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Multi-Beam UAV Communication in Cellular Uplink: Cooperative Interference Cancellation and Sum-Rate Maximization

Liang Liu, Shuowen Zhang, Rui Zhang

arXiv:1808.00189v1cs.ITmath.IT

TL;DR

Multi-beam UAV uplink sharing cellular resources with terrestrial users faces co-channel interference that can degrade communication. The paper proposes cooperative interference cancellation using adjacent-GBS backhaul links; numerical examples report DoF and sum-rate gains over schemes with no or local cancellation.

  • Problem

    Co-channel interference from multi-beam UAV uplink can degrade communication when aerial and terrestrial users share cellular resources.

    Source: §I · p. 3

  • Method

    The proposed strategy uses existing backhaul connections among adjacent GBSs for cooperative interference cancellation.

    Source: §VIII · p. 26

  • Results

    Numerical examples show significant DoF and sum-rate gains over benchmark schemes with no or local interference cancellation.

    Source: §VIII · p. 26

  • Takeaways & Limitations

    The cooperative cancellation strategy exploits existing backhaul links among adjacent GBSs.

    Source: §VIII · p. 26

Abstract

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Integrating unmanned aerial vehicles (UAVs) into the cellular network as new aerial users is a promising solution to meet their ever-increasing communication demands in a plethora of applications. Due to the high UAV altitude, the channels between UAVs and the ground base stations (GBSs) are dominated by the strong line-of-sight (LoS) links, thus severe interference may be generated to/from the GBSs in the uplink/downlink, which renders the interference management with coexisting terrestrial and aerial users a more challenging problem to solve. In this paper, we study the uplink communication from a multi-antenna UAV to a set of GBSs in its signal coverage region. Among these GBSs, we denote available GBSs as the ones that do not serve any terrestrial users at the assigned resource block (RB) of the UAV, and occupied GBSs as the rest that are serving their respectively associated terrestrial users in the same RB. We propose a new cooperative interference cancellation strategy for the multi-beam UAV uplink communication, which aims to eliminate the co-channel interference at each of the occupied GBSs and in the meanwhile maximize the sum-rate to the available GBSs. Specifically, the multi-antenna UAV sends multiple data streams to selected available GBSs, which in turn forward their decoded data streams to their backhaul-connected occupied GBSs for interference cancellation. To draw useful insights, the maximum degrees-of-freedom (DoF) achievable by the multi-beam UAV communication for sum-rate maximization in the high signal-to-noise ratio (SNR) regime is first characterized, subject to the stringent constraint that all the occupied GBSs do not suffer from any interference in the UAV's uplink transmission. Then, based on the DoF-optimal design, the achievable sum-rate at finite SNR is maximized, subject to given maximum allowable interference power constraints at each occupied GBS.

I. INTRODUCTION

The introduction frames cellular-enabled UAV uplink as a way to support high-rate aerial communication, but same-resource use can create severe interference for terrestrial users. It argues that existing terrestrial interference-management strategies do not directly fit this setting, where many GBSs may lie within a UAV’s coverage region.

I. INTRODUCTION

  • Cellular-enabled UAV communication leverages ground base stations to support high-performance UAV-ground communications.Source: §I · p. 2
  • Same-resource aerial and terrestrial transmissions can cause severe co-channel interference that degrades UAV and terrestrial-user communication performance.Source: §I · p. 3
  • The paper studies multi-beam cellular uplink in which a multi-antenna UAV sends streams to selected available GBSs while suppressing interference at occupied GBSs.Available GBSs do not serve terrestrial users on the UAV’s resource block; occupied GBSs do.Source: §I · p. 3

A. Prior Work

  • Prior terrestrial interference-management schemes raise an open question of applicability when aerial and terrestrial users share the system.Source: A. Prior Work · pp. 4–5
  • Cognitive beamforming can leave limited or zero UAV degrees of freedom when occupied GBS channels consume the UAV’s spatial dimensions.The cited discussion notes that occupied GBSs may outnumber the UAV antennas, preventing multi-beam spatial multiplexing even when many available GBSs exist.Source: A. Prior Work · p. 4
  • NOMA’s expected sum-rate advantage over cognitive beamforming is marginal at high SNR, while CoMP incurs substantial backhaul overhead and delay.Source: A. Prior Work · p. 5

B. Main Contributions

The paper proposes cooperative interference cancellation over existing backhaul links between adjacent GBSs, alongside DoF-optimal stream association and finite-SNR beamforming design. Its numerical results report DoF and sum-rate gains over schemes with no or local interference cancellation, and significant sum-rate gain over cognitive beamforming.

