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On the Impact of Phase Noise on Active Cancellation in Wireless Full-Duplex

Achaleshwar Sahai, Gaurav Patel, Chris Dick, Ashutosh Sabharwal

arXiv:1212.5462v1cs.IT

TL;DR

Full-duplex communication remains constrained by self-interference that existing designs do not eliminate completely. The paper classifies full-duplex architectures and analytically explains experimental bottlenecks, identifying local-oscillator phase noise as a major limitation.

  • Problem

    Self-interference remains the key challenge in full-duplex communications, and existing designs do not eliminate it completely.

  • Method

    The paper classifies known full-duplex architectures and incorporates phase noise into signal models to analytically explain observed cancellation performance.

  • Results

    Phase noise associated with transmitter and receiver local oscillators is identified as a major bottleneck, with cancellation limited by local-oscillator phase-noise properties.

  • Takeaways & Limitations

    Reducing the phase-noise figure of radio mixers could improve self-interference cancellation.

Abstract

from arXiv · show

Recent experimental results have shown that full-duplex communication is possible for short-range communications. However, extending full-duplex to long-range communication remains a challenge, primarily due to residual self-interference even with a combination of passive suppression and active cancellation methods. In this paper, we investigate the root cause of performance bottlenecks in current full-duplex systems. We first classify all known full-duplex architectures based on how they compute their cancelling signal and where the cancelling signal is injected to cancel self-interference. Based on the classification, we analytically explain several published experimental results. The key bottleneck in current systems turns out to be the phase noise in the local oscillators in the transmit and receive chain of the full-duplex node. As a key by-product of our analysis, we propose signal models for wideband and MIMO full-duplex systems, capturing all the salient design parameters, and thus allowing future analytical development of advanced coding and signal design for full-duplex systems.

I. INTRODUCTION

Full-duplex systems struggle to eliminate self-interference, which can remain above the thermal noise floor despite passive suppression and active cancellation. The paper classifies cancellation architectures and analytically identifies local-oscillator phase noise as the major bottleneck explaining observed behavior.

  • Motivation: 15 dB above the thermal noise floor remains after passive suppression and active cancellation in one reported design.The result illustrates why existing short-range full-duplex systems do not eliminate self-interference completely.
  • Approach: Known active analog cancellers are classified as pre-mixer or post-mixer according to where the cancelling signal is generated, with baseband analog cancellation added as another architecture.The classification enables systematic analysis and direct performance comparisons across architectures.
  • Main finding: Phase noise from transmitter and receiver local oscillators is identified as a major bottleneck and is used to explain published cancellation results.The analysis closely matches a reported cancellation number and conjectures that phase noise explains additional experimental results.
  • Main finding: More analog cancellation leaves phase-noise-dominated residual interference that digital cancellation cannot remove, whereas less analog cancellation leaves more correlated interference for digital cancellation.Thus, the two cancellation stages are interdependent rather than independently additive.
  • Main finding: Increasing passive suppression increases total suppression but reduces individual pre-mixer analog cancellation, so total reduction does not grow linearly.The paper attributes this dependence to phase noise.
  • Additional contribution: The paper proposes wideband and MIMO signal models whose noise depends on phase-noise statistics, channel-estimation quality, and thermal noise.These parameters determine the dominant noise regime and capture limits on full-duplex communication.

II. REDUCING SELF-INTERFERENCE IN FULL-DUPLEX

Full-duplex receivers combine passive suppression with active cancellation to reduce self-interference before or during analog reception, while digital cancellation follows quantization. Active analog cancellers are classified by where the cancelling signal is generated and injected.

