Performance Analysis of a Wireless Backhaul in a Three-Tier Hybrid Network With Directional Antennas

In this paper, a three-tier hybrid cellular heterogeneous network is considered using the microwave (<inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>Wave) links for the first two tiers and millimeter (mmWave) links for the last tier. The two-tiers with <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>Wave links form a wireless backhaul to the last tier with mmWave links. The main challenge in having a wireless backhaul is to suppress interference. Thus, we propose a novel and practical model where we can reuse the <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>Wave infrastructure, but equip the BSs with directional antennas to have a robust wireless backhaul network. To solve the bottleneck rate problem, we assume that the rate required by the mmWave users is comparable to that offered by the <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>Wave links. Different configurations based on the placement of the directional antennas at each tier are explored. The analysis of the key performance indicators, namely, the coverage probability, area spectral efficiency, and energy efficiency using the conventional minimum rate model, and the simulation results associated with these parameters are presented. In order to analyze this hybrid network with a wireless backhaul, an optimization problem for the overall area spectral efficiency and energy efficiency with respect to the optimal signal-to-interference ratio (SIR) threshold required for <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>Wave and mmWave links is investigated. Results indicate that the optimal SIR threshold required for the <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>Wave tiers (wireless backhaul) depends only on the path-loss exponent and that for the mmWave tier depends on the area of the line-of-sight region. Finally, instead of the conventional minimum rate model, we consider the average rate under coverage and show that the area spectral efficiency and energy efficiency are strictly decreasing functions with respect to the threshold, thereby concluding that they can be maximized by choosing the lowest possible SIR threshold available in the system.