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Millimeter Wave Beam-Selection Using Out-of-Band Spatial Information

Anum Ali, Nuria González-Prelcic, Robert W. Heath

arXiv:1702.08574v1cs.IT

TL;DR

mmWave link configuration creates substantial overhead, motivating methods that use more readily obtained sub-6 GHz spatial information for mmWave establishment. The paper develops weighted and multiple-measurement-vector sparse beam-selection with structured training under the stated sub-6 GHz and mmWave architectures. Rate results conclude that out-of-band information reduces in-band-only compressed beam-selection training overhead by 4x.

  • Problem

    mmWave link establishment through channel estimation or beam-selection has significant overhead, while the relevant mmWave channel state is difficult to acquire with large arrays and low pre-beamforming SNR.

  • Method

    The paper uses sub-6 GHz spatial information as out-of-band side information for weighted sparse recovery, structured random codebooks, and multiple-measurement-vector recovery across active OFDM subcarriers.

  • Results

    4x reduction in training overhead is reported for out-of-band-aided beam-selection compared with in-band-only compressed beam-selection.

  • Takeaways & Limitations

    Out-of-band spatial information can reduce the training overhead required for mmWave compressed beam-selection under the paper's modeled settings.

Abstract

from arXiv · show

Millimeter wave (mmWave) communication is one feasible solution for high data-rate applications like vehicular-to-everything communication and next generation cellular communication. Configuring mmWave links, which can be done through channel estimation or beam-selection, however, is a source of significant overhead. In this paper, we propose to use spatial information extracted at sub-6 GHz to help establish the mmWave link. First, we review the prior work on frequency dependent channel behavior and outline a simulation strategy to generate multi-band frequency dependent channels. Second, assuming: (i) narrowband channels and a fully digital architecture at sub-6 GHz; and (ii) wideband frequency selective channels, OFDM signaling, and an analog architecture at mmWave, we outline strategies to incorporate sub-6 GHz spatial information in mmWave compressed beam selection. We formulate compressed beam-selection as a weighted sparse signal recovery problem, and obtain the weighting information from sub-6 GHz channels. In addition, we outline a structured precoder/combiner design to tailor the training to out-of-band information. We also extend the proposed out-of-band aided compressed beam-selection approach to leverage information from all active OFDM subcarriers. The simulation results for achievable rate show that out-of-band aided beam-selection can reduce the training overhead of in-band only beam-selection by 4x.

I. INTRODUCTION

mmWave link establishment is challenging because large arrays, low pre-beamforming SNR, and frequent channel changes create substantial configuration overhead. The paper proposes using sub-6 GHz spatial information to guide compressed mmWave beam-selection, including weighted recovery and structured training designs.

  • Motivation: Large mmWave arrays and directional communication make link configuration a significant challenge.The paper frames configuration through channel estimation or beam-selection as an overhead source.
  • Proposed approach: The paper uses sub-6 GHz spatial information as out-of-band side information for establishing analog mmWave links.The approach assumes narrowband, fully digital sub-6 GHz MIMO and wideband frequency-selective, OFDM-based analog mmWave MIMO.
  • Applications: Frequent link reconfiguration is especially important for highly dynamic V2X channels and high-data-rate vehicular sensing exchange.The paper identifies V2X as a use case in which out-of-band-aided establishment may help address mmWave mobility requirements.
  • Motivation: Low pre-beamforming SNR makes reliable mmWave link establishment particularly difficult at large distances such as cell edges.Sub-6 GHz systems offer more favorable SNR for obtaining side information.
  • Proposed approach: Compressed beam-selection is formulated as weighted sparse recovery, with weights derived from out-of-band information and training shaped by structured random codebooks.The codebook design concentrates training precoder and combiner gains toward strong channel directions indicated by the side information.
  • Proposed approach: The all-subcarrier extension uses multiple measurement vector sparse recovery to jointly recover sparse signals with common support.This extends the weighted recovery and structured codebook designs beyond training on a single OFDM subcarrier.
  • Model and novelty: The proposed model considers frequency-selective wideband channels with multiple rays per cluster rather than the narrower assumptions of prior work.The paper also presents a structured random codebook design not present in the compared prior work.

