[Paper Review] Capacity and Delay Tradeoff of Secondary Cellular Networks with Spectrum Aggregation

Lingyu Chen, Chen Liu+4 more|arXiv (Cornell University)|Dec 28, 2016

Advanced MIMO Systems Optimization40 references4 citations

TL;DR

This paper proposes a stochastic geometry and queueing theory-based analytical framework to study the capacity-delay tradeoff in secondary cellular networks with spectrum aggregation. It derives closed-form expressions for mean delay and delay distribution, revealing that per-user throughput is bounded by a logarithmic function of the user-to-base station density ratio, with optimal spectrum allocation balancing bandwidth and access probability.

ABSTRACT

Cellular communication networks are plagued with redundant capacity, which results in low utilization and cost-effectiveness of network capital investments. The redundant capacity can be exploited to deliver secondary traffic that is ultra-elastic and delay-tolerant. In this paper, we propose an analytical framework to study the capacity-delay tradeoff of elastic/secondary traffic in large scale cellular networks with spectrum aggregation. Our framework integrates stochastic geometry and queueing theory models and gives analytical insights into the capacity-delay performance in the interference limited regime. Closed-form results are obtained to characterize the mean delay and delay distribution as functions of per user throughput capacity. The impacts of spectrum aggregation, user and base station (BS) densities, traffic session payload, and primary traffic dynamics on the capacity-delay tradeoff relationship are investigated. The fundamental capacity limit is derived and its scaling behavior is revealed. Our analysis shows the feasibility of providing secondary communication services over cellular networks and highlights some critical design issues.

Motivation & Objective

• To address the underutilization of redundant network capacity in cellular networks by enabling secondary, ultra-elastic traffic over existing infrastructure.
• To model and analyze the fundamental capacity-delay tradeoff for secondary traffic using a cross-layer framework combining stochastic geometry and queueing theory.
• To investigate how spectrum aggregation, user and base station densities, session payload, and primary traffic dynamics affect secondary traffic performance.
• To derive the fundamental capacity limit and its scaling behavior under interference-limited conditions.
• To provide design guidelines for maximizing secondary service throughput while meeting delay constraints.

Proposed method

• The framework integrates stochastic geometry to model spatial distribution of users and base stations, and queueing theory to model session-level traffic behavior.
• It assumes Poisson-distributed users and base stations, with active users randomly selecting bands for access based on coverage area and bandwidth allocation.
• The access probability per user is derived using a strict fairness assumption and the distribution of interfering users, leading to a closed-form expression involving the Gamma function.
• Throughput capacity is defined as the average traffic arrival rate that can be supported with finite delay, derived via the effective bandwidth concept and queueing delay analysis.
• The model accounts for multi-band spectrum aggregation, where system bandwidth is split across N bands, each with independent bandwidth and path loss.
• A numerical optimization is performed to find the optimal number of bands N that maximizes capacity, considering tradeoffs between bandwidth per band and access probability.

Experimental results

Research questions

• RQ1 How does spectrum aggregation impact the capacity-delay tradeoff for secondary, elastic traffic in large-scale cellular networks?
• RQ2 What is the fundamental capacity limit of secondary traffic under interference-limited conditions?
• RQ3 How do user and base station densities affect the achievable throughput and delay performance?
• RQ4 What is the optimal number of spectrum bands to maximize secondary user capacity, and how does this depend on user-to-BS density ratio?
• RQ5 How does session size and dynamic scheduling influence the capacity-delay tradeoff in low-delay regimes?

Key findings

• The per-user throughput per Hertz is upper bounded by a constant and decreases at a sub-linear rate proportional to the logarithm of the user-to-base station density ratio.
• A closed-form approximation for the maximum achievable capacity is derived: $ C^{* ext{max}}_{II} riangleq 0.6359 - 0.052 imes \log_2(\lambda_u / \lambda_b) $, valid for $ 2 < \lambda_u / \lambda_b < 500 $.
• For a fixed system bandwidth, capacity initially increases with the number of bands N but eventually declines due to reduced bandwidth per band, indicating an optimal N exists.
• When N increases, single-channel capacity decreases due to bandwidth reduction, but access probability increases due to more available bands, creating a tradeoff.
• Spectrum aggregation primarily affects capacity in the high-delay regime, while session size management and dynamic scheduling have greater impact in the low-delay regime.
• The derived capacity limit scales logarithmically with the user-to-base station density ratio, indicating diminishing returns at high densities.