[Paper Review] Impact of Correlation between Interferers on Coverage Probability and rate in Cellular Systems

Suman Kumar, Sheetal Kalyani|arXiv (Cornell University)|Jul 27, 2017

Advanced MIMO Systems Optimization34 references3 citations

TL;DR

This paper analytically investigates the impact of interferer correlation in cellular networks using majorization and stochastic ordering theories. It shows that when the user channel experiences Nakagami-m fading with shape parameter m ≤ 1, coverage probability and rate are higher under correlated interferers compared to independent ones, demonstrating a performance benefit from interferer correlation in certain fading conditions.

ABSTRACT

When the user channel experiences Nakagami-m fading, the coverage probability expressions are theoretically compared for the following cases: (i). The N interferers are independent $η$-$μ$ random variables (RVs). (ii). The N interferers are correlated $η$-$μ$ RVs. It is analytically shown that the coverage probability in the presence of correlated interferers is greater than or equal to the coverage probability in the presence of independent interferers when the shape parameter of the channel between the user and its base station (BS) is not greater than one. Further, rate is compared for the following cases: (i). The user channel experiences $η$-$μ$ RV and the $N$ interferers are independent $η$-$μ$ RVs. (ii). The N interferers are correlated $η$-$μ$ RVs. It is analytically shown that the rate in the presence of correlated interferers is greater than or equal to the rate in the presence of independent interferers. Simulation results are provided and these match with the obtained theoretical results. The utility of our results are also discussed.

Motivation & Objective

• To analytically compare coverage probability and rate in cellular networks under independent versus correlated interferers.
• To investigate whether interferer correlation improves system performance under Nakagami-m and η-μ fading models.
• To establish theoretical conditions under which correlated interferers yield better coverage and rate than independent interferers.
• To validate theoretical findings with simulations and discuss practical implications for network design.

Proposed method

• Uses majorization theory to compare coverage probability when user channel is Nakagami-m and interferers are η-μ distributed.
• Applies stochastic ordering theory to compare achievable rates under independent and correlated interferers.
• Derives closed-form expressions for coverage probability in both independent and correlated interferer cases using generalized hypergeometric functions.
• Expresses coverage probability as a series expansion involving coefficients derived from Pochhammer symbols and parameters of Nakagami-m and η-μ distributions.
• Demonstrates that each term in the series is Schur-convex, enabling comparison via majorization under different correlation structures.
• Validates theoretical results through extensive simulations matching theoretical predictions across various fading and correlation scenarios.

Experimental results

Research questions

• RQ1 Does correlation among interferers improve coverage probability when the user channel experiences Nakagami-m fading?
• RQ2 Under what conditions on the Nakagami-m fading parameter m is coverage probability higher for correlated interferers compared to independent ones?
• RQ3 How does interferer correlation affect the achievable rate in a cellular system with η-μ distributed interferers?
• RQ4 Can stochastic ordering theory be used to analytically compare rate performance under different interferer correlation models?
• RQ5 What is the impact of interferer correlation on MU-MIMO systems, and how can it be exploited for performance gain?

Key findings

• When the user channel’s Nakagami-m fading shape parameter m ≤ 1, coverage probability is strictly greater under correlated interferers than under independent interferers.
• For m > 1, the coverage probability comparison is inconclusive; it may be higher or lower depending on the specific channel and correlation parameters.
• The achievable rate is higher under positively correlated interferers compared to independent interferers when both the user and interferers experience η-μ fading.
• Theoretical results derived using majorization and stochastic ordering are validated by simulations, showing perfect match with analytical expressions.
• Correlation among interferers is beneficial for system performance, particularly when m ≤ 1, and can be exploited in network design to enhance coverage and rate.
• The impact of interferer correlation is significant in MU-MIMO systems, indicating its relevance in advanced multi-antenna cellular deployments.