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Energy Efficient User Clustering, Hybrid Precoding and Power Optimization in Terahertz MIMO-NOMA Systems

Haijun Zhang, Haisen Zhang, Wei liu, Keping Long, Jiangbo Dong, Victor C. M. Leung

arXiv:2005.01053v1eess.SP

TL;DR

The paper studies how to maximize energy efficiency in THz-NOMA-MIMO networks while handling high data demand, attenuation, low transmit power, imperfect SIC, and fronthaul constraints. It decomposes the problem into clustering, hybrid precoding, and power allocation, using enhanced K-means, sub-connected precoding, and distributed ADMM. Simulations report faster convergence and higher energy efficiency, lower precoding power consumption, and improved energy efficiency from power optimization.

  • Problem

    Resource optimization for user clustering, hybrid precoding, and power allocation has not been well investigated in THz-NOMA networks despite energy, attenuation, low-power, and fronthaul constraints.

  • Method

    The paper decomposes energy-efficiency maximization into clustering, hybrid precoding, and power optimization, using enhanced K-means, sub-connected hybrid precoding, and distributed ADMM.

  • Results

    Simulations report faster convergence and higher energy efficiency for user clustering, lower power consumption from sub-connected hybrid precoding, and higher energy efficiency from power optimization.

  • Takeaways & Limitations

    The proposed designs provide an integrated approach to energy-efficiency optimization in cache-enabled THz-NOMA-MIMO networks with imperfect SIC and fronthaul constraints.

Abstract

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Terahertz (THz) band communication has been widely studied to meet the future demand for ultra-high capacity. In addition, multi-input multi-output (MIMO) technique and non-orthogonal multiple access (NOMA) technique with multi-antenna also enable the network to carry more users and provide multiplexing gain. In this paper, we study the maximization of energy efficiency (EE) problem in THz-NOMA-MIMO systems for the first time. And the original optimization problem is divided into user clustering, hybrid precoding and power optimization. Based on channel correlation characteristics, a fast convergence scheme for user clustering in THz-NOMA-MIMO system using enhanced K-means machine learning algorithm is proposed. Considering the power consumption and implementation complexity, the hybrid precoding scheme based on the sub-connection structure is adopted. Considering the fronthaul link capacity constraint, we design a distributed alternating direction method of multipliers (ADMM) algorithm for power allocation to maximize the EE of THz-NOMA cache-enabled system with imperfect successive interference cancellation (SIC). The simulation results show that the proposed user clustering scheme can achieve faster convergence and higher EE, the design of the hybrid precoding of the sub-connection structure can achieve lower power consumption and power optimization can achieve a higher EE for the THz cache-enabled network.

I. INTRODUCTION

The paper addresses energy-efficiency optimization in cache-enabled THz-NOMA-MIMO networks, where high capacity, channel characteristics, power limits, and fronthaul constraints complicate resource design. It decomposes the problem into user clustering, hybrid precoding, and power optimization, proposing specialized methods for each stage.

  • Motivation and problem: Resource optimization in THz-NOMA networks remains insufficiently investigated despite the need to maximize energy efficiency under high data demand, attenuation, low transmit power, and fronthaul constraints.The paper focuses on a downlink heterogeneous THz-NOMA-MIMO network with caching.
  • Problem formulation: The original energy-efficiency maximization problem is divided into user clustering, hybrid precoding, and power optimization sub-problems.The study targets a downlink heterogeneous THz-NOMA-MIMO network with cached base stations and clustered single-antenna users.
  • Proposed methods: Enhanced K-means clustering uses channel correlation characteristics to accelerate convergence, while sub-connected hybrid precoding addresses power consumption and implementation complexity.The precoding design uses quantized phase shifters and a low-complexity ZF algorithm.
  • Proposed methods: A distributed ADMM power-allocation algorithm maximizes energy efficiency subject to fronthaul capacity constraints and imperfect SIC residual interference.The paper derives a data-rate expression for residual interference caused by imperfect SIC.
  • Reported outcomes: Simulations report faster convergence and higher energy efficiency for the proposed clustering scheme, lower power consumption from sub-connected hybrid precoding, and higher energy efficiency from power optimization.These results are reported for the THz-NOMA-MIMO and THz cache-enabled networks considered in the paper.

A. Hybrid Analog/Digital Precoding Model

The model combines NOMA signal superposition with sub-connected hybrid precoding, where RF chains connect to subsets of antennas to reduce energy consumption. It defines received signals, interference, SINR, achievable rate, and cluster power constraints for the THz-NOMA system.

