Digital Self-Interference Canceler

• Digital self-interference cancellation is a signal processing technique that subtracts transmitted leakage to enhance full-duplex communication.
• Adaptive algorithms such as LS, RLS, and NLMS estimate linear, multipath, and nonlinear SI impairments dynamically.
• Hybrid implementations using FPGA/ASIC and photonic-assisted methods balance complexity and performance to achieve high SI suppression.

A digital self-interference canceler is a signal processing subsystem in in-band full-duplex or simultaneous-transmit-and-receive (STAR) wireless systems, designed to regenerate and subtract the self-interference (SI) signal that results from the transmitter’s own emissions coupling into its receiver chain. The digital canceler operates downstream of any analog or photonic cancellation front-end and implements adaptive or algorithmic estimation of the SI path—including linear, multipath, and nonlinear impairments—using digital filtering, parameter estimation, and reference regeneration. The goal is to reduce the residual SI to below the noise floor or as close as possible, thereby enabling robust detection of the signal-of-interest (SOI) in the presence of strong co-located transmissions. Recent research has demonstrated architectures ranging from sampled-data H-infinity design and polynomial or orthonormal adaptive filtering to neural-network and photonic-assisted hybrid domains, with complexity-performance trade-offs governed by system bandwidth, SI dynamic range, and hardware constraints.

1. Signal and System Models for Digital SIC

The digital self-interference canceler targets the analog-to-digital converted baseband signal, which contains the composite SI as well as the SOI and noise. The canonical SI model takes the form:

$$r[n] = \sum_{p=1}^{P} \sum_{\ell=0}^{L-1} h_{p,\ell}(n)\, \phi_p(x[n-\ell]) + v[n]$$

where $x[n]$ is the known transmit baseband sequence, $\phi_p(\cdot)$ are polynomial (or, in some approaches, orthonormal) nonlinearity bases (e.g., $x$, $|x|^2x$, etc.), $h_{p,\ell}(n)$ are (possibly time-varying) SI channel coefficients, $P$ is nonlinearity order, $L$ is SI channel memory, and $v[n]$ models noise and unmodeled effects (Kim et al., 2023, Kristensen et al., 2019).

A matrix-vector compactification is used for batch or adaptive filtering:

$r[n] = \mathbf{w}^T(n)\, \mathbf{u}[n] + v[n]$

where $\mathbf{u}[n]$ is the stacked regressor of basis functions over taps and orders, and $\mathbf{w}(n)$ the adaptation vector.

Specific impairments such as IQ mixer imbalance, power amplifier nonlinearity, multipath propagation, and hardware imperfections are incorporated through expanded basis sets—typically comprising widely linear and higher-order monomials (Anttila et al., 2014, Balatsoukas-Stimming, 2017, Li et al., 2017).

2. Digital Cancelation Algorithms: Adaptive Filtering and Reference Construction

Central to digital self-interference cancelation is the adaptive estimation of SI channel parameters. The predominant methodologies include:

• Least Squares (LS) / Recursive Least Squares (RLS): Minimizing the exponentially weighted error cost $J(n) = \sum_{k=0}^n \lambda^{n-k} |e(k)|^2$ with forgetting factor $\lambda \leq 1$ yields fast-converging parameter estimates in both linear and nonlinear SI models. The RLS update equations are:

$$\begin{align*} K(n) &= P(n-1)\, x(n) \, / \, [\lambda + x^T(n)\,P(n-1)\,x(n)] \ e(n) &= d(n) - w^T(n-1)\,x(n) \ w(n) &= w(n-1) + K(n)\,e(n) \ P(n) &= (1/\lambda)[P(n-1) - K(n)\, x^T(n)\,P(n-1)] \ \end{align*}$$

(Han et al., 2021, Emara et al., 2017)

