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Millimeter Wave and Sub-Terahertz Spatial Statistical Channel Model for an Indoor Office Building

Shihao Ju, Yunchou Xing, Ojas Kanhere, Theodore S. Rappaport

arXiv:2103.17127v1cs.IT

TL;DR

Indoor mmWave and sub-THz channel models need broader measurement support across emerging frequencies and realistic office environments. This paper uses extensive 28 and 140 GHz measurements to build a unified 3-D spatial statistical model, finding frequency-dependent channel sparsity and good agreement between simulated and measured delay-spread distributions. The model and simulator support directional, omnidirectional, and MIMO channel generation up to 150 GHz.

  • Problem

    Existing indoor THz measurements were often limited to a few meters and a single room, while accurate models across emerging frequencies are needed for 6G design and evaluation.

  • Method

    The paper derives path-loss and channel statistics from extensive 28 and 140 GHz office measurements and incorporates them into a NYUSIM-based 3-D indoor spatial statistical channel model.

  • Results

    The number of time clusters follows a Poisson distribution and the number of within-cluster subpaths follows a composite exponential distribution across LOS and NLOS environments at 28 and 140 GHz.

  • Takeaways & Limitations

    The resulting model and simulator can recreate 3-D omnidirectional, directional, and MIMO channels for carrier frequencies up to 150 GHz.

Abstract

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Millimeter-wave (mmWave) and sub-Terahertz (THz) frequencies are expected to play a vital role in 6G wireless systems and beyond due to the vast available bandwidth of many tens of GHz. This paper presents an indoor 3-D spatial statistical channel model for mmWave and sub-THz frequencies based on extensive radio propagation measurements at 28 and 140 GHz conducted in an indoor office environment from 2014 to 2020. Omnidirectional and directional path loss models and channel statistics such as the number of time clusters, cluster delays, and cluster powers were derived from over 15,000 measured power delay profiles. The resulting channel statistics show that the number of time clusters follows a Poisson distribution and the number of subpaths within each cluster follows a composite exponential distribution for both LOS and NLOS environments at 28 and 140 GHz. This paper proposes a unified indoor statistical channel model for mmWave and sub-Terahertz frequencies following the mathematical framework of the previous outdoor NYUSIM channel models. A corresponding indoor channel simulator is developed, which can recreate 3-D omnidirectional, directional, and multiple input multiple output (MIMO) channels for arbitrary mmWave and sub-THz carrier frequency up to 150 GHz, signal bandwidth, and antenna beamwidth. The presented statistical channel model and simulator will guide future air-interface, beamforming, and transceiver designs for 6G and beyond.

I. INTRODUCTION

Emerging mmWave and sub-THz systems offer large bandwidths for indoor applications, but their propagation differs from sub-6 GHz and remains insufficiently measured across relevant frequencies. This paper addresses the need for accurate indoor channel models with extensive measurements and a unified statistical framework.

  • Motivation: Indoor applications such as 8K streaming and centimeter-level positioning are motivating mmWave and sub-THz systems because of their vast available bandwidths.Mobile data traffic was predicted to reach 77 exabytes per month by 2022.
  • Research gap: Only a few indoor measurement and modeling studies cover emerging frequencies such as 28, 73, and 142 GHz.Existing work has concentrated mainly on sub-6 GHz and 60 GHz environments.
  • Propagation challenges: MmWave and THz signals experience weak diffraction and increased sensitivity to human blockage, requiring directional steerable antennas and beamforming.These propagation properties make time-variant directional channel models relevant to beam tracking and system design.
  • Research gap: Many existing THz channel models rely on free-space, reflection, and scattering measurements collected over a few meters in a single room.This measurement scope differs from the entire-floor office measurements used in the present work.
  • Contribution: The paper derives empirical statistics from extensive 28 and 140 GHz office-floor measurements and proposes a 3GPP-like indoor spatial statistical model following NYUSIM.The model can generate directional and omnidirectional wideband channel impulse responses from 28 to 140 GHz.

