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Widely-Linear Digital Self-Interference Cancellation in Direct-Conversion Full-Duplex Transceiver

Dani Korpi, Lauri Anttila, Ville Syrjälä, Mikko Valkama

arXiv:1402.6083v4cs.IT

TL;DR

Full-duplex direct-conversion transceivers can suffer strong self-interference shaped by transmitter and receiver IQ imbalance and PA nonlinearities. The paper models these effects and develops widely-linear digital cancellation with least-squares parameter estimation. Simulations show that widely-linear processing outperforms classical linear cancellation, while PA-induced IMD remains a residual limitation.

  • Problem

    Self-interference in practical full-duplex transceivers includes IQ image components that classical linear cancellation does not efficiently suppress.

  • Method

    The paper models IQ imaging and PA nonlinearities across the transceiver and estimates a two-filter widely-linear canceller using least-squares fitting.

  • Results

    The proposed widely-linear cancellation substantially improves SI cancellation performance over classical purely linear processing in extensive simulations.

  • Takeaways & Limitations

    Processing transmit data and its complex conjugate can attenuate IQ-induced image SI and prevent the associated decrease in SINR.

  • Takeaways & Limitations

    The widely-linear least-squares model does not model PA-induced IMD, which limits cancellation at higher transmit powers.

Abstract

from arXiv · show

This article addresses the modeling and cancellation of self-interference in full-duplex direct-conversion radio transceivers, operating under practical imperfect radio frequency (RF) components. Firstly, detailed self-interference signal modeling is carried out, taking into account the most important RF imperfections, namely transmitter power amplifier nonlinear distortion as well as transmitter and receiver IQ mixer amplitude and phase imbalances. The analysis shows that after realistic antenna isolation and RF cancellation, the dominant self-interference waveform at receiver digital baseband can be modeled through a widely-linear transformation of the original transmit data, opposed to classical purely linear models. Such widely-linear self-interference waveform is physically stemming from the transmitter and receiver IQ imaging, and cannot be efficiently suppressed by classical linear digital cancellation. Motivated by this, novel widely-linear digital self-interference cancellation processing is then proposed and formulated, combined with efficient parameter estimation methods. Extensive simulation results demonstrate that the proposed widely-linear cancellation processing clearly outperforms the existing linear solutions, hence enabling the use of practical low-cost RF front-ends utilizing IQ mixing in full-duplex transceivers.

I. INTRODUCTION

The paper examines self-interference in practical full-duplex transceivers and identifies IQ imaging as a limitation of linear cancellation, motivating widely-linear processing.

  • Self-interference can be 60–100 dB stronger than the received signal of interest at the receiver input.The stated range applies to separate-antenna configurations, depending on antenna separation and transmit power.
  • Linear cancellation is limited by analog/RF circuit non-idealities, including phase noise, nonlinear distortion, and IQ imbalance.Prior work considered phase noise and nonlinearities; this paper focuses especially on IQ imaging in IQ-based architectures.
  • Transmitter and receiver IQ imbalance introduce additional inband image interference into the self-interference path.The paper notes that transmitter image attenuation specifications of 25 dB or 28 dB may still leave image interference relevant to full-duplex operation.
  • The paper models transmitter and receiver IQ images, transmitter PA nonlinearities, coupling, RF cancellation, and receiver cancellation across the SI path.The analysis combines detailed waveform modeling with calculations of the powers of different residual SI components.
  • A widely-linear digital canceller processes both transmit data and its complex conjugate, with parameters estimated through widely-linear least-squares fitting.The proposed approach is evaluated against classical purely linear processing through analysis and extensive simulations.

II. FULL-DUPLEX TRANSCEIVER AND SELF-INTERFERENCE

The paper analyzes a direct-conversion full-duplex architecture using a baseband-equivalent model to characterize signal propagation and self-interference components.

  • The analyzed transceiver uses a typical direct-conversion architecture selected for its simple structure and wide applications in modern wireless transceivers.The paper attributes the IQ imaging problem to amplitude and phase mismatches between I- and Q-branches in the transmitter and receiver mixers.
  • A baseband-equivalent model represents the transceiver blocks, propagating signals, and principal mathematical or behavioral component models.The model is used to analyze the self-interference waveform at different stages of the transceiver.
  • The signal characterization includes transmitter IQ imaging, PA distortion, multipath coupling, RF cancellation, receiver IQ imaging, and receiver linear cancellation.The resulting powers of different self-interference terms are analyzed at receiver digital baseband.

A. Self-Interference Signal Model with Practical RF Components

The modeled digital-baseband SI contains linear, conjugate, and PA-induced distortion components, explaining why classical linear cancellation can leave substantial interference.

