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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

arXiv:1511.06938v2cs.IT

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.

    Source: §I · p. 1

  • 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.

    Source: §I · pp. 1–2

  • 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.

    Source: B. Analysis of Small-Scale Fading of… · p. 4, §IV · pp. 5–6

  • Takeaways & Limitations

    The provided models can recreate wideband multipath-amplitude statistics over local areas for multi-element antenna simulations and channel-impulse-response studies.

    Source: §I · p. 2, §IV · p. 6

Abstract

from arXiv · show

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.Source: §I · p. 1
  • 28 GHz outdoor measurements were used to obtain mmWave small-scale fading statistics over a local area.Source: §I · p. 1
  • The paper extracts spatial fading models for individual multipath voltage amplitudes in LOS and NLOS environments with co- and cross-polarization scenarios.Source: §I · pp. 1–2
  • 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.Source: §I · p. 2

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.Source: §II · p. 2
  • Measurements covered LOS, NLOS, and transitional LOS-to-NLOS environments with V-V and V-H antenna polarization scenarios.Source: §II · p. 2
  • One TX location and four RX locations were used to investigate spatial and temporal fading and autocorrelations of received multipath amplitudes over local areas.Source: §II · p. 2
  • The RX antenna moved along tracks toward the TX and laterally across the static TX beam, capturing fading over two orthogonal receiver directions.Source: §II · p. 2

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.Source: §III · pp. 2–3
  • Measurement-based distributions are extracted for path powers, delays, departure angles, and arrival angles, while multipath phases are modeled uniformly between 0 and 2π.Source: §III · p. 3
  • The directional impulse response modifies the omnidirectional model for fixed TX and RX beam pointing directions during real-time mmWave communication links.Source: §III · p. 3
  • Directional antenna patterns weight the resolvable multipath components selected by the beam pointing direction.Source: §III · p. 3

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.

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.Source: B. Analysis of Small-Scale Fading of… · pp. 3–4
  • 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.Source: B. Analysis of Small-Scale Fading of… · p. 4
  • 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.Source: B. Analysis of Small-Scale Fading of… · p. 4
  • 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.Source: B. Analysis of Small-Scale Fading of… · p. 4
  • 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.Source: B. Analysis of Small-Scale Fading of… · p. 4
  • 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.Source: B. Analysis of Small-Scale Fading of… · p. 4

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.Source: Figure 5 · p. 4

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.Source: Figure 6 · p. 4

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.Source: C. Spatial Autocorrelation of… · p. 4

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.Source: Figure 7 · p. 5, Table I · p. 5
  • The measurements summarize Rician K-factors for path-voltage gains across V-V and V-H polarization configurations and multiple environments.Source: Table I · p. 5

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.Source: §28 · p. 5

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.Source: §IV · p. 5
  • 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.Source: §IV · p. 6
  • Individual multipath signal amplitudes typically reach zero spatial correlation after 2 wavelengths in LOS and 5 wavelengths in NLOS V-V scenarios.Source: Figure 8 · p. 5, Figure 9 · p. 5, §IV · p. 6
  • The reported models support simulation of wideband multipath-amplitude statistics over local areas for multi-element antenna diversity studies.Source: Table II · p. 5, §IV · p. 6
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