A Unified Prediction Framework for Signal Maps: Not All Measurements are Created Equal

Abstract

Signal maps are essential for the planning and operation of cellular networks. However, the measurements needed to create such maps are expensive, often biased, not always reflecting the performance metrics of interest, and posing privacy risks. In this paper, we develop a unified framework for predicting cellular performance maps from limited available measurements. Our framework builds on a state-of-the-art random-forest predictor, or any other base predictor. We propose and combine three mechanisms that deal with the fact that not all measurements are equally important for a particular prediction task. First, we design <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">quality-of-service functions (<inline-formula><tex-math notation="LaTeX">$Q$</tex-math></inline-formula>)</i> , including signal strength (RSRP) but also other metrics of interest to operators, such as number of bars, coverage (improving recall by 76%-92%) and call drop probability (reducing error by as much as 32%). By implicitly altering the loss function employed in learning, quality functions can also improve prediction for RSRP itself where it matters ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g.</i> MSE reduction up to 27% in the low signal strength regime, where high accuracy is critical). Second, we introduce <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">weight functions</i> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$W$</tex-math></inline-formula> ) to specify the relative importance of prediction at different locations and other parts of the feature space. We propose re-weighting based on importance sampling to obtain unbiased estimators when the sampling and target distributions are different. This yields improvements up to 20% for targets based on spatially uniform loss or losses based on user population density. Third, we apply the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Data Shapley</i> framework for the first time in this context: to assign values ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\phi$</tex-math></inline-formula> ) to individual measurement points, which capture the importance of their contribution to the prediction task. This can improve prediction ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g.</i> from 64% to 94% in recall for coverage loss) by removing points with negative values and storing only the remaining data points ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> as low as 30%), which also has the side-benefit of helping privacy. We evaluate our methods and demonstrate significant improvement in prediction performance, using several real-world datasets.