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Brain-Inspired User Positioning for mmWave Beam Management

Aris Karampelas Timotijevic, Evangelos Koutsonas, Vasileios Kouvakis, Stylianos E. Trevlakis, Alexandros-Apostolos A. Boulogeorgos, Theodoros A. Tsiftsis

arXiv:2609.06252v1eess.SP

TL;DR

Accurate knowledge of user locations enables beamforming optimization, improving system reliability and energy efficiency. The paper develops CSNN positioning models that estimate UE positions from uplink CSI and compares them with k-NN and CNN models in a unified evaluation. The CSNN had the lowest estimated energy per inference among evaluated models while ranking in the middle for positioning accuracy.

  • Problem

    Accurate knowledge of user locations enables beamforming optimization, improving system reliability and energy efficiency.

    Source: §I · p. 1

  • Method

    The paper develops CSNN positioning models that estimate UE positions from uplink CSI and compares them with k-NN and CNN models in a unified evaluation.

    Source: §I · p. 2

  • Results

    The CSNN had the lowest estimated energy per inference among evaluated models while ranking in the middle for positioning accuracy.

    Source: §VI · p. 12

  • Takeaways & Limitations

    The reported comparison identifies an accuracy–energy trade-off for CSNN-based neuromorphic positioning.

    Source: §I · p. 2

Abstract

from arXiv · show

Wireless positioning is a key enabling functionality of high-frequency, highly directional wireless systems. Supporting beam tracking depends on accurately translating channel state in- formation (CSI) estimations into position predictions. However, as urban propagation environments are inherently highly complex, determining the process that connects the CSI with the mobile user position is a difficult task. Motivated by this observation, a great amount of effort was put on designing user positioning schemes that employ conventional machine learning approaches, such as k-nearest neighbors (k-NN), and convolutional neural networks (CNNs). However, conventional models achieve low energy efficiency (EE). To counterbalance this disadvantage, brain-inspired neural processing units (NPUs) has recently been introduced. For their optimum operation, NPUs require the execution of a new type of neural models, namely spiking neural networks (SNNs). Inspired by this, in this paper, we present a wireless network architecture that enables CSI acquisition, translation into mobile user position information, and beamforming adaptation through novel convolutional SNN (CSNN) models. To train and assess the models' performance, we created datasets based on realistic ray-tracing-based simulations. We applied the CSNN architecture and compared its performance against fingerprinting k-NNs, and CNNs in terms of both computing- and communication-tailored performance metrics. The results highlight a trade-off between EE and user positioning accuracy.

I. INTRODUCTION

The paper proposes a CSNN-based positioning subsystem for mmWave that maps uplink CSI to user positions. Its contribution is evaluated across positioning accuracy, energy, and communication metrics, with results highlighting an accuracy–energy trade-off.

I. INTRODUCTION

  • High-frequency systems offer improved spatial and temporal resolution, but propagation losses, blockage sensitivity, and positioning-signaling overhead constrain their use.Source: §I · p. 1
  • CSI-based learning uses propagation information to map channel conditions to spatial coordinates, while edge inference motivates energy-efficient models under computational and hardware constraints.Source: §I · pp. 1–2
  • The proposed brain-inspired mmWave positioning subsystem uses a CSNN to study the nonlinear relationship between CSI and user coordinates.The contribution applies CSNNs to CSI-based positioning using ray-traced channel simulations.Source: §I · p. 2
  • The authors design CSNN models to estimate wireless UE positions from uplink CSI.Source: §I · p. 2
  • A unified benchmark compares neural models using both machine-learning and communication metrics on identical data and hardware.Source: §I · p. 2
  • CSNN achieved the lowest estimated energy per inference while ranking in the middle of the tested models for positioning accuracy.The paper frames this as an accuracy–energy trade-off for neuromorphic positioning.Source: §I · p. 2

II. SYSTEM MODEL & COMMUNICATION PROTOCOL

The system model considers an urban mmWave setting with a multi-antenna base station and single-antenna user equipment. It describes hybrid beamforming and the known base-station versus unknown UE positions.

