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Millimeter Wave Beamforming for Wireless Backhaul and Access in Small Cell Networks
Sooyoung Hur, Taejoon Kim, David J. Love, James V. Krogmeier, Timothy A. Thomas, Amitava Ghosh
TL;DR
Outdoor millimeter-wave small-cell links face severe path loss and beam misalignment from environmental movement. This paper develops adaptive beam alignment with hierarchical codebooks and finds improved performance with reduced search time, while documenting an array-size–wind-movement tradeoff.
Problem
Outdoor millimeter-wave systems face severe path loss and propagation challenges, motivating efficient beamforming for small-cell links.
Method
The paper develops computationally efficient beam alignment using adaptive subspace sampling and hierarchical beam codebooks, with analysis of wind-induced impairments.
Results
The proposed alignment outperforms non-adaptive joint and single-sided methods while substantially improving system performance and reducing search time.
Takeaways & Limitations
The paper documents a tradeoff between array size and wind-induced movement, limiting the benefits of larger arrays when beam misalignment increases.
Abstract
from arXiv · showhide
Recently, there has been considerable interest in new tiered network cellular architectures, which would likely use many more cell sites than found today. Two major challenges will be i) providing backhaul to all of these cells and ii) finding efficient techniques to leverage higher frequency bands for mobile access and backhaul. This paper proposes the use of outdoor millimeter wave communications for backhaul networking between cells and mobile access within a cell. To overcome the outdoor impairments found in millimeter wave propagation, this paper studies beamforming using large arrays. However, such systems will require narrow beams, increasing sensitivity to movement caused by pole sway and other environmental concerns. To overcome this, we propose an efficient beam alignment technique using adaptive subspace sampling and hierarchical beam codebooks. A wind sway analysis is presented to establish a notion of beam coherence time. This highlights a previously unexplored tradeoff between array size and wind-induced movement. Generally, it is not possible to use larger arrays without risking a corresponding performance loss from wind-induced beam misalignment. The performance of the proposed alignment technique is analyzed and compared with other search and alignment methods. The results show significant performance improvement with reduced search time.
I. INTRODUCTION
The paper targets scalable millimeter-wave backhaul and access for dense small-cell networks, where outdoor propagation and wind-induced movement make high-gain beam alignment difficult. It proposes adaptive hierarchical beam alignment and analyzes wind-related beam misalignment and array-size limits.
- Motivation: Dense small-cell deployments require cost-effective, reliable, and scalable backhaul because wired backhaul is expensive and existing cellular spectrum is unsuitable for large-scale in-band backhaul.Millimeter-wave bands are presented as a scalable alternative for backhaul and access, offering substantial underutilized spectrum and line-of-sight propagation.
- Contributions: The proposed adaptive alignment outperforms non-adaptive joint alignment and single-sided alignment while avoiding exhaustive transmit–receive beam-pair sampling.It adaptively samples channel subspaces with hierarchical codebooks to maximize receive SNR within constrained time.
- Contributions: Wind-induced pole movement makes larger arrays increasingly sensitive to beam misalignment, limiting achievable beamforming gain despite increasing antenna-array size.The paper uses pole-movement analysis to assess backhaul failure and determine required alignment frequency.
II. SYSTEM OVERVIEW AND MOTIVATION
Millimeter-wave frequencies can support wireless backhaul between small cells and access within cells while reducing interference on sub-3 GHz bands. However, severe outdoor path loss, environmental movement, narrow beams, and limited channel observability motivate large-array beamforming and subspace-sampling-based beam alignment.
- Network motivation: Millimeter-wave communication can provide wireless backhaul between small-cell access points and access within cells, reducing interference on sub-3 GHz mobile-broadband bands.Picocell access points are expected to be separated by less than 100 meters, mitigating oxygen absorption and rain attenuation.
- System requirements: Outdoor millimeter-wave systems suffer severe path loss, requiring large array gains and potentially tens, hundreds, or thousands of antennas.Large arrays could provide both backhaul and access and be mounted on road signs, lampposts, and other urban traffic-control structures.
- Link budget: A 100 m link requires an additional 32 dB or more gain for reliable communication compared with an indoor millimeter-wave system.The link-budget calculation is summarized in Table I and illustrated in Fig. 2.
- Beam-alignment challenge: Environmental movement and narrow beam widths make small propagation-geometry changes large enough to cause pointing errors that affect link performance.The relevant movement includes wind and moving vehicles, especially for access nodes mounted on urban structures.
- Beam-alignment formulation: Analog beamforming limits observations to noisy subspace samples z*Hf, so transmitters and receivers must collaborate to select the beamformer-combiner pair without full channel-matrix estimation.The alignment objective is to maximize beamforming gain |z*Hf|^2, while practical transmission may impose regulatory beam-width constraints.