  • A. Hybrid Analog/Digital Precoding Model: Sub-connected hybrid precoding connects each RF chain to only part of the antennas, using a phase-shifter count equal to the antenna count.The number of antennas connected to each RF chain is equal.
  • A. Hybrid Analog/Digital Precoding Model: The number of RF chains is set equal to the number of clusters to obtain multiplexing gain.
  • A. Hybrid Analog/Digital Precoding Model: Users in each cluster transmit a superposed signal with cluster power and per-user power-control factors subject to separate constraints.The cluster contains Lb,n users, and its transmit power and control factors are constrained.
  • A. Hybrid Analog/Digital Precoding Model: The superposed signal is processed by a digital baseband precoder and phase shifters before transmission through the THz channel.The analog precoding matrix and digital precoding vector determine the hybrid precoder.
  • A. Hybrid Analog/Digital Precoding Model: The system accounts for intra-cluster and multi-cluster interference when defining users’ received signals, SINR, and achievable rates.The bandwidth W is used in the achievable-rate model.

B. THz Indoor Communication Channel Model

The THz channel model incorporates atmospheric transmission attenuation, water-vapor absorption, path loss, antenna gains, and array steering. It also distinguishes LOS and NLOS propagation while emphasizing blockage and the dominance of path-loss effects.

  • B. THz Indoor Communication Channel Model: The THz channel model uses atmospheric transmission attenuation and experiential water-vapor continuum absorption.
  • B. THz Indoor Communication Channel Model: THz propagation includes LOS and NLOS links, but weak scattering makes the channel sensitive to blockage by obstacles.Scattered and diffracted paths are generally ignored because they receive less power.
  • B. THz Indoor Communication Channel Model: The channel gain depends on frequency- and distance-dependent path loss, antenna gains, and the array steering vector.The model assumes transmitter–receiver distances are known by the SBS to reduce computational complexity.
  • B. THz Indoor Communication Channel Model: THz path gain includes spreading loss and molecular absorption loss caused by electromagnetic-wave expansion and atmospheric molecular collisions.
  • B. THz Indoor Communication Channel Model: For a uniform linear array, the steering vector is determined by the array structure and angle of departure.

C. Cache Model and Fronthaul Link

The cache model uses predetermined binary cache states and accounts for cached and uncached file retrieval over the fronthaul. Limited fronthaul capacity and cache availability constrain user transmission rates, while cache-efficiency modeling remains outside the paper’s scope.

  • C. Cache Model and Fronthaul Link: The cache state variable is binary: it equals 1 when file f is cached by BS b and 0 otherwise.
  • C. Cache Model and Fronthaul Link: A cached requested file is retrieved directly at the SBS, whereas an uncached file is fetched from the MBS through the fronthaul link.
  • C. Cache Model and Fronthaul Link: Cache efficiency represents the long-term utility of files requested from the cache, but its modeling remains beyond the paper’s scope.The paper focuses on a caching strategy with known cache efficiency.
  • C. Cache Model and Fronthaul Link: Limited fronthaul capacity restricts the rate available for data that must be fetched from the MBS.The fronthaul capacity constraint is part of the cache-enabled system model.
  • C. Cache Model and Fronthaul Link: Only infinite fronthaul capacity can reach the cached-network rate; finite capacity and absent local files jointly limit transmission rate.

D. Power Consumption Model

The energy-efficiency formulation relates long-term capacity utility to total power consumption. Total BS power includes transmission and circuit components, with the sub-connected structure reducing phase-shifter requirements relative to a fully connected structure.

  • D. Power Consumption Model: BS power consumption combines transmit power with circuit power consumption and power-amplifier inefficiency.
  • D. Power Consumption Model: Circuit power includes baseband, RF-chain, phase-shifter, and power-amplifier components.The model gives separate per-component power terms.
  • D. Power Consumption Model: For the sub-connected structure, the phase-shifter count is NT rather than NT NR in the fully connected structure.
  • D. Power Consumption Model: The resource-allocation problem jointly studies user clustering, hybrid precoding, and power allocation under normalization, fronthaul, and power constraints.The constraints limit beam power and normalize per-beam user power-control factors.
  • D. Power Consumption Model: System energy efficiency is defined as the long-term capacity utility divided by total power consumption.

III. USER CLUSTERING AND HYBRID PRECODING

The paper designs user clustering and hybrid precoding around THz channel-correlation characteristics, using enhanced K-means to accelerate clustering and reduce interference. The clustering procedure selects correlation-informed initial heads and iterates assignments until convergence.

  • III. USER CLUSTERING AND HYBRID PRECODING: The section combines correlation-based clustering with hybrid precoding to reduce user interference and improve performance in THz-NOMA systems.
  • A. User Clustering: The clustering objective is to group users with strong channel correlation, thereby reducing inter-beam interference.The algorithm assigns each user to the cluster with the smallest distance and outputs cluster heads and user sets.
  • A. User Clustering: Enhanced K-means user clustering uses channel correlation and initial cluster-head settings to achieve faster convergence.The method addresses K-means sensitivity to initialization by selecting initial cluster heads using channel-correlation information.
  • A. User Clustering: The enhanced scheme has asymptotic complexity O(tNBU), compared with O(tNBU^2) for cluster-head selection and O(BU^(2N+1)) for exhaustive search.

