Modeling and Analysis of K-Tier Downlink Heterogeneous Cellular Networks (1103.2177v4)

Abstract: Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In this paper, we develop a tractable, flexible, and accurate model for a downlink heterogeneous cellular network (HCN) consisting of K tiers of randomly located BSs, where each tier may differ in terms of average transmit power, supported data rate and BS density. Assuming a mobile user connects to the strongest candidate BS, the resulting Signal-to-Interference-plus-Noise-Ratio (SINR) is greater than 1 when in coverage, Rayleigh fading, we derive an expression for the probability of coverage (equivalently outage) over the entire network under both open and closed access, which assumes a strikingly simple closed-form in the high SINR regime and is accurate down to -4 dB even under weaker assumptions. For external validation, we compare against an actual LTE network (for tier 1) with the other K-1 tiers being modeled as independent Poisson Point Processes. In this case as well, our model is accurate to within 1-2 dB. We also derive the average rate achieved by a randomly located mobile and the average load on each tier of BSs. One interesting observation for interference-limited open access networks is that at a given SINR, adding more tiers and/or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same target-SINR.

• The paper derives a general coverage probability expression using stochastic geometry, showing that under equal SINR thresholds, additional BSs do not impact performance.
• It models multi-tier base station deployments with independent Poisson Point Processes to achieve closed-form results in high SINR regimes that closely match real-world data.
• The analysis contrasts open versus closed access and computes average data rates, providing key insights for scalable network planning and effective interference management.

Modeling and Analysis of $K$-Tier Downlink Heterogeneous Cellular Networks

Introduction

The paper "Modeling and Analysis of $K$-Tier Downlink Heterogeneous Cellular Networks" authored by Harpreet S. Dhillon, Radha Krishna Ganti, François Baccelli, and Jeffrey G. Andrews, explores the mathematical modeling and probabilistic analysis of heterogeneous cellular networks (HCNs). Given the shift from homogeneous cellular networks with large, well-distributed macro base-stations (BSs) to heterogeneous infrastructures composed of macro, micro, pico, and femtocells, there is a pressing need for a robust analytical framework to evaluate their performance. The authors introduce a new tractable model for such multi-tier (heterogeneous) networks that captures key aspects influencing network performance, such as BS density, transmit power, and supported data rates.

System Model and Methodology

The core of the modeling approach is based on stochastic geometry, where the locations of BSs in each tier are assumed to be distributed according to independent Poisson Point Processes (PPPs). This model is particularly apt because it encapsulates the spatial randomness inherent in the deployment of femtocells and picocells better than traditional grid or deterministic models.

Key assumptions of the model are:

1. Independent PPPs for BS Locations: The BSs of each tier are distributed as independent PPPs, denoted $\Phi_i$ for the $i$-th tier, with density $\lambda_i$.
2. Rayleigh Fading and Path Loss: The channel model assumes Rayleigh fading with a path loss characterized by exponent $\alpha$.
3. Signal-to-Interference-plus-Noise Ratio (SINR): A typical user connects to the BS that supplies the highest SINR, where the SINR accounts for interference from all other BSs in the network.
4. Coverage and Outage Probabilities: The key performance metrics of interest are the coverage probability $P_c$ (probability that a user is in a state of adequate SINR for communication) and the associated outage probability.

Main Contributions and Results

1. General Formulation:

The authors derive a general expression for the probability of coverage, which is reliant on the cumulative distribution function of the SINR. This expression simplifies considerably in the high SINR regime, providing insight into the behavior of networks when noise power is negligible compared to interference power.

2. Closed-Form Results Under High SINR:

When thermal noise is ignored, the coverage probability simplifies to a form that illustrates the trade-offs between the number of tiers, BS density, and respective SINR thresholds. Specifically, the result shows that if all tiers have the same SINR threshold, adding more BSs does not change the coverage probability, indicating that the network is ideally scalable.

3. Comparison with Real Data:

The authors validate their model by comparing it against actual LTE network deployments and show that despite the randomness assumption for BS locations, the model retains high accuracy, often within 1-2 dB of empirical data.

4. Open vs Closed Access:

Two access strategies are considered: open access, where users can connect to any BS, and closed access, where users are restricted to a subset of BSs. Predictably, open access outperforms closed access in terms of coverage probability.

5. Average Rate:

The average data rate within coverage is derived, considering Shannon capacity with interference treated as noise. This complements the coverage probability by giving a holistic view of user experience in terms of achievable data rates.

Implications and Future Work

The analytical results derived from this model hold significant implications for the design and optimization of heterogeneous cellular networks:

• Scalability and Network Planning: The independence of coverage probability from the density of BSs suggests practical approaches to network scaling, making the model valuable for future network expansions.
• Interference Management: Insights into SINR distribution and coverage probability provide a foundation for developing advanced interference management schemes.

For future developments, extending the model to incorporate advanced physical layer and MAC layer technologies such as MIMO, resource allocation strategies, and more complex interference alignment techniques can provide deeper insights. Additionally, modeling the BS deployments with more sophisticated point processes such as determinantal or Matérn processes could potentially yield even more accurate performance estimates. Furthermore, considering realistic user distributions and traffic models may enhance the applicability of the model to practical scenarios.

Conclusion

This paper introduces a flexible, analytical framework for evaluating and understanding the performance of $K$-tier heterogeneous cellular networks. Through comprehensive probabilistic analysis using stochastic geometry, it provides pivotal insights into the performance, scalability, and optimization of emerging cellular architectures.