II. MULTI-BAND CHANNEL CHARACTERISTICS AND SIMULATION

The paper reviews frequency-dependent channel behavior to assess sub-6 GHz/mmWave spatial similarity and motivate a simulation strategy for multi-band channels. It also identifies scenarios where out-of-band-aided establishment may be unreliable.

  • Motivation: The section motivates extracting sub-6 GHz spatial information as out-of-band side information for mmWave link establishment.This requires understanding similarities and differences between the two frequency bands and simulating frequency-dependent multi-band channels.
  • Simulation strategy: The proposed simulation strategy is designed to generate multi-band frequency-dependent channels consistent with prior observations.The review provides the basis for selecting channel relationships and parameter behavior across frequencies.
  • Limitation: Out-of-band-aided establishment is expected to perform poorly when sub-6 GHz propagation is LOS but mmWave propagation is NLOS.The spatial information can differ in this case, so the paper suggests detecting such scenarios and reverting to in-band-only establishment.

A. Review of multi-band channel characteristics

Prior work reports substantial, though imperfect, similarity between channels at different frequencies, while also documenting frequency-dependent changes in several channel characteristics. These observations guide the paper’s multi-band channel model.

  • Frequency dependence: Several channel characteristics vary with frequency, including delay spread, AoA-cluster count, shadow fading, cluster angle spread, and late-path behavior.Late-arriving multipath is more frequency-dependent because of greater environmental interaction, and some paths may occur at only one frequency.
  • Related evidence: Measurements found small dominant-path AoA deviations between 1935 MHz uplink and 2125 MHz downlink channels, supporting spatial congruence across links.This spatial congruence has been used to reduce or eliminate feedback in FDD systems.
  • Cross-frequency similarity: Directional power distributions were reported as almost identical for 5.8 GHz, 14.8 GHz, and 58.7 GHz LOS channels.Other studies found similar cluster counts, subpath decay constants, and AoD-cluster counts at 28 and 73 GHz.
  • Cross-frequency similarity: Sub-6 GHz and mmWave channels are likely to exhibit significant but imperfect spatial congruence, even across large frequency separations.Prior measurements reported similar directional power distributions and related channel statistics across several frequency pairs.
  • Modeling implications: The simulation model uses frequency-dependent cluster and path parameters, with higher-frequency channels generally assigned fewer clusters, fewer rays, smaller maximum delay spreads, and narrower angular spreads.The numerical parameters are examples chosen to comply with observations from prior work.
  • Channel model: The channel formulation represents clusters with delays and mean angles, rays with relative delays and angular shifts, and complex path gains.The continuous-time impulse response is not band-limited, but pulse shaping produces a band-limited response that can be sampled into a discrete-time channel.

1) First Stage:

The first simulation stage generates coupled cluster parameters for two frequencies, introduces common and uncommon clusters, and perturbs one channel to model frequency-dependent offsets.

  • Generation: The algorithm first generates mean cluster delays and mean AoAs/AoDs for both frequencies, using frequency-specific channel parameters.The initial cluster parameter sets are drawn before cross-frequency coupling is imposed.
  • Replacement: Clusters are coupled across frequencies by replacing selected clusters so that some clusters co-occur in both channels.Replacement is more likely for early-arriving clusters and less likely as percent frequency separation increases.
  • Replacement: Replacement index sets identify candidate co-occurring clusters and update the channel with the larger delay spread using the other channel’s cluster parameters.The procedure stores the relevant indices and replaces corresponding delay and angle parameters.
  • Perturbation: Frequency-dependent perturbations then offset the delays and angles of clusters in one channel.The perturbation scales with mean cluster delay and percent center-frequency separation, with deterministic modifiers applied to delays and angles.
  • Perturbation: The same underlying perturbation is transformed for delay, azimuth, and elevation offsets to preserve coupling among these physical channel parameters.The modified perturbations are added to the corresponding cluster parameters before both channel parameter sets are returned.
  • Algorithm summary: Algorithm 1 summarizes the first stage as generation, replacement-index updating, and perturbation of cluster delays and angles.Its output is the coupled set of cluster parameters for both frequency channels.

2) Second Stage:

The second stage independently generates rays within the coupled clusters, while the system model assumes co-located sub-6 GHz and mmWave arrays with distinct signaling and hardware architectures.

