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Hybrid Precoding-Based Millimeter-Wave Massive MIMO-NOMA with Simultaneous Wireless Information and Power Transfer

Linglong Dai, Bichai Wang, Mugen Peng, Shanzhi Chen

arXiv:1809.07682v1cs.IT

TL;DR

The paper addresses integrating SWIPT with hybrid-precoded mmWave massive MIMO-NOMA, where joint transceiver and power-splitting design is challenging. It proposes a clustered hybrid-precoding and iterative optimization framework, and reports higher spectrum and energy efficiency than corresponding OMA-based systems.

  • Problem

    Integrating SWIPT into HP-based mmWave massive MIMO-NOMA requires joint power-allocation and power-splitting optimization under coupled inter-group and intra-group interference.

  • Method

    The paper combines CHS-based user grouping, hybrid precoding, NOMA power allocation, and power-splitting-factor optimization, solved through an iterative algorithm.

  • Results

    The proposed HP-based mmWave massive MIMO-NOMA with SWIPT achieves higher spectrum and energy efficiency than HP-based mmWave massive MIMO-OMA with SWIPT.

  • Takeaways & Limitations

    The proposed integration supports spectrum- and energy-efficient mmWave massive MIMO-NOMA while exploiting fewer RF chains and simultaneous information decoding and energy harvesting.

Abstract

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Non-orthogonal multiple access (NOMA) has been recently considered in millimeter-wave (mmWave) massive MIMO systems to further enhance the spectrum efficiency. In addition, simultaneous wireless information and power transfer (SWIPT) is a promising solution to maximize the energy efficiency. In this paper, for the first time, we investigate the integration of SWIPT in mmWave massive MIMO-NOMA systems. As mmWave massive MIMO will likely use hybrid precoding (HP) to significantly reduce the number of required radio-frequency (RF) chains without an obvious performance loss, where the fully digital precoder is decomposed into a high-dimensional analog precoder and a low-dimensional digital precoder, we propose to apply SWIPT in HP-based MIMO-NOMA systems, where each user can extract both information and energy from the received RF signals by using a power splitting receiver. Specifically, the cluster-head selection (CHS) algorithm is proposed to select one user for each beam at first, and then the analog precoding is designed according to the selected cluster heads for all beams. After that, user grouping is performed based on the correlation of users' equivalent channels. Then, the digital precoding is designed by selecting users with the strongest equivalent channel gain in each beam. Finally, the achievable sum rate is maximized by jointly optimizing power allocation for mmWave massive MIMO-NOMA and power splitting factors for SWIPT, and an iterative optimization algorithm is developed to solve the non-convex problem. Simulation results show that the proposed HP-based MIMO-NOMA with SWIPT can achieve higher spectrum and energy efficiency compared with HP-based MIMO-OMA with SWIPT.

I. INTRODUCTION

The paper integrates SWIPT with hybrid-precoded mmWave massive MIMO-NOMA to address spectrum- and energy-efficiency goals while reducing RF-chain requirements. It jointly designs transceivers, power allocation, and power splitting, building on NOMA and SWIPT mechanisms.

  • Hybrid precoding reduces the required RF chains in mmWave massive MIMO, lowering hardware cost and base-station energy consumption without obvious performance loss.
  • NOMA supports multiple users per beam through superposition coding and successive interference cancellation, increasing spectrum efficiency relative to conventional OMA.
  • SWIPT lets users simultaneously decode information and harvest energy from received RF signals through power-splitting receivers.
  • The paper proposes integrating SWIPT into HP-based mmWave massive MIMO-NOMA and jointly optimizing user grouping, hybrid precoding, power allocation, and power splitting.
  • The joint optimization is formulated to maximize achievable sum rate under rate and energy-harvesting QoS constraints, with an iterative algorithm developed for the non-convex problem.

II. SYSTEM MODEL

The system is a single-cell downlink mmWave massive MIMO-NOMA architecture with hybrid precoding and power splitting at every user. NOMA allows multiple users per beam, while SWIPT divides received signals between information decoding and energy harvesting.

