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Rate Gain Region and Design Tradeoffs for Full-Duplex Wireless Communications

Elsayed Ahmed, Ahmed Eltawil, Ashutosh Sabharwal

arXiv:1303.1795v5cs.ITmath.IT

TL;DR

The paper asks when practical full-duplex can achieve higher rates than half-duplex despite uncancelled self-interference caused by the power differential between self-interference and the signal of interest. The paper models transmitter and receiver impairments and analytically derives a piecewise-linear, log-domain approximation of the full-duplex rate-gain region. For applications such as class-3 Bluetooth, −60dBc in-band phase noise combined with 40dB passive self-interference suppression could achieve a rate of ∼1.2x to ∼1.4x times that of half-duplex systems.

  • Problem

    The paper asks when practical full-duplex can achieve higher rates than half-duplex despite uncancelled self-interference caused by the power differential between self-interference and the signal of interest.

    Source: §I · p. 2

  • Method

    The paper models transmitter and receiver impairments and analytically derives a piecewise-linear, log-domain approximation of the full-duplex rate-gain region.

    Source: §VI · p. 28

  • Results

    For applications such as class-3 Bluetooth, −60dBc in-band phase noise combined with 40dB passive self-interference suppression could achieve a rate of ∼1.2x to ∼1.4x times that of half-duplex systems.

    Source: §VI · p. 29

  • Takeaways & Limitations

    The derived rate-gain region provides an analytical way to characterize where full-duplex outperforms half-duplex as received signal-of-interest strength varies.

    Source: §III · p. 12, §VI · p. 28

Abstract

from arXiv · show

In this paper, we analytically study the regime in which practical full-duplex systems can achieve larger rates than an equivalent half-duplex systems. The key challenge in practical full-duplex systems is uncancelled self-interference signal, which is caused by a combination of hardware and implementation imperfections. Thus, we first present a signal model which captures the effect of significant impairments such as oscillator phase noise, low-noise amplifier noise figure, mixer noise, and analog-to-digital converter quantization noise. Using the detailed signal model, we study the rate gain region, which is defined as the region of received signal-of-interest strength where full-duplex systems outperform half-duplex systems in terms of achievable rate. The rate gain region is derived as a piece-wise linear approximation in log-domain, and numerical results show that the approximation closely matches the exact region. Our analysis shows that when phase noise dominates mixer and quantization noise, full-duplex systems can use either active analog cancellation or base-band digital cancellation to achieve near-identical rate gain regions. Finally, as a design example, we numerically investigate the full-duplex system performance and rate gain region in typical indoor environments for practical wireless applications.

I. INTRODUCTION

The paper examines when imperfect full-duplex transmission can outperform half-duplex and models several hardware noise sources to analyze that question. It derives an approximate rate-gain region and uses it to identify system tradeoffs and indoor design requirements.

I. INTRODUCTION

  • The analysis models transmitter and receiver phase noise, LNA noise figure, mixer noise figure, and ADC quantization noise alongside passive suppression and active cancellation.It examines dominant noise components for analog and digital self-interference cancellation.Source: §I · pp. 2–4
  • The rate-gain region is the received signal-of-interest strength range where full-duplex outperforms half-duplex, approximated by a closed-form piecewise-linear relation in the log domain.The approximation is intended to reveal behavior across different operating conditions.Source: §I · pp. 3–4
  • The rate-gain region is inversely proportional to transmit power, so reducing transmit power makes full-duplex more likely to outperform half-duplex.The paper relates this trend to prior relay-system results.Source: §I · p. 4
  • With −60dBc in-band phase noise and 40dB passive suppression, full-duplex achieves about 1.2x–1.4x the half-duplex rate in typical indoor environments.The improvement also highlights design challenges involving strong passive self-interference suppression and low-noise restrictions.Source: §I · p. 4
  • The paper motivates a detailed impairment model because the dominant noise source can change with operating conditions, including when strong self-interference makes ADC quantization noise limiting.Small ADC bit counts can make this effect especially relevant; lower LNA gain also changes the noise-figure balance.Source: §I · p. 5

II. SIGNAL MODEL

The signal model represents narrowband full- and half-duplex operation with transmitter and receiver impairments. It also distinguishes analog from digital self-interference cancellation and states the channel knowledge assumptions used in the analysis.

