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28 GHz Millimeter-Wave Ultrawideband Small-Scale Fading Models in Wireless Channels
Mathew K. Samimi, George R. MacCartney,, Shu Sun, Theodore S. Rappaport
TL;DR
The paper addresses limited small-scale fading evidence for outdoor mmWave channels by measuring 28 GHz ultrawideband links over local spatial tracks with fixed directional beams. It extracts fading and spatial-correlation models, finding Rician path-amplitude behavior across LOS, NLOS, and polarization scenarios, with correlation reaching zero after 2 wavelengths in LOS and 5 wavelengths in NLOS V-V channels. These models support local-area channel-impulse-response and multi-element antenna simulations.
Problem
Small-scale fading statistics at mmWave frequencies were limited despite their importance for estimating local-area path amplitudes in MIMO simulations.
Method
The paper measures 28 GHz outdoor ultrawideband channels over local areas and extracts spatial fading models for individual multipath amplitudes across propagation and polarization scenarios.
Results
Rician distributions best fit the voltage path amplitudes, with K-factors of 9 - 15 dB in LOS V-V, 5 - 8 dB in NLOS V-V, and 3 - 7 dB in both LOS and NLOS V-H scenarios.
Takeaways & Limitations
The provided models can recreate wideband multipath-amplitude statistics over local areas for multi-element antenna simulations and channel-impulse-response studies.
Abstract
from arXiv · showhide
This paper presents small-scale fading measurements for 28 GHz outdoor millimeter-wave ultrawideband channels using directional horn antennas at the transmitter and receiver. Power delay profiles were measured at half-wavelength spatial increments over a local area (33 wavelengths) on a linear track in two orthogonal receiver directions in a typical base-to-mobile scenario with fixed transmitter and receiver antenna beam pointing directions. The voltage path amplitudes are shown to follow a Rician distribution, with K-factor ranging from 9 - 15 dB and 5 - 8 dB in line of sight (LOS) and non-line of sight (NLOS) for a vertical-to-vertical co-polarized antenna scenario, respectively, and from 3 - 7 dB in both LOS and NLOS vertical-to-horizontal cross-polarized antenna scenario. The average spatial autocorrelation functions of individual multipath components reveal that signal amplitudes reach a correlation of 0 after 2 and 5 wavelengths in LOS and NLOS co-polarized V-V antenna scenarios. The models provided are useful for recreating path gain statistics of millimeter-wave wideband channel impulse responses over local areas, for the study of multi-element antenna simulations and channel estimation algorithms.
I. INTRODUCTION
Existing mmWave work established path-loss models, but small-scale fading statistics at mmWave frequencies remained limited despite their importance for local-area MIMO simulations. This paper addresses that gap with 28 GHz outdoor measurements and models for individual multipath amplitudes across propagation and polarization scenarios.
- Small-scale fading statistics at mmWave frequencies had received little attention despite their importance for estimating local-area path amplitude gains in MIMO simulations.
- 28 GHz outdoor measurements were used to obtain mmWave small-scale fading statistics over a local area.
- The paper extracts spatial fading models for individual multipath voltage amplitudes in LOS and NLOS environments with co- and cross-polarization scenarios.
- The models can be implemented in channel emulators to recreate channel impulse responses and narrowband fading amplitude envelopes over short sub-wavelength distances in multi-element antenna simulations.
II. 28 GHZ SMALL-SCALE FADING MEASUREMENTS
The measurements characterize 28 GHz street-canyon small-scale fading across realistic LOS, NLOS, and transitional environments. A broadband sliding-correlator sounder and directional horn antennas sampled multipath amplitudes over local-area tracks and two receiver directions.
- 28 GHz street-canyon measurements used a 400 megachips-per-second broadband sliding correlator channel sounder and 15 dBi directional horn antennas.TX-to-RX local-area distances ranged from 8 m to 12.9 m, with maximum TX power of 27 dBm.
- Measurements covered LOS, NLOS, and transitional LOS-to-NLOS environments with V-V and V-H antenna polarization scenarios.
- One TX location and four RX locations were used to investigate spatial and temporal fading and autocorrelations of received multipath amplitudes over local areas.
- The RX antenna moved along tracks toward the TX and laterally across the static TX beam, capturing fading over two orthogonal receiver directions.
III. CHANNEL IMPULSE RESPONSE MODEL
The channel model represents the impulse response as resolvable multipath components with amplitudes, phases, delays, and directional parameters. A directional form incorporates fixed TX/RX beam pointing and antenna patterns to model the measured mmWave link.
- The channel impulse response is modeled as a superposition of multipath components, each described by a complex voltage amplitude, phase, delay, departure angles, and arrival angles.
- Measurement-based distributions are extracted for path powers, delays, departure angles, and arrival angles, while multipath phases are modeled uniformly between 0 and 2π.
- The directional impulse response modifies the omnidirectional model for fixed TX and RX beam pointing directions during real-time mmWave communication links.