III. 28 GHZ AND 140 GHZ WIDEBAND INDOOR CHANNEL MEASUREMENTS

The study measured wideband directional channels across a large office floor at 28 and 140 GHz using sliding-correlation sounders and steerable horn antennas. Directional sweeps and ray-tracing-assisted timing enabled synthesis of omnidirectional power delay profiles.

  • Measurement procedure: A sliding-correlation channel sounder transmitted a 2047-chip pseudorandom sequence through steerable horns and recorded averaged power delay profiles.The systems provided measurable path-loss dynamic ranges of 152 dB at 28 GHz and 145 dB at 140 GHz.
  • Measurement environment: Measurements covered a 65.5 m × 35 m × 2.7 m office environment containing offices, conference rooms, classrooms, hallways, cubicles, and elevators.Obstructions included desks, chairs, cubicle partitions, glass doors, and drywall walls with metal studs.
  • Measurement environment: Five transmit locations and 33 receive locations were used at 28 GHz, while 140 GHz measurements reused the five transmit locations and 13 NLOS receive pairs.The 28 GHz campaign included nine LOS and 35 NLOS pairs; the 140 GHz campaign included nine LOS and 13 NLOS pairs.
  • Measurement procedure: Eight unique antenna azimuth sweeps per transmitter–receiver pair characterized spatial arrival and departure statistics.Six receive-antenna sweeps and two transmit-antenna sweeps were performed at half-power beamwidth increments.
  • Measurement procedure: Equivalent omnidirectional received power was synthesized by summing measurements from all unique pointing angles in the 3-D space.The sweep steps were 30° at 28 GHz and 8° at 140 GHz, corresponding to 12 and 45 azimuth rotations.

B. Synthesizing Omnidirectional PDPs

The paper aligns directional power delay profiles using ray-tracing-predicted first-arrival times before combining them into omnidirectional channels. It models path loss with a 1 m close-in reference and compares directional behavior across 28 and 142 GHz.

  • Synthesizing omnidirectional PDPs: NYURay predicts candidate propagation rays and supplies the absolute time of flight for the first arriving multipath component in each measured directional profile.This prediction resolves the absolute timing needed to align directional profiles.
  • Synthesizing omnidirectional PDPs: Directional profiles assigned to the same predicted ray are summed in power to form partial omnidirectional profiles and avoid double counting.The extracted multipath component direction is assigned from the measured profile closest to the predicted ray.
  • Path-loss modeling: The close-in path-loss model anchors measurements at 1 m free-space path loss and fits distance dependence using a single path-loss exponent.Shadow fading is modeled as a zero-mean lognormal random variable in dB.
  • Directional path loss: The directional LOS path-loss exponents at 28 and 142 GHz are 1.7 and 2.1, respectively.The difference may reflect the 30° and 8° antenna half-power beamwidths used at the two frequencies.
  • Directional path loss: The directional NLOS-Best path-loss exponent is about 3.0 at both 28 and 142 GHz.The reported result indicates strong NLOS paths are available for link-margin support and may be leveraged by intelligent reflecting surfaces.

B. Omnidirectional Path Loss Modeling

The omnidirectional CI path loss model synthesizes received power from all measured directions and provides a reference for indoor channel modeling. At 28 and 142 GHz, NLOS path loss exponents are comparable, while LOS behavior differs across frequencies and locations.

  • Omnidirectional path loss is synthesized from received powers measured across the 3-D space.
  • The omnidirectional model serves as a fundamental reference model for channel models and standards.
  • 28 GHz has a LOS path loss exponent of 1.2, attributed to waveguide effects in some corridor locations.
  • 28 and 142 GHz have comparable NLOS path loss exponents of about 2.7.

V. 3-D SPATIAL STATISTICAL CHANNEL MODEL

The model represents indoor propagation as clustered multipath in temporal and angular domains, while separating time clusters from spatial lobes. It uses measured channel structure and NYUSIM-style statistics to support 3-D channel generation and validation.