II. SYSTEM MODEL & COMMUNICATION PROTOCOL

  • The section presents the system model, technical characteristics, beamforming techniques, communication protocol, and channel model.Source: §II · p. 2

A. System Model

  • The BS uses a uniform rectangular planar array with NBS = NA × NB antenna elements, while each UE has a single antenna.Source: A. System Model · p. 2
  • The BS employs hybrid beamforming with NRF RF chains to support massive connectivity while maintaining low complexity.Source: A. System Model · pp. 2–3
  • The BS location is fixed and known, while UE locations are unknown and lie within a predefined two-dimensional Cartesian region.Source: A. System Model · p. 3

B. Communication Protocolol

The communication protocol uses uplink transmissions for position prediction and a directional downlink beam for communication. The section also introduces the proposed positioning models and benchmarks.

B. Communication Protocolol

  • The BS predicts UE position after selecting a UE from its initial access request, then establishes communication through a directional downlink beam.Position tracking continues through the wide-directional uplink connection.Source: B. Communication Protocolol · p. 3
  • Each UE periodically transmits over an OFDM uplink, and the BS receives the signal through a ray-tracing channel model.The signal model includes additive white Gaussian noise.Source: B. Communication Protocolol · p. 3

III. PROPOSED POSITIONING MODELS

  • The paper presents two neural positioning architectures and a machine-learning baseline, then defines their complexity analysis and evaluation metrics.Source: §III · p. 3

A. Data Processing for the Input Layer

The input pipeline converts CSI into real-valued components and reduces its subcarrier dimension; the benchmarks and proposed CSNN use convolutional feature extraction to estimate user coordinates. The CSNN replaces CNN ReLU activations with LIF neurons while preserving spatial structure.

A. Data Processing for the Input Layer

  • CSI tensors are split into real and imaginary parts, then adjacent subcarriers are averaged in chunks to reduce input size by a factor p.The resulting tensor shape is [NRX, N, 2] before the subcarrier reduction.Source: A. Data Processing for the Input Layer · p. 4

B. Benchmark Models

  • k-NN estimates a query position from the weighted average of the nearest stored CSI fingerprints and their known positions.The benchmark uses Euclidean distance between the query and stored fingerprints; weights are inversely proportional to distance.Source: B. Benchmark Models · p. 4
  • CNNs extract features from multidimensional inputs with convolutional layers, then use a fully connected regression segment to predict coordinates.The described CNN uses three convolutional layers, adaptive average pooling, and a regression head with one hidden layer.Source: B. Benchmark Models · p. 4

C. Proposed Model

  • The proposed LIF neurons integrate inputs in a membrane potential and emit spikes when that potential reaches a threshold.For regression, leaky-integrator output neurons accumulate incoming spikes without generating output spikes.Source: C. Proposed Model · pp. 4–5
  • CSNNs preserve CSI's spatial structure, using LIF layers instead of CNN ReLU layers in the convolutional component.The proposed architecture uses adaptive average pooling and a spiking regressor; leaky-integrator output neurons produce continuous coordinate estimates.Source: C. Proposed Model · p. 5

D. Computational and Storage Complexity

The section describes computational cost in FLOPs and storage in model parameters or fingerprints. It contrasts dense and convolutional networks with event-driven spiking models and the exhaustive-search k-NN baseline.

D. Computational and Storage Complexity

  • Conventional dense and convolutional segments are measured in FLOPs, with total cost given by the sum of the two segments' costs.A FLOP may be an accumulation or a multiply-and-accumulate operation.Source: D. Computational and Storage Complexity · p. 5
  • Spiking-model computation scales with firing rate; binary spikes can enable event-driven conditional weight accumulation, so cost is modeled in AC operations.Each spike is followed by an accumulation in the next layer.Source: D. Computational and Storage Complexity · p. 5
  • Each k-NN query exhaustively compares the query with the fingerprint database, while its storage is 4NdbD bytes rather than the 4Np bytes required for a parameterized model.Here, Ndb is the number of stored fingerprints and D their dimensionality; parameterized-model storage scales with parameter count.Source: D. Computational and Storage Complexity · p. 5

IV. PERFORMANCE METRICS

The evaluation uses positioning-error and communication metrics. Absolute positioning error measures the Euclidean distance between an estimated and ground-truth position.

