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Millimeter Wave Channel Modeling and Cellular Capacity Evaluation

Mustafa Riza Akdeniz, Yuanpeng Liu, Mathew K. Samimi, Shu Sun, Sundeep Rangan, Theodore S. Rappaport, Elza Erkip

arXiv:1312.4921v3cs.NI

TL;DR

Conventional cellular bands face severe spectrum shortages, motivating mmW systems with wider bandwidth and large antenna arrays. This paper uses 28 and 73 GHz New York City measurements to build spatial channel models and evaluate capacity and outage. The models predict at least an order-of-magnitude capacity increase, while the analysis remains bounded by outdoor street-level measurements and limited treatment of indoor users.

  • Problem

    Conventional cellular spectrum is severely limited, motivating careful assessment of mmW systems for next-generation micro- and picocellular networks.

  • Method

    The paper uses 28 and 73 GHz New York City propagation measurements to derive statistical models of path loss, spatial clusters, angular characteristics, and outage for system evaluation.

  • Results

    At least an order-of-magnitude higher system capacity is predicted under reasonable bandwidth and beamforming assumptions, including a 25-times cell-throughput example over 20+20 MHz FDD LTE.

  • Takeaways & Limitations

    MmW systems can provide substantial capacity gains without increased cell density, while multiple measured clusters indicate potential spatial multiplexing gains.

  • Takeaways & Limitations

    The measurements and derived models use outdoor street-level locations, so system performance with indoor mobiles requires further study.

Abstract

from arXiv · show

With the severe spectrum shortage in conventional cellular bands, millimeter wave (mmW) frequencies between 30 and 300 GHz have been attracting growing attention as a possible candidate for next-generation micro- and picocellular wireless networks. The mmW bands offer orders of magnitude greater spectrum than current cellular allocations and enable very high-dimensional antenna arrays for further gains via beamforming and spatial multiplexing. This paper uses recent real-world measurements at 28 and 73 GHz in New York City to derive detailed spatial statistical models of the channels and uses these models to provide a realistic assessment of mmW micro- and picocellular networks in a dense urban deployment. Statistical models are derived for key channel parameters including the path loss, number of spatial clusters, angular dispersion and outage. It is found that, even in highly non-line-of-sight environments, strong signals can be detected 100 m to 200 m from potential cell sites, potentially with multiple clusters to support spatial multiplexing. Moreover, a system simulation based on the models predicts that mmW systems can offer an order of magnitude increase in capacity over current state-of-the-art 4G cellular networks with no increase in cell density from current urban deployments.

I. INTRODUCTION

The paper evaluates whether mmW cellular systems can address spectrum and capacity demands using measured 28 and 73 GHz New York City channels. It develops statistical channel models and predicts substantial capacity gains despite path loss and outage concerns.

  • Motivation: 30–300 GHz mmW bands provide much wider bandwidth than today’s cellular allocations and support large antenna arrays for beamforming and spatial multiplexing.The available spectrum can be approximately 200 times greater than current cellular allocations.
  • Approach: 28 and 73 GHz New York City measurements are used to derive statistical models for channel parameters needed in mmW system evaluation.The models cover spatial characteristics, cluster parameters, path loss, and outage probabilities.
  • Key findings: 20 to 25 dB higher omnidirectional path loss at mmW frequencies can be compensated by proportional antenna gain without increasing physical antenna size.With appropriate beamforming, non-outage locations may experience no effective path-loss increase.
  • Key findings: Up to four spatial clusters were observed, averaging approximately two, indicating potential spatial multiplexing and diversity gains.The clusters arrive from multiple distinct angular directions, presumably through different scattering or reflection paths.
  • Capacity evaluation: 25 times greater cell throughput is predicted for a hypothetical 1 GHz TDD mmW system with 100 m cell radii than for a 20+20 MHz FDD LTE system with similar cell density.The broader prediction is at least an order-of-magnitude system-capacity increase under reasonable bandwidth and beamforming assumptions, without including spatial multiplexing gains.
  • Capacity evaluation: System performance appears robust when outage levels are similar to or slightly worse than those observed in the New York City measurements.Significantly worse outages can greatly impact performance, particularly the cell-edge rate.

II. MEASUREMENT METHODOLOGY

The study measures 28 and 73 GHz urban microcellular channels from rooftop transmitters to street-level receivers and estimates path loss from angularly sampled received power. It fits LOS and NLOS behavior separately while modeling measured distances and observed channel variability.

