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Full-Duplex Transceiver System Calculations: Analysis of ADC and Linearity Challenges

Dani Korpi, Taneli Riihonen, Ville Syrjälä, Lauri Anttila, Mikko Valkama, Risto Wichman

arXiv:1401.3538v3cs.ITcs.ET

TL;DR

The paper addresses limited understanding of nonlinear and ADC-related nonidealities in full-duplex transceivers. It develops component-wise system calculations incorporating self-interference cancellation and validates them with waveform simulations. The results identify PA nonlinearity, receiver nonlinearities with low-cost components, and ADC quantization noise as important constraints.

  • Problem

    Limited knowledge of full-duplex transceiver-chain nonlinearities and ADC dynamic-range requirements leaves practical self-interference-limited devices insufficiently characterized.

  • Method

    The paper combines component properties into complete transceiver system calculations covering RF and digital self-interference cancellation, transmitter and receiver nonlinearities, and ADC effects.

  • Results

    PA nonlinearity is a significant issue; receiver nonlinearities become considerable with cheaper, less-linear components; and ADC quantization noise becomes significant with digitally intensive cancellation.

  • Takeaways & Limitations

    Full-duplex design must account for transmitter and receiver linearity together with ADC dynamic range, and nonlinear digital cancellation is motivated for low-cost RF electronics.

Abstract

from arXiv · show

Despite the intensive recent research on wireless single-channel full-duplex communications, relatively little is known about the transceiver chain nonidealities of full-duplex devices. In this paper, the effect of nonlinear distortion occurring in the transmitter power amplifier (PA) and the receiver chain is analyzed, alongside with the dynamic range requirements of analog-to-digital converters (ADCs). This is done with detailed system calculations, which combine the properties of the individual electronics components to jointly model the complete transceiver chain, including self-interference cancellation. They also quantify the decrease in the dynamic range for the signal of interest caused by self-interference at the analog-to-digital interface. Using these system calculations, we provide comprehensive numerical results for typical transceiver parameters. The analytical results are also confirmed with full waveform simulations. We observe that the nonlinear distortion produced by the transmitter PA is a significant issue in a full-duplex transceiver and, when using cheaper and less linear components, also the receiver chain nonlinearities become considerable. It is also shown that, with digitally-intensive self-interference cancellation, the quantization noise of the ADCs is another significant problem.

I. INTRODUCTION

Full-duplex transceivers face strong self-interference and component nonidealities that complicate practical realization. The paper analyzes transmitter and receiver nonlinearities, RF and digital cancellation, and ADC dynamic-range requirements.

  • Practical challenges: Self-interference can be 60–100 dB stronger than the received signal of interest, especially near receiver sensitivity.Unknown coupling channels and nonlinear component effects make perfect cancellation unrealistic in practice.
  • Practical challenges: Nonlinear distortion is a significant bottleneck in practical full-duplex radios, particularly with low-cost integrated circuits.Receiver RF components must tolerate high-power self-interference that is gradually suppressed through the receive chain.
  • Paper scope: The paper provides component-wise system calculations covering transmitter and receiver nonlinearities, RF and digital cancellation, and detector-input distortion.The analysis derives explicit second- and third-order distortion powers for essential RF components.
  • Key findings: PA nonlinearity can limit operation at transmit powers of 5–10 dBm, especially when the RF-cancellation reference is taken from the PA input.This makes transmitter-chain linearity a major design concern alongside receiver-chain linearity.
  • Key findings: Digital cancellation requires additional ADC dynamic range because residual self-interference can reduce the effective resolution of the weak desired signal.The paper derives ADC requirements so detector-input SINR stays within a specified implementation margin.

A. Analysis Principles and Performance Measures

The analysis evaluates two principal receiver interfaces: the ADC input, where self-interference affects quantization and effective resolution, and the detector input, where residual interference and distortion determine overall SINR.

  • ADC input: The ADC input is analyzed through SINR, quantization noise, and the dynamic-range allocation among desired signal, self-interference, noise, and distortion.Automatic gain control keeps total ADC input power fixed, so stronger self-interference leaves less effective resolution for the desired signal.
  • Detector input: The detector input provides the overall receiver-performance measure after digital self-interference cancellation.At this interface, self-interference is attenuated and quantization noise can become a significant remaining distortion component.
  • Modeling assumptions: All distortion types are modeled additively, and the analytical approach is later checked against full waveform simulations.The additive model is used for transceiver system calculations and is reported to have good accuracy in later validation.
  • System calculations: The SINR expressions combine receiver gain, desired-signal power, thermal noise, antenna attenuation, RF cancellation, transmit power, PA distortion, and receiver nonlinearities.The second- and third-order receiver distortion powers are accumulated at the relevant interface.
  • Reference performance: Receiver sensitivity is defined from thermal noise, receiver noise figure, bandwidth, and detector SNR requirement.The study uses two reference sensitivity values for its numerical examples.