  • Measured multipath components arrive in clusters across delay and angular domains at 28 and 140 GHz.
  • The time-cluster spatial-lobe approach characterizes temporal and angular domains separately.
  • A time cluster groups multipath components close in time, whereas a spatial lobe represents a main arrival or departure direction.
  • The cluster-based omnidirectional CIR is parameterized by time clusters, subpaths, delays, powers, phases, and 3-D departure and arrival angles.
  • The PDP and APS are partitioned using a minimum inter-cluster time interval and a spatial-lobe threshold, respectively.
  • Primary statistics drive channel generation, while secondary statistics support validation against measured channels.

VI. STATISTICS OF CHANNEL GENERATION PARAMETERS

Channel-generation parameters are extracted from measured power delay profiles and angular power spectra using matched 28 and 140 GHz location sets. The number of time clusters is modeled with a shifted Poisson distribution.

  • Temporal parameters include time-cluster and subpath counts, delays, and powers; spatial parameters include spatial-lobe counts, mean angles, and angular offsets.
  • The 28 GHz common set matches the 140 GHz common set in transmitter–receiver location pairs for fair comparison.
  • Histograms of time-cluster counts for the three datasets and both propagation scenarios are fitted with Poisson distributions using a 6 ns MTI.
  • Because observed time-cluster counts start at one, the fitted variable is N′ = N − 1 and the simulated count is recovered as N = N′ + 1.
  • The 28 GHz channel has about three more time clusters than the 140 GHz channel in both NLOS and LOS scenarios.

2) Number of Cluster Subpaths:

Cluster subpath counts depend on the MTI and are modeled with discrete exponential or composite distributions. The results indicate larger 28 GHz clusters, especially in NLOS, while 140 GHz channels are sparser.

  • Number of Cluster Subpaths:: Larger MTI values produce fewer time clusters and more subpaths per cluster, whereas smaller MTI values produce the opposite pattern.
  • Number of Cluster Subpaths:: A composite distribution is used because about half of the measured 28 GHz clusters contain only one subpath.
  • Number of Cluster Subpaths:: For 28 GHz NLOS all-set data, the composite distribution has µs = 5.3 and β = 0.7.
  • Number of Cluster Subpaths:: For 28 GHz LOS all-set data, µs = 3.7 and β = 0.7, indicating larger NLOS clusters than LOS clusters.
  • Number of Cluster Subpaths:: At 140 GHz, a simple discrete exponential distribution fits both LOS and NLOS common-set histograms, with clusters averaging about two subpaths.
  • Number of Cluster Subpaths:: 140 GHz clusters are much smaller than 28 GHz clusters, indicating greater channel sparsity at 140 GHz.

3) Inter-cluster Excess Delay:

Inter-cluster delays characterize timing gaps between time clusters, while intra-cluster delays describe subpath dispersion within each cluster. Measurements show exponential delay behavior in several scenarios, with larger intra-cluster delays in NLOS conditions.

  • Inter-cluster Excess Delay: 140 GHz inter-cluster delays fit exponential distributions with means of 14.6 ns in LOS and 21.0 ns in NLOS scenarios.The 28 GHz and 140 GHz LOS distributions differ, with lognormal behavior at 28 GHz and exponential behavior at 140 GHz.
  • Inter-cluster Excess Delay: Large inter-cluster delays mainly occurred in corridor environments, attributed to a waveguide effect.
  • Intra-cluster Excess Delay: Intra-cluster excess delay is the time difference between the first arriving subpath and a targeted subpath within the same time cluster.
  • Intra-cluster Excess Delay: 28 GHz intra-cluster excess delays fit exponential distributions, with means of 3.4 ns for LOS and 22.7 ns for NLOS scenarios.The larger NLOS mean indicates greater intra-cluster delay in that scenario.
  • Cluster Power: Cluster power is modeled as an exponentially decaying function of cluster excess delay with lognormal shadowing.For 28 GHz NLOS, the first cluster occupies about 68% of total received power, and expected cluster power falls below 34% beyond 23.6 ns.
  • Subpath Power: Subpath power decays exponentially with intra-cluster excess delay and includes lognormal shadowing.The first subpath averages about 42% of cluster power, while expected subpath power falls below 21% beyond 9.2 ns.