B. Analog Precoding

The analog precoder uses a sub-connected antenna structure with quantized phase shifters, designed from cluster-head channel vectors to increase antenna gain while reducing implementation burden.

  • B. Analog Precoding: The sub-connection structure reduces the number of phase shifters associated with each RF chain.
  • B. Analog Precoding: The design uses a two-stage hybrid precoder with Q-bit quantized phase shifters in each antenna subarray.
  • B. Analog Precoding: Sub-connected analog precoding uses cluster-head channel vectors to increase antenna gain for each user cluster.

C. Digital Precoding

The digital precoder operates on a low-dimensional equivalent channel after clustering and analog precoding, using low-complexity zero forcing to mitigate inter-cluster interference.

  • C. Digital Precoding: The baseband precoder changes the amplitude and phase of input complex symbols after analog precoding.
  • C. Digital Precoding: Low-complexity zero-forcing digital precoding is applied to the equivalent channel formed from cluster-head information.
  • C. Digital Precoding: Users are reordered within each cluster according to equivalent channel gain before decoding and power optimization.

IV. POWER OPTIMIZATION

The power-optimization stage maximizes energy efficiency under low THz transmit power, imperfect SIC, and fronthaul-capacity constraints. It transforms the fractional objective and solves distributed power allocation with ADMM.

  • IV. POWER OPTIMIZATION: Distributed ADMM power allocation addresses coupled user powers under fronthaul-capacity constraints and imperfect SIC.The formulation accounts for residual interference from imperfect cancellation and allocates power after clustering and hybrid precoding.
  • IV. POWER OPTIMIZATION: Imperfect SIC is modeled through residual cancellation error, which contributes residual interference to each user’s received signal and SINR.
  • IV. POWER OPTIMIZATION: A Dinkelbach-style transformation converts the fractional energy-efficiency objective into a parameterized subtractive form.
  • IV. POWER OPTIMIZATION: ADMM separates distributed power variables from a global auxiliary vector and iteratively updates the primal, auxiliary, and dual variables until convergence.
  • IV. POWER OPTIMIZATION: The total complexity of the power-allocation algorithm is O(T((1 + T*)BU)) when the outer process uses T iterations and the inner update converges within T* iterations.

V. NUMERICAL SIMULATION AND ANALYSIS

Simulations evaluate user clustering, ADMM power allocation, hybrid precoding, NOMA versus OMA, and caching under the stated THz-NOMA-MIMO settings. The proposed methods converge faster and achieve higher energy efficiency in the reported comparisons.

  • User clustering: The enhanced K-means clustering algorithm converges faster than K-means and achieves lower initial MSE than K-means and the cluster-head selection algorithm.The clustering objective is to minimize the sum of MSE by maximizing channel correlation within clusters.
  • User clustering: The proposed clustering algorithm achieves higher EE than other algorithms as SIC cancellation error increases.Larger cancellation error increases intra-cluster interference and decreases system EE.
  • Power optimization: The ADMM power-allocation algorithm converges to approximately 2.3×10^11 bps/J/Hz from 2.2×10^11 bps/J/Hz and stabilizes after 10 iterations.The simulation uses 64 transmitting antennas and partial-connected hybrid precoding.
  • Multiple access and phase-shifter power: NOMA-MIMO achieves higher EE than OMA-MIMO, while 20 mW phase-shifter power yields higher EE than 30 mW.The comparison varies users from 4 to 20 with four clusters and sub-connected hybrid precoding.
  • Hybrid precoding: Sub-connected hybrid precoding achieves higher EE than digital ZF, and lower phase-shifter quantization bits produce higher EE.Higher quantization bits increase power consumption and reduce energy efficiency.
  • Caching: EE increases with cache efficiency but decreases as the number of transmitting antennas increases.Higher cache efficiency raises users’ sum rate by enabling more files to be retrieved locally at the base station.

VI. CONCLUSIONS

The paper maximizes energy efficiency in THz-NOMA-MIMO systems through enhanced user clustering, sub-connected hybrid precoding, and distributed ADMM power allocation. Simulations report faster convergence, lower power consumption, and higher EE for the proposed designs.

  • Conclusion: The proposed framework jointly addresses user clustering, hybrid precoding, and power optimization for energy-efficient THz-NOMA-MIMO communication.It uses enhanced K-means clustering, sub-connected hybrid precoding, and distributed ADMM power allocation with imperfect SIC and fronthaul constraints.
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