B. Main Contributions

  • The proposed strategy uses existing backhaul connections between adjacent GBSs for cooperative interference cancellation.Selected available GBSs decode UAV streams and forward the decoded messages to connected occupied GBSs for cancellation.Source: B. Main Contributions · p. 5
  • The paper characterizes maximum achievable DoF under a stringent no-harmful-interference constraint by jointly choosing stream count and available-GBS associations.Source: B. Main Contributions · p. 6
  • A zero-forcing design achieves the maximum DoF, analytically exceeding the DoF of cognitive beamforming and NOMA.Source: B. Main Contributions · p. 6
  • For finite SNR, the DoF-optimal association yields a multi-group multicast problem addressed by a successive-convex-approximation beamforming algorithm.The paper reports significant sum-rate gain over cognitive beamforming.Source: B. Main Contributions · p. 6

C. Organization

The paper proceeds from a cellular-uplink model distinguishing occupied and available GBSs and a cooperative interference-cancellation strategy to constrained sum-rate optimization, DoF analysis, finite-SNR algorithms, simulations, and conclusions. The strategy is intended to control air-to-ground interference and make interference-temperature constraints easier to satisfy at occupied GBSs.

C. Organization

  • The paper outlines its system model, cancellation strategy, interference-constrained sum-rate formulation, DoF analysis, finite-SNR algorithm, simulations, and conclusion.The organization passage assigns these topics to Sections II–VIII, respectively.Source: C. Organization · p. 6

II. SYSTEM MODEL

  • The system has one M-antenna UAV and N GBSs; occupied GBSs serve terrestrial users on the UAV’s resource block, while available GBSs do not.The model treats each GBS as effectively single-antenna under a fixed beam pattern and assumes the UAV’s assigned resource block is given.Source: §II · pp. 7–8
  • The UAV is modeled at a fixed location with Rician fading channels comprising line-of-sight and Rayleigh components, and its channel vectors are assumed known.The model notes that multi-antenna GBSs with flexible three-dimensional beamforming are left for future work.Source: §II · pp. 7–8
  • The UAV sends streams to selected available GBSs, whose decoded data can be forwarded to occupied GBSs for interference cancellation.The system model assumes terrestrial interference at available GBSs is well mitigated and negligible compared with the UAV signal, but the UAV’s interference at occupied GBSs is strong.Source: §II · pp. 8–9
  • Interference power at each occupied GBS must remain below its given temperature constraint, while nonzero beamforming may be infeasible when constraints are stringent and occupied GBSs outnumber UAV antennas.The passage specifically notes the case N1 ≥ M and explains that total interference cancellation then generally leaves no feasible nonzero beamforming solution.Source: §II · p. 10
  • The proposed strategy aims to improve air-to-ground interference control and ease interference-temperature constraint satisfaction at occupied GBSs.Source: §II · p. 10

III. COOPERATIVE INTERFERENCE CANCELLATION

Available GBSs decode UAV streams and forward them over backhaul to connected occupied GBSs, which subtract those streams; the UAV controls residual interference through beamforming. The strategy can permit transmission where zero-forcing alone cannot, while relaxing occupied-GBS interference constraints.

Cooperative interference cancellation

  • The UAV need only control residual interference from streams that connected available GBSs cannot deliver to an occupied GBS.For each occupied GBS, these streams form the set Γ; streams that can be forwarded are canceled after their decoded messages arrive.Source: §III · p. 11
  • Available GBSs forward decoded UAV streams to connected occupied GBSs, which subtract them before decoding terrestrial uplink signals.Each available GBS forwards only to an occupied GBS connected by a one-hop backhaul link; the UAV controls interference from streams that cannot be forwarded.Source: §III · pp. 11–12
  • Cooperative cancellation generally makes the interference-temperature constraint easier to satisfy, particularly with many occupied GBSs and small thresholds.The strategy may require multicasting each stream to more than one available GBS to use the backhaul connections.Source: §III · pp. 11–12
  • In the example with N1 = 3, M = 2, and linearly independent channels to occupied GBSs 1–3, the proposed strategy sends at least one stream to an available GBS; cooperative interference cancellation alone cannot do so without interference to all three occupied GBSs.Source: §III · p. 12

IV. SUM-RATE MAXIMIZATION UNDER INTERFERENCE CONSTRAINTS

The section formulates UAV sum-rate maximization over stream count, available-GBS associations, beamformers, and multicast rates, subject to decoding, interference, and power constraints. It then uses a DoF-optimal design to develop finite-SNR beamforming.

