Effective User-Pair Association Schemes for Relay-Based Multi-tier Heterogeneous Networks with Physical Layer Security

This paper focuses on relay-assisted multi-tier heterogeneous networks (HetNets) in term of feasible user-pair association (UPA) criterions and physical layer secrecy analysis. In the interesting relay-assisted multi-tier HetNets, the randomly located mobile user-pair communicates with the help of the relay of its associated tier. We model the locations of all network elements as independent Poisson point process. For such relay-assisted HetNets, similar to the nearest relay defined for user association in traditional single-hop HetNets, we define the so-called best relay in each tier for a typical mobile user-pair by using the equivalent end-to-end biased received power (BRP). Then based on the defined best-relay, we first propose the max–min user-pair association (MM-UPA) criterion. Due to the fact that the MM-UPA criterion is dominated by the bottleneck link’s BRP and does not exploit the joint effect of both the source-relay and relay-destination links, we present the maximum harmonic mean user-pair association (MHM-UPA) criterion, again. For the two UPA criterions, by using feasible mathematical analysis, we derive the corresponding UPA probabilities. Finally, as an implement of the two proposed UPA criterions, by using stochastic geometry, we perform the secrecy performance analysis of the considered relay-assisted multi-tier HetNets. The presented numerical analysis first validates our derivations through the comparison analysis with traditional single-hop user association criterion. At the same time, we also present the comparison analysis between the two proposed MM-UPA and MHM-UPA criterions. It is found that when the transmission power \(P_{R(S)}^{k}\) is small, the MHM-UPA scheme outperforms the MM-UPA one in term of UPA probability. On the contrary, the two schemes achieve approximately the same UPA probability. For the total secrecy probability, we find that when transmit power is small, the MHM-UPA achieves the higher secrecy probabilities. Moreover, the achieved gain by MHM-UPA is increasing with the decrease of transmission power. Contrarily, when the transmission power is large, although the MM-UPA outperforms the MHM-UPA, the achieved gain by MM-UPA cover MHM-UPA is small.