- Directional antenna patterns weight the resolvable multipath components selected by the beam pointing direction.
A. Measured Power Impulse Reponses
Power-delay-profile tracks measured small-scale multipath behavior over 33 wavelengths in LOS and NLOS V-V settings. LOS components were relatively stable, whereas selected NLOS components fluctuated strongly because unresolved multipath components coherently summed.
- 33-wavelength PDP tracks sampled LOS and NLOS V-V channels at half-wavelength increments using directional horn antennas.
- LOS individual multipath power amplitudes remained relatively constant along the spatial dimension.
- Three strong NLOS multipath components were detected, with the first path diffracting around a building corner and showing little fading.
- 27 ns and 47 ns NLOS components fluctuated more strongly because different multipath components coherently summed within the system pulse-time resolution.
B. Analysis of Small-Scale Fading of Path Amplitudes
The study extracts local-area small-scale fading distributions for individual multipath amplitudes at 28 GHz and finds that Rician models best fit the measurements.
- Small-scale spatial fading describes random amplitude fluctuations of individual multipath components over a few wavelengths.The analysis groups measured path amplitudes across delay bins after normalization by mean bin power, assuming delay-independent fading.
- Rician distributions provided the best fit to the measured amplitudes, outperforming Rayleigh and lognormal alternatives.The comparison uses empirical CDFs of normalized individual path amplitudes.
- 9–15 dB and 5–8 dB bound the V-V Rician K-factors in LOS and NLOS, respectively.These ranges describe the co-polarized measurements.
- 3–7 dB bounds the V-H Rician K-factors in both LOS and NLOS environments.The cross-polarized empirical CDFs lie between Rician distributions with these K-factor values.
- 4–6 dB and 6–10 dB bound the LOS-to-NLOS Rician K-factors for V-V and V-H scenarios, respectively.These ranges are reported for the transitional environment.
- Rayleigh distributions underestimate the measurement data when the 800 MHz RF bandwidth resolves individual or few-component paths.The observation links the distributional mismatch to the measurement system’s path resolution.
28 GHz Small−Scale Fading, V−V Scenario
Figure 5 presents CDFs of individual 28 GHz path-voltage amplitudes for LOS and NLOS co-polarized V-V measurements, alongside Rayleigh and Rician models.
- Figure 5 compares LOS and NLOS V-V path-amplitude CDFs with Rician K-factors from 5 dB to 15 dB.The plotted K-factors increase in 1 dB increments and are shown with a Rayleigh reference.
28 GHz Small−Scale Fading, V−H Scenario
The V-H analysis presents cross-polarized path-amplitude CDFs and summarizes their measured Rician K-factor ranges.
- Figure 6 compares LOS and NLOS V-H path-amplitude CDFs with Rician K-factors from 3 dB to 7 dB.The candidate distributions are plotted in 1 dB increments alongside a Rayleigh distribution.
C. Spatial Autocorrelation of Individual Multipath Amplitudes
The paper uses spatial autocorrelation to quantify similarity in multipath amplitudes across sub-wavelength receiver separations and support spatial channel modeling.
- Spatial autocorrelation measures multipath-amplitude similarity over fractions of wavelengths and supports realistic spatial correlations in multi-element antenna simulations.The coefficients are averaged across receiver locations and environments for co- and cross-polarized configurations.
28 GHz Small−Scale Fading, LOS−to−NLOS Scenario
The paper characterizes 28 GHz path-amplitude fading in transitional LOS-to-NLOS conditions using CDFs and Rician models, and models spatial autocorrelation with an exponential form.
- Fading distributions: Rayleigh and Rician CDFs are compared for transitional LOS-to-NLOS path-voltage amplitudes across co- and cross-polarization scenarios.The plotted Rician K-factors range from 4 dB to 11 dB in 1 dB increments.
- Fading distributions: The measurements summarize Rician K-factors for path-voltage gains across V-V and V-H polarization configurations and multiple environments.
- Spatial autocorrelation: The empirical spatial autocorrelation functions are averaged over excess-delay bins for LOS and NLOS V-V scenarios.The corresponding figures show typical receiver-side autocorrelation behavior for individual multipath amplitudes.
IV. CONCLUSION
The paper presents 28 GHz ultrawideband outdoor fading measurements and models for LOS and NLOS channels. It reports Rician path-amplitude statistics and spatial autocorrelation behavior for recreating local-area multipath fading.
- Conclusion: The study presents 28 GHz ultrawideband outdoor small-scale fading measurements performed in LOS and NLOS environments.
- Conclusion: Rician K-factors range from 9 - 15 dB in LOS V-V, 5 - 8 dB in NLOS V-V, and 3 - 7 dB in both V-H environments.
- Conclusion: Individual multipath signal amplitudes typically reach zero spatial correlation after 2 wavelengths in LOS and 5 wavelengths in NLOS V-V scenarios.
- Conclusion: The reported models support simulation of wideband multipath-amplitude statistics over local areas for multi-element antenna diversity studies.