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Uplink Cooperative NOMA for Cellular-Connected UAV

Weidong Mei, Rui Zhang

arXiv:1809.03657v3cs.IT

TL;DR

Cellular-connected UAV uplinks create severe interference through strong LoS channels, while conventional local NOMA can provide limited gains. The paper proposes cooperative NOMA over BS backhaul links, optimizes rate and power allocations, and reports higher achievable rates than the benchmark schemes, especially under high traffic or UAV rate demand.

  • Problem

    Strong LoS A2G channels create severe uplink interference, while non-cooperative NOMA can be limited by the worst UAV-to-BS channel.

  • Method

    The paper proposes cooperative NOMA that forwards decoded UAV signals among backhaul-connected BSs and optimizes UAV rate and power allocations using alternating optimization and SCA.

  • Results

    The proposed cooperative NOMA yields higher achievable rates than non-orthogonal transmission and non-cooperative NOMA, especially at high ground traffic or UAV rate demand.

  • Takeaways & Limitations

    Larger cancellation size improves the UAV–ground-user achievable-rate trade-off, with higher complexity and processing delay.

Abstract

from arXiv · show

Aerial-ground interference mitigation is a challenging issue in the cellular-connected unmanned aerial vehicle (UAV) communications. Due to the strong line-of-sight (LoS) air-to-ground (A2G) channels, the UAV may impose/suffer more severe uplink/downlink interference to/from the cellular base stations (BSs) than the ground users. To tackle this challenge, we propose to apply the non-orthogonal multiple access (NOMA) technique to the uplink communication from a UAV to cellular BSs, under spectrum sharing with the existing ground users. However, for our considered system, traditional NOMA with local interference cancellation (IC), termed non-cooperative NOMA, may provide very limited gain compared to the OMA. This is because there are many co-channel BSs due to the LoS A2G channels and thus the UAV's rate performance is severely limited by the BS with the worst channel condition with the UAV. To improve the UAV's achievable rate, a new cooperative NOMA scheme is proposed by exploiting the backhaul links among BSs. Specifically, some BSs with better channel conditions are selected to decode the UAV's signals first, and then forward the decoded signals to their backhaul-connected BSs for IC. To investigate the optimal design of cooperative NOMA, we maximize the weighted sum-rate of the UAV and ground users by jointly optimizing the UAV's rate and power allocations over multiple resource blocks. However, this problem is hard to be solved optimally. To obtain useful insights, we first consider two special cases with egoistic and altruistic transmission strategies of the UAV, respectively, and solve their corresponding problems optimally. Next, we consider the general case and propose an efficient suboptimal solution via the alternating optimization. Numerical results show that the proposed cooperative NOMA yields significant throughput gains than the OMA and the non-cooperative NOMA benchmark.

I. INTRODUCTION

Cellular-connected UAVs face severe aerial-ground interference because strong LoS A2G channels reach many BSs. The paper proposes cooperative NOMA using BS backhaul links and optimizes UAV rate and power allocations to improve the UAV–ground-user trade-off.

  • Motivation: Cellular-connected UAVs are motivated by applications requiring ubiquitous coverage, low latency, reliability, and high throughput.These requirements support command-and-control traffic and rate-demanding payload communication.
  • Interference challenge: Strong LoS A2G channels let the UAV associate with multiple BSs while generating severe interference at many non-associated co-channel BSs.This creates a distinctive coexistence challenge compared with conventional terrestrial systems.
  • Benchmark limitations: OMA protects ground UEs by restricting UAV transmissions to unused RBs, but increasing ground-UE density rapidly reduces the RBs available to the UAV.NOMA can reuse occupied RBs, making it attractive when ground-UE density is high.
  • Proposed approach: The proposed cooperative NOMA selects BSs with better UAV channels to decode signals and forwards them over backhaul links for interference cancellation.The scheme extends local cancellation by exploiting cooperative IC among BSs.
  • Optimization: The paper maximizes weighted sum-rate by jointly optimizing UAV rate and power allocations over multiple RBs, with special-case optimal solutions and a general alternating-optimization method.The general problem is non-convex and includes discrete allocation difficulty, motivating reformulation and efficient local optimization.
  • Positioning: Prior NOMA work largely targets terrestrial settings or UAVs acting as aerial BSs, whereas this paper studies NOMA for a UAV acting as an aerial uplink UE.The paper addresses cooperative IC for the UAV uplink, a setting distinguished by LoS channels and macro-diversity.