IV. SUM-RATE MAXIMIZATION UNDER INTERFERENCE CONSTRAINTS

  • The formulation requires each stream to be decoded by its assigned available GBSs, limits interference at occupied GBSs, and caps total UAV transmit power.It also requires each stream to reach at least one available GBS and each available GBS to decode at most one stream.Source: §IV · p. 13
  • Finding the optimum entails exhaustive searches over stream counts and feasible stream-to-GBS associations, followed by beamforming optimization.Even with stream count and associations fixed, the beamforming sum-rate problem is described as NP-hard.Source: §IV · p. 13
  • The section first studies the infinite-power limit, where the problem reduces to DoF maximization with zero-forcing constraints, to guide lower-complexity finite-SNR design.The authors say this analysis clarifies the rate gain over schemes with local or no interference cancellation.Source: §IV · pp. 13–14
  • The finite-SNR design builds on the DoF-optimal available-GBS associations to maximize the UAV’s achievable sum-rate.The optimization jointly considers the number of streams, their receiving GBSs, beamforming vectors, power allocation, and multicast rates.Source: §IV · pp. 12, 14

V. DOF ANALYSIS

The DoF analysis characterizes high-SNR stream capacity under the requirement of zero interference at occupied GBSs. Its formulation tests feasible stream associations and beamformers against decoding and interference conditions.

V. DOF ANALYSIS

  • The high-SNR analysis characterizes maximum achievable DoF and compares the cooperative strategy with CoMP/C-RAN, NOMA, and cognitive beamforming.The authors motivate the regime by the strong LoS channels between the UAV and GBSs and use the DoF-optimal design in the finite-SNR solution.Source: §V · p. 14

A. Problem Formulation

  • As transmit power tends to infinity, the formulation maximizes the number of streams while requiring each stream to reach an available GBS and avoid interference at occupied GBSs unable to receive it for cancellation.The zero-interference condition follows because, at infinite power, interference under the temperature constraints must be zero rather than finite and nonzero.Source: A. Problem Formulation · pp. 14–15
  • For each candidate stream count, the method tests whether associations and beamformers satisfy the formulation, then uses bisection over [1, min(M, N2)] to find the maximum feasible DoF.In the most favorable case with no occupied GBSs, the maximum DoF is min(M, N2).Source: A. Problem Formulation · p. 15

B. Feasibility Check

A DoF of J ≤ min(M, N2) is achievable exactly when a stream-to-GBS assignment satisfies the stated conditions, reducing feasibility to the assignments alone. The section then gives a zero-forcing beamforming design and contrasts cooperative cancellation with full cooperation and schemes without backhaul exchange.

B. Feasibility Check

  • A DoF of J ≤ min(M, N2) is achievable if and only if a stream assignment satisfies the stated conditions, including |Λi| < M.The theorem characterizes DoF feasibility through the assignments Λj alone; the associated finite search considers (J + 1)^N2 assignments.Source: B. Feasibility Check · pp. 15–16
  • The assignment-only feasibility test avoids beamforming variables and permits exhaustive search over the finite set of possible assignments.Each available GBS can be assigned to decode one of J streams or none.Source: B. Feasibility Check · p. 16

C. DoF-Optimal Beamforming Design

  • Zero-forcing beamforming places each stream’s beam in the null space of channels to occupied GBSs that cannot cancel that stream.The design uses the assignment obtained in the preceding feasibility step.Source: C. DoF-Optimal Beamforming Design · p. 16

