[Paper Review] Max-Min Rates in Self-backhauled Millimeter Wave Cellular Networks

Mandar N. Kulkarni, Amitava Ghosh+1 more|arXiv (Cornell University)|May 2, 2018

Millimeter-Wave Propagation and Modeling35 references16 citations

TL;DR

This paper proposes a tractable analytical framework to maximize the minimum end-to-end data rate in self-backhauled mmWave cellular networks using a k-ring urban-canyon model. It derives closed-form expressions for max-min rates under various configurations—such as IAB vs. OAB, half/full duplex, and dual connectivity—showing that OAB often outperforms IAB due to simpler implementation and comparable performance under realistic load conditions.

ABSTRACT

This paper considers the following question for viable wide-area millimeter wave cellular networks. What is the maximum extended coverage area of a single fiber site using multi-hop relaying, while achieving a minimum target per user data rate? We formulate an optimization problem to maximize the minimum end-to-end per user data rate, and exploit unique features of millimeter wave deployments to yield a tractable solution. The mesh network is modeled as a $k-$ring urban-canyon type deployment, where $k$ is the number of hops back to the fiber site. The total number of relays per fiber site grows as $k^2$. We consider both integrated access-backhaul (IAB) and orthogonal access-backhaul (OAB) resource allocation strategies, as well as both half and full duplex base stations (BSs). With a few validated simplifications, our results are given as simple closed-form expressions that are easy to evaluate even for large networks. Several design guidelines are provided, including on the choice of routing and scheduling strategy, the maximum allowable self-interference in full duplex relays and role of dual connectivity to reduce load imbalance across BSs. For example, we show that for certain load conditions there is very little gain to IAB (as considered for 5G) as opposed to tunable OAB (using separate spectrum for access and backhaul links); the latter being significantly simpler to implement.

Motivation & Objective

• To determine the maximum extended coverage area of a single fiber site in mmWave cellular networks while ensuring a minimum per-user data rate.
• To address the trade-off between deployment cost (via multi-hop relaying) and end-user data rate degradation in self-backhauled mmWave networks.
• To develop a tractable optimization framework for max-min rate maximization in noise-limited mmWave mesh networks with directional transmissions.
• To evaluate the impact of resource allocation strategies (IAB vs. OAB), duplexing modes (half/full duplex), and dual connectivity on network performance.
• To provide design guidelines for practical deployment based on closed-form expressions and simplified assumptions validated through simulation and modeling.

Proposed method

• Models the mmWave network as a k-ring urban-canyon deployment with BSs on a 2D square grid, where the number of relays grows as $k^2$.
• Assumes noise-limited operation due to directional beamforming, high path loss, and limited diffraction, simplifying interference modeling.
• Derives a closed-form upper bound on the max-min rate $\gamma^*$ using time-fraction constraints: $\gamma^* = \left(\frac{w_{0,0}}{R_a} + \frac{f(0,0) - w_{0,0}}{R_1}\right)^{-1}$, where $w_{0,0}$ is the number of UEs served by the MBS and $f(0,0)$ is the total backhaul load.
• Proposes a near-neighbor highway routing (NNHR) strategy that ensures all users achieve the theoretical max-min rate $\gamma^*$ by allocating time fractions proportionally to user and backhaul demands.
• Validates the optimality of NNHR by showing that any alternative routing using lower-rate backhaul links reduces the achievable max-min rate.
• Analyzes the performance of integrated access-backhaul (IAB) and orthogonal access-backhaul (OAB) strategies, demonstrating that OAB often provides comparable or better performance with lower complexity.

Experimental results

Research questions

• RQ1 What is the maximum coverage radius (in terms of k rings) a single fiber site can support while maintaining a minimum per-user data rate in a self-backhauled mmWave network?
• RQ2 How do different resource allocation strategies—integrated access-backhaul (IAB) versus orthogonal access-backhaul (OAB)—affect the max-min user rate in mmWave mesh networks?
• RQ3 Does full-duplex relaying provide significant gains over half-duplex relaying in terms of max-min rate, and what are the constraints on self-interference suppression?
• RQ4 To what extent does dual connectivity improve load balancing and per-user rates in self-backhauled mmWave networks?
• RQ5 Can a tractable, closed-form expression for the max-min rate be derived under realistic mmWave deployment assumptions, such as directional beams and urban canyon propagation?

Key findings

• The max-min rate $\gamma^*$ is achieved when the fiber site uses nearest-neighbor highway routing (NNHR), and the upper bound $\gamma^* = \left(\frac{w_{0,0}}{R_a} + \frac{f(0,0) - w_{0,0}}{R_1}\right)^{-1}$ is tight and achievable.
• OAB outperforms IAB in terms of max-min rate under typical load conditions, with only marginal gains from IAB, making OAB a more practical choice due to lower implementation complexity.
• Full-duplex relays do not significantly improve max-min rates unless self-interference is suppressed below a threshold, which is challenging in practice.
• Dual connectivity helps reduce load imbalance across base stations and improves fairness, especially in high-load scenarios.
• The use of a k-ring model with noise-limited assumptions enables closed-form solutions, making the framework scalable and suitable for network design without requiring large-scale optimization.
• Any routing strategy that uses backhaul links with data rates lower than $R_1$ (the rate of the nearest neighbor link) results in a lower max-min rate than $\gamma^*$, proving the optimality of NNHR.