Wireless Personal Communications

, Volume 104, Issue 1, pp 149–171 | Cite as

Min–Max User-Pair Association Criterion and Outage Performance of K-Tier Relay-Based Heterogeneous Networks

  • Xiangdong Jia
  • Wenjuan Xu
  • Mangang Xie
  • Meng Zhou
  • Longxiang Yang


This paper focuses on the user-pair association for multi-tier relay-based dual-hop heterogeneous networks (HetNets) and proposes a novel min–max user-pair association (MM-UPA) criterion by integrating the bias factors, which is an evolution of conventional single-hop user association based on receive signal strength (RSS). The core idea of the proposed MM-UPA is that, in each tier the nearest relay to a typical user-pair is characterized by the maximum of the RSS reciprocals \({1 / {P_{SR}^{j} }}\) and \({1/ {P_{RD}^{j} }}\) by the source and destination from relay. Then, a typical user-pair is associated to the relay based on minimizing these maximums of each tier. This proposed MM-UPA criterion is fit especially for the relay-based HetNets due to effectively exploiting the source-relay and relay-destination links simultaneously. With the MM-UPA criterion, by using stochastic geometry and homogeneous Poisson point processes, we present the analytical expression of the probability that a typical user-pair is associated with a relay of the kth tier as well as the corresponding statistical description of the distances from the source and destination of a typical user-pair to its associated relay. Finally, the average outage probability of a typical user-pair relay communication link is derived. The presented simulations and numerical results validate the derivations.


5G Heterogeneous networks Relay User association Association probability Outage probability 



This work was supported by the Natural Science Foundation of China under Grant 61561043, 61861039, 61261015, the Science and technology plan Foundation of Gansu Province of China under Grant 18YF1GA060, the program of improving the scientific research ability of young teachers in Northwest Normal University: “Key technologies of next generation wireless networks”, and by the Foundation Research Funds for the University of Gansu Province: ‘Massive MIMO channels modeling and estimation over millimeter wave band for 5G’.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Xiangdong Jia
    • 1
    • 2
  • Wenjuan Xu
    • 1
  • Mangang Xie
    • 1
  • Meng Zhou
    • 1
  • Longxiang Yang
    • 2
  1. 1.College of Computer Science and EngineeringNorthwest Normal UniversityLanzhouChina
  2. 2.Wireless Communication Key Lab of Jiangsu ProvinceNanjing University of Posts and TelecommunicationsNanjingChina

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