D. Comparison with Other Techniques

  • With every GBS connected, the maximum DoF is min(M, N2), but this requires many backhaul links and can introduce delay that is problematic for a mobile UAV.The paper contrasts this full-cooperation benchmark with a strategy requiring fewer, adjacent-GBS connections.Source: D. Comparison with Other Techniques · p. 17
  • Without backhaul exchange, the maximum DoF is min(max(M − N1, 0), N2), and successive interference cancellation does not increase NOMA’s DoF.The paper’s cooperative strategy achieves a DoF gain over NOMA and cognitive beamforming with a reasonable backhaul requirement, and is described as more robust to NOMA’s SIC error propagation.Source: D. Comparison with Other Techniques · pp. 17–18

VI. PROPOSED SOLUTION AT FINITE SNR

The finite-SNR design separates stream-count and association selection from beamforming and rate allocation, using DoF maximization as a high-SNR approximation. It then applies successive convex approximation to the remaining multicast sum-rate problem, whose iterative algorithm converges monotonically to a solution satisfying KKT conditions.

VI. PROPOSED SOLUTION AT FINITE SNR

  • The finite-SNR problem couples discrete stream count and associations with beamforming and rates, so the design decouples these choices to reduce complexity.The selected stream count and associations maximize DoF, which the paper says approximates the original problem at high SNR.Source: §VI · p. 18, A. Data Stream Association Design · p. 18

A. Data Stream Association Design

  • Choosing the DoF-maximizing stream count and associations separates that design from beamforming and rate allocation, with the DoF objective serving as a high-SNR approximation.The paper identifies high-rate multi-stream UAV transmission over strong LoS channels as the setting motivating this approximation.Source: A. Data Stream Association Design · p. 18

B. Beamforming and Rate Allocation Design

  • The remaining sum-rate task is a multi-group multicast problem that the authors describe as open even without the interference-temperature constraint.Each stream is decoded by an exclusive subset of available GBSs; the paper notes that MIMO broadcast-channel sum-rate results do not directly apply because of a minimum-rate operation.Source: B. Beamforming and Rate Allocation… · p. 19
  • Successive convex approximation replaces the non-convex rate constraint with a concave lower-bound constraint, enabling joint optimization of beamformers and rates under the stated constraints.The resulting approximated problem is convex and is solved iteratively while updating the auxiliary reference values.Source: B. Beamforming and Rate Allocation… · pp. 19–20
  • Algorithm 1 converges monotonically, and its converged solution satisfies all Karush-Kuhn-Tucker conditions.Each iteration solves the approximated convex problem before updating the reference variables.Source: B. Beamforming and Rate Allocation… · pp. 20–21

VII. NUMERICAL EXAMPLES

The numerical examples evaluate the proposed cooperative interference-cancellation strategy in an eight-GBS cellular topology, with three occupied and five available GBSs. The UAV is positioned above cell 6, and the section includes a plot of maximum achievable DoF against UAV antenna count.

VII. NUMERICAL EXAMPLES

  • The simulated network has 8 GBSs: 3 occupied and 5 available, with specified backhaul connections between the two groups.Each cell has a 200-meter radius.Source: §VII · p. 21
  • The UAV is placed 100 meters above the center of cell 6, and the channel setup uses a Rician factor of 5.The examples use a 10 MHz resource block and AWGN power spectral density of −169 dBm/Hz.Source: §VII · pp. 21–22
  • Figure 3 plots maximum achievable DoF against the number of antennas at the UAV.The examples assess the proposed strategy in the cellular topology described for this section.Source: §VII · p. 21, Figure 3 · p. 22

A. Achievable DoF

In the high-SNR examples, the proposed strategy’s DoF is 3, compared with 5 for full-cooperation CoMP and 2 for cognitive beamforming; its finite-SNR sum-rate also exceeds cognitive beamforming, while its relative performance depends on the interference constraint. The examples show monotonic algorithm convergence and a trade-off between beamforming gain and cooperative interference cancellation across stream assignments.

