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Hierarchical Codebook based Multiuser Beam Training for Millimeter Wave Massive MIMO
Chenhao Qi, Kangjian Chen, Octavia A. Dobre, Geoffrey Ye Li
TL;DR
Exhaustive beam sweeping requires testing all possible BS–UE codeword pairs, creating substantial training overhead. The paper proposes constant-modulus UE codebook design and adaptive hierarchical training that trains multiple UEs simultaneously; simulations show performance can approach beam sweeping with reduced overhead.
Problem
Exhaustive beam sweeping tests all possible BS–UE codeword pairs and requires NBSNUE time slots, motivating lower-overhead beam training.
Source: §II · p. 3Method
The paper designs UE hierarchical codebooks with AMCF and Zadoff-Chu initialization, and adaptively designs multi-mainlobe BS codewords from prior-layer training results for simultaneous multiuser training.
Source: §I · p. 2, A. Simultaneous Multiuser Hierarchical… · p. 6Results
The proposed simultaneous multiuser beam training can approach beam-sweeping performance with considerable reduction in training overhead.
Source: §VI · p. 11Takeaways & Limitations
Except for the bottom layer, the adaptive BS codebook uses two codewords per layer and requires only two simultaneous training rounds for all UEs, regardless of their number.
Source: §VI · pp. 10–11Avoiding beam conflicts between users that share a BS codeword requires beam allocation, which is outside the paper’s scope.
Source: B. Digital Precoding · p. 8
Abstract
from arXiv · showhide
In this paper, multiuser beam training based on hierarchical codebook for millimeter wave massive multi-input multi-output is investigated, where the base station (BS) simultaneously performs beam training with multiple user equipments (UEs). For the UEs, an alternative minimization method with a closed-form expression (AMCF) is proposed to design the hierarchical codebook under the constant modulus constraint. To speed up the convergence of the AMCF, an initialization method based on Zadoff-Chu sequence is proposed. For the BS, a simultaneous multiuser beam training scheme based on an adaptively designed hierarchical codebook is proposed, where the codewords in the current layer of the codebook are designed according to the beam training results of the previous layer. The codewords at the BS are designed with multiple mainlobes, each covering a spatial region for one or more UEs. Simulation results verify the effectiveness of the proposed hierarchical codebook design schemes and show that the proposed multiuser beam training scheme can approach the performance of the beam sweeping but with significantly reduced beam training overhead.
I. Introduction
The introduction motivates hierarchical beam training as a way to reduce overhead in mmWave massive MIMO and introduces simultaneous multiuser training based on an adaptive hierarchical codebook. The system model contrasts exhaustive beam sweeping with hierarchical training and describes the multiuser hybrid-precoding setup.
I. Introduction
- Hybrid precoding uses a small number of RF chains connected to many antennas through phase shifters to compensate for mmWave path loss while reducing hardware complexity and energy consumption.The system model specifies one RF chain per UE and K ≤ NRF simultaneously served users.Source: §I · p. 1, §II · p. 2
- Sequential TDMA hierarchical training reduces exhaustive-search overhead, but its total overhead grows linearly with the number of users.Prior simultaneous training for partially connected BS architectures performs beam training independently at each subarray.Source: §I · p. 1, §II · p. 4
- The JOINT codebook forms wide beams by weighted subarray summation but may power off half the antennas; EJOINT avoids antenna deactivation.The introduction notes that JOINT’s antenna deactivation can weaken signal strength and reduce coverage.Source: §I · p. 1
- The paper proposes simultaneous multiuser hierarchical beam training based on an adaptively designed codebook.The introduction identifies this as the proposed scheme, but the supplied passage does not include further design details.Source: §I · pp. 1–2
II. System Model
- Exhaustive beam sweeping tests all BS–UE codeword pairs, requiring NBSNUE time slots, although UEs can test and report their best codewords simultaneously.The number of slots is independent of K.Source: §II · p. 3
- For K = 4, NBS = 64, and NUE = 16, TDMA hierarchical training reduces overhead by 92.2% compared with exhaustive beam training.The cited passage gives the TDMA hierarchical-training overhead as 2K(log2 NBS + log2 NUE), versus NBSNUE for exhaustive training.Source: §II · p. 4
III. Hierarchical Codebook Design for UEs
This section designs the hierarchical codebook for the UEs; the BS codebook is addressed in the following section alongside beam training.
III. Hierarchical Codebook Design for UEs
- The section focuses on designing the UEs’ hierarchical codebook, leaving the BS codebook for the next section together with beam training.Source: §III · p. 4
A. Codebook Design Based on Alternative Minimization Method
The UE codebook design uses alternative minimization under a constant-modulus constraint. Its updates include a closed-form solution, avoiding the iterative algorithms used by earlier approaches for that subproblem.
