Heterogeneous Cellular Networks with Flexible Cell Association: A Comprehensive Downlink SINR Analysis (1107.3602v1)

Abstract: In this paper we develop a tractable framework for SINR analysis in downlink heterogeneous cellular networks (HCNs) with flexible cell association policies. The HCN is modeled as a multi-tier cellular network where each tier's base stations (BSs) are randomly located and have a particular transmit power, path loss exponent, spatial density, and bias towards admitting mobile users. For example, as compared to macrocells, picocells would usually have lower transmit power, higher path loss exponent (lower antennas), higher spatial density (many picocells per macrocell), and a positive bias so that macrocell users are actively encouraged to use the more lightly loaded picocells. In the present paper we implicitly assume all base stations have full queues; future work should relax this. For this model, we derive the outage probability of a typical user in the whole network or a certain tier, which is equivalently the downlink SINR cumulative distribution function. The results are accurate for all SINRs, and their expressions admit quite simple closed-forms in some plausible special cases. We also derive the \emph{average ergodic rate} of the typical user, and the \emph{minimum average user throughput} -- the smallest value among the average user throughputs supported by one cell in each tier. We observe that neither the number of BSs or tiers changes the outage probability or average ergodic rate in an interference-limited full-loaded HCN with unbiased cell association (no biasing), and observe how biasing alters the various metrics.

• The paper develops an analytical framework using a Poisson Point Process to derive per-tier association probabilities and user load distributions.
• It analytically characterizes SINR distributions and outage probabilities under various biasing strategies in multi-tier networks.
• The study advances spectral efficiency analysis by calculating average ergodic rates and minimum user throughput for optimal network performance.

Heterogeneous Cellular Networks with Flexible Cell Association: A Comprehensive Downlink SINR Analysis

The paper "Heterogeneous Cellular Networks with Flexible Cell Association: A Comprehensive Downlink SINR Analysis" by Han-Shin Jo et al. develops a rigorous analytical framework for the Signal-to-Interference-and-Noise Ratio (SINR) analysis in downlink heterogeneous cellular networks (HCNs). The paper addresses a multi-tier cellular network configuration wherein each tier's base stations (BSs) differ in terms of transmit power, path loss exponent, spatial density, and cell association biasing. The focus is on understanding the impact of these differences on SINR distribution, outage probability, and spectral efficiency.

Methodology and Contributions

The authors effectively model HCNs as multi-tier networks; each tier's BSs are randomly located according to a Poisson Point Process (PPP). This abstraction embraces the inherent randomness and variability in practical BS deployments, which contrasts with the traditional, deterministic hexagonal grid models. The PPP approach permits tractable mathematical analysis, making it possible to derive meaningful insights into SINR distributions analytically.

Key theoretical contributions include:

1. Derivation of Per-Tier Association Probability: The authors derive probabilities that a typical user will associate with a BS from a specific tier, based on the BS density, transmit power, and biases. This probability is further used to calculate the average number of users per BS in each tier.
2. SINR Distribution and Outage Probability: The paper provides outage probabilities across all SINR values for a typical user, with analytical expressions simplified for certain scenarios, such as interference-limited networks. Notably, the work extends existing models to incorporate arbitrary biasing and per-tier SINR distribution.
3. Spectral Efficiency Metrics: The paper derives the average ergodic rate of a typical user and the minimum average user throughput, which are pivotal for evaluating the spectral efficiency of HCNs. These metrics are examined under various network conditions, such as different BS densities, path loss exponents, and bias factors.

Numerical Results and Observations

The numerical results validated the theoretical findings and provided several practical insights, which include:

• Impact of BS Density:

Increasing BS density, particularly for lower-tier BSs (e.g., picocells), without considering noise, does not affect SINR distribution in unbiased cases due to the interference-limited nature of HCNs. However, higher path loss exponents in lower-tier BSs can further improve SINR and spectral efficiency.

• Bias Factor Influence:

While unbiased association leads to uniform performance regardless of the number of tiers, introducing bias can improve SINR at cell edges by pushing users from heavily loaded macrocells to less loaded picocells. However, this comes at a cost of potentially degrading overall network performance under fully-loaded conditions.

Implications and Future Directions

The robust analytical framework developed in this paper allows for a comprehensive understanding of SINR behavior in complex multi-tier HCNs. The findings suggest that while randomly adding small cells to an existing macro network does not inherently degrade network performance, strategic biasing needs careful consideration to balance load and optimize throughput.

For future research, there are avenues to explore the dynamic and adaptive biasing strategies under varying traffic conditions to further enhance network efficiency. Additionally, expanding the model to incorporate factors such as non-orthogonal multiple access or user mobility could provide deeper insights into real-world applicability.

In summary, this work enriches the theoretical foundation for analyzing HCNs and sets the stage for future exploration into optimizing network deployment and user association strategies in next-generation cellular networks.