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Throughput Analysis for Full-Duplex Wireless Networks with Imperfect Self-interference Cancellation

Zhen Tong, Martin Haenggi

arXiv:1502.07404v1cs.ITmath.IT

TL;DR

Full-duplex can enable simultaneous bidirectional transmission, but additional interference and residual self-interference make its throughput advantage over half-duplex dependent on network conditions. This paper uses stochastic geometry to analyze and optimize throughput in networks with both modes. It finds that ALOHA throughput is maximized by using a single mode, with the preferred mode depending on self-interference cancellation and link distance.

  • Problem

    Full-duplex can raise throughput through simultaneous bidirectional transmission, but added interference and imperfect self-interference cancellation leave its advantage over half-duplex uncertain.

    Source: §I · p. 2, A. Problem statement · p. 17

  • Method

    The paper uses stochastic geometry to analyze and optimize throughput in a network whose nodes can operate in half- or full-duplex mode.

    Source: §I · p. 2, §II · p. 3

  • Results

    With perfect cancellation under ALOHA, full-duplex always outperforms half-duplex, but its throughput gain is bounded at 0–33% for practical path-loss exponents α ∈ (2, 4].

    Source: §I · p. 3

  • Takeaways & Limitations

    Under ALOHA, maximum throughput is achieved by choosing full-duplex or half-duplex operation according to the amount of self-interference cancellation and link distance.

    Source: B. Throughput optimization · pp. 20–21, §V · p. 24

    The network model assumes an interference-limited case and ignores thermal noise, while the paper states that noise cancels in the throughput gain.

    Source: §V · p. 24

Abstract

from arXiv · show

This paper investigates the throughput for wireless network with full-duplex radios using stochastic geometry. Full-duplex (FD) radios can exchange data simultaneously with each other. On the other hand, the downside of FD transmission is that it will inevitably cause extra interference to the network compared to half-duplex (HD) transmission. Moreover, the residual self-interference has negative effects on the network throughput. In this paper, we focus on a wireless network of nodes with both HD and FD capabilities and derive and optimize the throughput in such a network. Our analytical result shows that if the network is adapting an ALOHA protocol, the maximal throughput is achieved by scheduling all concurrently transmitting nodes to work in either FD mode or HD mode depending on one simple condition. Moreover, the effects of imperfect self-interference cancellation on the signal-to-interference ratio (SIR) loss and throughput are also analyzed based on our mathematical model. We rigorously quantify the impact of imperfect self-interference cancellation on the throughput gain, transmission range, and other metrics, and we establish the minimum amount of self-interference suppression needed for FD to be beneficial.

I. INTRODUCTION

Full-duplex transmission can increase throughput by enabling simultaneous bidirectional communication, but its additional interference and residual self-interference can reduce the gain over half-duplex. This paper analyzes throughput in a network with both modes and finds that, under ALOHA with perfect self-interference cancellation, full-duplex always outperforms half-duplex, although its gain is bounded.

I. INTRODUCTION

  • Full-duplex enables simultaneous bidirectional communication and can potentially double throughput when self-interference is well mitigated.The paper contrasts this potential gain with the extra interference from full-duplex transmissions and imperfect cancellation.Source: §I · p. 2
  • Earlier ad hoc network capacity analyses assumed perfect self-interference cancellation and equal distances from the receiver to both nodes of an interfering full-duplex link.The paper studies throughput while accounting for imperfect cancellation.Source: §I · p. 2
  • Under ALOHA with perfect self-interference cancellation, full-duplex always outperforms half-duplex, but its throughput gain is bounded at 0–33% for practical path-loss exponents α ∈ (2, 4].The bound is 2α/(α+2) and holds for arbitrary node densities, link distances, and SIR regimes.Source: §I · p. 3

II. NETWORK MODEL

The model represents links as independently marked points in a Poisson point process, with each link silent, half-duplex, or full-duplex. It includes residual self-interference in full-duplex links and uses a power-law path-loss model.

II. NETWORK MODEL

  • Each link is independently assigned to silence, half-duplex, or full-duplex, with probabilities p0, p1, and p2 that sum to one.Half-duplex links transmit in one direction per slot; full-duplex links transmit in both directions concurrently.Source: §II · p. 3
  • The network is modeled as an independently marked Poisson point process whose ground process has density λ.Each point is associated with a communication partner at link distance R, and link angles are independent and uniform on [0, 2π].Source: §II · p. 3
  • Residual self-interference in a full-duplex link is βP for transmit power P, with β = 0 denoting perfect cancellation and β = 1 no cancellation.The cancellation amount in dB is −10 log10 β.Source: §II · p. 4
  • The path-loss function is l(x, y) = ∥x − y∥^−α, with α > 2.The model also defines a network configuration by (λ, θ, R, α).Source: §II · p. 5

III. SUCCESS PROBABILITY

The paper uses success probability as a metric for evaluating wireless links and relating their performance to throughput.

