy rate always increases in the number of antennas. This is due to the improved array gain from multi-antenna communications, and hence, stronger useful signal power, whilst the interference level remains the same. Furthermore, the FD over HD small- cell network PHYLS performance gain always increases in the number of antennas. In point of fact, even with SIC capability and perfect SI suppression, only negligible FD versus HD improvements in ergodic secrecy performance can be achieved when the small-cell BSs are equipped with a few antennas. This trend highlights the essential role of MIMO in harnessing the full potential of FD technology through enhancing the system robustness against the increased interference level versus that in the HD operation [114, 115]. The presence of significant residual SI (e.g., variance > −30 dB), would typi- cally result in secrecy outage (even when the number of antennas is relatively large). The current SI cancellation capabilities can achieve orders of magnitude greater cancellation (e.g., in the range 60 − 100 dB [12]), hence, the FD operation is cer- tainly feasible. It is important to note that in such cases the impact of residual SI becomes negligible compared to the MI [17], [107]. It may be useful to note that to achieve higher FD versus HD PHYLS performance gains in the UL, the transmit power of the small-cell BSs should be reduced. It can be observed that the MC simulations confirm the validity of our theoretical findings in Theorems 1-4.
Passive Eavesdroppers. Next, we derive explicit expressions for the ergodic rates of the most malicious passive EDs in the DL and UL. Note that in this case the EDs act independently (do not exchange information).
Passive Eavesdroppers. Next, we derive explicit expressions for the ergodic rates of the most malicious passive EDs in the DL and UL. Note that in this case the EDs act independently (do not exchange information).
Theorem 3. The DL ergodic rates (in b/s/Hz) of the most malicious passive ED v in the FD and HD small-cell networks over two resource blocks are given by I I p v I I p I v α I d u α α Proof: See Appendix C.
Theorem 4. The UL ergodic rates (in b/s/Hz) of the most malicious passive ED c in the FD and HD small-cell networks over two resource blocks are given by s s d u α α α . (2.24) I
2 Γ 1 − 2 Γ 1 + 2 ! Γ(1) L d,u [s] = exp −πλd (spd) α α α
2.4 Numerical Results We provide several numerical examples in order to assess the PHYLS performance of FD and HD small-cell networks in the presence of a Poisson field of EDs. The spatial density of the small-cell BSs is set to be λ (d) = 4 per km2. The (per-user) BS and UE transmit powers are kept fixed at pd = 23 dBm and pu = 20 dBm, respectively. The noise spectral density at all receivers is −170 dBm/Hz and the total system bandwidth is W = 10 MHz. The MC simulations are obtained from 20 k trials in a circular region of radius 10 km. Note that all results correspond to the per-user ergodic secrecy performance over two resource blocks. In the FD small-cell network, the DL and UL run simultaneously, whereas in the HD small- cell network, the DL and UL occur over different resource blocks. Furthermore, in the FD system, we take into account different interference cancellation schemes. In particular, in the DL, we consider the cases with and without SIC capability at the UE side. Moreover, in the UL, we capture the performance under different perfect SI cancellation.