  • IQ mixer imbalance creates widely-linear transformations in which direct and complex-conjugated signals are separately filtered and summed.The transmitter model uses direct and image responses, with complex conjugation denoted by (·)∗.
  • The transmitter IQ mixer is characterized by an image rejection ratio, with analogous characterization for the receiver IQ mixer.The transmitter and receiver image responses are represented in the frequency domain by their respective direct and image transfer functions.
  • The PA is modeled with a Hammerstein nonlinearity, focusing on the third-order distortion component as the strongest PA nonlinearity in practice.The analysis acknowledges that actual PAs also contain distortion components beyond third order.
  • RF cancellation is modeled as attenuating only the direct coupling component through a one-tap filter representing delay, phase, and attenuation.The analysis uses realistic attenuation and delay errors to model practical RF cancellation.
  • Receiver IQ imbalance produces an image component of the total signal entering the receiver IQ mixer, including self-interference.The receiver output then passes through VGA amplification and ADC digitization, with quantization noise included in the digital signal model.
  • The total SI includes linear SI, conjugate SI, PA-induced IMD, and conjugate IMD.These components arise alongside the total noise term in the receiver digital-baseband waveform.
  • Classical linear cancellation estimates only the linear SI channel, leaving conjugate SI and distortion that can remain substantial relative to the desired signal.Thermal noise is also present but is typically not the main performance limitation under the stated circumstances.

B. Principal System Calculations for Different Distortion Terms

The section derives simplified power expressions for the different self-interference and noise components after RF and linear digital cancellation. These formulas expose how component powers depend on transmit power, antenna isolation, RF cancellation, digital cancellation, and receiver noise assumptions.

  • Model simplifications: The analysis approximates frequency-dependent impulse responses by scalar gains or delta functions to obtain compact average-power expressions.This simplification is justified for comparing average distortion powers rather than frequency-dependent behavior.
  • Power terms: The power definitions include transmit-signal power, nonlinear-distortion power, total-noise power, and ADC quantization-noise power.ADC quantization noise is parameterized by input signal power, ADC bit depth, and PAPR through the stated ADC SNR expression.
  • Noise model: Receiver noise is simplified by assigning most of the receiver noise factor F to the LNA and assuming no additional noise later in the chain.Under this approximation, total noise is related to thermal-noise power at the receiver input through the LNA gain and noise factor.
  • Cancellation chain: The self-interference chain is modeled through transmitter distortion, antenna coupling, RF cancellation, receiver processing, and linear digital cancellation.The linear component changes from h1(n)⋆x(n) before cancellation to approximately (h1−w1)x(n) afterward.
  • Derived powers: Equations (37)–(43) provide the powers of the different distortion components at detector input as functions of the system parameters.The derivation assumes static deterministic RF-component gains and circularly distributed RF-channel-estimation error.

System Calculations Example:

The example evaluates distortion powers for a representative low-cost wideband transceiver across transmit-power and analog-cancellation settings. Under typical parameters, conjugate self-interference dominates after linear digital cancellation, while weaker analog cancellation also makes PA nonlinear distortion important at higher transmit powers.

  • Example parameters: The example uses system parameters representing a typical wideband transceiver with low-cost mass-product components.The image attenuation is selected based on 3GPP LTE specifications, and the receiver VGA is assumed to match ADC-input waveform dynamics.
  • Reference signal: The reference signal-of-interest power is set 5 dB above receiver sensitivity to contextualize the calculated distortion powers.The signal of interest is shown in the figures but is not included in the self-interference signal model.
  • Typical setting: 27–57 dB of linear digital cancellation is required across transmit powers from −5 dBm to 25 dBm to place linear self-interference below the thermal-noise floor.This cancellation range is selected to approximate realistic digital-cancellation performance.
  • Typical setting: Above 9 dBm transmit power, conjugate self-interference exceeds the signal-of-interest power and prevents the ideal 15 dB SINR across the evaluated range.Conjugate self-interference is the most dominant distortion over a wide transmit-power range in this parameter setting.
  • Altered parameters: With 30 dB antenna separation, 20 dB RF cancellation, and 35 dB mixer image rejection, conjugate self-interference becomes even larger relative to the signal of interest.Above 15 dBm, PA-generated intermodulation distortion also becomes significant, so attenuating only linear and conjugate self-interference may be insufficient.

III. PROPOSED WIDELY-LINEAR DIGITAL CANCELLATION

The proposed canceller targets the conjugate self-interference component produced by IQ imbalance, because it dominates after classical linear digital cancellation. The section focuses on this component while treating PA-induced nonlinear distortion as weaker under the stated assumption.

  • Proposed approach: Widely-linear digital cancellation is introduced to attenuate the IQ-imbalance-induced self-interference image in addition to the direct component.The motivation is the observed dominance of conjugate self-interference after classical linear cancellation.
  • Scope assumption: The analysis assumes PA-generated intermodulation distortion and conjugate intermodulation distortion are clearly weaker than conjugate self-interference.This assumption focuses the proposed processing on the dominant conjugate component under the considered conditions.
  • Scope assumption: A combined canceller for PA intermodulation distortion and conjugate self-interference is left for future work.The section acknowledges that PA-induced nonlinear self-interference may require further suppression under some circumstances.