A. Achievable DoF

  • The proposed scheme achieves DoF 1 for M = 1 or 2, DoF 2 for M = 3, DoF 3 for M = 4 or 5, DoF 4 for M = 6, and DoF 5 for M ≥ 7.For M ≥ 7, this equals min(M, N2) in the example with five available GBSs.Source: A. Achievable DoF · p. 22
  • The example’s optimal stream-to-GBS assignment is not always unique; when M = 1, Λ1 = {5, 7} is also optimal.The listed assignments vary with the UAV antenna count.Source: A. Achievable DoF · p. 22
  • Compared with cognitive beamforming and uplink NOMA, the cooperative strategy’s DoF gain is especially pronounced as the UAV antenna count increases.The comparison also finds a reasonable DoF relative to full-cooperation CoMP, which is described as difficult to implement in practice.Source: A. Achievable DoF · p. 23

1) Convergence of Algorithm 1:

  • Algorithm 1’s sum-rate converges monotonically over iterations, consistent with Theorem 2.The plotted example uses a 23 dBm UAV transmit-power constraint and the association Λ1 = {4, 7}, Λ2 = {5, 8}, Λ3 = {6}.Source: 1) Convergence of Algorithm 1 · p. 23, Figure 4 · p. 24

2) Performance Comparison:

  • At a 23 dBm transmit-power constraint, the proposed strategy using all available GBSs for cooperative interference cancellation achieves higher sum-rate below −80 dBm interference-temperature constraint, but lower sum-rate above −70 dBm.Source: 2) Performance Comparison · p. 24, Figure 5 · p. 25
  • The two tested stream associations trade off multicast beamforming gain against interference-cancellation gain, so association should be designed to balance them.One association removes the interference-temperature constraint from beamformer design but multicasts two streams; the other uses one nearby GBS per stream but leaves that constraint in the design.Source: 2) Performance Comparison · pp. 24–25
  • The proposed strategy achieves higher sum-rate than cognitive beamforming, while CoMP achieves the maximum sum-rate through fully cooperative interference cancellation.CoMP requires a massive number of backhaul links, whereas the proposed strategy requires connections between adjacent cells.Source: 2) Performance Comparison · p. 25
  • At high SNR, the DoF is 3 for the proposed scheme, 5 for CoMP, and 2 for cognitive beamforming, so the proposed scheme and CoMP sum-rates increase faster with transmit power than cognitive beamforming.The comparison uses an interference-temperature constraint of −60 dBm.Source: 2) Performance Comparison · p. 25, Figure 6 · p. 26

VIII. CONCLUSION

The paper proposes multi-beam UAV uplink communication with cooperative interference cancellation using existing backhaul links between adjacent GBSs. It characterizes DoF through data-stream association, maximizes finite-SNR sum-rate through beamforming, and reports gains over schemes with no or local interference cancellation.

VIII. CONCLUSION

  • The work addresses severe aerial interference to terrestrial uplink communications arising from strong UAV–GBS LoS channels.Source: §VIII · p. 26
  • The UAV sends multiple streams to available GBSs, which forward decoded messages over backhaul links to occupied GBSs for interference cancellation before terrestrial-user decoding.The scheme uses existing backhaul connections between adjacent GBSs.Source: §VIII · p. 26
  • The paper characterizes the proposed strategy’s DoF by optimizing the association between each data stream and its decoding available GBSs.Source: §VIII · p. 26
  • At finite SNR, proper beamforming design maximizes the UAV uplink sum-rate based on the data-stream association.Source: §VIII · p. 26
  • Numerical examples show significant DoF and sum-rate gains over benchmark schemes with no or local interference cancellation.Source: §VIII · p. 26
  • Future work will extend DoF and/or sum-rate optimization to multi-antenna GBSs with flexible 3D beamforming and uplink NOMA.The proposed extensions include both cooperative and local interference cancellation.Source: §VIII · p. 26

APPENDIX

The proof establishes Theorem 1 by showing that its stated conditions yield the required beamforming vectors and that vectors meeting the beamforming conditions imply those conditions. Its construction uses null spaces formed from occupied- and available-GBS channels.

A. Proof of Theorem 1

  • Each beamforming vector wj is required to lie in the null space of the combined occupied- and available-GBS channel matrices.Source: A. Proof of Theorem 1 · p. 27
  • Under condition (14), the rank bound ensures that this null space exists for each j, allowing J beamforming vectors to satisfy conditions (13c) and (13d).Source: A. Proof of Theorem 1 · p. 27
  • Under the Rician channel model, the channel vectors are linearly independent, supporting the proof that the constructed zero-forcing vectors satisfy condition (13b) with probability one.Source: A. Proof of Theorem 1 · p. 27
  • The proof also shows the converse: beamforming vectors satisfying conditions (13b)–(13d), (11d), and (11e) imply conditions (11d), (11e), and (14), completing Theorem 1.Source: A. Proof of Theorem 1 · p. 27
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