  • Motivation: 50-100 dB larger self-interference can overwhelm the weaker signal of interest and degrade its effective digital-baseband SNR.Automatic gain control is governed by self-interference, so the signal of interest occupies a much smaller quantized range.
  • Passive suppression: Passive suppression reduces electromagnetic coupling before the self-interference reaches the receive antenna through separation, directionality, or polarization decoupling.These methods increase pathloss, reduce mutual coupling, or use orthogonal polarizations.
  • Active analog cancellation: Active analog cancellers generate a cancelling signal before or after upconversion, forming pre-mixer and post-mixer classes respectively.RF cancellation requires the cancelling signal to be upconverted, whereas baseband analog cancellation occurs before RF transmission.
  • RF active cancellers: Parallel radio cancellation processes a digital estimate of self-interference and adds its RF negative to the received signal through a power combiner.Perfect cancellation follows when the estimated channel equals the actual self-interference channel.
  • RF active cancellers: BALUN cancellation uses amplified and delayed RF copies to create a null when g1δ(t) + g2δ(t −τ) = hsi(t).Because generation and cancellation occur at carrier frequency, BALUN cancellation is classified as post-mixer.
  • Other cancellers: Antenna cancellation transmits opposite signals from symmetrically placed antennas, producing a perfect null when the two self-interference channels are equal.Baseband analog cancellers instead process the self-interference before adding its negative in analog baseband and may require less RF hardware.

3) Digital cancellation:

The conventional narrowband, time-invariant channel model predicts that channel-estimation error should quickly become negligible, but it does not explain reported residual cancellation limits.

  • Digital cancellation: Digital cancellation is applied after the received signal has been quantized by an analog-to-digital converter and is the final reduction step.The model represents the received signal as self-interference, desired signal, and AWGN thermal noise.
  • Signal model: The narrowband model uses single-tap delayed channels and assumes time invariance within channel coherence times.Transmitter average power is nominally limited to 1.
  • Estimation error: With a perfect self-interference-channel estimate, the residual in the model consists only of thermal noise.Equation (6) subtracts the estimated delayed channel response from the actual response.
  • Estimation error: Channel-estimation error decays inversely with training length, and with Ttrain = 5 the residual is no more than 3 dB above thermal noise.As training length tends to infinity, the model predicts residual self-interference composed only of thermal noise.
  • Model limitation: The reported 15 dB residual above thermal noise, and higher values in other studies, are not explained by the conventional signal model.This motivates considering additional dominant radio impairments.

IV. IDENTIFYING THE BOTTLENECK IN ACTIVE CANCELLATION

A controlled experiment separates measurement and implementation effects from cancellation limits by comparing delayed copies of a shared signal and varying the cancellation delay.

  • Candidate impairments: Quantization noise is ruled out as the bottleneck because a 14-bit ADC provides an 84 dB signal-to-quantization-noise ratio.IQ imbalance is also considered calibratable, while power-amplifier nonlinearity is absent in the linear operating regime.
  • Experimental setup: The experiment compares a WARP radio chip at 2.4 GHz with a high-precision vector signal generator at 2.2 GHz.A digitally generated 1 MHz narrowband signal is upconverted, split, and sent through wired paths to two analyzer inputs.
  • Experimental setup: The experiment mimics active cancellation by subtracting a scaled delayed version of y2[iT] from y1[iT].The scaling coefficient is computed from the received complex-valued sequences.

D. Experiment: Results and their explanation

The experiment shows that phase noise explains both delay-dependent cancellation and source-dependent floors, while measurement dynamic range limits the best observed cancellation. Estimation error accounts for only a smaller variation.

  • Upper bound of cancellation: 55-60 dB is the upper cancellation range for both signal sources because the VSA dynamic range limits the measurement.The received signals themselves have an SNR of no more than 55-60 dB.
  • Phase-noise explanation: WARP cancellation decreases with increasing delay and floors near 35 dB, observations explained by phase-noise perturbations in the upconverted signal.The transmitter dominates total phase noise because receiver phase noise from the VSA is small.
  • Phase-noise mechanism: In the absence of phase noise, cancellation depends only on thermal noise; with phase noise, residual self-interference depends on delay and phase-noise variance.Increasing delay reduces temporal phase-noise correlation until only phase-noise variance and thermal noise remain.
  • Estimation error: 20 dB of observed delay-dependent cancellation variation is explained by phase noise, while estimation error explains at most 6 dB.This supports phase noise as the dominant bottleneck in active cancellation.

