[Paper Review] Fixed Rank Kriging for Cellular Coverage Analysis

Hajer Braham, Sana Ben Jemaa+3 more|arXiv (Cornell University)|May 26, 2015

Advanced MIMO Systems Optimization4 citations

TL;DR

This paper proposes Fixed Rank Kriging (FRK) to efficiently predict LTE RSRP coverage maps from geo-located measurements, reducing the O(N³) computational complexity of standard Kriging. It extends FRK to multicell scenarios with directive antennas, enabling accurate coverage prediction and reliable best-serving cell detection using real and simulated MDT data, achieving a strong balance between accuracy and computational efficiency.

ABSTRACT

Coverage planning and optimization is one of the most crucial tasks for a radio network operator. Efficient coverage optimization requires accurate coverage estimation. This estimation relies on geo-located field measurements which are gathered today during highly expensive drive tests (DT); and will be reported in the near future by users' mobile devices thanks to the 3GPP Minimizing Drive Tests (MDT) feature~\cite{3GPPproposal}. This feature consists in an automatic reporting of the radio measurements associated with the geographic location of the user's mobile device. Such a solution is still costly in terms of battery consumption and signaling overhead. Therefore, predicting the coverage on a location where no measurements are available remains a key and challenging task. This paper describes a powerful tool that gives an accurate coverage prediction on the whole area of interest: it builds a coverage map by spatially interpolating geo-located measurements using the Kriging technique. The paper focuses on the reduction of the computational complexity of the Kriging algorithm by applying Fixed Rank Kriging (FRK). The performance evaluation of the FRK algorithm both on simulated measurements and real field measurements shows a good trade-off between prediction efficiency and computational complexity. In order to go a step further towards the operational application of the proposed algorithm, a multicellular use-case is studied. Simulation results show a good performance in terms of coverage prediction and detection of the best serving cell.

Motivation & Objective

• Address the high computational cost of traditional Kriging in large-scale radio coverage mapping.
• Enable efficient and accurate prediction of LTE RSRP coverage maps using massive geo-located measurements from 3GPP Minimization of Drive Tests (MDT).
• Extend the Fixed Rank Kriging framework to multicell environments with directional antennas.
• Improve operational feasibility of Radio Environment Maps (REMs) by reducing complexity while maintaining prediction accuracy.
• Ensure robust detection of the best-serving cell in multicell scenarios through spatial interpolation.

Proposed method

• Apply Fixed Rank Kriging (FRK) to reduce the O(N³) complexity of standard Kriging by approximating the spatial covariance structure using a low-rank basis.
• Use a spatial random effects model with a fixed number of basis functions to represent spatial variation, significantly reducing computational load.
• Estimate unknown model parameters via Maximum Likelihood Estimation (MLE), replacing the method of moments which fails in this context.
• Incorporate directional antenna patterns into the FRK model to reflect realistic propagation in multicell environments.
• Apply the Expectation-Maximization (EM) algorithm to iteratively estimate parameters and improve model fit on both simulated and real MDT data.
• Use spatial interpolation to predict RSRP values at unmeasured locations, enabling full-coverage map generation.

Experimental results

Research questions

• RQ1 Can Fixed Rank Kriging effectively reduce the computational complexity of Kriging-based coverage prediction while preserving accuracy?
• RQ2 How does FRK perform in predicting coverage and identifying the best-serving cell in a multicell environment with directional antennas?
• RQ3 What is the impact of using MLE instead of the method of moments for parameter estimation in FRK for radio coverage data?
• RQ4 How does the FRK model perform on real-world MDT measurements compared to simulated data?
• RQ5 Can FRK-based prediction maps support operational network optimization tasks such as coverage planning and interference management?

Key findings

• FRK achieves a significant reduction in computational complexity compared to standard Kriging, making large-scale coverage mapping feasible.
• The FRK model with MLE-based parameter estimation provides more accurate and stable predictions than the method of moments, which fails in this context.
• In multicell scenarios with directive antennas, FRK enables accurate prediction of RSRP and reliable detection of the best-serving cell.
• Simulation results show that FRK maintains high prediction accuracy even with sparse or irregularly distributed MDT measurements.
• Performance evaluation on both simulated and real MDT data confirms that FRK offers a strong trade-off between computational efficiency and prediction accuracy.
• The method is robust to location uncertainty and can be extended to include real antenna patterns for further performance gains.