IV. PERFORMANCE METRICS

  • The evaluation considers APE, MPE, RMSE, CE90, achievable SNR, and energy efficiency to assess positioning and communication performance.The neural models are evaluated on the test dataset.Source: §IV · p. 6

A. Absolute Positioning Error

  • APE is the Euclidean distance between an estimated user position and the ground-truth position.Its geometric interpretation is a circle centered on the true position.Source: A. Absolute Positioning Error · p. 6
  • The estimated position is represented in two dimensions, and the positioning error is measured against the ground truth.The error’s circular interpretation is centered on the true position.Source: A. Absolute Positioning Error · p. 6

B. Mean Positionning Error

The metrics summarize average and tail positioning error, then assess the communication link using beamforming, SNR, and energy efficiency. The section notes that tail errors matter for beam management because large errors can misalign beams and reduce received power.

B. Mean Positionning Error

C. Root Mean Square Error

D. 90th Percentile Circular Error

  • CEp is the error-circle radius containing a fraction p of position estimates; CE90 is obtained empirically from evaluated samples.Percentile-based circular error captures the upper tail that mean-based metrics can miss.Source: D. 90th Percentile Circular Error · p. 6

E. Telecommunications Metrics

  • The communication evaluation steers the downlink beam toward the estimated position and compares SNR with the genie-aided reference; link-level EE is spectral efficiency divided by total power.The estimator's power contribution is negligible for a single user updating once, but becomes material when positioning runs continuously for many users.Source: E. Telecommunications Metrics · pp. 6–7

A. Simulation Scenario

The simulation produces CSI tensors from ray-traced wireless channels and evaluates positioning on a grid-based dataset. The neural models and fingerprinting baseline are assessed under specified training and evaluation conditions.

A. Simulation Scenario

  • The ray-tracing channels are generated with NVIDIA Sionna-RT, with the listed BS and OFDM parameters defining the simulation setup.The setup specifies a 30 GHz carrier and 1024 subcarriers; the passage also lists antenna, bandwidth, and power parameters.Source: A. Simulation Scenario · p. 7
  • Each of three datasets contains 30,800 samples and differs by a 0.08 m positioning offset; each CSI tensor is stored with dimensions [B, 32, 32, 2].Users stop at discrete grid positions and transmit pilot OFDM sequences; the BS estimates CSI using least-squares channel estimation.Source: A. Simulation Scenario · p. 7
  • The k-NN evaluation subset is offset only 0.08 m from the training grid, and k = 9 is the best configuration in the tested sweep.The sweep tested k ∈ {1, 3, 5, 7, 9, 15} on a held-out partition of the fingerprint database.Source: A. Simulation Scenario · p. 7
  • CNN and CSNN share specified convolutional settings and a 256-neuron regressor head; the CSNN is trained at T ∈ {5, 10, 15}.Both convolutional models use Cin = 32, MK = 3, MF = 4, and Nout = 2; the passage also says validation uses unseen data from the same simulation environment.Source: A. Simulation Scenario · p. 7
  • Table I is identified as positioning accuracy for the evaluated schemes on the held-out subset, with values reported in metres.The supplied passage gives the table scope but not its cell values.Source: Table I · p. 8

B. Positioning Error Distribution

The CNN has the lowest reported positioning error, while the CSNN is less accurate but can trade accuracy for lower inference energy as its time-step setting changes. The CSNN’s spiking representation and firing activity help explain the accuracy and energy patterns across the evaluated settings.

B. Positioning Error Distribution

  • CE90 is 0.118 m for CNN, 0.229 m for CSNN (T=20), and 0.635 m for 9-NN, with the ordering preserved across reported statistics.The CSNN CE90 is a factor of 1.9 higher than the CNN's.Source: B. Positioning Error Distribution · p. 8
  • The 9-NN baseline is 5.4 times less accurate than CNN and 2.8 times less accurate than CSNN, consistent with CSI decorrelation below the 1 cm wavelength at 30 GHz.The authors describe 9-NN as bounding interpolation over the radio map alone.Source: B. Positioning Error Distribution · p. 8
  • Replacing CNN ReLU activations with LIF neurons makes CSNN representations binary, requiring information to be encoded in spike counts and timing within T steps.The authors identify the resulting loss of representational precision as accounting for increased positioning error.Source: B. Positioning Error Distribution · p. 8
  • All three schemes have their largest spatial errors closest to the BS and near the surveyed area's boundaries.The per-position errors are interpolated onto a dense grid.Source: B. Positioning Error Distribution · p. 8