B. Spatial Channel Parameters

The spatial channel model represents angular energy using spatial lobes and their mean directions, with measured lobe counts showing a small number of dominant arrival directions.

  • Spatial Lobe Representation: A spatial lobe represents a main direction of arrival or departure, and measured angular resolution depends on antenna HPBW.The HPBW values are 30° at 28 GHz and 8° at 140 GHz; directional powers are interpolated at 1° resolution in azimuth and elevation.
  • Number of Spatial Lobes: At most two main azimuth arrival directions were measured, except for a few 28 GHz NLOS locations with three.A simple DU distribution characterizes the number of spatial lobes.
  • Lobe Mean Directions: Each spatial lobe has mean azimuth and elevation directions, with elevation modeled as a normal random variable.The azimuth plane can be partitioned into sectors corresponding to individual spatial lobes.

3) Subpath Angular Offset:

Subpath angular offsets are generated around spatial-lobe mean directions, and the resulting simulator is evaluated against measured temporal and angular statistics using directional antenna patterns.

  • Subpath Angular Offset: Subpath angles are generated by assigning each subpath to a spatial lobe and adding normally distributed angular offsets around the lobe mean angle.The offset standard deviation is the median measured RMS lobe angular spread.
  • Frequency Dependence: At 140 GHz, channels have fewer time clusters and fewer subpaths per cluster than at 28 GHz, despite similar fitted distributions.Higher partition and first-meter path loss reduce propagation range and place some 140 GHz receiver locations in outage.
  • RMS Delay-Spread Validation: Omnidirectional RMS delay-spread validation produced simulated and measured medians of 10.8 and 10.8 ns for 28 GHz LOS, and 17.0 and 16.7 ns for 28 GHz NLOS.
  • RMS Delay-Spread Validation: For 140 GHz, simulated and measured omnidirectional RMS delay-spread medians were 3.0 and 2.6 ns in LOS, and 9.2 and 6.7 ns in NLOS.The simulated CDFs agreed well with empirical CDFs across all four frequency scenarios.
  • Directional Simulation: Directional channel simulations use arbitrary 3-D antenna patterns, with horn antennas applied to compare simulated and measured directional RMS delay spreads.The directional simulations generate one RMS delay spread for each MPC by pointing the simulated horn antenna toward that MPC.
  • Directional Validation: Measured and simulated directional RMS delay-spread medians show good agreement in 28 and 140 GHz LOS and NLOS scenarios.

B. Simulated RMS Angular Spreads

Global and lobe angular spreads assess angular dispersion at different spatial scales. Simulations reproduce lobe spreads closely, while global-spread agreement depends on frequency and spatial-lobe statistics.

  • Global Angular Spread: Global azimuth and elevation angular spreads measure dispersion over the entire 4π steradian sphere.
  • Global Angular Spread: Simulated and measured median global AOA spreads match well at 140 GHz but not at 28 GHz.The 28 GHz mismatch is attributed to differences in spatial-lobe statistics and limited data samples.
  • Global Angular Spread: At 140 GHz, the cumulative probability rising from 0 to 0.6 within 10° indicates one observed main arrival direction at the receiver.With one spatial lobe, global RMS angular spread approaches lobe RMS angular spread.
  • Lobe Angular Spread: Lobe angular spread measures dispersion in a particular direction after applying a -15 dB spatial-lobe threshold.
  • Lobe Angular Spread: Measured and simulated median lobe AOA spreads agree within 0.5° for 28 and 140 GHz NLOS scenarios.
  • Overall Validation: The unified model and simulator reproduce measured global and lobe angular-spread statistics, alongside temporal statistics.

APPENDIX

The appendix identifies the processed data used to generate and calibrate the omnidirectional channel models, documenting channel statistics at 28 and 140 GHz.

  • Processed data for generating and calibrating the omnidirectional channel models are provided in Tables VI and VII.
  • Table VI reports 28 GHz omnidirectional statistics, including environment, transmitter and receiver IDs, separation distance, path loss, time clusters, subpaths, and RMS delay spread.
  • Table VII reports 140 GHz omnidirectional statistics using the same channel-statistics categories as Table VI.
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