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Multi-Beam NOMA for Hybrid mmWave Systems

Zhiqiang Wei, Lou Zhao, Jiajia Guo, Derrick Wing Kwan Ng, Jinhong Yuan

arXiv:1806.04919v1cs.ITmath.IT

TL;DR

Hybrid mmWave systems face limits on concurrent users from narrow beams and scarce RF chains, while prior single-beam NOMA is constrained by user angles. This paper introduces beam-split multi-beam NOMA and two-stage resource allocation, reporting close-to-optimal allocation performance and higher spectral efficiency than single-beam NOMA and OMA.

  • Problem

    Hybrid mmWave systems have limited RF chains and narrow analog beams, while single-beam NOMA serves users within the same beam and depends on their AOD distribution.

    Source: §I · p. 3

  • Method

    The scheme splits antennas into subarrays to form multiple NOMA beams and uses two-stage resource allocation for grouping, antenna assignment, and QoS-aware power allocation.

    Source: §I · p. 5

  • Results

    The resource allocation performs close to optimal in each stage, and multi-beam mmWave-NOMA achieves higher spectral efficiency than single-beam mmWave-NOMA and mmWave-OMA.

    Source: §I · p. 5

  • Takeaways & Limitations

    Arbitrary-AOD user pairing gives the scheme flexibility to form more NOMA groups and exploit multi-user diversity.

    Source: §I · p. 5

Abstract

from arXiv · show

In this paper, we propose a multi-beam non-orthogonal multiple access (NOMA) scheme for hybrid millimeter wave (mmWave) systems and study its resource allocation. A beam splitting technique is designed to generate multiple analog beams to serve multiple users for NOMA transmission. Compared to conventional mmWave orthogonal multiple access (mmWave-OMA) schemes, the proposed scheme can serve more than one user on each radio frequency (RF) chain. Besides, in contrast to the recently proposed single-beam mmWave-NOMA scheme which can only serve multiple NOMA users within the same beam, the proposed scheme can perform NOMA transmission for the users with an arbitrary angle-of-departure (AOD) distribution. This provides a higher flexibility for applying NOMA in mmWave communications and thus can efficiently exploit the potential multi-user diversity. Then, we design a suboptimal two-stage resource allocation for maximizing the system sum-rate. In the first stage, assuming that only analog beamforming is available, a user grouping and antenna allocation algorithm is proposed to maximize the conditional system sum-rate based on the coalition formation game theory. In the second stage, with the zero-forcing (ZF) digital precoder, a suboptimal solution is devised to solve a non-convex power allocation optimization problem for the maximization of the system sum-rate which takes into account the quality of service (QoS) constraint. Simulation results show that our designed resource allocation can achieve a close-to-optimal performance in each stage. In addition, we demonstrate that the proposed multi-beam mmWave-NOMA scheme offers a higher spectral efficiency than that of the single-beam mmWave-NOMA and the mmWave-OMA schemes.

I. INTRODUCTION

The introduction motivates NOMA for hybrid mmWave systems, where limited RF chains and narrow analog beams constrain multi-user service. It proposes multi-beam NOMA with two-stage resource allocation; the system model focuses on an overloaded, fully connected hybrid architecture.

I. INTRODUCTION

  • Hybrid mmWave systems face multi-user constraints from limited RF chains and narrow beams, while practical multi-beam NOMA realization remained an open design problem.The cited prior multi-beam proposal offered conceptual discussion, while existing single-beam schemes depended on users sharing a beam.Source: §I · pp. 3–4
  • Beam splitting divides an RF chain’s antenna array into subarrays that form multiple analog beams, allowing NOMA users with arbitrary AODs to be served.The authors contrast this flexibility with single-beam mmWave-NOMA, which groups users within the same beam.Source: §I · pp. 4–5
  • The two-stage resource allocation uses coalition formation for user grouping and antenna allocation, then D.C. programming for QoS-aware power allocation.The first stage maximizes conditional system sum-rate; the second maximizes system sum-rate based on the first-stage decisions.Source: §I · p. 5
  • The proposed resource allocation is reported to perform close to optimal in both stages, and multi-beam mmWave-NOMA achieves higher spectral efficiency than single-beam mmWave-NOMA and mmWave-OMA.These are simulation results reported in the introduction.Source: §I · p. 5

II. SYSTEM MODEL

  • The system model considers a single-cell downlink with K users and N_RF RF chains in an overloaded scenario where K ≥ N_RF.The BS uses a fully connected hybrid structure, and the model assumes the users’ LOS channel state information is known at the BS.Source: §II · pp. 6–7

III. THE MULTI-BEAM NOMA SCHEME

The framework groups users by RF chain, allocates antennas within each group, and uses beam splitting to form multiple analog beams for downlink NOMA. Unlike single-beam NOMA, its users need not share the same analog beam.