A. Cellular Network with Ground UEs Only

The system models a cellular region with ground UEs served by BSs over reused RBs, while assuming terrestrial inter-cell interference is well mitigated. A UAV then shares these RBs and creates additional received interference at BSs through its LoS-dominated channels.

  • Ground-UE network: Each BS serves K_j ground UEs over N RBs, with the total ground-UE count K equal to the sum of users across BSs.The model assumes K_j ≥ 1 for every BS.
  • Resource reuse: Because frequency reuse usually gives N < K, ground UEs in different cells may transmit simultaneously on the same RB.The model assumes existing ICIC techniques have largely mitigated this terrestrial inter-cell interference.
  • RB notation: For each RB, J(n) contains BSs serving ground UEs, while J^c(n) contains BSs not occupied by a ground-UE transmission.The serving ground UE at BS j on RB n is indexed by k_j(n).
  • Ground links: The ground-UE channel h_j(n) incorporates antenna gain, path loss, shadowing, and small-scale fading, with transmit power p_j(n).The corresponding received model includes the transmitted symbol and aggregate background noise plus terrestrial ICI.
  • Ground-link performance: The ground-UE serving-BS SNR and achievable sum-rate are defined from the channel and noise model, with bandwidth B denoting the per-RB bandwidth.The paper sets B = 1 Hz unless stated otherwise.
  • UAV link: The UAV-to-BS links are modeled as frequency-flat because LoS propagation dominates, so f_j(n) = f_j across RBs.The UAV transmits with nonnegative RB power p_n, producing a received signal at each BS.

C. Cooperative NOMA

Cooperative NOMA uses decodable BSs and backhaul forwarding to cancel UAV interference at additional occupied BSs. The cancellation sets depend on UAV rate, power, and the selected BSs’ neighboring relationships.

  • Cooperative NOMA lets decodable BSs forward decoded UAV signals over backhaul links for interference cancellation at neighboring BSs.With M = 0, the scheme reduces to non-cooperative NOMA with local IC; larger M enables cancellation across more BS tiers.
  • At each RB, decodable BSs are identified from the UAV’s rate and power, and selected BSs can decode and forward the UAV signal when their cancellation neighborhoods contain occupied BSs.The decodable set shrinks as UAV rate increases and expands as UAV power increases.
  • The cancelling set contains occupied BSs reached through the M-tier neighborhoods of BSs that decode the UAV signal.Thus, enlarging the forwarding neighborhoods generally enlarges the set of BSs performing IC.
  • With cooperative cancellation, fewer BSs suffer UAV interference than under non-cooperative NOMA when the cancellation set is nonempty.For M = 0, cancelling BSs are only the intersection of decodable and occupied BSs, which is generally smaller than with M ≥ 1.
  • In the illustrative RB, J = 37 and M = 1, decodable BSs 1 and 3 leave occupied BSs 19 and 32 exposed after cooperative IC.For M = 0, no occupied BS can cancel the UAV interference in that RB.

III. PROBLEM FORMULATION

The paper formulates a weighted sum-rate optimization balancing UAV throughput against ground-user throughput under cooperative NOMA. It analyzes egoistic and altruistic special cases, including how cancellation size affects ground-user rates.

  • III. PROBLEM FORMULATION: The objective maximizes the weighted sum-rate of the UAV and ground UEs by jointly optimizing UAV rate and transmit power across RBs.The weight μ controls the emphasis on ground-UE sum-rate, while UAV power is bounded by Pmax.
  • III. PROBLEM FORMULATION: Higher UAV rates improve UAV throughput but shrink the decodable and cancelling BS sets, potentially degrading the ground UEs’ sum-rate.Higher UAV power enlarges those sets but can also strengthen interference at occupied BSs outside the cancelling set.
  • III. PROBLEM FORMULATION: The general optimization is nonconvex and difficult to solve optimally because UAV power and rate allocations have non-trivial effects on the objective.The paper therefore first studies the limiting cases μ → 0 and μ → +∞.
  • III. PROBLEM FORMULATION: The terrestrial UE transmit powers are fixed, allowing the proposed scheme to be combined with terrestrial uplink ICIC designs that determine those powers.This assumption reflects the paper’s focus on integrating the UAV with an existing cellular network.
  • A. Egoistic Scheme: In the egoistic scheme, the UAV maximizes its own achievable rate, with each RB decoded at the BS having the highest normalized UAV channel gain.The resulting optimal UAV power allocation is water-filling over RBs, and rate constraints hold with equality.
  • A. Egoistic Scheme: Egoistic UAV power and rate allocations are independent of M, so non-cooperative NOMA can match cooperative NOMA in UAV rate performance.Cooperative NOMA can nevertheless improve ground-UE sum-rate by cancelling interference at more BSs.
  • A. Egoistic Scheme: Ground-UE sum-rate under the egoistic scheme is monotonically non-decreasing with cancellation size M and reaches the no-UAV-interference maximum when M ≥ M0.At that threshold, all occupied BSs can receive the decoded UAV signal for cancellation.
  • A. Egoistic Scheme: When M is small, including M = 0, the egoistic scheme may overlook occupied BSs outside the cancelling sets, leaving them exposed to UAV interference.Increasing M enlarges the cancellation neighborhoods and improves the ground-UE sum-rate.