• Normalized LMS (NLMS) and Orthonormal Polynomial LMS: Standard and orthonormalized LMS algorithms are effective for both memory-polynomial and spatio-temporal bases. Adaptive orthonormalization yields robust convergence even with non-Gaussian or nonstationary transmit data (Kim et al., 2023).
• Total Least Mean Squares (MTLS): For jointly estimating SI and remote (SOI) channels under high dynamic-range or impulsive-noise scenarios, multi-layered M-estimate TLS is used, iteratively whitening SI contributions (Song et al., 2023).
• Photonic/Digital Hybrid Reference Construction: In photonic analog-cancellation architectures, a direct-path analog reference (for the strongest SI component) is combined with a digitally synthesized reference for weak multipath reflections, reconstructed adaptively via linear estimation (RLS/LS), and combined optically for pre-digitization cancellation (Han et al., 2021, Han et al., 2022).
• Reference Receiver Schemes: In MIMO radios, dedicated reference receiver chains tap the PA output, enabling analog-correct analog impairment capture (PA, IQ, etc.) and facilitating simple linear cancellation in DSP by estimating channel convolutions via LS (Korpi et al., 2014, Ahmed et al., 2014).

3. Hardware Architectures and Implementation Aspects

Implementations span both software-defined and hardware-accelerated platforms:

• FPGA/ASIC: Resource and energy efficiency are critical factors. Direct polynomial canceller implementations scale in complexity as $O(LP^2)$ (memory depth $L$, nonlinearity order $P$), often resulting in hundreds to thousands of real multiplications/additions per sample (Kurzo et al., 2020, Kurzo et al., 2018). Neural-network-based cancellers can realize equivalent cancellation with up to $8\times$ less area and $7\times$ less power, reducing per-sample arithmetic by $\sim$30–36% (Kristensen et al., 2019, Balatsoukas-Stimming, 2017, Kurzo et al., 2020).
• Hybrid Photonic/Electrical Realizations: Coherent photonic analog front ends, leveraging dual-drive or dual-parallel Mach-Zehnder modulators, provide wideband cancellation and RF-to-IF downconversion ahead of digital processing; digital blocks generate reference signals with adaptive LS/RLS, with experimental setups utilizing AWGs, high-speed ADCs (e.g., 8–12 bits, 10–64 GSa/s), and external control (Han et al., 2021, Han et al., 2022).
• ADC Dynamic Range: For high cancellation depth (≥90 dB) in multicarrier OFDM radios, 14-bit ADCs are commonly necessary, particularly when analog suppression is limited ($<50$ dB) (Kwak et al., 2019). At lower bit depths, architectures such as modulo ADCs (unlimited sensing framework) capture out-of-range SI waveforms via digital unfolding, enabling up to 40 dB SIC with 4–6 bits, provided proper modulo-domain channel estimation (Liu et al., 2024).
• Complexity Trade-off: For highly dynamic SI channels, RLS and model-based neural networks achieve near-optimal cancellation (>50 dB) at a fraction (1/1000×) the arithmetic complexity of full WLMP-RLS adaptive filters, given adequate retraining frequency (Kristensen et al., 2021).

4. Multi-Antenna and MIMO Extensions

Digital SIC in MIMO and multi-antenna full-duplex systems must manage self-crosstalk and impairment coupling across streams. The principal approaches include:

• Spatio-temporal Nonlinear Cancelers: Expand the SI model to account for multiplexed transmit/receive paths, IQ imbalance, and PA nonlinearity across antennas, typically leading to high-dimensional LS estimation problems over composite polynomial bases (Anttila et al., 2014).
• Reference Receiver MIMO Architectures: Each transmit stream is accompanied by a dedicated reference receiver that captures the impairment-rich output, and digital cancellation is performed via a block-Toeplitz formulation, with complexity limited to that of linear MIMO convolution (Korpi et al., 2014).
• Joint Age/Beamforming and Cancellation: Unified A/D cancellation designs optimize analog tap placement, digital beamforming, and joint channel estimation to render SI below ADC noise floors while minimizing hardware (Islam et al., 2019). Photonic multipath SIC can also be extended via LS with adaptive filter order to track channel delay spread under MIMO (Han et al., 2022).
• Far-field and Environmental SI: In distributed or multi-scatterer environments, DSIC leverages per-path least squares estimation and a scatterer map, dynamically updating delayed/angled SI components and choosing between spatial, digital, and inaction-based suppression according to communication-centric metrics (Kurt et al., 2024).