A. User Grouping and Antenna Allocation

B. Multiple Analog Beams with Beam Splitting

  • Beam splitting steers separate subarray beams toward users in one NOMA group, so their AODs need not fall within the same analog beam.This provides greater flexibility in user grouping than single-beam NOMA.Source: B. Multiple Analog Beams with Beam… · pp. 8–9

A. User Grouping and Antenna Allocation

B. Multiple Analog Beams with Beam Splitting

  • Beam splitting reduces each beam’s main-response magnitude and increases its beamwidth, while allowing more users to be accommodated on an RF chain.A phase shift synchronizes the phases between the two subarrays.Source: B. Multiple Analog Beams with Beam… · pp. 8–9

C. Effective Channel Estimation

The system estimates effective channels using uplink pilots and TDD reciprocity, then uses the estimated channel matrix to design the digital precoder and power allocation. Users in each NOMA group share a digital precoder, subject to the base station’s sum-power constraint.

C. Effective Channel Estimation

D. Digital Precoder and Power Allocation Design

  • The estimated effective channel matrix is used to design the digital precoder and power allocation, with users in each NOMA group sharing a digital precoder.The digital precoder has one column per RF chain.Source: D. Digital Precoder and Power… · p. 10
  • The user powers are constrained by the base station’s total power budget.The received signal includes the superimposed NOMA signal and additive white Gaussian noise.Source: D. Digital Precoder and Power… · p. 11

E. SIC Decoding at Users

SIC decoding is performed by the strong user in each NOMA group, while the weak user treats the strong user’s signal as noise. The framework describes RF-chain association as spatial degree-of-freedom allocation and uses beam splitting to multiplex users in the beam domain.

E. SIC Decoding at Users

  • The strong user decodes the weaker user’s message before decoding its own, while the weak user treats the strong user’s signal as noise.Strong and weak users are ordered by LOS path gain.Source: E. SIC Decoding at Users · pp. 11–12
  • With a digital precoder, RF-chain association represents allocation of a spatial degree of freedom, and each NOMA group or OMA user has one such degree of freedom.The signals are multiplexed across all RF chains in this hybrid setting.Source: E. SIC Decoding at Users · p. 11
  • Beam splitting multiplexes users on one RF chain in separate beam-domain virtual tunnels, allocating array beamforming gain among users.Allocating more antennas to a user gives that user higher beamforming gain.Source: E. SIC Decoding at Users · p. 12
  • The framework relies on LOS-path AODs and complex path gains, and its performance depends on user grouping, antenna allocation, power allocation, and digital precoder design.The paper distinguishes this reliance on LOS information from fully digital MIMO-NOMA.Source: E. SIC Decoding at Users · p. 13

IV. RESOURCE ALLOCATION DESIGN

This section separates coupled hybrid-beamforming resource allocation into two stages: coalition-based user grouping and antenna allocation, followed by ZF-based QoS-constrained power allocation.

IV. RESOURCE ALLOCATION DESIGN

  • The two-stage design first optimizes grouping and antenna allocation with analog beamforming, then uses a ZF digital precoder for QoS-constrained power allocation.The stages address the coupling between effective-channel acquisition and the analog beamformer structure.Source: §IV · p. 13

1) Problem Formulation:

  • With identity digital precoding and equal power, the first-stage objective is to maximize the conditional system sum-rate through joint user grouping and antenna allocation.The first stage assumes only analog beamforming is available.Source: §IV · p. 13, 1) Problem Formulation · pp. 13–14
  • The first-stage formulation is a non-convex integer program whose trigonometric effective-channel gain makes global optimization difficult.Exhaustive search can solve it optimally, but its computational complexity is prohibitively high.Source: 1) Problem Formulation · p. 14
  • A coalition formation game provides a compromise solution for user grouping and antenna allocation.The proposed algorithm seeks an efficient suboptimal solution.Source: 1) Problem Formulation · p. 14

2) The Proposed Coalition Formation Algorithm:

The algorithm models users as cooperative players forming NOMA groups, then iteratively changes group membership and antenna allocation to improve conditional system sum-rate.