V. ANSWER 1. IMPACT OF PHASE NOISE ON ACTIVE ANALOG CANCELLATION

The analysis quantifies how transmitter and receiver phase noise limits active analog cancellation across canceller architectures. Matched local oscillators and correlated phase noise can improve cancellation, while phase-noise residuals become dominant at higher self-interference power.

  • Active analog cancellation is analytically limited by transmitter and receiver phase noise across the studied canceller types.The paper quantifies this impact for different active analog cancellers.
  • Independent local oscillators make phase-noise contributions uncorrelated, limiting pre-mixer cancellation by the inverse phase-noise variance.The paper gives 1/(2σ^2_si) as an upper bound in the stated case.
  • Matched local oscillators and small self-interference delay allow phase-noise correlation to reduce residual self-interference in pre-mixer cancellers.For a 42 ns delay, measurements predict 45 dB cancellation with matched oscillators.
  • Matching local oscillators yields 10 dB higher active analog cancellation than unmatched oscillators in the reported WARP measurements.The paper connects this improvement to the measured canceller behavior.
  • Phase-noise-dependent residual strength scales linearly with self-interference strength, becoming dominant at higher received self-interference powers.This identifies phase noise as the dominant residual source after pre-mixer cancellation in that regime.

B. Performance of different active analog cancellers with imperfect channel estimates

With imperfect channel estimates, all analog cancellers retain estimation-dependent and phase-noise-dependent residuals. Their cancellation differs because phase noise interacts differently with delay, oscillator placement, and transmitter-receiver paths.

  • Active cancellation in pre-mixer, post-mixer, and baseband cancellers depends on the inverse of phase-noise variance.The phase-noise residual scales with both phase-noise variance and self-interference strength.
  • All analog cancellers produce residuals comprising a channel-dependent component and a phase-noise-dependent component when channel estimates are imperfect.The channel-dependent term vanishes for a perfect attenuation and delay estimate.
  • Post-mixer cancellers: Post-mixer cancellers reduce phase-noise residuals by improving delay estimates, because their residual is scaled by 1 − R_φsi(∆si − τ).Unlike pre-mixer cancellers, post-mixer performance continues improving as channel-estimation error decreases.
  • The predicted 20 dB cancellation for USRP radios is attributed to their likely higher phase-noise variance than WARP radios.The comparison is presented as an explanation of the reported experimental result.
  • Baseband cancellers: Baseband cancellers have phase-noise residuals independent of self-interference delay and bounded even with perfect channel estimates.Their residual scales with the sum of transmitter and receiver phase-noise variances.

A. Digital cancellation when active analog cancellation uses perfect channel estimate

When analog cancellation uses perfect channel estimates, its phase-noise residual is uncorrelated with the self-interference signal and cannot be further reduced digitally. With imperfect estimates, digital cancellation can remove the correlated component, but cascaded performance remains phase-noise limited.

  • Perfect analog channel estimates leave phase-noise residuals that are uncorrelated with the self-interference signal, preventing further digital cancellation.This conclusion applies to pre-mixer and post-mixer cancellers, with perfect estimates leaving only thermal noise in the latter case.
  • With imperfect analog estimates, digital cancellation removes the residual component correlated with the self-interference signal.Digital cancellation therefore reduces residual strength when analog estimation is imperfect.
  • The phase-noise residual behaves as a zero-mean fast-fading component that changes every sample and cannot be estimated digitally.Its independence from the self-interference signal prevents digital cancellation from reducing it.
  • The cascaded analog-plus-digital cancellation is limited by phase-noise properties and the analog channel-estimation error.This limitation is stated for the sum of the active cancellation stages.
  • Even perfect digital channel estimation cannot overcome the phase-noise lower bound when analog cancellation is poor.Poor analog cancellation leaves a larger residual channel, increasing the receiver phase-noise contribution.

2) Post-mixer cancellers:

For post-mixer cancellers, digital cancellation can exploit correlated residuals after imperfect analog cancellation, while the cascaded total remains bounded by phase noise. Unlike some other architectures, post-mixer residuals do not explicitly depend on analog cancellation quality in the stated formulation.