II. SIGNAL MODEL

  • The modeled transceiver includes transmitter-side carrier up-conversion and phase error, followed by power amplification, and receiver-side gain adjustment and down-conversion.Nodes A and B are separated by distance D, and the model covers circulator-based systems using one antenna for transmission and reception.Source: §II · pp. 5–6
  • The model includes transmitter and receiver phase errors, receiver-circuit noise, and ADC quantization noise, with the ADC noise parameterized by its number of bits.The receiver chain down-converts the signal and then quantizes it using an m-bit ADC.Source: §II · pp. 6–7
  • The analysis assumes frequency-flat fading and perfectly known channel state information for all transmitter-receiver links at the receiver.The same analysis applies to both nodes because the model assumes hardware symmetry.Source: §II · pp. 6, 8
  • Digital cancellation removes self-interference after the signal passes through the radio section, while analog cancellation subtracts an up-converted baseband estimate before the LNA.Removing interference before the LNA allows it to operate at higher gain than in digital cancellation.Source: §II · p. 8

A. Digital cancellation scheme

Digital cancellation subtracts a reconstructed self-interference signal using knowledge of the interference channel. The resulting full-duplex SINR accounts for residual phase noise and receiver and quantization noise.

A. Digital cancellation scheme

  • Digital cancellation subtracts the self-interference signal reconstructed from the transmitted signal and interference channel in the digital domain.The remaining received signal still includes receiver noise and ADC quantization noise.Source: A. Digital cancellation scheme · p. 8
  • The digital-cancellation full-duplex SINR includes signal-of-interest power and residual phase-noise, receiver-noise, and quantization-noise terms.The phase-noise powers are calculated for self-interference and signal-of-interest components.Source: A. Digital cancellation scheme · pp. 9–10
  • The model calculates total phase-noise power by integrating its power spectral density over system bandwidth; the PSD depends on PLL architecture and design.The passage notes that precise phase-noise PSD is usually obtained by measurement of a fabricated PLL tuner.Source: A. Digital cancellation scheme · p. 9
  • Receiver and quantization noise powers depend on LNA gain, which the variable-gain amplifier sets according to received signal power at the LNA input.The model distinguishes a system noise floor independent of incoming signal power from a signal-power-dependent noise component.Source: A. Digital cancellation scheme · p. 10

B. Analog cancellation scheme

Analog cancellation removes self-interference before the LNA, allowing high-gain operation that reduces receiver and quantization noise. The resulting SINR differs from digital cancellation only in receiver and quantization noise power.

B. Analog cancellation scheme

  • The analog-cancellation SINR is formed from the residual signal after cancellation and the resulting impairment terms.The paper identifies AC as analog cancellation.Source: B. Analog cancellation scheme · pp. 10–11
  • The only SINR difference between digital and analog cancellation is the receiver and quantization noise power.Source: B. Analog cancellation scheme · p. 11
  • Analog cancellation removes self-interference before the LNA, which lets the LNA operate at high gain and reduces receiver and quantization noise.Receiver and quantization noise power are inversely proportional to LNA gain.Source: B. Analog cancellation scheme · p. 11

III. RATE GAIN REGION FOR DIGITAL AND ANALOG CANCELLATION SCHEMES

The paper defines the rate-gain region using per-link full-duplex rates exceeding their half-duplex counterparts, then derives the condition for that comparison. For digital cancellation, it approximates the region as piecewise linear in the log domain, with three regimes whose boundaries vary with system parameters.

III. RATE GAIN REGION FOR DIGITAL AND ANALOG CANCELLATION SCHEMES

  • The paper defines rate gain conservatively: each full-duplex communication link must exceed its own half-duplex rate.This avoids a sum-rate definition under which one link could lose rate even when the overall sum improves.Source: §III · pp. 12–13
  • The rate comparison reduces to SINR_FD^2 + 2SINR_FD > SNR_HD, which is used with the signal model to derive the rate-gain region.The derivation considers received signal-of-interest strength and supports other architectures with one full-duplex node communicating with two half-duplex nodes.Source: §III · pp. 12–13

A. Rate gain region for digital cancellation scheme

  • The digital-cancellation approximation is derived by solving the rate-gain inequality across operation regimes set by self-interference strength.The full expression includes system parameters and radio impairments, but its complexity makes behavior difficult to interpret without numerical simulations.Source: A. Rate gain region for digital… · pp. 14–15
  • The digital-cancellation rate-gain region has three distinct linear-trend regimes, and their boundaries change with system parameters.The piecewise-linear approximation is in the log domain.Source: A. Rate gain region for digital… · p. 14, Figure 3 · p. 15

1) Strong self-interference regime:

In the strong self-interference regime, self-interference-induced noise exceeds the receiver noise floor. The impairment factor combines phase, receiver, and quantization noise, whose components are typically much less than one in practical fabricated circuits.