  • Second Stage: The second stage independently generates paths within clusters for each frequency channel.It takes per-cluster path counts, RMS intra-cluster time spread, and RMS relative-angle spreads as inputs.
  • Second Stage: Relative path delays, angle shifts, and complex gains are sampled using suitable PDP, APS, and fading models.Examples include exponential or uniform PDPs, uniform or truncated angular spectra, and Rayleigh or Ricean fading.
  • System model: The system uses co-located, aligned sub-6 GHz and mmWave arrays with comparable apertures operating simultaneously.Uniform linear arrays of isotropic point sources are adopted for exposition, with extensions to other geometries requiring suitable modifications.
  • Sub-6 GHz system: The sub-6 GHz system has one RF chain per antenna, enabling fully digital precoding, and assumes narrowband signaling.Only directional information is expected to vary little across sub-6 GHz bandwidth, allowing extension to wideband sub-6 GHz systems.

M RXM TX

The paper models sub-6 GHz communication with narrowband, fully digital precoding and mmWave communication with wideband OFDM and analog beamforming. It then formulates beam selection as sparse recovery using limited training measurements.

  • M RXM TX: The sub-6 GHz system uses array-response-based MIMO modeling with narrowband signaling and fully digital precoding.
  • M RXM TX: The mmWave system uses OFDM over frequency-selective channels with a single RF chain and phase-shifter-based analog precoding and combining.
  • M RXM TX: Analog beamforming constrains precoder entries to constant modulus with quantized phases, enabling DFT codebooks.
  • M RXM TX: The virtual channel representation is approximately sparse because mmWave propagation has limited scattering, despite possible grid-offset leakage.
  • M RXM TX: The dominant virtual-channel coefficient determines the selected transmit and receive codewords, while analog beams remain independent of subcarrier.
  • M RXM TX: Compressed beam-selection uses a few random measurements to estimate the dominant beam pair instead of exhaustive reconstruction.

B. Proposed two-stage OOB-aided compressed beam-selection

The proposed two-stage procedure extracts coarse spatial directions from a sub-6 GHz channel and uses them to support mmWave compressed beam-selection. Fourier-based spatial spectra provide this information without additional out-of-band retrieval overhead.

  • First stage: The first stage extracts dominant angle-of-arrival and angle-of-departure information from the sub-6 GHz channel.
  • First stage: The sub-6 GHz channel is already required for that system, so Fourier-based direction estimation adds no out-of-band information-retrieval overhead.
  • First stage: The sub-6 GHz channel estimate can be obtained from training observations using least-squares or minimum-mean-squared-error estimation.
  • Second stage: The resulting spatial spectrum is used in weighted sparse recovery, while its dominant direction indices support structured codebook design.
  • First stage: Sub-6 GHz spatial Fourier analysis produces a coarse estimate of dominant mmWave directions despite unavoidable cross-frequency mismatch.

2) Second stage (OOB-aided compressed beam-selection):

The second stage incorporates sub-6 GHz spatial information into mmWave compressed beam-selection through prior weighting, structured codebooks, and joint recovery across OFDM subcarriers.

  • Weighted sparse recovery: Sub-6 GHz spatial spectra are scaled and converted into prior probabilities for weighted sparse recovery.
  • Weighted sparse recovery: The probability-scaling constant represents the reliability of out-of-band information, which depends on spatial congruence and operating SNR.
  • Structured random codebooks: Structured precoder and combiner codebooks concentrate training around mmWave angle bins associated with dominant sub-6 GHz directions while respecting analog constraints.
  • Structured random codebooks: The structured codebook selects random codewords having the highest correlation with a deterministic codebook formed from the candidate angle set.
  • Joint weighted sparse recovery: Measurements from all active subcarriers are jointly recovered using their approximately common sparse support in an MMV formulation.
  • Joint weighted sparse recovery: The OOB-informed joint method uses logit-weighted SOMP, with structured codebooks yielding the structured LW-SOMP variant.

V. SIMULATION RESULTS

The simulations evaluate out-of-band-aided beam-selection under specified sub-6 GHz and mmWave channel, array, OFDM, and training conditions. Performance is measured using effective achievable rate, which accounts for training time.