  • Post-mixer digital cancellation can reduce residual self-interference when preceding analog cancellation uses imperfect channel estimates.The digital stage acts on the residual channel left by the analog stage.
  • Active analog cancellation can cancel only the residual component correlated with the self-interference signal.Uncorrelated phase-noise residuals remain outside this cancellation mechanism.
  • The total cascaded cancellation in post-mixer systems is bounded by an inverse phase-noise-variance term.The bound is described as depending solely on phase noise.
  • The lower bound is achievable when the digital canceller has a perfect estimate of the residual self-interference channel.This bound corresponds to the residual after perfect analog channel estimation in the baseband analysis.
  • In post-mixer cancellers, residual performance does not explicitly depend on analog cancellation quality but depends on digital channel-estimation error.The formulation uses the difference between the residual channel and its digital estimate.

VII. ANSWER 3. INFLUENCE OF PASSIVE SUPPRESSION ON ACTIVE CANCELLATION

Passive suppression changes the balance between line-of-sight and reflected self-interference components, thereby affecting achievable active analog cancellation. Greater passive suppression lowers active analog cancellation in pre-mixer cancellers while maximizing total cancellation.

  • The analysis models self-interference with line-of-sight and reflected taps having delays Δ1 < Δ2 and average strengths E(|h1|2) and E(|h2|2).
  • Higher passive suppression can result in lower active analog cancellation in pre-mixer cancellers.Passive suppression reduces the line-of-sight component, changing the ratio between the two channel-tap strengths.
  • 2E(|h1|2)(1 − Rφsi(∆1)) + 2E(|h2|2)(1 − Rφsi(∆2)) approximates residual self-interference strength under phase noise.
  • When the line-of-sight component dominates, active analog cancellation approaches 1/(1 − Rφsi(∆1)); when it is negligible, it approaches 1/(1 − Rφsi(∆2)).
  • Because ∆1 < ∆2 implies 1/(1−Rφsi(∆1)) > 1/(1−Rφsi(∆2)), more passive suppression implies less active analog cancellation.
  • Total cancellation is maximized when passive suppression is maximum, even though active analog cancellation decreases as passive suppression increases.

B. Wideband signal model

The wideband model treats the channel as multiple narrowband systems across coherence-bandwidth-sized subchannels and extends the model to MIMO transmissions. The resulting framework incorporates phase noise, channel structure, and antenna-dependent residual interference.

  • Wideband full-duplex is modeled as a combination of K narrowband channels, with overall bandwidth W and self-interference coherence bandwidth w.
  • For W << ωc, phase jitter over the band can be assumed independent of bandwidth.
  • In each narrowband channel, phase-noise contribution scales with transmit power in that band, whereas the thermal noise floor remains constant.
  • With equal total power P and equal channel magnitudes across bands, the model compares residual phase-noise and thermal-noise effects between narrowband and wideband systems.
  • The MIMO extension represents self-interference from M transmit antennas to N receivers and assigns per-transmitter signal and self-interference power constraints.
  • With independent local oscillators across transmit antennas, phase-noise residual self-interference is the sum of M independent SISO residuals.
  • The paper analytically explains observed full-duplex bottlenecks, identifies phase noise as a major bottleneck, and proposes wideband and MIMO signal models.

X. APPENDIX

The appendix derives phase-noise and cancellation expressions for different canceller architectures and relates phase-noise spectra to phase jitter. It also characterizes residual interference from imperfect cancellation estimates.

  • The appendix derives phase jitter from the phase-noise power spectral density L(f), carrier frequency fc, and integration offsets f1 and f2.
  • For WARP at 2.4 GHz, the measured time jitter is 0.83 picoseconds, corresponding to σφ = 0.717°.
  • For the 2.2 GHz signal generator, the computed phase-noise variance is σφ = 0.066.
  • The pre-mixer, baseband analog, and post-mixer sections express residual self-interference as combinations of imperfect channel estimates and phase-noise terms.
  • E(|yresidue−analog(t)|2) ≥ |hsi|2(1 + ρ2 − 2|ρ|Rxsi(∆si − τ)) gives a lower bound associated with imperfect estimation.
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