  • The base station uses N antennas and N_RF RF chains to serve K single-antenna users, each equipped with a power-splitting receiver for SWIPT.
  • Fully digital MIMO assigns one RF chain per antenna, whereas hybrid-precoding architectures use fewer RF chains than antennas.
  • The number of beams is set to G = N_RF, and each beam may serve multiple users through NOMA rather than only one user.
  • Hybrid precoding decomposes beamforming into an N × N_RF analog matrix A and an N_RF × 1 digital vector d_g for each beam, with ||Ad_g||_2 = 1.
  • The fully-connected and sub-connected architectures differ in analog connectivity, with each sub-connected RF chain serving M = N/N_RF antennas.
  • Each power-splitting receiver divides the received signal between information decoding and energy harvesting using a factor β_g,m satisfying 0 < β_g,m < 1.

III. USER GROUPING AND HYBRID PRECODING

Because more users than RF chains share a limited set of analog precoding vectors, the paper organizes users and designs hybrid precoding through cluster-head selection and equivalent-channel relationships.

  • The system has K > N_RF users but only N_RF simultaneous analog precoding vectors, motivating structured user grouping and hybrid-precoding design.
  • The CHS algorithm selects one user per beam, after which analog precoding is designed to obtain antenna array gain from the selected cluster heads.
  • Remaining users are grouped using equivalent-channel correlation with cluster heads, and digital precoding selects the strongest equivalent-channel users to cancel inter-user interference.

A. The proposed CHS algorithm

The proposed CHS algorithm selects beam cluster heads by balancing channel strength and inter-beam channel correlation. Its adaptive threshold restricts candidates, and its complexity is polynomial in the number of beams and users.

  • Cluster heads are selected by minimizing channel correlation so users assigned to different beams have low correlation for inter-beam interference cancellation.
  • The first cluster head has the highest channel gain, while later candidates must have channel correlation below the adaptive threshold δ.
  • O(GK^2) is the complexity of the CHS algorithm, with per-iteration operations bounded by expressions in K − 1.

B. Analog precoding

The analog precoder is designed in two stages: cluster-head selection identifies one representative user per beam, then phase-quantized analog vectors are chosen to maximize array gain for the selected users.

  • Analog precoder design: With B-bit phase shifters, the nonzero analog-precoder entries are restricted to quantized phase changes.The paper considers a practical two-stage HP scheme in which phase-shifter constraints limit the analog precoder.
  • Scope: More sophisticated hybrid-precoding schemes could further enhance mmWave massive MIMO-NOMA performance.This is identified as a scope boundary of the considered analog-precoding design.
  • Cluster-head selection: The CHS algorithm selects a cluster-head set by processing user channel norms and normalized channel vectors across the available beams.The algorithm takes the user count, beam count, channel vectors, and an initial threshold as inputs, then outputs the cluster-head set Γ.
  • Analog precoder design: The selected cluster heads determine the analog precoding design for all beams.Analog precoding vectors are obtained from the channel vectors of users in Γ.
  • Analog precoder design: Analog precoding maximizes the array gain |h^H_g a_g|^2 separately for fully-connected and sub-connected architectures.The fully-connected and sub-connected architectures use different analog precoding vectors and antenna-index ranges.

C. User grouping

After analog precoding, users are grouped by equivalent-channel correlation so that users sharing a beam are highly correlated while different beams remain weakly correlated.

  • Equivalent channels: Equivalent channel vectors are formed for all users after analog precoding.These equivalent channels provide the basis for assigning users to beams.
  • Correlation-based grouping: Each non-cluster-head user is assigned to the beam whose equivalent channel has the specified strongest correlation.The assignment uses the beam index selected through the correlation-based grouping rule.
  • Grouping outcome: Users in the same beam have high equivalent-channel correlation, whereas users in different beams have low correlation.The resulting separation supports inter-beam interference cancellation and improves multiplexing gains.

D. Digital precoding

Digital precoding uses the strongest equivalent-channel user in each beam to construct low-complexity zero-forcing precoders that suppress inter-beam interference, followed by SIC-compatible user ordering.

  • Digital precoder construction: Digital precoding becomes a conventional MIMO-NOMA problem after analog precoding and user grouping.The remaining design objective is to eliminate inter-beam interference.
  • Digital precoder construction: The user with the highest equivalent channel gain in each beam is selected for zero-forcing digital precoding.The resulting digital precoding matrix has size N_RF × N_RF.
  • Digital precoder construction: The digital precoding vectors are normalized after generating the digital precoding matrix.A normalized vector is obtained for each beam.
  • User ordering: Users in each beam are reordered according to their effective channel gains to support the SIC ordering assumed in the model.This completes the hybrid-precoding and grouping design before joint power and splitting optimization.

