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Energy Efficiency Optimization for NOMA UAV Network with Imperfect CSI

Haijun Zhang, Jianmin Zhang, Keping Long

arXiv:2005.02046v1cs.ITeess.SPmath.IT

TL;DR

Energy efficiency in NOMA UAV networks with imperfect CSI has received limited study, despite channel estimation errors in low-altitude links. The paper transforms the probability-constrained problem and uses two-stage user scheduling and power allocation. Simulations report higher energy efficiency than comparison schemes, including a reported 19% advantage over FTPA at 1 W hovering power.

  • Problem

    Energy-efficiency optimization for NOMA UAV networks with imperfect CSI is underexplored, although low-altitude links experience small-scale fading and channel estimation errors.

    Source: §I · p. 2

  • Method

    The paper transforms the probability-constrained problem and decouples it into user scheduling by DC programming and power allocation by successive convex approximation.

    Source: §I · p. 2, §IV · p. 7, §VI · p. 11

  • Results

    At 1 W hovering power, the proposed algorithm's energy efficiency exceeds FTPA by 19% and is far superior to OFDMA.

    Source: §V · p. 10

  • Takeaways & Limitations

    The study concludes that two-step resource allocation can optimize NOMA UAV network energy efficiency while accounting for imperfect CSI and operational constraints.

    Source: §I · p. 2, §VI · p. 11

Abstract

from arXiv · show

Unmanned aerial vehicles (UAVs) are developing rapidly owing to flexible deployment and access services as air base stations. However, the channel errors of low-altitude communication links formed by mobile deployment of UAVs cannot be ignored. And the energy efficiency of the UAVs communication with imperfect channel state information (CSI) hasnt been well studied yet. Therefore, we focus on system performance optimization in non-orthogonal multiple access (NOMA) UAV network considering imperfect CSI between the UAV and users. A suboptimal resource allocation scheme including user scheduling and power allocation is designed for maximizing energy efficiency. Because of the nonconvexity of optimization function with an probability constraint for imperfect CSI, the original problem is converted into a non-probability problem and then decoupled into two convex subproblems. First, a user scheduling method is applied in the two-side matching of users and subchannels by the difference of convex programming. Then based on user scheduling, the energy efficiency in UAV cells is optimized through a suboptimal power allocation algorithm by successive convex approximation method. The simulation results prove that the proposed algorithm is effective compared with existing resource allocation schemes.

I. INTRODUCTION

The paper addresses energy-efficiency optimization for NOMA UAV networks with imperfect CSI, a setting the authors say had not been studied. It proposes user scheduling and power allocation under UAV power, outage, and macro-user interference constraints.

I. INTRODUCTION

  • The study targets the gap in energy-efficiency optimization for NOMA UAV networks with imperfect CSI, which is affected by estimation errors and finite feedback.The paper considers dense urban low-altitude links, where small-scale fading accompanies path loss.Source: §I · p. 2
  • The proposed approach optimizes UAV-user energy efficiency through user scheduling and power allocation after converting the non-convex problem into two convex subproblems.The formulation accounts for imperfect CSI, UAV transmit-power limits, and interference to macro users.Source: §I · p. 2

II. SYSTEM MODEL

  • The network model includes UAV air base stations and a ground macro base station sharing spectrum across UAV and macro users.Each hovering UAV serves a UAV cell within the macrocell.Source: §II · p. 3
  • The low-altitude UAV-user channel includes small-scale fading, with imperfect CSI modeled through an estimation error on the fading coefficient.The model assumes large-scale fading can be estimated perfectly.Source: §II · pp. 3–4
  • Energy efficiency accounts for successful transmission rate relative to power consumption, including transmit power and the UAV's hovering power.The paper optimizes user-subchannel matching and power allocation to improve network energy efficiency.Source: §II · p. 4
  • The optimization is constrained by each UAV's transmit-power limit, interference imposed on macro users, and an outage-probability threshold.Each subchannel is limited to at most two users to reduce computational complexity.Source: §II · pp. 4–5

III. ENERGY EFFICIENCY OPTIMIZATION AND RESOURCE ALLOCATION

The energy-efficiency problem under imperfect CSI is non-convex and includes a probability constraint. The paper removes that constraint and separates resource allocation into user-subchannel matching and power control.