A. Widely-Linear Cancellation Principle

The widely-linear principle extends digital self-interference cancellation by processing both the transmitted samples and their complex conjugates. The conjugated samples are filtered with an estimate of the effective image channel to cancel conjugate self-interference.

  • Signal model: The starting signal model includes a direct transmit-data term and a residual term z(n) containing other signal components.The general formulation retains frequency-dependent antenna coupling and IQ imbalance without approximation.
  • Conjugate cancellation: Conjugate self-interference is canceled by conjugating the known transmitted samples and filtering them with an estimate w2(n) of the effective image channel.This produces a cancellation signal for the mirror-image component.
  • Widely-linear principle: Widely-linear cancellation processes both the direct transmit data and its complex conjugate to account for the mirror-image component.The procedure estimates the effective conjugate channel and convolves it with the conjugated transmit samples.

B. Widely-Linear Least-Squares Parameter Estimation

The proposed estimator models both the transmit signal and its conjugate using augmented convolution data, enabling separate estimation of direct and image channels for widely-linear cancellation.

  • Ordinary least squares estimates the augmented channel from observed ADC samples using both x(n) and x*(n).
  • The observed baseband signal combines convolutions of transmit data and its complex conjugate with noise.
  • The estimation matrix includes delayed, non-causal FIR taps to capture RF-cancellation delay errors and timing misalignment.The first K taps represent pre-cursor channel components.
  • The augmented convolution matrix stacks the transmit-data matrix with its elementwise complex-conjugated counterpart.
  • The direct and image channel estimates are extracted from the augmented estimate and assigned as the two WL cancellation filters.

IV. PERFORMANCE SIMULATIONS AND EXAMPLES

Full-scale OFDM simulations compare widely-linear and traditional linear digital cancellation under varying analog attenuation, transmit power, filter length, and training duration. Widely-linear processing provides substantially greater cancellation, while PA-induced distortion, quantization, and estimation accuracy bound performance.

  • The simulations model a complete full-duplex transceiver with explicit RF nonidealities and realistic OFDM waveforms.Matlab simulations avoid simplifications regarding the modeled nonidealities.
  • The simulated SI channel contains a line-of-sight component and two weak multipath components delayed by one and two samples.The main component exceeds the total multipath power by 35.8 dB on average.
  • For higher analog attenuation, WL cancellation maintains approximately the ideal 15 dB SINR below 15 dBm, whereas linear cancellation declines steadily.
  • With 10 dB less analog attenuation, WL residual SI degrades SINR above 7 dBm, while the linear model reaches -5 dB at the lowest considered transmit power.PA-induced IMD and quantization noise contribute to the WL degradation.
  • WL processing achieves 35 dB or 50 dB more digital SI attenuation than linear processing, whose attenuation remains below 25 dB.Linear cancellation is limited by conjugate SI, whereas WL cancellation is limited by channel-estimate accuracy.
  • SINR shows no significant difference for filter lengths M ≥4 with at least 1000 training samples, and saturates near 3000 samples for the chosen parameters.Longer filters may be needed under different coupling-channel characteristics.
  • Digital attenuation saturates near 58 dB for N > 10000, while approximately 55 dB suffices below 15 dBm to suppress total SI below the noise floor.The saturation is mainly set by PA-induced IMD, which the WL least-squares model cannot represent.

V. CONCLUSION

The paper proposes widely-linear processing to compensate self-interference image components caused by transmitter and receiver IQ imbalances. Simulations show that this approach attenuates the image component digitally and improves full-duplex transceiver performance.

  • The proposed method compensates self-interference image components caused by IQ imbalances in the transmitter and receiver IQ mixers.
  • Widely-linear least-squares estimation and widely-linear digital cancellation attenuate the image component in the digital domain.The method prevents the decrease in SINR attributed to the image component.
  • Extensive full-waveform simulations demonstrate significant performance improvement for a typical full-duplex transceiver.

APPENDIX ANALYSIS OF BIAS

The appendix analyzes how nonlinear transmitter PA distortion affects widely-linear parameter estimation. Because the nonlinear distortion depends on the transmit-data regressors, it introduces estimator bias.

  • The augmented estimation model represents digital-baseband self-interference as linear, conjugate, nonlinear-IMD, and noise components.The simplified model is y_ADC(n) ≈ h_1x(n) + h_2x*(n) + h_IMDx_IMD(n) + u(n).
  • For large sample size N, the augmented regressor covariance is approximated by the ensemble augmented covariance matrix of transmit data.
  • Assuming second-order circular transmit data, the second-order complementary moment satisfies c = E[x(n)^2] = 0.
  • Dependence between the augmented regressors and nonlinear IMD makes the average estimation error nonzero, so the estimator is biased.The derivation additionally assumes fourth-order circular transmit data.
  • The nonlinear transmitter PA IMD causes bias in the estimator, reducing estimation accuracy.
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