2) The Proposed Coalition Formation Algorithm:

  • Users form coalitions representing NOMA groups, with each player's payoff given by its individual conditional data rate.Because payoffs depend on antenna allocation and other coalitions, the game has nontransferable utility and partition-form structure.Source: 2) The Proposed Coalition Formation… · p. 15
  • A user prefers a coalition change when the resulting conditional system sum-rate is at least as large as before, with antenna allocation optimized for the involved coalition.The defined preference relation also distinguishes strict preference.Source: 2) The Proposed Coalition Formation… · p. 16
  • Leaving-and-joining and switch operations let users change groups while respecting the maximum coalition size of two.A switch exchanges users between two groups when a direct move would make a group too large.Source: 2) The Proposed Coalition Formation… · pp. 17–18
  • Starting from singleton coalitions, the algorithm tests possible leaving-and-joining or switch operations and stops when none is preferred.The singleton initialization corresponds to OMA.Source: 2) The Proposed Coalition Formation… · p. 18

3) Effectiveness, Stability, and Convergence:

The coalition algorithm makes sum-rate-increasing changes and terminates at a stable grouping after a finite number of operations.

3) Effectiveness, Stability, and Convergence:

  • The algorithm terminates when no strictly preferred operation remains, and its conditional system sum-rate is bounded above.The paper attributes the bound to limited RF chains and time resources.Source: 3) Effectiveness, Stability, and… · p. 19
  • Each approved leaving-and-joining or switch operation increases the conditional system sum-rate, and the terminal grouping is stable because no user has an incentive to leave.Stability is defined by the absence of an incentive to leave the final coalition.Source: 3) Effectiveness, Stability, and… · p. 19
  • Because feasible grouping and antenna-allocation combinations are finite and every approved operation increases sum-rate, the algorithm converges to a final stable coalitional structure.The final stable structure is reached within a limited number of iterations.Source: 3) Effectiveness, Stability, and… · pp. 19–20

4) Computational Complexity:

The section compares the coalition algorithm's per-iteration complexity with exhaustive search and analyzes the costs of its two move types.

4) Computational Complexity:

B. Second Stage: Digital Precoder and Power Allocation Design

The second stage uses the effective channels produced by the first-stage grouping and antenna allocation to construct a ZF digital precoder. For each NOMA group, an equivalent channel is formed using its leading left singular vector.

1) ZF Digital Precoder:

  • ZF digital precoding uses the effective channel matrix obtained after first-stage user grouping and antenna allocation.The precoder is shared by users within each NOMA group and is designed to suppress inter-group interference.Source: 1) ZF Digital Precoder · p. 20
  • For each NOMA group, the equivalent channel is formed from the first left singular vector associated with the largest singular value.The group’s equivalent channel is obtained by applying SVD to its equivalent channel matrix; for a single-user group, it is the effective channel.Source: 1) ZF Digital Precoder · p. 20
  • The resulting group precoders are assembled into G, with each g_r shared by the users in group S*_r.The passage defines G as the collection of digital precoders, one for each RF chain.Source: 1) ZF Digital Precoder · p. 20, 2) Power Allocation Design · p. 21

2) Power Allocation Design:

The second-stage power allocation maximizes system sum-rate under base-station power, SIC-decoding, and minimum-rate constraints. The non-convex problem is handled through D.C. programming and an iterative convex optimization procedure.