  • Measurement setup: 28 and 73 GHz measurements emulate microcellular deployments with rooftop transmitters and street-level receivers up to 500 m away.Transmitters were placed 7 and 17 m high, approximately 2 to 5 stories above ground.
  • Measurement setup: Directional horn antennas with approximately 10° beamwidths characterize both bulk path loss and spatial channel structure.The horns provided 30 dBm transmit power and 24.5 dBi gain at both transmitter and receiver.
  • Measurement procedure: Angular sampling sweeps transmitter and receiver azimuth and elevation offsets, while paths exceeding a 5 dB SNR threshold are included in the power-delay profile.The received power at each angular location is aggregated across delays.
  • Path-loss estimation: The omnidirectional path loss is estimated from total transmit power, integrated received power over all angular directions, and horn antenna gains.This path-loss measure excludes beamforming gains from directing the transmitter or receiver.
  • Path-loss modeling: NLOS path loss is fit with a floating-intercept linear model over measured distances of 30 to 200 m, with lognormal shadowing variance.The fitted parameters are α, β, and σ².
  • Path-loss results: For LOS points below 100 m, theoretical free-space path loss from Friis’ law provides a good fit.Two 28 GHz LOS points beyond 100 m show higher path loss and are not well fit by free-space propagation.

B. Spatial Cluster Detection

The paper detects spatial path clusters from angular-domain receive-power measurements and fits statistical models for their number, power fractions, and angular characteristics. The measurements support Poisson modeling of detected cluster counts and a fitted model for significant cluster power fractions.

  • Cluster representation: The channel model represents each path cluster by power fraction, departure and arrival angles, angular beamspread, and delay characteristics.This work models spatial and power characteristics but does not study temporal characteristics such as relative propagation times or delay profiles.
  • Measurement and detection: Angular measurements sample a four-dimensional transmit-receive angle space, but practical scans cover only subsets of angular offsets.Insufficiently detected power is treated as zero, and a location with no valid angular points is classified as outage.
  • Measurement and detection: The clustering algorithm uses power-weighted K-means and stops when clusters overlap within two standard deviations or when a cluster is empty.It estimates the number of resolvable clusters, their central angles, rms angular spreads, and receive powers.
  • Cluster parameters: Detected cluster counts range from 1 to 4, and a Poisson distribution with the empirical mean fits the measured distribution well, particularly at 28 GHz.The empirical and modeled distributions are compared for both 28 and 73 GHz.
  • Cluster parameters: For K = 2, cluster power fractions use exponentially distributed delays, lognormal per-cluster variations, normalization to unity, and latent relative delays in the measurements.The fitted model is accurate for clusters carrying more than 10% of the energy, while very low-energy clusters may be missed by detection.
  • Cluster parameters: The weaker-cluster power-fraction distributions for K = 2 are compared with the theoretical model fit using approximate maximum likelihood estimation.The estimated parameters at 28 and 73 GHz are reported as very similar.
  • Cluster parameters: Rms angular spreads are estimated after excluding the lowest 10% of each cluster’s power, which introduces a small bias.The distributions of horizontal azimuth AoA and AoD spreads are compared with exponential distributions sharing the empirical mean.

D. LOS, NLOS, and Outage Probabilities

The paper extends conventional LOS/NLOS link modeling with an explicit outage state to represent complete mmW link loss. Models fitted to 28 GHz measurements provide a good fit, but their parameters should not be generalized broadly because outage is environmentally dependent.

  • Outage motivation: Outages were frequently undetectable at locations particularly beyond 200 m, likely because environmental obstructions occluded all reflected or scattered paths.The measurements considered locations with detected signal separately from outage locations.
  • Three-state model: Conventional cellular evaluation generally models each link as either LOS or NLOS, with outage occurring implicitly when path loss becomes sufficiently large.The LOS and NLOS probabilities and link characteristics depend on distance and link state.
  • Three-state model: The proposed model adds outage as a third state, assigning links to LOS, NLOS, or outage and treating outage as no link with infinite path loss.The three state probabilities are modeled statistically from measurement data.
  • Model fitting: The LOS, NLOS, and outage probability functions were fitted by maximum likelihood to 42 TX-RX pairs at 28 GHz and fit the observed state fractions well.The simulations assume the same probabilities at 73 GHz.
  • Scope: The fitted parameter values should not be generalized to other scenarios because outage conditions are highly environmentally dependent.Further study is needed to identify parameters valid across a range of circumstances.

E. Small-Scale Fading Simulation

The simulation generates time-varying narrowband channel matrices from measured large-scale spatial parameters and synthesized small-scale subpaths. The resulting model excludes delay-spread characterization and is therefore narrowband.