A. Codebook Design Based on Alternative Minimization Method
- AMCF designs UE codewords under the constant-modulus constraint imposed by phase-shifter hardware.The design minimizes mean-squared error between a predefined beam gain and the codeword’s practical beam gain.Source: A. Codebook Design Based on… · p. 4
- The method alternates between optimizing the phase vector Θ with v fixed and optimizing v with Θ fixed until the iteration limit is reached.The method alternatively updates v and Θ for at most M iterations.Source: A. Codebook Design Based on… · pp. 4–5
- Unlike earlier approaches using successive closed-form or Riemannian optimization algorithms, the phase update has a closed-form solution and requires no such algorithm.The paper states that this gives the phase-update subproblem very low computational complexity.Source: A. Codebook Design Based on… · p. 4
- The v update has a closed-form expression obtained by dividing the problem into NUE independent subproblems.The resulting codeword entries are given by [v]n = [u]n + j[u]n+NUE.Source: A. Codebook Design Based on… · p. 5
B. Zadoff-Chu Sequence Initialization
The Zadoff-Chu initialization is used to speed AMCF convergence, while AMCF’s output—not the initial sequence—is used as the UE codeword. The hierarchical codebook is built layer by layer by shifting the designed beam across different coverage regions.
B. Zadoff-Chu Sequence Initialization
- The initial Zadoff-Chu-based vector covers the target angle space but has transition-zone fluctuations that can deteriorate beam-training performance.An earlier approach smooths the transition zone with unequal power dividers.Source: B. Zadoff-Chu Sequence Initialization · p. 5
- AMCF-ZCI uses the Zadoff-Chu-based vector only to initialize AMCF and uses AMCF’s output as the UE codeword, avoiding additional hardware.The initialization is proposed to speed AMCF convergence.Source: B. Zadoff-Chu Sequence Initialization · p. 5
- The UE codebook is constructed layer by layer, shifting the first codeword’s beam coverage to obtain the other codewords at each layer.The process repeats until the bottom layer is reached.Source: B. Zadoff-Chu Sequence Initialization · p. 5
IV. Simultaneous Beam Training based on Adaptive
The section proposes simultaneous multiuser hierarchical beam training using an adaptive codebook to reduce overhead relative to existing hierarchical beam training.
IV. Simultaneous Beam Training based on Adaptive
- The proposed scheme performs hierarchical beam training simultaneously for multiple users.It is based on an adaptively designed codebook.Source: §IV · p. 6
- The codebook is adaptive rather than fixed throughout the beam-training process.Source: §IV · p. 6
- The scheme is intended to considerably reduce training overhead compared with existing hierarchical beam training.Source: §IV · p. 6
A. Simultaneous Multiuser Hierarchical Beam Training
The BS codebook adapts its intermediate-layer codewords to previous beam-training results, allowing two multi-mainlobe codewords per layer to cover regions associated with the UEs. The scheme iterates through user feedback and finishes with uplink training at the bottom layer.
A. Simultaneous Multiuser Hierarchical Beam Training
- The top layer divides the full AoD range into two codewords, the intermediate layers contain two codewords each, and the bottom layer matches the existing hierarchical codebook.Intermediate-layer coverage need not span the full range when some regions have no channel path.Source: A. Simultaneous Multiuser Hierarchical… · p. 6
- The BS forms upper-layer codewords by combining bottom-layer codewords, using weighted channel-steering-vector sums and phase choices to help avoid low gain within the covered region.Practical codewords approximate the ideal ones given the number of RF chains and phase-shifter resolution.Source: A. Simultaneous Multiuser Hierarchical… · pp. 6–7
- Intermediate layers use two codewords whose intermittent beam coverage is adapted from previous-layer results, with multiple mainlobes covering regions where one or more UEs may lie.The number of codewords remains two per intermediate layer as the number of UEs increases, although the number of mainlobes may grow.Source: A. Simultaneous Multiuser Hierarchical… · pp. 6–7
- UEs report the stronger of two codewords, and the BS uses the resulting indices to group refined coverage for the next layer; UEs sharing a prior-layer AoD can be trained together.For differing prior-layer AoDs, users are distinguishable by their coverage regions, and the scheme also trains them simultaneously.Source: A. Simultaneous Multiuser Hierarchical… · pp. 6–7
- At each intermediate layer, the BS transmits two codewords to all UEs, while bottom-layer uplink training tests two BS codewords per UE to identify each UE’s best codeword.The BS can use multiple RF chains for parallel reception at the bottom layer.Source: A. Simultaneous Multiuser Hierarchical… · p. 7
- In the NBS = 128, NUE = 16, K = 4 example, feedback directs the construction of later codewords, and both third-layer codewords have three mainlobes.The example gives Γ1 = {1, 1, 2, 2} and Γ2 = {1, 2, 4, 4}.Source: A. Simultaneous Multiuser Hierarchical… · pp. 7–8
B. Digital Precoding
After beam training, the paper designs digital precoding for data transmission using the effective channel formed from the channel, analog precoder, and UE combiners. It notes that users sharing a BS codeword can make this channel rank deficient, a beam-allocation issue outside the paper’s scope.