2) RF Cancellation:

The paper compares RF-cancellation reference signals taken from the PA output or input and quantifies how self-interference affects ADC resolution and digital cancellation.

  • RF cancellation: A multi-tap RF-cancellation circuit uses fixed delay lines with adjustable weights to suppress self-interference before the receiver chain.The analysis considers antenna attenuation and RF cancellation as distinct contributors to self-interference suppression.
  • Case A: Case A takes the RF-cancellation reference from the PA output, but requires a bulky attenuator to match the incoming self-interference level.The attenuation is selected according to the estimated path loss between transmit and receive antennas.
  • Case B: Case B takes the reference from the PA input, avoiding the additional RF attenuator but leaving PA-generated nonlinear distortion outside RF cancellation.That uncancelled distortion produces lower analog-domain SINR and also represents scenarios using a separate low-power TX reference chain.
  • ADC quantization: ADC signal-to-quantization-noise ratio depends on ADC bit width and estimated peak-to-average power ratio under proper AGC without clipping.The expression assumes the ADC’s full range is used while signal peaks remain unclipped.
  • ADC quantization: Self-interference bit loss is determined by how far the desired signal lies below total ADC-input power, with 6.02 dB representing one bit of dynamic range.The resulting bit loss increases with transmit power and decreases with antenna attenuation or RF cancellation, independently of total ADC bits.
  • Digital cancellation: Digital cancellation subtracts a linearly filtered estimate of the transmitted waveform using an estimate of the overall TX-to-RX coupling channel.The channel estimate includes transmitter, antenna-coupling, and receiver effects.

D. Nonlinear Distortion in Receiver Chain

The paper models receiver-chain and transmitter-PA nonlinearities, quantization noise, and signal components at the detector input to assess full-duplex transceiver behavior.

  • Receiver-chain nonlinear distortion: IIP2 and IIP3 model second- and third-order nonlinear distortion in receiver components such as the LNA, mixers, and baseband VGA.The component model uses input-referred intercept points and analytically accumulates distortion across the chain.
  • PA-induced distortion: Linear digital cancellation suppresses neither transmitter-PA nonlinear distortion nor distortion absent from its digital reference, while RF cancellation may attenuate it.Further nonlinear cancellation is outside the paper’s scope.
  • Accumulated detector-input powers: The detector-input power accounting includes the desired signal, residual self-interference, quantization noise, thermal noise, receiver nonlinearities, and transmitter-PA distortion.These components are combined after applying the relevant gains, cancellation, and coupling effects.
  • Quantization noise: ADC quantization noise depends on the ADC maximum input power and bit count for a given peak-to-average power ratio.Ptarget denotes the maximum average ADC-input power allowed to avoid clipping.
  • Receiver gain and self-interference: At high transmit powers, self-interference can dominate the receiver input, allowing total receiver gain to be approximated from self-interference power.Near sensitivity, self-interference is described as several orders of magnitude stronger than other signal components.
  • Receiver gain and self-interference: For high transmit powers, the linear self-interference power at the detector is approximated by PSI = Ptarget − Adig.This follows when the receiver gain is approximated using the self-interference-dominated input power.

III. SYSTEM CALCULATIONS AND RESULTS

The system calculations combine component models under a sensitivity-level received-signal assumption and evaluate quantization noise, nonlinear distortion, and full-duplex SINR loss.

  • System-calculation scope: The analysis targets the challenging case in which the received signal is only slightly above receiver sensitivity.It examines how ADC quantization noise and nonlinear distortion affect overall transceiver performance.
  • Performance criterion: A 3 dB SINR-loss threshold defines the maximum tolerable full-duplex degradation relative to half-duplex operation.The threshold is reached when effective noise-plus-interference power more than doubles.
  • Performance interpretation: At low SINR loss, full-duplex operation can approximately double spectral efficiency, whereas high SINR loss can reduce effective spectral efficiency below half-duplex performance.The paper uses the 3 dB point as indicating continued capacity gain over half-duplex operation.
  • Scope boundary: A detailed system- or network-level comparison of practical half-duplex and full-duplex radios under implementation impairments is outside the paper’s scope.The passage identifies this analysis as possible future work.

A. Parameters for Numerical Results

The numerical analysis uses two transceiver parameter sets, representative of modern performance and a more challenging lower-linearity scenario, to evaluate receiver, transmitter, cancellation, and ADC behavior.