  • Large-scale parameters: The statistical parameters represent large-scale fading characteristics associated with the macro-scattering environment and changing relatively slowly.These parameters are summarized in the proposed model based on NYC measurements.
  • Channel synthesis: Channel synthesis first generates distance-based path loss, cluster count, cluster power fractions, central angles, and angular beamspreads from the statistical model.Each cluster is then represented using multiple subpaths, such as L = 20 subpaths.
  • Channel synthesis: For antenna arrays with n_rx receive and n_tx transmit antennas, the model represents the narrowband time-varying TX-RX channel as a matrix formed from subpath gains and array response vectors.The response vectors encode angular arrivals and departures at the RX and TX arrays.
  • Small-scale fading: Small-scale subpath gains include Doppler dependence through the maximum Doppler shift and subpath arrival angle, with scaling by omnidirectional path loss.The mobile array orientation determines the relation between subpath motion angles and angular arrivals.
  • Scope: The model is narrowband because the measurements do not yet characterize delay spread or temporal delay profiles.Relative propagation times from different angular directions require further analysis.

IV. COMPARISON TO 3GPP CELLULAR MODELS

The paper compares empirically derived 28 and 73 GHz path-loss models with free-space propagation and the 2.5 GHz 3GPP UMi model. Although mmW omnidirectional losses are higher, beamforming can compensate for the difference at equal physical antenna size.

  • The Empirical NYC curves represent omnidirectional path loss from the paper’s linear model and are compared against free-space and 3GPP UMi models.Figure 8 compares distance-based models at the stated frequencies.
  • At d = 100 m, free-space path loss is approximately 30 dB less than the experimentally measured mmW model.This suggests capacity predictions based on free-space propagation may be optimistic.
  • 20 to 25 dB higher omnidirectional path loss is predicted at 28 and 73 GHz than by the 2.5 GHz 3GPP UMi model.The comparison applies over most relevant distances.
  • 10 to 30 times smaller wavelengths at 28 and 73 GHz allow sufficient beamforming to compensate for the higher path loss with the same physical antenna size.Beamforming at both ends can make effective mmW path loss even lower.

B. Spatial Characteristics

The measured mmW channels exhibit multiple angular clusters and spatial structure that can support beamforming and multiplexing. The analysis therefore contrasts instantaneous and long-term beamforming, while noting practical CSI and hardware constraints.

  • Spatial clusters: Up to four clusters were observed, with an average of approximately two, indicating multiple angular paths for spatial multiplexing and diversity.The cluster angular spreads are similar to those in the 3GPP UMi model, although UMi has somewhat more clusters.
  • Spatial clusters: The delay scaling parameters r_τ = 2.8 and 3.0 are in the same range as 3GPP UMi values.The paper says this suggests similar power-delay behavior, but requires confirmation using actual relative cluster delays.
  • Practical constraints: High Doppler and analog beamforming may make maintaining transmitter CSI and obtaining full receiver CSI infeasible.These constraints motivate the more conservative long-term beamforming analysis.
  • Beamforming: Instantaneous beamforming can provide up to approximately 30 dB gain for n_tx = 64 and n_rx = 16 under the stated bound.The maximum occurs when the channel is rank one and energy is concentrated in a single direction.
  • Beamforming: Long-term beamforming adapts to slowly varying large-scale parameters rather than instantaneous small-scale fading.Covariance matrices average out small-scale fading and can be estimated over longer periods.
  • Beamforming: Median interfering beamforming gain is approximately 6 dB lower at the receiver and 9 dB lower at the transmitter.The paper connects this difference with directional isolation from typical interferers.

C. Spatial Degrees of Freedom

The spatial-degree analysis measures how much channel energy is captured by optimal r-dimensional transmit and receive subspaces. The measured channels retain substantial energy beyond one spatial dimension, supporting multiple streams.

  • Energy across spatial dimensions: φ(r) is the fraction of channel energy captured by optimal r-dimensional subspaces at both receiver and transmitter.Under the Kronecker approximation, it is determined by the largest eigenvalues of the spatial covariance matrices.
  • Energy across spatial dimensions: Multiple clusters with nonzero angular dispersion distribute significant channel energy across higher spatial dimensions.With no angular dispersion, a rank-one covariance would concentrate all energy in one dimension.
  • Energy across spatial dimensions: In the median 28 GHz channel, one spatial dimension captures approximately 50% of channel energy.The distribution is shown for r = 1, ..., 4.
  • Energy across spatial dimensions: Two spatial dimensions capture 80% of channel energy, while three dimensions capture 95% in the median channel.The paper interprets these values as indicating potential single-user MIMO gains with two or three streams at many locations.