B. Altruistic Scheme

The altruistic scheme preserves the maximum ground-UE sum-rate while selecting strong decodable BSs to improve the UAV’s transmission rate as cancellation size M increases.

  • Altruistic transmission strategy: The UAV preserves the maximum ground-UE sum-rate by cancelling its interference at every occupied BS in each resource block.For occupied RBs, each BS must have an available decodable BS, selected from its cancellation-connected set.
  • Altruistic transmission strategy: Each occupied BS selects as decodable BS the candidate with the maximum normalized UAV channel gain within its cancellation set.The resulting decodable-BS set contains one selected BS for every occupied BS.
  • Altruistic transmission strategy: The altruistic scheme uses water-filling power allocations across resource blocks, with corresponding rate allocations determined by the selected decodable BSs.The supplied passages identify water-filling for the optimal altruistic power allocation and define the decodable-BS construction.
  • Effect of cancellation size: Unlike the egoistic scheme, altruistic power and rate allocations depend on M, so cooperative NOMA with M ≥1 generally outperforms non-cooperative NOMA for UAV rate.Increasing M enlarges the candidate sets from which decodable BSs can be selected.
  • Effect of cancellation size: The altruistic UAV transmit rate increases monotonically with M and converges to the egoistic-scheme rate when M ≥M0.For sufficiently large cancellation size, the altruistic solution also becomes optimal for the general problem for any µ ≥0.
  • Effect of cancellation size: With small M, the UAV rate is severely limited by the occupied BS having the worst normalized channel power gain with the UAV.This limitation makes the altruistic-scheme rate practically low in the non-cooperative case M = 0.

V. PROPOSED SOLUTION TO (P1)

The general problem is addressed by reformulating the original optimization and then solving the equivalent problem efficiently.

  • General case: The general case targets problem (P1) with finite weight 0 < µ < +∞ and cancellation size M < M0.The solution procedure first develops an equivalent reformulation of (P1).
  • General case: The proposed solution transforms the general optimization into an equivalent problem that can be solved efficiently.The passage states the reformulation and efficient solution as the section’s two-step approach.
  • General case: The reformulated problem is designed for the practically relevant regime where cancellation size remains below M0.The section explicitly restricts the general case to M < M0.

A. Equivalent Reformulation of (P1)

The original joint rate-and-power optimization is reformulated by replacing rate allocations with BS associations, reducing the power subproblem to a more tractable form for alternating optimization.

  • Motivation: The original problem is difficult because jointly optimizing UAV rate and power allocations requires an exhaustive search over many discrete power levels.The resulting worst-case complexity is O(JN), which is prohibitive when the numbers of BSs or resource blocks are large.
  • Equivalent reformulation: For any fixed power allocation, each resource block has an associated decodable BS that characterizes the optimal UAV rate allocation.The optimal rate can be mapped to a unique BS association through the reformulation.
  • Equivalent reformulation: The associated BS decodes the UAV signal, while other BSs with larger normalized UAV channel gains may also decode it.This defines the relationship between the association and the broader set of decodable BSs.
  • Equivalent reformulation: Problem (P1) is therefore replaced by problem (P2), which jointly optimizes BS associations and UAV power allocations across resource blocks.The reformulation uses BS associations {jn} and power allocations {pn} as the optimization variables.
  • Solution structure: The reformulation converts the power allocation subproblem from discrete to continuous optimization.This change enables efficient numerical treatment of the power variables.
  • Solution structure: An alternating optimization method iteratively optimizes power allocations and BS associations until the two variable blocks are updated alternately.Power allocation is optimized with associations fixed, and associations are then optimized in the alternating procedure.

B. Power Allocation Optimization with Given BS Association

With BS associations fixed, the power allocation problem is handled through successive convex approximation, producing a locally optimal solution with monotonic convergence.