III. PERFORMANCE ANALYSIS OF THE BEAM ALIGNMENT CRITERION
This section characterizes beam-alignment performance using pairwise error probability and measures wind-vibration effects through beam outage probability and beam coherence time.
- Beam-alignment performance is characterized in terms of pairwise error probability.
- Wind-induced vibration is modeled for a small cell mounted on a lamppost.
- Vibration effects on beam alignment are measured using beam outage probability and beam coherence time.
A. Performance Analysis of Beam Alignment
Under a rank-one channel model, the analysis characterizes beam misalignment through pairwise error probabilities and derives asymptotic approximations. Fig. 4 validates that the bounds and approximations closely match the analyzed misalignment behavior, with pairwise and overall probabilities coinciding at high SNR.
- A. Performance Analysis of Beam Alignment: The analysis assumes a rank-one channel, motivated by line-of-sight backhaul channels, and models each sounding observation as a noisy subspace-pair measurement.The optimal sounding pair is defined as the pair selected under noiseless sounding, with a uniform prior over candidate pairs.
- A. Performance Analysis of Beam Alignment: Beam misalignment is expressed through pairwise misalignment probabilities, whose bounds converge as ρ increases and admit tractable asymptotic approximations.The approximations use modified Bessel, Marcum Q, and complementary error functions before simplifying the dominant exponential dependence.
- A. Performance Analysis of Beam Alignment: The beam-alignment analysis yields pairwise exponential decay in beam misalignment as ρ, γ̂ℓopt, and γℓopt increase.This follows because γ̂ℓopt exceeds γℓopt.
- A. Performance Analysis of Beam Alignment: Fig. 4 shows that the pair-wise misalignment probability coincides with Pmis at increasing SNR, while the asymptotic expression tightly models the bound.The plotted slope approximation also closely models the beam-misalignment rate behavior.
B. Wind Induced Impairments in Beam Alignment
Wind-induced pole motion can deflect narrow millimeter-wave beams, making larger arrays more outage-prone and requiring frequent realignment. Beam coherence time therefore constrains alignment search time and achievable beamforming gain.
- B. Wind Induced Impairments in Beam Alignment: Wind-induced movement is on the order of hundreds of wavelengths, and narrow beam patterns make outdoor millimeter-wave links vulnerable to beam misalignment.The analysis models wind-induced vibration in a lamppost deployment and computes pole-top trajectories to characterize resulting beam deflection.
- B. Wind Induced Impairments in Beam Alignment: Beam outage is defined by the beam deflection angle exceeding θL,max, and coherence time is defined as Tc = E[Tout].Power fluctuation from relative displacement is negligible for large link distance D, so outage probability depends only on angular deflection.
- B. Wind Induced Impairments in Beam Alignment: On the order of 100s of milliseconds, the expected beam coherence time is reported for the M = 64 system.Alignment search time must be somewhat smaller than the order of milliseconds to avoid beam outage.
IV. SUBSPACE SAMPLING FOR BEAM ALIGNMENT
Because prior beam-selection algorithms are limited to observed data, this section emphasizes judicious subspace sampling and reviews both non-adaptive and adaptive approaches.
- Subspaces must be chosen judiciously because beam-selection algorithms are limited to observed data.
- The section overviews both non-adaptive and adaptive subspace sampling.
A. Non-Adaptive Subspace Sampling
Non-adaptive subspace sampling sounds the channel using every possible transmit–receive beam pair, making it straightforward but time-intensive. The selected beam pair is the one whose received sample achieves the largest sup norm.
- A. Non-Adaptive Subspace Sampling: The method exhaustively sounds the channel with all possible pairs of beamforming and combining vectors.This is described as the most time-intensive but most obvious sampling method.
- A. Non-Adaptive Subspace Sampling: The total sounding time is L = card(Z)card(F).
- A. Non-Adaptive Subspace Sampling: The selected beam pair corresponds to the index achieving the sup norm ∥y∥∞.
B. Adaptive Sampling
The section develops adaptive subspace sampling to avoid exhaustive beam-pair searches in large millimeter-wave codebooks. It combines ping-pong transmitter–receiver probing with hierarchical subcodebooks that progressively refine beam alignment while controlling codebook size and covering distance.
- Ping-Pong Adaptive Sampling: Ping-pong sampling alternates transmitter- and receiver-assisted subspace probing, using each LK-sample half-round to update the corresponding optimal beam estimate.After successive rounds, the final transmit and receive beam pair is estimated from all L observations.
- Adaptive Subspace Sampling using Hierarchical Subcodebooks: Adaptive subspace sampling addresses the impracticality of exhaustively searching large transmit and receive beam codebooks.The method is motivated by codebooks whose sizes can become extremely large in large-array millimeter-wave systems.