2) Power Allocation Design:

  • The power-allocation objective is system sum-rate, subject to total base-station power, successful SIC decoding, and a minimum-rate requirement for each user.The passage states that the SIC constraint is inactive when the specified user-scheduling condition holds.Source: 2) Power Allocation Design · p. 21
  • The formulated power-allocation problem is non-convex but can be transformed into a canonical D.C. programming form.The functions H1(p) and H2(p) are differentiable and convex with respect to the power vector p.Source: 2) Power Allocation Design · p. 21
  • Each iteration solves a convex upper-bound problem, updating the power allocation until the iteration limit or a small change between adjacent solutions is reached.The algorithm initializes from a feasible solution obtained using H1(p) as the objective.Source: 2) Power Allocation Design · p. 22
  • The proposed power-allocation algorithm converges to a stationary point with polynomial-time computational complexity.The stated convergence result follows from the D.C. programming procedure.Source: 2) Power Allocation Design · p. 22

V. SIMULATION RESULTS

The simulations evaluate the proposed multi-beam mmWave-NOMA scheme and its two-stage resource allocation against optimal benchmarks and OMA and single-beam NOMA baselines. The experiments use a specified mmWave cell and channel setting, with results averaged over channel and minimum-rate realizations.

V. SIMULATION RESULTS

  • The simulations use a 28 GHz, 200 m-radius hexagonal cell with 100 base-station antennas and 10 antennas per user terminal.The channel model includes one LOS path and 10 NLOS paths; users are randomly and uniformly distributed unless otherwise specified.Source: §V · p. 23
  • Simulation results are averaged across realizations of large-scale fading, small-scale fading, and minimum-rate requirements.The minimum-rate requirement is drawn from a uniform distribution over (0, 5] bit/s/Hz.Source: §V · p. 23
  • The first-stage coalition algorithm is benchmarked against exhaustive user grouping and antenna allocation, while second-stage precoding and power allocation are compared with DPC.The DPC comparison uses the same first-stage grouping and antenna allocation as the proposed design.Source: §V · p. 23
  • The scheme comparisons include mmWave-OMA, which serves at most one user per RF chain, and single-beam mmWave-NOMA, which groups users whose LOS AODs fall within the same main beamwidth.For fairness, all schemes use LOS channel-state information; OMA users are scheduled in two time slots when needed.Source: §V · pp. 23–24

A. Convergence of the Proposed Coalition Formation Algorithm

Across the reported simulations, multi-beam mmWave-NOMA outperforms the single-beam NOMA and OMA baselines, while the two-stage resource allocation approaches its corresponding optimal benchmarks. The results also examine convergence, transmit power, antenna count, user density, and the effect of ignoring NLOS information in the first stage.

A. Convergence of the Proposed Coalition Formation Algorithm

  • The coalition formation algorithm’s average conditional sum-rate rises monotonically and reaches close-to-optimal performance against exhaustive search within 10 iterations on average.The exhaustive-search comparison covers cases with NRF = 3, K = 5 and NRF = 6, K = 8.Source: A. Convergence of the Proposed… · p. 24
  • Ignoring NLOS-path information in first-stage grouping and antenna allocation causes only limited performance degradation, especially with few RF chains and users.The passage relates this limited impact to stronger LOS paths and analog beamforming that focuses energy on the LOS AODs.Source: A. Convergence of the Proposed… · p. 25

B. Average System Sum-rate versus Transmit Power at the BS

  • The proposed scheme approaches the DPC benchmark and provides higher spectral efficiency than single-beam NOMA and OMA as transmit power varies.The reported explanation highlights AOD-aware grouping, ZF suppression of inter-group interference, SIC, and power allocation.Source: B. Average System Sum-rate versus… · pp. 25–26, Figure 5 · p. 25

C. Average System Sum-rate versus Number of Antennas at the BS

  • Average system sum-rate increases with the number of base-station antennas, and multi-beam NOMA achieves higher spectral efficiency than the two baselines.With few antennas, single-beam NOMA is only slightly better than OMA, as the wider beamwidth raises the chance of placing multiple users in one beam.Source: C. Average System Sum-rate versus… · p. 26, Figure 6 · p. 27

D. Average System Sum-rate versus User Density

VI. CONCLUSION

  • The proposed resource allocation achieves close-to-optimal performance in each stage, and multi-beam mmWave-NOMA provides substantial sum-rate improvement over OMA and single-beam NOMA.The conclusion attributes the scheme’s flexibility to pairing NOMA users with arbitrary AOD distributions and forming more NOMA groups.Source: §VI · p. 28
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