  • Power allocation subproblem: Fixing BS associations reduces (P2) to a power allocation problem over the UAV powers across resource blocks.The associated decodable and cancelling BS sets are fixed in this subproblem.
  • Power allocation subproblem: The resulting continuous power problem remains difficult because its objective is non-concave in the UAV power allocations.The non-concavity arises from the ground-UE sum-rate term.
  • Successive convex approximation: SCA approximates the non-concave objective by a concave function at each local point and iteratively solves the resulting convex problems.The approximation uses a first-order Taylor lower bound of the convex ground-UE sum-rate component.
  • Successive convex approximation: The SCA iterations update UAV power allocations by solving the convex approximated problem at each iteration.The algorithm computes a new solution from the current local power point and repeats the update until the objective increase falls below a threshold.
  • Convergence: The proposed SCA algorithm guarantees monotonic convergence because the objective value is non-decreasing over iterations.The convergence statement follows from the cited SCA convergence result.

C. BS Association Optimization with Given Power Allocation

With fixed power allocations, the BS association problem separates into N parallel subproblems. A partial enumeration algorithm finds the optimal association with polynomial worst-case complexity.

  • Fixed power allocations decouple the BS association problem into N parallel subproblems, one for each resource block.
  • When no candidate cancelling BS exists, the optimal association is the BS with the largest normalized UAV channel power gain.
  • Full enumeration solves each association subproblem, while partial enumeration obtains the optimum more efficiently.
  • The partial algorithm sorts BSs by normalized channel gain, updates cancelling sets when possible, and retains the association with the highest objective value.
  • The algorithm can terminate early when cancelling sets cannot expand; its worst-case complexity is O(JN), which is polynomial.

D. Overall Algorithm and Convergence

The overall algorithm alternates power-allocation and BS-association optimization. Its objective is non-decreasing across iterations and therefore converges because it is upper-bounded.

  • Power allocations and BS associations are alternately optimized by solving problems (30) and (36) while fixing the other variable block.
  • Each iteration initializes the power-allocation solver with the previous powers, then solves BS association using the updated powers.
  • The algorithm repeats these updates until convergence and outputs the resulting associations, powers, and rate allocation.
  • The objective value is non-decreasing after each iteration, and the proposed AO algorithm is guaranteed to converge because the objective is upper-bounded.
  • Although the power-allocation subproblem is solved only locally optimally, monotonic convergence remains guaranteed.

VI. NUMERICAL RESULTS

Numerical evaluations compare cooperative NOMA with non-orthogonal transmission and non-cooperative NOMA. Cooperative NOMA improves rate trade-offs and is especially beneficial when ground traffic or UAV rate demand is high.

  • The evaluation uses an OFDMA system with terrestrial ICIC to mitigate inter-cell interference before assigning resource blocks to ground UEs.
  • With increasing active ground UEs, OMA’s UAV rate degrades toward zero because fewer resource blocks remain available; non-cooperative NOMA offers only marginal gain over OMA.
  • Non-cooperative and non-orthogonal transmission have similar network sum-rates, which become constant at high UAV transmit power as ground-UE rate loss offsets UAV-rate increases.
  • At Pmax = 20 dBm and K = 150, increasing cancellation size M improves the achievable rate trade-off, with cooperative NOMA enlarging the region especially at high UAV rates.
  • When M = 3, all occupied BSs can receive decoded UAV signals, allowing UAV interference cancellation at every occupied BS without ground-UE sum-rate loss.
  • For M = 1, the first five ground UEs’ rates decrease with UAV rate demand, whereas the last five remain unchanged because their BSs can cancel UAV interference.

VII. CONCLUSIONS

The paper proposes cooperative NOMA for uplink interference mitigation in cellular-connected UAV communications and optimizes UAV and ground-user rates jointly. Simulations show higher achievable rates than benchmark schemes, particularly under high ground traffic or UAV rate demand, while larger cancellation size increases complexity and delay.

  • Cooperative NOMA uses BS backhaul cooperation to mitigate severe uplink interference caused by UAV LoS channels, including non-cooperative NOMA as a special case.
  • The study jointly optimizes UAV uplink rate and power allocations over multiple resource blocks to maximize the weighted sum-rate of UAV and ground UEs.
  • Optimal solutions are obtained for egoistic and altruistic UAV strategies, while the general case uses AO and SCA to derive a locally optimal solution.
  • Cooperative NOMA achieves higher rates than non-orthogonal transmission and non-cooperative NOMA, especially when ground traffic or UAV rate demand is high.
  • Increasing cancellation size improves the UAV–ground-UE rate trade-off but incurs higher complexity and processing delay.
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