III. SUCCESS PROBABILITY

  • Success probability is the complementary cumulative distribution function of the SIR and helps determine throughput.The analysis may place the receiver at the origin without changing the point-process distribution.Source: §III · p. 5

A. Derivation of the success probability and its bounds

The analysis derives conditional success probabilities for half- and full-duplex links, then combines them into an unconditional probability and bounds the results. Residual self-interference adds a multiplicative penalty to full-duplex success probability, while the bounds have a constant horizontal gap under the stated conditions.

A. Derivation of the success probability and its bounds

  • Residual self-interference adds an exponential factor to full-duplex success probability relative to half-duplex, with equality when cancellation is perfect.The analysis derives the conditional probabilities separately for links in each mode.Source: A. Derivation of the success… · pp. 5, 8
  • The unconditional success probability averages the conditional half- and full-duplex probabilities according to their link-state probabilities.The conditional full-duplex interference includes residual self-interference in addition to interference from half- and full-duplex nodes.Source: A. Derivation of the success… · pp. 7–8
  • The paper provides lower and upper bounds for conditional and unconditional success probabilities because the exact expressions include an integral.The lower bound models the two dependent point processes from full-duplex links as independent processes with the same density.Source: A. Derivation of the success… · pp. 8–10
  • The upper bound matches the approximation that treats the two interfering nodes in each full-duplex link as equally distant from the receiver.The cited passage states that equality holds for the Cauchy-Schwarz inequality under this condition.Source: A. Derivation of the success… · p. 10
  • For the unconditional success-probability bounds, the horizontal gap is 1.58 dB when p1 = p2 = 0.5 and δ = 2/α = 1/2.The gap is independent of the SIR threshold and target success probability, and depends only on δ and the transmit probabilities.Source: A. Derivation of the success… · p. 11, Figure 2 · p. 12
  • For θ > 0, R > 0, and α > 2, the ratio F/H lies between 1 + δ and 2.The ratio is independent of link distance R.Source: A. Derivation of the success… · pp. 11–12
  • The upper bound on success probability is asymptotically exact as the SIR threshold θ tends to infinity.The paper also identifies the bounds and their gap as useful for calculating SIR loss and maximal throughput.Source: A. Derivation of the success… · p. 13

B. SIR loss due to FD operation

The section compares FD-only and HD-only networks by the horizontal SIR-threshold gap between their success-probability curves, then bounds that loss and examines imperfect cancellation.

B. SIR loss due to FD operation

  • SIR loss is the horizontal gap between FD-only and HD-only SIR distributions at the same target success probability.Figure 3 compares success probabilities as a function of SIR threshold; the section evaluates the all-HD and all-FD cases.Source: B. SIR loss due to FD operation · pp. 13–14
  • With imperfect cancellation, the SIR-loss bounds depend on the SIR threshold, and loss grows as residual self-interference increases.The passage attributes the additional loss to γ(θFD) > 0 under imperfect cancellation.Source: B. SIR loss due to FD operation · p. 15
  • With perfect cancellation, the SIR-loss bounds depend only on the path-loss exponent, not the SIR threshold, target success probability, or link distance.The bounds are constant horizontal gaps between the FD-only and HD-only success-probability curves.Source: B. SIR loss due to FD operation · pp. 15–17
  • At α = 4, FD-only operation can incur up to 6.0 dB SIR loss under perfect cancellation; imperfect cancellation adds loss, especially at high SIR thresholds.For α = 4, the upper and lower bounds correspond to 3.5 dB and 6.0 dB left shifts, respectively.Source: B. SIR loss due to FD operation · p. 17

A. Problem statement

The problem is to choose between HD and FD operation to maximize network-wide throughput despite the trade-off between link throughput and interference. The section sets up throughput optimization over the densities of HD and FD links.