III. ENERGY EFFICIENCY OPTIMIZATION AND RESOURCE ALLOCATION

  • The imperfect-CSI energy-efficiency problem has a non-convex objective and an outage-probability constraint.The method separates user-subchannel matching from power control.Source: §III · p. 5
  • An outage threshold is introduced to remove the probability constraint from the optimization problem.The resulting allocation is performed based on user scheduling.Source: §III · p. 5
  • The problem is decoupled into subchannel-user matching and power control to optimize energy efficiency under imperfect CSI.Source: §III · p. 5

A. Optimization Problem Transformation

The transformation replaces the probability-constrained formulation with an outage-threshold-based one. It uses actual and maximum achievable SINR quantities to express the imperfect-CSI outage condition before formulating energy efficiency for subchannels with up to two users.

A. Optimization Problem Transformation

  • The method simplifies the probability-constrained problem using the outage threshold εout and formulates actual and maximum achievable SINR quantities.The outage event is expressed as the actual instantaneous rate exceeding the maximum achievable capacity.Source: A. Optimization Problem Transformation · p. 5
  • The imperfect-CSI outage probability is constrained to be no greater than εout, yielding stricter constraints for the transformed problem.Source: A. Optimization Problem Transformation · p. 5
  • The resulting energy-efficiency formulation assumes at most two users per subchannel and uses user power-proportion factors.The paper then addresses resource allocation through user scheduling and power allocation.Source: A. Optimization Problem Transformation · p. 6

B. Energy-Efficient User Scheduling

User scheduling matches users to subchannels using imperfect-CSI channel gains and energy efficiency. A DC-programming search selects the most energy-efficient user pair and its power-proportion factor for each subchannel.

B. Energy-Efficient User Scheduling

  • The scheduling procedure first ranks user-subchannel choices by estimated imperfect-CSI channel gain, then matches each subchannel with an energy-efficient user pair.The method assumes equal power per subchannel at the start of matching.Source: B. Energy-Efficient User Scheduling · p. 6
  • Because the matching objective is non-convex in the power-proportion factor, the paper applies difference-of-convex programming to search for a suboptimal solution.The objective is expressed as a difference of two convex functions and approximated iteratively.Source: B. Energy-Efficient User Scheduling · p. 6
  • When a subchannel has fewer than two users, the procedure adds an unassigned user and compares the resulting three pairs, assigning the pair with the highest energy efficiency.The DC algorithm searches for the power-proportion factor for each pair.Source: B. Energy-Efficient User Scheduling · p. 7

C. Energy-Efficient Power Allocation

Power allocation is non-convex in the subchannel powers, so the section applies successive convex approximation to obtain a convex problem and rewrite the energy-efficiency function.

C. Energy-Efficient Power Allocation

IV. RESOURCE OPTIMIZATION ALGORITHM DESIGN

The resource optimization design combines user scheduling with cross-subchannel power allocation, using DC programming for user-pair selection and successive convex approximation for power optimization.

IV. RESOURCE OPTIMIZATION ALGORITHM DESIGN

  • Two suboptimal algorithms are proposed: user scheduling and cross-subchannel power allocation for UAV-network performance optimization.Source: §IV · p. 7
  • Users select subchannels according to priority order, with a new user assigned when a subchannel has fewer than two users.Source: §IV · p. 7
  • When a subchannel has two users, DC programming selects the user pair to maximize energy efficiency through iterative optimization of the power proportion factor.Source: §IV · p. 7

A. User Scheduling Algorithm

User scheduling matches users and subchannels using imperfect-CSI channel gain, then uses DC programming to select energy-efficient pairs and their power proportions.

A. User Scheduling Algorithm

B. Power Allocation Algorithm

After user scheduling, an iterative successive-convex-approximation algorithm allocates power across subchannels under UAV power and macro-user interference constraints.