  • System and component parameters: Two parameter sets model state-of-the-art wideband performance and a more challenging scenario with lower received power, decreased linearity, and slightly weaker SI cancellation.Parameter Set 1 is used for most of the analysis because it better represents modern transceiver bandwidth and linearity.
  • System and component parameters: Parameter Set 1 has receiver sensitivity Psens = −88.9 dBm, while Parameter Set 2 has Psens = −100.1 dBm.For Parameter Set 2, the received signal is assumed to be close to sensitivity; for Parameter Set 1, it is assumed to be 5 dB above sensitivity.
  • System and component parameters: The assumed antenna isolation and RF cancellation are both 40 dB for Parameter Set 1, with the RF value described as optimistic for a single-tap canceller but feasible for multi-tap cancellation.The passage states that similar antenna-isolation values have been reported and that multi-tap circuits can achieve RF cancellation of this magnitude.
  • Receiver and transmitter models: The receiver model uses typical component parameters and yields total IIP2 = 10.8 dBm and IIP3 = −17.1 dBm for Parameter Set 1, versus IIP2 = 10.8 dBm and IIP3 = −20.1 dBm for Parameter Set 2.The component values are selected to obtain reliable and feasible results for the direct-conversion receiver chain.
  • Receiver and transmitter models: The ADC model assumes VGA-controlled full-range utilization, 10 dB PAPR, and SNRADC = 6.02b − 5.24 for b ADC bits.The transmitter model includes only third-order nonlinear distortion because second-order products do not fall within the actual signal band.
  • Results with Case A: With Parameter Set 1 and Case A, the maximum transmit power is approximately 15 dBm, where SI becomes equal to thermal noise and causes more than 3 dB SINR loss beyond that point.Case A takes the RF-cancellation reference after the PA, so PA-generated nonlinear distortion is included in the RF reference and attenuated by RF cancellation.
  • Results with Case A: Approximately 3 ADC bits are lost to SI at 15 dBm, increasing to 4 bits at 20 dBm; higher transmit powers therefore require a high-bit ADC.At maximum transmit power, quantization noise is almost 10 dB lower than the SI-related limitation in this scenario.

2) Variable Amount of Digital Cancellation and Pushing the Performance Limits:

The analysis varies digital cancellation to identify when self-interference, ADC quantization noise, or nonlinear distortion limits full-duplex performance. For Parameter Set 1, digital cancellation requirements and ADC resolution determine the maximum transmit power before nonlinearities become dominant.

  • Digital cancellation limits: Arbitrarily increasing digital cancellation can remove the remaining linear self-interference, but quantization noise and nonlinearities may still prevent the required SINR.The analysis uses this assumption to expose the limits of DSP-based cancellation.
  • Digital cancellation limits: Increasing antenna separation or RF cancellation decreases the required amount of digital cancellation.
  • Digital cancellation limits: Approximately 23 dBm is the maximum transmit power for Parameter Set 1 while sustaining a 3 dB SINR loss through linear digital cancellation.Beyond this point, the required digital cancellation tends toward perfect linear cancellation, while quantization noise and nonlinearities limit SINR.
  • ADC and distortion limits: Quantization noise becomes limiting at higher transmit powers because digitally cancelled self-interference occupies most of the ADC dynamic range and reduces desired-signal resolution.
  • ADC and distortion limits: 25.02 dBm is the nonlinear-distortion-limited maximum transmit power for Parameter Set 1 when ADC quantization noise is negligible.The corresponding value for Parameter Set 2 is 10.29 dBm.
  • ADC and distortion limits: A 10-bit ADC is sufficient for Parameter Set 1 to make quantization noise negligibly low, after which maximum transmit power saturates at the nonlinear-distortion limit.Further improvement requires more linear components or greater analog SI attenuation.

3) Calculations with Parameter Set 2:

Parameter Set 2 models cheaper, less linear receiver components with weaker RF cancellation and a 12-bit ADC. Receiver nonlinear distortion, rather than quantization noise, becomes the principal transmit-power limitation.

  • Parameter assumptions: Parameter Set 2 assumes 20 dB RF cancellation, reduced bandwidth and SNR requirement, and a 12-bit ADC to preserve desired-signal resolution.
  • Performance limits: Approximately 10 dBm is the maximum transmit power for Parameter Set 2 because receiver nonlinear distortion limits the required SINR.After this point, mitigating only linear self-interference cannot sustain the required SINR.
  • Performance limits: Lower analog/RF SI cancellation substantially increases lost ADC bits because more self-interference reaches the ADC interface.
  • Performance limits: Parameter Set 2 achieves about 10 dBm versus 25 dBm for Parameter Set 1, with the difference attributed to lower receiver linearity and reduced RF cancellation.