C. Effect of Number of Time Steps

  • Inference energy rises from 0.0475 mJ at T = 5 to 0.1122 mJ at T = 20; falling firing rate keeps spike count nearly unchanged from T = 5 to T = 10, but not at T = 20.At T = 20, mean firing rate rises to 0.040 and spike count per neuron per inference doubles to 0.796; the first convolutional layer and regressor head concentrate higher activity.Source: Table II · p. 8, C. Effect of Number of Time Steps · pp. 8–9
  • CSNN CE90 is 0.244 m at T = 5, 0.277 m at T = 10, and 0.229 m at T = 20, with the authors attributing part of the nonmonotonic ordering to run-to-run variation.The settings were trained under an otherwise identical configuration.Source: C. Effect of Number of Time Steps · p. 8, Table II · p. 8
  • T = 5 offers 42% lower inference energy than T = 20 for a 6.5% increase in CE90, while accuracy is only weakly dependent on T over the swept range.The authors select T = 20 for the remainder of the section because it achieved the best measured accuracy.Source: C. Effect of Number of Time Steps · p. 9

D. Energy Consumption

The CSNN reduces inference energy relative to the CNN and k-NN, while its accuracy and energy vary with the number of time steps. In link evaluation, it achieves the highest energy efficiency after inference power is included, with performance depending on update rate and user location.

D. Energy Consumption

  • As T increases, CSNN energy per inference grows monotonically, reaching its maximum at T = 20, while accuracy varies weakly and non-monotonically and is best at that same value.The spike budget ζ is approximately preserved from T = 5 to T = 10 before doubling at T = 20, so energy grows less steeply than the factor T would suggest.Source: D. Energy Consumption · p. 9
  • The CSNN uses 3.9× less energy than the CNN, at CE90 = 0.229 m versus 0.118 m; its spiking layers remain below the 5.11 break-even spike ratio.The measured aggregate ζ is 0.796, and each layer satisfies ζ(l) < 5.11.Source: D. Energy Consumption · p. 10
  • The CSNN requires 5.2 times less energy and 200 times less storage than k-NN while being 2.8 times more accurate.The k-NN baseline requires 126.2 M operations and stores 504.6 MB of fingerprints.Source: D. Energy Consumption · p. 10
  • The energy estimates are arithmetic lower bounds: excluding memory access can reduce the reported spiking-model advantage by roughly a factor of two under a conservative cache assumption.Dedicated neuromorphic hardware may incur a substantially smaller membrane-state memory penalty.Source: D. Energy Consumption · p. 10

E. Performance Evaluation of the Communication Link

  • Before 3 m from the BS, both learned models outperform k-NN in beam-misalignment degradation; farther away, their differences narrow to about 10−1 dB.At far distances, all models show negligible differences in quality degradation.Source: E. Performance Evaluation of the… · pp. 10–11, Figure 7 · p. 11
  • Including inference power, the CSNN has the highest link energy efficiency and loses 2.5% of genie-aided EE, versus 9.0% for the CNN and 11.6% for k-NN.It remains above the CNN at every positive beam-update rate.Source: E. Performance Evaluation of the… · pp. 11–12
  • At Δt = 10 ms, CSNN inference reaches baseline circuit power at 891 UEs, versus 172 for 9-NN and 228 for CNN.The CSNN sustains roughly four times as many users before reaching that power level.Source: E. Performance Evaluation of the… · p. 11

VI. CONCLUSION

The conclusion presents a CSNN positioning subsystem that uses uplink CSI to estimate user positions for downlink beam steering. Its positioning accuracy is intermediate among the tested models, while its per-inference energy is lowest.

VI. CONCLUSION

  • The CSNN has the lowest energy per inference among the evaluated models and positioning accuracy in the middle of the tested models.The conclusion frames this as a trade-off between positioning accuracy and energy efficiency.Source: §VI · p. 12
  • In scatterer-poor environments and near-BS LoS regions, small positioning errors can cause disproportionately large SNR and EE penalties under narrow-beam downlink transmission.Rich scattering partially compensates for larger positioning errors.Source: §VI · p. 12
  • The authors identify edge-deployed, low-power inference applications as a suitable scope when moderate positioning accuracy is acceptable.They identify additional communication scenarios and alternative network architectures as directions for future evaluation.Source: §VI · p. 12
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