Reciprocity-Aware Convolutional Neural Networks for Map-Based Path Loss Prediction

Path loss modeling is a widely used technique for estimating point-to-point losses along a communications link from transmitter (Tx) to receiver (Rx). Accurate path loss predictions can optimize use of the radio frequency spectrum and minimize unwanted interference. Modern path loss modeling often leverages data-driven approaches, using machine learning to train models on drive test measurement datasets. Drive tests primarily represent downlink scenarios, where the Tx is located on a building and the Rx is located on a moving vehicle. Consequently, trained models are frequently reserved for downlink coverage estimation, lacking representation of uplink scenarios. In this paper, we demonstrate that data augmentation can be used to train a path loss model that is generalized to uplink, downlink, and backhaul scenarios, training using only downlink drive test measurements. By adding a small number of synthetic samples representing uplink scenarios to the training set, root mean squared error is reduced by > 8 dB on uplink examples in the test set.

💡 Research Summary

Path loss prediction is a cornerstone of modern wireless network planning, influencing spectrum allocation, interference management, and overall system performance. While traditional empirical models have long been used, recent advances in data‑driven techniques—particularly convolutional neural networks (CNNs) that ingest high‑resolution geographic information—have demonstrated superior accuracy. However, most existing CNN‑based approaches are trained exclusively on downlink (base‑station‑to‑user‑equipment) drive‑test measurements. This creates a critical gap: the models are not guaranteed to respect the physical principle of electromagnetic reciprocity, which states that the path loss should be identical when the transmitter (Tx) and receiver (Rx) are swapped, assuming passive, non‑magnetic surroundings. Consequently, such models perform poorly for uplink (UE‑to‑BS) or backhaul (BS‑to‑BS) scenarios.

The paper addresses this limitation by introducing a simple yet effective data‑augmentation strategy that injects synthetic “reflected” samples into the training set. The authors start from a previously published CNN architecture that consumes four channels: (1) a direct‑path height map (terrain plus antenna heights interpolated along the line‑of‑sight), (2) a 2‑D distance‑from‑Tx map, (3) a surface‑height map derived from open‑source digital surface models (DSMs), and (4) a frequency channel. The network is trained on six UK cities (Boston, London, Merthyr Tydfil, Nottingham, Southampton, Stevenage) using 10 000 randomly selected measurements per frequency band (six bands ranging from 449 MHz to 5850 MHz), for a total of 360 000 samples. A rigorous geographic cross‑validation holds out an entire city at a time, ensuring that performance reflects true generalisation to unseen regions.

Two transformations are defined: Identity, which leaves the original downlink sample unchanged, and Reflection, which flips the entire 2‑D input image across both horizontal axes (equivalent to a 180° rotation). The Reflection operation swaps the Tx and Rx positions while preserving the surrounding environment, thereby creating a synthetic uplink sample that, according to reciprocity, should have the same loss as the original. The authors also evaluate a separate CRC dataset (Ottawa, Canada) containing 71 BS‑to‑BS measurements at 3455 MHz, used solely for testing backhaul performance.

Training augmentation is performed at three levels: (i) no augmentation (0 % of the original training/validation set), (ii) a modest 4 % augmentation (500 reflected samples per city), and (iii) a more aggressive 25 % augmentation (3000 reflected samples per city). Each configuration is cross‑validated ten times. The models are then tested on three groups: (a) the original Identity hold‑out (downlink), (b) the reflected hold‑out (uplink), and (c) the CRC BS‑to‑BS set.

Results are striking. For the downlink test, augmentation has negligible impact—RMSE remains around 7.3 dB, confirming that the original model already performs well in its native scenario. For the uplink test, however, the baseline model exhibits a disastrous RMSE of 16.2 dB (with a large standard deviation). Adding just 4 % reflected samples reduces the mean RMSE to 7.76 dB, a >8 dB improvement, and further increasing to 25 % brings it down to 7.42 dB. The backhaul (BS‑to‑BS) test also benefits modestly, dropping from 7.33 dB to 7.16 dB (4 % augmentation) and 7.09 dB (25 % augmentation). Kernel density estimation of prediction bias shows that, without augmentation, the model systematically underestimates loss in uplink cases, likely because the original training data over‑emphasises obstacles near the Rx (the vehicle) while neglecting those near the Tx (the tower). The reflected samples force the network to learn that obstacles around both ends can affect loss, thereby aligning predictions with physical reality.

The discussion highlights that a tiny fraction of synthetic, physically‑consistent data can dramatically improve model generalisation, effectively teaching the CNN the reciprocity property without altering its architecture or loss function. This approach is computationally cheap (no extra measurement campaigns) and readily applicable to any existing drive‑test dataset. It also suggests that future work could explore richer augmentations (e.g., varying antenna heights, polarisation effects, or multi‑frequency joint training) and could integrate actual uplink measurements to further validate the reciprocity learning.

In conclusion, the paper demonstrates that map‑based CNN path‑loss models, when trained with a modest amount of reciprocity‑aware synthetic data, become robust across downlink, uplink, and backhaul scenarios. This advancement bridges the gap between data‑driven performance and fundamental electromagnetic theory, offering network planners a versatile, accurate tool that can be deployed using only the conventional downlink drive‑test data already collected by operators.