B. Power Allocation Algorithm

  • The power-allocation algorithm initializes with equal subchannel powers and iteratively minimizes the objective from (47) using successive convex approximation.Source: B. Power Allocation Algorithm · p. 8
  • The power problem is converted into a convex function based on the existing subchannel-user matching state, with UAV-power and macro-user interference constraints.Source: B. Power Allocation Algorithm · p. 8
  • Macro users provide interference feedback to the macro BS, which sends the cross-tier interference constraint to the UAV for the next iteration.Source: B. Power Allocation Algorithm · p. 8

C. Complexity Analysis

The section compares exhaustive user–subchannel matching with the proposed DC-based scheduling algorithm, which reduces computational complexity while seeking a user schedule.

C. Complexity Analysis

  • Exhaustive search can obtain the optimal match for all users and subchannels, while Algorithm 1 uses a DC algorithm for scheduling.The passage gives the exhaustive-search complexity only in a truncated expression.Source: C. Complexity Analysis · p. 8
  • In the worst case, Algorithm 1 compares a new user with two previous users across all subchannels, with complexity no more than O(K^2).Source: C. Complexity Analysis · p. 8
  • The authors conclude that their user-scheduling algorithm reduces computational complexity relative to exhaustive search.Source: C. Complexity Analysis · p. 8

V. NUMERICAL SIMULATION AND ANALYSIS

Simulations compare the proposed NOMA resource-allocation method with existing schemes across user counts, channel-estimation errors, hovering power, and UAV heights. The reported results favor the proposed method in several comparisons, while energy efficiency also varies with these operating conditions.

V. NUMERICAL SIMULATION AND ANALYSIS

  • The simulation uses 4 UAVs at 200 m height, serving 10–40 users per UAV cell over K = N/2 subchannels.The scenario also includes one ground BS and 20 macro users.Source: §V · p. 8
  • At 30 users per UAV cell, energy efficiency improves 3.6% over NOMA-DC and 17% over FTPA; NOMA energy efficiency is much higher than OFDMA.Fig. 2 compares energy efficiency across 10–40 users per cell under NOMA and OFDMA.Source: Figure 2 · p. 9, §V · p. 9
  • After 4 iterations, energy efficiency reaches a stable value for the power-allocation method; the 30-user case has higher efficiency than the 10-user case.Fig. 3 shows the iteration behavior for both user counts.Source: Figure 3 · p. 9, §V · p. 9
  • The network energy efficiency declines as estimation error increases; poorer UAV-channel sensing makes maximum channel capacity harder to calculate accurately, so instantaneous rate may exceed it and outage probability rises.Source: §V · p. 9
  • At 40 users per UAV cell, perfect-CSI energy efficiency is 6% higher than with σ²_e = 0.2, and the proposed algorithm outperforms FTPA under both CSI conditions.The paper defines perfect CSI as zero channel estimation error.Source: §V · p. 9, Figure 5 · p. 10
  • At 1 W hovering power, the proposed algorithm's energy efficiency exceeds FTPA by 19% and is far above OFDMA, with Pmax = 10 W.Source: Figure 6 · p. 10, §V · p. 10
  • At 0.5 W hovering power, the proposed algorithm improves 18% over FTPA with Pmax = 5 W, 10 users per cell, and estimation error 0.05.Energy efficiency degrades as hovering power increases.Source: Figure 7 · p. 10, §V · p. 10
  • At 150 m UAV height, energy efficiency is 8.8% higher than NOMA-FTPA and 34% higher than OFDMA.Across algorithms, energy efficiency first rises and then falls with height; the height yielding maximum efficiency depends on the environment.Source: §V · pp. 10–11, Figure 9 · p. 11

VI. CONCLUSIONS

The proposed suboptimal resource-allocation algorithm improves UAV-network energy efficiency compared with existing algorithms under imperfect CSI. It converts the probability-constrained problem and separates user scheduling from power allocation at a fixed UAV hovering height.

VI. CONCLUSIONS

  • The simulations show higher UAV-network energy efficiency with the proposed algorithm than with existing algorithms.Source: §VI · p. 11
  • The method first removes the probability constraint, then matches users to subchannels and optimizes power using successive convex approximation.Source: §VI · p. 11
  • The optimization includes UAV power, outage-probability, and macro-user interference constraints, with UAV hovering height fixed.Source: §VI · p. 11
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