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This paper presents findings from an extensive 28 GHz mmWave measurement campaign conducted in New York City. The study includes over 20 million power measurements collected from two key scenarios: around-corner (non-line-ofsight due to building blockages) and same-street (nominally lineof-sight without obstructions from street furniture or foliage), covering over 1,300 unique links. For urban macro-cell (UMa) rooftop base stations above local clutter, the dominant angle of arrival (AoA) deviates by only 2 to 3.5 degrees from the direct transmitter/receiver direction. This small deviation allows for effective spatial separation between users, facilitating the future development of Multi-User MIMO algorithms for Beyond5G networks. In the urban micro-cell (UMi) dataset, with base stations below local clutter, a path gain drop of over 20 dB was observed in around-corner segments just 20 meters into a corner. Our Street-Clutter-NLOS path loss model achieves an RMSE of 6.4 dB, compared to 11.9 dB from NLOS 3GPP models. Using the best path loss model to estimate coverage for 90% of users traveling around corners, downlink rates could drop by over 10 times after 50 meters, highlighting the challenges in maintaining consistent user experience over mmWave networks in urban street canyons. 

1-parameter persistent homology, a cornerstone in Topological Data Analysis (TDA), studies the evolution of topological features such as connected components and cycles hidden in data. It has been applied to enhance the representation power of deep learning models, such as Graph Neural Networks (GNNs). To enrich the representations of topological features, here we propose to study 2-parameter persistence modules induced by bi-filtration functions. In order to incorporate these representations into machine learning models, we introduce a novel vector representation called Generalized Rank Invariant Landscape (GRIL) for 2-parameter persistence modules. We show that this vector representation is 1-Lipschitz stable and differentiable with respect to underlying filtration functions and can be easily integrated into machine learning models to augment encoding topological features. We present an algorithm to compute the vector representation efficiently. We also test our methods on synthetic and benchmark graph datasets, and compare the results with previous vector representations of 1-parameter and 2-parameter persistence modules. Further, we augment GNNs with GRIL features and observe an increase in performance indicating that GRIL can capture additional features enriching GNNs. We make the complete code for the proposed method available at https://github.com/soham0209/mpml-graph. 

https://jmlr.org/papers/ v22/18-780