  • V. SIMULATION RESULTS: The simulations use 3.5 GHz sub-6 GHz and 28 GHz mmWave systems with 4 and 32 antennas, respectively, and shared half-wavelength-spaced ULAs.
  • V. SIMULATION RESULTS: The OFDM configuration uses K = 256 subcarriers and a cyclic prefix of length Lc = 64.
  • V. SIMULATION RESULTS: The sub-6 GHz channel is frequency flat, whereas the mmWave channel is frequency selective with L = 63 taps.
  • V. SIMULATION RESULTS: The experiments vary spatial congruence between sub-6 GHz and mmWave channels in addition to evaluating fixed channel parameters.
  • V. SIMULATION RESULTS: The channel model includes four sub-6 GHz clusters and three mmWave clusters, each contributing ten rays.
  • V. SIMULATION RESULTS: Effective achievable rate accounts for the fraction of coherence blocks consumed by training.

A. OOB-aided compressed beam-selection

The proposed OOB-aided compressed beam-selection methods use structured training and multi-subcarrier information to improve effective rate while reducing training overhead. Gains are strongest for shorter channel coherence times and can extend to rapidly varying channels.

  • Effective-rate evaluation: OOB-aided LW-OMP achieves a higher effective rate than OMP, while structured LW-OMP further improves LW-OMP.These results support using structured random codebooks to tailor training to out-of-band information.
  • Effective-rate evaluation: As channel coherence time decreases, the proposed approach gains an increasing advantage over exhaustive-search.For medium coherence, the method reduces exhaustive-search overhead by over 20x and LW-OMP overhead by 4x.
  • Effective-rate evaluation: The proposed approach is suitable for applications with rapidly varying channels, including V2X.The conclusion follows from its stronger relative advantage at smaller coherence times.
  • Success percentage: Structured LW-OMP recovers a top-five beam-pair approximately 75% of the time, compared with approximately 80% for exhaustive-search.For the single best beam-pair, structured LW-OMP succeeds approximately 50% of the time versus approximately 74% for exhaustive-search.
  • Multi-subcarrier extension: Using training information from all subcarriers lets structured LW-SOMP achieve a better effective rate than LW-SOMP and approach exhaustive-search with few measurements.At low coherence times, compressed beam-selection approaches, especially OOB-aided methods, can outperform exhaustive-search.

B. Impact of mismatch in spatial parameters

OOB-aided performance depends on spatial congruence between sub-6 GHz and mmWave channels. Increasing mismatch in angles or angular spread reduces the benefit and can make the method inferior to in-band-only selection.

  • Spatial congruence: The OOB-aided performance depends on congruence between sub-6 GHz and mmWave angular and angular-spread parameters.The experiments vary mismatch in mean AoA/AoD and angular spread while holding other settings fixed.
  • AoA/AoD mismatch: When the sub-6 GHz and mmWave mean AoA match, structured LW-OMP achieves its highest rate.The experiment fixes the mmWave cluster mean angle and varies the sub-6 GHz mean AoA.
  • AoA/AoD mismatch: When mean AoA mismatch exceeds approximately 0.5 rad, structured LW-OMP becomes inferior to in-band-only OMP.This identifies a practical boundary for the angular mismatch tested.
  • Angular-spread mismatch: The gain of structured LW-OMP decreases as sub-6 GHz angular spread increases relative to mmWave.In the tested setting, performance becomes inferior to in-band-only OMP when sub-6 GHz angular spread reaches approximately 0.368 rad, or approximately 10.5x the mmWave spread.

VI. CONCLUSION

The paper uses sub-6 GHz spatial information to reduce mmWave beam-selection training overhead through weighted sparse recovery and structured random codebooks. Simulations with frequency-dependent multiband channels show a 4x reduction in overhead for out-of-band-aided selection.

  • Conclusion: The paper uses sub-6 GHz spatial information to reduce training overhead for beam-selection in analog mmWave systems.The evaluation uses multiband frequency-dependent channels generated consistently with prior observations.
  • Conclusion: Compressed beam-selection is formulated as weighted sparse recovery with structured random codebooks incorporating out-of-band information.The method also includes a structured precoder/combiner design for out-of-band-tailored training.
  • Conclusion: 4x reduction in training overhead is obtained for out-of-band-aided beam-selection compared with in-band-only compressed beam-selection.This is the paper’s principal achievable-rate conclusion.
  • Future work: Future work includes calibrating channel generation, extending beyond uniform linear arrays, and studying hybrid or fully digital low-resolution mmWave architectures.These directions define the evaluated method’s current scope boundary.
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