IV. JOINT OPTIMIZATION OF POWER ALLOCATION AND POWER SPLITTING

The paper jointly optimizes NOMA power allocation and SWIPT power splitting under rate, transmit-power, and harvested-energy constraints. An iterative block-optimization procedure converts the non-convex subproblems into solvable convex programs and converges to at least a local optimum.

  • Problem formulation: Joint power allocation and power splitting introduces coupling among users’ allocation factors and between allocation and splitting factors.Existing MIMO-SWIPT optimization methods cannot be directly applied to the MIMO-NOMA setting.
  • Problem formulation: The optimization maximizes achievable sum rate subject to nonnegative user powers, a maximum total transmit power, minimum data rates, and minimum harvested energy.The constraints include the transmitted-power limit, per-user rate requirement, and energy-harvesting QoS requirement.
  • Problem formulation: The original problem is non-convex because of the objective and the data-rate and energy-harvesting constraints.The paper therefore develops an iterative optimization algorithm for sub-optimal solutions.
  • Iterative solution: The algorithm separately updates equalization coefficients, auxiliary variables, power allocation, and power splitting factors across iterations.Convexification uses variable transformations and the Schur complement lemma before numerical convex optimization is applied.
  • Iterative solution: The reformulated subproblem is a standard convex optimization problem solvable by numerical convex-program solvers.The iterative updates increase or maintain the objective value and yield at least a local optimal solution.
  • Complexity: The joint optimization algorithm has polynomial complexity, with per-iteration coefficient updates linear in K and the convex subproblem bounded by O(T_max K^4.5 log^2(1/ε)).The stated bound depends on the maximum iteration count T_max, user count K, and solution accuracy ε.

V. SIMULATION RESULTS

Simulations evaluate convergence and compare spectrum and energy efficiency across fully connected, sub-connected, and fully digital SWIPT architectures. The proposed HP-based MIMO-NOMA schemes outperform corresponding OMA schemes in spectrum efficiency, while sub-connected HP offers higher energy efficiency than fully connected HP.

  • Simulation setup: The simulations use a 64-antenna BS with 4 RF chains, 4-bit phase shifters, and a 30 mW maximum transmitted power.Each user must achieve at least R_fm/10 achievable rate and 0.1 mW harvested energy.
  • Convergence: Spectrum efficiency stabilizes after 10 iterations for both fully-connected and sub-connected HP under joint power allocation and power splitting optimization.The convergence test uses K = 6 users and SNR = 0 dB; subsequent simulations use 10 iterations.
  • Spectrum efficiency: The proposed HP-based MIMO-NOMA systems with SWIPT achieve higher spectrum efficiency than corresponding HP-based MIMO-OMA systems with SWIPT.The comparison is shown against SNR for K = 6 users.
  • Spectrum efficiency: Fully digital MIMO has the highest spectrum efficiency, while fully-connected HP exceeds sub-connected HP because it exploits the full array gain at every RF chain.The fully digital benchmark uses one RF chain per antenna to exploit multiplexing gains.
  • Energy efficiency: The proposed HP-based MIMO-NOMA systems with SWIPT achieve higher energy efficiency than both HP-based MIMO-OMA and fully digital MIMO with SWIPT.Reducing RF chains lowers RF-chain power consumption relative to fully digital MIMO, where each RF chain consumes 300 mW.
  • Energy efficiency: Sub-connected HP achieves higher energy efficiency than fully-connected HP because it uses fewer phase shifters.With SNR = 10 dB, sub-connected HP-OMA remains more energy-efficient than all other schemes as the user count becomes very large.

VI. CONCLUSIONS

The proposed HP-based mmWave massive MIMO-NOMA system integrates user grouping, hybrid precoding, power allocation, and power splitting to balance spectrum and energy efficiency. Joint power and power-splitting optimization maximizes achievable sum rate, and simulations show higher spectrum and energy efficiency than HP-based MIMO-OMA with SWIPT.

  • CHS selects one cluster head per beam, after which analog precoding follows the selected heads and users are grouped by equivalent-channel correlation.
  • Digital precoding selects users with the strongest equivalent channel gain in each beam.
  • Joint power allocation and power splitting are optimized to maximize achievable sum rate through an iterative algorithm for the non-convex problem.
  • The proposed mmWave massive MIMO-NOMA system with SWIPT achieves higher spectrum and energy efficiency than the corresponding MIMO-OMA system with SWIPT.
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