1) Strong self-interference regime:

  • The strong regime assumes self-interference is high enough that its introduced noise exceeds the receiver noise floor: ηRSSIA > ζ.Equivalently, the passage gives RSSIA > ζ/η.Source: 1) Strong self-interference regime · p. 15
  • The impairment factor η combines phase, receiver, and quantization noise, and these components are typically much less than one in practical fabricated circuits.Source: 1) Strong self-interference regime · p. 15

2) Weak self-interference regime:

For analog cancellation, the rate-gain region is approximated piecewise and closely matches the unapproximated analysis except near regime transitions. The weak digital regime is defined by self-interference-induced noise below the receiver noise floor.

2) Weak self-interference regime:

  • The weak self-interference regime assumes ηRSSIA < ζ, so self-interference-induced noise is below the receiver noise floor.Source: 2) Weak self-interference regime · p. 16
  • Under the weak-regime assumptions, the authors derive a simplified digital rate-gain region from the preceding approximations.They state that an additional simplification condition contradicts the weak-regime condition when η is typically much less than one.Source: 2) Weak self-interference regime · p. 17

B. Rate gain region for analog cancellation scheme

  • For analog cancellation, the piecewise-linear rate-gain approximation follows the digital derivation using Equation (17) instead of Equation (10).The resulting approximation predicts where full-duplex outperforms half-duplex for given system parameters and operating conditions.Source: B. Rate gain region for analog… · pp. 17–18
  • The analog rate-gain approximation closely fits the unapproximated region, with a small 0–3 dBm error at transitions between operation regimes.Simulation closely matches the unapproximated analysis, validating the analysis.Source: B. Rate gain region for analog… · p. 18

IV. KEY OBSERVATIONS AND DESIGN TRADEOFFS

Analog cancellation reduces mixer and quantization noise, but its advantage depends on which impairment dominates: it matches digital cancellation when phase noise dominates and outperforms it when mixer or quantization noise dominates. A wider rate-gain region trades off passive suppression, hardware complexity, and transmission range.

  • Analog cancellation reduces mixer and quantization noise by removing most self-interference before the LNA, but it does not affect phase noise.Source: §IV · pp. 18–19
  • When phase noise dominates, analog and digital cancellation have identical rate-gain regions; when mixer or quantization noise dominates, analog cancellation performs better, sometimes at added hardware complexity.Analog cancellation's performance enhancement in the latter case comes with additional hardware.Source: §IV · pp. 19–20
  • The analog scheme is limited by phase noise, while the digital scheme is limited by the dominant component among phase, quantization, and mixer noise.Source: §IV · p. 20
  • A wide rate-gain region requires both lower self-interference and reduced analog-front-end noise, but passive suppression has limited mitigation and circuit noise reduction is challenging.Source: §IV · pp. 20–21
  • Reducing received self-interference expands the rate-gain region, but lowering transmit power to achieve this also reduces signal-of-interest power and transmission range.Source: §IV · p. 21
  • For a fixed rate-gain target, passive suppression and noise reduction can trade off; for analog cancellation, each x dB of extra suppression permits x dB higher phase noise.Source: §IV · pp. 21–22

V. NUMERICAL RESULTS

The numerical design analysis evaluates indoor full-duplex requirements against a −80dBm rate-gain target, including a Bluetooth example. Analog cancellation matches digital cancellation when phase noise dominates, but at −85dB phase noise and 10dBm transmit power it requires 8dB less passive suppression.

V. NUMERICAL RESULTS

  • The numerical analysis uses an indoor cluster-based channel model with log-normal shadowing and 2.4GHz, 1MHz system parameters reflecting industry-standard chipsets.Source: §V · pp. 22–23

A. Design requirements for feasible full-duplex transmission

B. Achievable Rate gain

The achievable-rate analysis finds full-duplex gains over half-duplex under specific signal and suppression conditions. At fixed distance, increasing transmit power reduces the full-duplex rate gain, while the full-duplex rate eventually saturates as residual self-interference limits SINR.

VI. CONCLUSION

The paper models key radio impairments and derives a piecewise linear, log-domain approximation of the rate-gain region for analog and digital self-interference cancellation. In typical indoor settings, the required phase-noise and passive-suppression levels depend on the application range.

  • The SISO narrowband full-duplex signal model captures transmitter and receiver phase noise, LNA and mixer noise figures, and ADC quantization noise.Source: §VI · p. 28
  • The model supports an analytical piecewise linear, log-domain approximation of the rate-gain region under analog and digital self-interference cancellation.Source: §VI · p. 28
  • The study examines full-duplex behavior across operating conditions to illustrate system design space, tradeoffs, and indoor design requirements for rate gains over half-duplex.Source: §VI · p. 28
  • For short-range class-3 Bluetooth, −60dBc in-band phase noise with 40dB passive self-interference suppression achieves about 1.2x–1.4x the half-duplex rate; class-1 requires −70dB phase noise with 50dB suppression for the same gain.Source: §VI · pp. 28–29
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