B. Digital Precoding
- The BS stacks the received signals and designs a digital precoder under the zero-forcing criterion for data transmission.The analog combiner is obtained using existing hierarchical beam training; details are omitted.Source: B. Digital Precoding · p. 8
- The effective channel matrix combines each UE’s channel with the BS analog precoder and UE analog combiner, and its entries are obtained through bottom-layer uplink beam training.Source: B. Digital Precoding · p. 8
- Geographically close users may share a BS codeword, making the effective channel rank deficient; avoiding this conflict requires beam allocation, which the paper leaves out of scope.Digital precoding requires the effective channel to be full rank.Source: B. Digital Precoding · p. 8
C. Overhead Analysis
The proposed scheme reduces beam-training time slots relative to both beam sweeping and TDMA hierarchical training in the stated example.
C. Overhead Analysis
- The proposed scheme requires (2K + 2 log2(NUE NBS) − 2) time slots across the described training stages.The stages include top and intermediate layers, followed by two bottom-layer slots per UE.Source: C. Overhead Analysis · p. 8
- With NBS = 128, NUE = 16, and K = 8, the proposed scheme requires 36 time slots, versus 2048 for scheme and 176 for TDMA hierarchical beam training, reducing training overhead by 98.2% and 79.6%, respectively.Source: C. Overhead Analysis · p. 9
- The proposed scheme uses K fewer feedback occasions than TDMA hierarchical beam training because it requires feedback at the bottom layer.Source: C. Overhead Analysis · p. 9
V. Simulation Results
The paper evaluates its schemes by simulation for multiuser mmWave massive MIMO systems.
V. Simulation Results
- The proposed schemes are evaluated by simulation in multiuser mmWave massive MIMO systems.Source: §V · p. 9
A. Evaluation of codeword design schemes for each UE
The UE codeword evaluation finds that AMCF-ZCI produces more favorable beam patterns and higher beam-training success rates than JOINT and EJOINT in the reported comparisons.
A. Evaluation of codeword design schemes for each UE
- The beam-pattern comparison evaluates codeword designs in a single-user mmWave massive-MIMO setup with a 128-antenna BS, 32-antenna UE, and beam width B = 1/2.Source: A. Evaluation of codeword design… · p. 9
- AMCF-ZCI has narrower transition bands than JOINT and EJOINT, while JOINT has lower beam gain and EJOINT has a nonmonotonic transition band that may cause beam-training failure.AMCF-ZCI can also design arbitrary beam widths, unlike JOINT or EJOINT.Source: A. Evaluation of codeword design… · p. 9, Figure 4 · p. 9
- AMCF-ZCI achieves better beam-training success-rate performance than JOINT and EJOINT, with EJOINT outperforming JOINT at lower SNR but underperforming it at high SNR.The reported comparison uses a BS codebook designed according to.Source: A. Evaluation of codeword design… · pp. 9–10, Figure 5 · p. 9
B. Evaluation of simultaneous multiuser beam training
In the multiuser simulations, the proposed simultaneous hierarchical scheme approaches TDMA hierarchical training in sum-rate while using less training overhead, though beam sweeping performs better in success rate.
B. Evaluation of simultaneous multiuser beam training
- The simulation uses a BS with 128 antennas serving eight UEs, each equipped with 16 antennas, and assumes three channel paths per UE.Each channel has one LOS path and two NLOS paths.Source: B. Evaluation of simultaneous… · p. 10
- Beam sweeping achieves better success-rate performance than the other compared schemes, while its training overhead is much higher.The authors note that starting hierarchical training from a lower codebook layer may improve its performance by enlarging codeword beam gain.Source: B. Evaluation of simultaneous… · p. 10
- At SNR = 15 dB, the proposed scheme’s averaged sum-rate gap from beam sweeping is no more than 0.5 bps/Hz; its averaged sum-rate curves almost overlap TDMA hierarchical training.Source: B. Evaluation of simultaneous… · p. 10
- The proposed scheme uses 36 time slots versus 176 for TDMA hierarchical training, a 79.6% overhead reduction.Source: B. Evaluation of simultaneous… · p. 10
VI. Conclusion
The paper combines constant-modulus hierarchical codebook design for UEs with adaptive multiuser beam training at the BS. Simulations show performance approaching beam sweeping with reduced training overhead.
VI. Conclusion
- For UEs, AMCF-ZCI designs hierarchical codebooks under a constant-modulus constraint.Source: §VI · p. 10
- At the BS, codewords in each current layer are designed adaptively from the previous layer’s beam-training results.Source: §VI · p. 10
- BS multi-mainlobe codewords cover spatial regions where one or more UEs are probably located.Source: §VI · p. 10
- Simulations verify the codebook designs and show simultaneous multiuser beam training can approach beam-sweeping performance with considerably reduced training overhead.Source: §VI · p. 11
- Future work will reduce UE-to-BS feedback and extend the scheme from narrowband to wideband mmWave channels.Source: §VI · p. 11