A. System Model

The system model evaluates small-cell networks by randomly dropping base stations and users according to a 3GPP UMi-like urban deployment. The default layout uses hexagonal sectors over a 2 km by 2 km area.

  • Evaluation framework: Base stations and user equipments are randomly dropped, and performance metrics are measured over multiple network realizations.The evaluation follows a standard cellular methodology adapted to small-cell networks.
  • Deployment: The deployment uses a uniform hexagonal pattern with three sectors per site and a 200 m inter-site distance.This configuration covers a 2 km by 2 km area.
  • Deployment: 130 cell sites and 390 cells are included per network drop.The three-sector-per-site layout produces the stated cell count.
  • Deployment: User equipments are uniformly distributed at a density of 10 UEs per cell.This matches the 3GPP UMi assumption used for comparison.
  • Transmit assumptions: Maximum transmit powers are 20 dBm at the UE and 30 dBm at the base station.The paper describes these values as reasonable for current mmW CMOS power amplifiers.

B. Beamforming Modeling

The evaluation models mmW links with effective path losses and simplified single-stream processing, then compares SINR and rates across frequencies and antenna-array sizes. Results show that array size and physical antenna area strongly shape the 28-versus-73 GHz trade-off, while directional beams compensate for higher path loss.

  • Beamforming Model: Single-stream processing uses beamforming to maximize SNR without interference nulling, while each TX-RX pair is modeled as an effective SISO channel.The effective path loss accounts for received power across path clusters and beamforming at both link ends.
  • Rate Evaluation: The simulation converts effective path losses into average SINR and then rates using a simplified spectral-efficiency model.The model uses Shannon capacity with a loss factor and maximum spectral efficiency, with Δ = 3 dB and ρmax = 4.8 bps/Hz for mmW.
  • MAC Layer Assumptions: Proportional-fair scheduling with full-buffer traffic gives each UE an equal fraction of time-frequency resources under the no-multi-user-diversity assumption.The uplink additionally allows simultaneous scheduling of multiple UEs, requiring the BS to receive multiple beams.
  • Frequency and Array Size: 73 GHz rates are approximately half those at 28 GHz for the same antenna-element count, but a 73 GHz 8x8 array has rate and SNR distributions close to a 28 GHz 4x4 array.Both arrays occupy roughly 1.5 × 1.5 cm2 when the physical antenna area is held approximately constant.
  • SINR Results: Only about 5 to 10% of mobiles fall below 0 dB SINR, indicating that short cells and highly directional beams compensate for mmW path loss relative to conventional cellular frequencies.The cited comparison reports SINR distributions slightly better than those in traditional cellular evaluation studies.
  • Capacity Comparison: > 25-fold overall cell-throughput increase is predicted for the mmW system over LTE under the stated bandwidth and scheduling assumptions.The comparison uses 1 GHz mmW bandwidth versus 20+20 MHz LTE bandwidth, with a 50-50 UL-DL TDD split and 20% control overhead.

E. Directional Isolation

The paper examines how directional transmission, outage conditions, and line-of-sight availability affect mmW network performance. Directionality limits interference, while severe outage shifts and loss of LOS links create important coverage and rate penalties.

  • Directional Isolation: Thermal noise exceeds interference on 90% of links, showing that directional transmissions and short cell radii produce relatively high-SINR links with limited interference.The paper notes that thermal noise is often dramatically larger than interference.
  • Outage Sensitivity: A 50 m shift making outages occur closer than predicted does not significantly affect performance, but a 75 m shift causes many UEs to lose connection to any BS.With a 100 m cell radius, the larger outage radius sharply reduces cell-edge rates and may force mobiles to connect to more distant cells.
  • LOS Dependence: Removing LOS links causes a significant rate drop, yet the mmW system still provides greater than 20-fold higher rate than the comparison LTE system.The result applies when links are restricted to NLOS or outage states.
  • Urban Propagation: The models report detectable signals 100 m to 200 m from potential cell sites even without LOS, with multiple reflected path clusters supporting spatial multiplexing and diversity.These models are based on real experimental data collected at 28 and 73 GHz in New York City.
  • Capacity Implications: Capacity evaluations predict an order-of-magnitude increase over current 4G systems under reasonable assumptions about antennas, bandwidth, and beamforming.The findings support the viability of small-cell outdoor mmW systems in challenging urban-canyon environments.
  • Scope Boundary: The analysis is limited to outdoor street-level measurements, so indoor-mobile coverage and penetration remain unevaluated.The paper identifies relaying or fallback to conventional microwave cells as possible ways to serve indoor locations and coverage holes.
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