C. Results with Case B

Case B takes the RF-cancellation reference before the PA, so PA-generated nonlinear distortion is not attenuated. The results show that PA distortion limits transmit power and that nonlinear digital cancellation can substantially improve performance.

  • Case B setup: In Case B, the RF-cancellation reference is taken from the PA input, leaving PA-generated nonlinear distortion unattenuated by RF cancellation.
  • Case B results: PA nonlinear distortion becomes the most significant distortion component above 11 dBm transmit power.
  • Case B results: Mitigating nonlinear as well as linear self-interference digitally can significantly increase maximum transmit power compared with linear cancellation alone.The comparison varies total digital cancellation and PA IIP3.
  • Case B results: At 25 dB digital cancellation, nonlinear digital cancellation increases maximum transmit power by as much as 5 dB.The gain is smaller with a more linear PA and remains significant for a less linear PA.
  • Implications: The findings motivate nonlinear estimation and processing mechanisms for future digital self-interference cancellation.

IV. WAVEFORM SIMULATIONS AND COMPARISONS

The paper validates its analytical full-duplex transceiver calculations with a complete waveform simulator and examines how cancellation, transmit power, and nonlinearities affect operation. The comparisons show strong agreement while identifying practical limits from PA distortion, receiver nonlinearities, and ADC quantization noise.

  • Waveform simulator: The Matlab/Simulink simulator models a direct-conversion full-duplex transceiver with parameters corresponding to Parameter Set 1.It uses the SimRF component library and considers Case A for compactness.
  • Waveform simulator: The simulated OFDM waveform uses parameters essentially similar to WLAN specifications for generating transmitted and received signals.
  • Cancellation model: Digital cancellation estimates the SI coupling channel by linear least-squares fitting between ideal TX data and RX observations during calibration.Its achievable amount depends on channel-estimation accuracy rather than being freely tunable.
  • Cancellation model: Higher transmit power improves digital cancellation through stronger SI-based channel estimates, but above 17 dBm PA-induced distortion reduces the achievable cancellation.
  • Analytical validation: The analysis compares SINR at the detector input from analytical calculations and full waveform simulations.The simulator derives SINR from effective ideal-signal and total noise-plus-interference powers.
  • Practical limitations: With PA-output RF reference, quantization noise and achievable linear digital cancellation limit operation for high-quality components, while low-cost components make chain nonlinearities considerable.With PA-input reference, PA linearity becomes the major bottleneck above 10 dBm; the findings motivate nonlinear digital SI cancellation for 20–30 dBm terminals.

APPENDIX A DERIVATION OF BIT LOSS DUE TO SI

This appendix derives the loss of ADC resolution attributable specifically to self-interference by comparing full-duplex and half-duplex operation under automatic gain control. The resulting expression relates bit loss to signal, noise, and SI-dependent receiver gain.

  • Derivation: Bit loss due to SI is obtained by subtracting the bits lost under HD operation from those lost under FD operation.
  • Derivation: Because AGC keeps total ADC-input power constant, the derivation expresses SI-related bit loss using the desired-signal powers under FD and HD operation.Ptarget is the constant total ADC-input power, while PSOI,FD and PSOI,HD denote desired-signal powers with and without SI.
  • Gain formulation: The bit-loss expression can be written in terms of the total receiver-chain gains GFD and GHD under FD and HD operation.The gain reduction under FD operation incorporates SI through AGC.
  • Power formulation: The derivation introduces SI and PA-distortion input powers through pSI,in = ptx aantaRF and p3rd,PA,in = p3rd,PA,tx.

APPENDIX B DERIVATIONS OF RECEIVER NONLINEAR DISTORTION

The appendix derives cumulative receiver nonlinear-distortion powers by combining component-level distortion with subsequent receiver gains. It distinguishes the components producing in-band second-order distortion from those producing third-order distortion and verifies the approximations numerically.

  • Distortion model: Only the mixer and VGA are assumed to produce SI-induced in-band second-order distortion, whereas all receiver components produce third-order distortion.
  • Distortion model: The derivation expresses receiver input power as the sum of signal of interest, self-interference, and thermal noise while omitting receiver-generated thermal-noise increase.The omission is justified because it has no significant effect on nonlinear-distortion power.
  • Component derivations: The mixer and VGA derivations calculate second- and third-order nonlinear-distortion powers from their component input powers and nonlinear characteristics.
  • Cumulative distortion: Total second- and third-order receiver distortion is obtained by summing each component’s output distortion after accounting for the gains of subsequent components.
  • Approximation check: 0.7% error is observed above 5 dBm when the derived equations are compared with calculations without approximations.The stated error indicates that the approximations have no notable effect on equation reliability for the chosen parameter range.
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