- Adaptive Subspace Sampling using Hierarchical Subcodebooks: Each subcodebook is designed by quantizing the array manifold to maximize the minimum beamforming gain, with covering distance minimized offline.The same hierarchical construction applies to transmit beamformers and receive combiners.
- Adaptive Subspace Sampling using Hierarchical Subcodebooks: Hierarchical subcodebooks increase resolution across K rounds, sounding only the LK beams closest to the previously selected beam.The nested codebooks satisfy N1 < N2 < · · · < NK with FK = F and Nk ≤ (LK)^k.
- Adaptive Subspace Sampling using Hierarchical Subcodebooks: For a one-dimensional ULA, equally divided angular sectors provide a bound on the subcodebook covering distance, while ideal nonoverlapping beam patterns remain generally unrealizable.The construction therefore seeks collective beam patterns that approximate sectorized, flattened coverage.
V. SIMULATIONS AND DISCUSSIONS
The simulations compare beamforming methods using Monte Carlo trials over a street-geometry spatial channel with angular spread and multipath. The comparison assumes no wind misalignment and uses a K-factor of 13.2 dB.
- V. SIMULATIONS AND DISCUSSIONS: Monte Carlo simulations compare the performance of various beamforming methods.The comparison is conducted without wind-induced beam misalignment.
- V. SIMULATIONS AND DISCUSSIONS: The spatial channel is modeled with a street geometry including one LOS path and first-order non-LOS reflections from both sides of the street.Delays and reflected-path angular spreads are calculated from distance differences and ray tracing.
- V. SIMULATIONS AND DISCUSSIONS: The simulated channel uses a K-factor K of 13.2 dB, representing the LOS-to-non-LOS energy ratio.The K-factor is defined as the ratio of LOS energy to the summed energy of other paths.
A. Performance Comparison
The proposed adaptive sampling and beam alignment achieves higher beamforming gain than single-sided and non-adaptive joint alignment while requiring substantially less search time. Its benefits persist across array sizes, but larger arrays are more vulnerable to wind-sway misalignment.
- Performance Comparison: At high SNR, adaptive alignment improves beamforming gain by around 4 dB over single-sided alignment and by more than 13 dB over non-adaptive joint alignment.This comparison uses M = 32 arrays and L = 48.
- Performance Comparison: For a 26 dB target, adaptive alignment requires L ≈25, versus L ≈47 for single-sided and L ≈585 for non-adaptive joint alignment.The method estimates optimal beamformer-combiner pairs through hierarchical adaptive sampling and uses less search time than IEEE 802.11ad alignment.
- Performance Comparison: Increasing a linear array to M = 96 can cause up to 10 dB of wind-sway-induced degradation at 40 m/s wind speed.Increasing array size in only one dimension can impose a severe beamforming penalty from wind-sway misalignment.
VI. CONCLUSIONS
The paper addresses millimeter-wave beam alignment for small-cell backhaul and access through subspace sampling, including adaptive methods that improve performance. It also examines wind-induced beam misalignment, documenting a tradeoff between array size and movement and motivating more resilient two-dimensional arrays.
- Millimeter-wave path loss over longer links makes transmit–receive beam alignment a challenging and important problem.
- Adaptive subspace sampling leverages previous received data to substantially improve beam alignment performance in simulations.The simulations compared the proposed beam alignment and subspace sampling algorithms.
- The paper documents a tradeoff between array size and wind-induced movement, including the resulting effect on achievable receive SNR.Wind-induced impairments were modeled and their effect on the millimeter-wave beamforming system was evaluated.
- When many antenna elements are required, large uniform linear arrays may be insufficient because of wind-induced beam misalignment.The paper identifies this as an area requiring further work.
- A two-dimensional array architecture is proposed as a more resilient design because spacing the array across two dimensions limits beam-misalignment effects.
APPENDIX A WIND VIBRATION MODELING
The model represents wind as mean flow plus orthogonal turbulence components and maps resulting drag and vortex-shedding forces through a mechanical pole model. It assumes planar pole motion at 10 m and computes pole-response spectra in the frequency domain up to 10 Hz.
- Wind and turbulence model: Wind velocity is modeled as a time-varying spatial random field with surface coordinates x and y, height z, and mean vector u.The model fixes z = 10 m and assumes approximately constant surface variation over a short link.
- Wind and turbulence model: Orthogonal along-wind and across-wind turbulence components are zero-mean, wide-sense stationary, uncorrelated processes, with no vertical turbulence or pole motion.The pole top is constrained to move in the (x, y) plane.
- Pole-response simulation: Independent along-wind and across-wind forces drive uncoupled spring-mass-damper pole models, and spectral simulation with inverse FFT represents responses up to 10 Hz.The mechanical model is characterized by damping coefficient ζ and natural frequency fn.