A. Problem statement

  • The optimization asks how nodes with both capabilities should choose HD or FD operation to maximize network-wide throughput as network configuration varies.The stated motivation is a trade-off between link throughput and interference.Source: A. Problem statement · p. 17
  • Throughput is defined for a typical link that operates in HD with probability p1 or FD with probability p2, assuming spectral efficiency log(1 + θ).The passage introduces the throughput definition and its spectral-efficiency assumption.Source: A. Problem statement · p. 17
  • The optimization can use HD-link and FD-link densities λ1 and λ2, tuned through mode-transmission probabilities at fixed node density.This reparameterization lets the throughput be optimized over link densities rather than only p1 and p2.Source: A. Problem statement · p. 18
  • HD-only and FD-only networks are the two extreme cases whose throughputs are compared with the mixed-mode network.The passage identifies the extreme-case throughputs and the maxima of HD-only, FD-only, and mixed-mode throughput as objects of interest.Source: A. Problem statement · p. 18

B. Throughput optimization

For an ALOHA network, maximum throughput is attained by scheduling nodes in HD, FD, or a mixed mode according to a condition comparing F with 2κH. Imperfect self-interference cancellation creates a critical SIPR threshold that determines whether FD or HD has higher throughput.

B. Throughput optimization

  • For ALOHA, maximum throughput is attained by all-HD, all-FD, or mixed scheduling, depending on the condition comparing F with 2κH.The theorem gives the maximal throughput and corresponding optimal HD and FD densities.Source: B. Throughput optimization · p. 19
  • At F = 2κH, HD and FD have the same throughput, and every density pair on L is stationary.The stated break-even means a typical link has the same throughput in either mode.Source: B. Throughput optimization · p. 20
  • When F > 2κH, HD-only scheduling is optimal; when F < 2κH, FD-only scheduling is optimal.For F > 2κH, the maximum is achieved at the HD-only density; for F < 2κH, it is the FD-only maximum.Source: B. Throughput optimization · p. 20
  • With perfect self-interference cancellation, FD-only scheduling maximizes throughput for every network configuration considered.This holds despite the additional interference from FD nodes.Source: B. Throughput optimization · p. 20
  • For imperfect cancellation, FD has higher throughput when β < βc, while HD is better when β > βc.The critical SIPR βc scales as R^-α.Source: B. Throughput optimization · p. 21
  • Figure 5 identifies the link-distance boundary: below the curve FD is preferable, while above it HD is preferable.At θ = 0 dB and α = 4, 80 dB cancellation favors FD only below link distance 10; reaching distance 100 requires 120 dB for α = 4 or 100 dB for α = 3.Source: Figure 5 · p. 21, B. Throughput optimization · pp. 21–22

C. Comparison of FD with HD

The paper compares the optimized throughput of FD-only and HD-only networks using their throughput gain. The gain stays below its stated bound, approaches its upper bound at high SIR thresholds, and can fall below one when cancellation is insufficient.

C. Comparison of FD with HD

  • Figure 6 plots throughput gain against θ and shows bounds for different SIPRs at α = 4 and R = 1.Source: Figure 6 · p. 23, C. Comparison of FD with HD · p. 24
  • FD throughput gain stays below its stated bound and converges to its upper bound as the SIR threshold θ tends to infinity.The gain is defined as the ratio of maximal FD-only to HD-only throughput under the same network parameters.Source: C. Comparison of FD with HD · pp. 22–23
  • With imperfect cancellation, throughput gain decreases in the high-SIR regime and can fall below 1 when cancellation is insufficient.A gain below 1 means the HD-only network has higher throughput.Source: C. Comparison of FD with HD · p. 24

V. CONCLUSION

With perfect self-interference cancellation, FD outperforms HD under ALOHA, but the throughput gain is less than a doubling. With imperfect cancellation, FD and HD reach a break-even point that depends on cancellation and link distance; the paper also motivates MAC decisions that adapt to surrounding interference.

V. CONCLUSION

  • Under ALOHA with perfect self-interference cancellation, FD is preferable to HD, but the throughput gain is not a doubling and is 2α α+2 for path-loss exponent α.The conclusion also states that imperfect cancellation creates a break-even point whose location depends on cancellation and link distance.Source: §V · p. 24
  • With imperfect self-interference cancellation, the required cancellation in dB grows logarithmically with link distance, which sets the maximum distance at which FD is beneficial.The break-even point depends on both the amount of cancellation and link distance.Source: §V · p. 24
  • Ignoring thermal noise does not affect the throughput gain because its common exponential factor cancels between HD and FD throughput expressions.The network model is interference-limited, but the paper states that the gain is independent of thermal noise.Source: §V · p. 24
  • A MAC scheme tailored to mixed FD/HD networks should let nodes choose their mode according to surrounding interference to maximize network throughput.The paper notes that protocols beyond ALOHA or interference management for pairwise FD-link interferers may yield larger gains.Source: §V · p. 25
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