5. Nonlinear and Machine Learning Approaches

Residual SI components due to PA nonlinearity, IQ mismatch, DAC/ADC distortion, and hardware memory effects limit the effectiveness of classical linear-canceller paradigms. Recent directions include:

• Polynomial and Memory Polynomial Cancellers: Parallel Hammerstein or memory-polynomial models represent the SI as a sum of polynomial and delayed basis functions. Batch LS or adaptive LMS/RLS algorithms fit coefficients offline or online, enabling up to 45 dB digital SIC in standard OFDM radios (Kristensen et al., 2019, Kwak et al., 2019).
• Neural Network Cancellers: Small feedforward or complex-valued neural networks are trained (typically after linear cancellation) to reconstruct nonlinear SI residues, achieving the same or superior cancellation depths (44–45 dB) as memory-polynomial models, but with $\sim$30% fewer arithmetic operations and parameters in inference (Kristensen et al., 2019, Balatsoukas-Stimming, 2017, Kurzo et al., 2018). Hardware-efficient neural networks attain $>37$ dB digital SIC at up to $2\times$-better energy efficiency vs. polynomial approaches (Kurzo et al., 2020).
• Data-Driven and Model-Free Methods: Deep neural networks and kernel methods are explored for SI channel modeling under time-varying and nonstationary conditions; however, these typically carry higher training complexity and require substantial offline data. Adaptive orthonormal polynomial LMS (AOP-LMS) approaches maintain optimal performance with $O(M)$ computational complexity and robust convergence under arbitrary symbol distributions (Kim et al., 2023).

6. Performance Limits, Trade-offs, and Practical Guidelines

Performance is fundamentally constrained by hardware impairments, quantization, incomplete SI modeling, and environmental factors:

• Maximum Cancellation Depth: Integrated analog plus digital chains consistently achieve 90–110 dB total SI suppression with a judicious balance of analog cancellation ($\sim$40–70 dB) and digital cancellation ($\sim$30–50 dB) (Kwak et al., 2019, Emara et al., 2017). For challenging nonlinear SI, the digital chain's performance is bottlenecked by PA nonlinearity and quantization.
• Computational and Hardware Limits: Complexity grows cubically in polynomial model order and linearly to quadratically with the number of RF taps, antennas, or SI channel memory. Efficient implementations, including neural networks and photonic analog cancellation, are essential for high-datarate, wideband, or low-power operation (Kristensen et al., 2021, Kurzo et al., 2020).
• Adaptive and Hybrid Schemes: Adaptive algorithms, especially RLS and AOP-LMS, are necessary in time-varying SI environments; batch LS suffices for quasi-static cases (Kim et al., 2023). Photonic or analog front-end cancellation relieves ADC and DSP requirements but increases hardware complexity and alignment burden.
• Specialized Scenarios: In applications with strong multipath or phase noise, such as relay stations or environmental scatterers, multichannel or multi-tap reference architectures and robust adaptive algorithms (e.g., sampled-data H-infinity design, masked NLMS banks, multi-path photonic cancellation) are required to avoid residual error floors (Sasahara et al., 2015, Ferrand et al., 2017, Han et al., 2021, Kurt et al., 2024).
• Reference Receiver and All-Digital Approaches: Digital cancelers leveraging impairment-rich reference receiver paths, sharing common local oscillators, and implementing per-subcarrier LS channel estimation, robustly suppress SI to within ≃3 dB of the noise floor, even at high transmit power, with up to 76% throughput gains over conventional half-duplex operation (Ahmed et al., 2014, Korpi et al., 2014).

7. Comparative Assessment and Current Challenges

Digital self-interference cancellation, whether combined with analog/photonic SIC or implemented purely in DSP, is a multi-dimensional design space featuring strong trade-offs among cancellation depth, hardware and computational complexity, adaptability, and environmental robustness. Innovative architectures—including photonic-assisted, neural network-based, reference receiver-based, and orthonormal/adaptive filter approaches—push the boundaries in full-duplex, in-band MIMO and STAR systems, but ongoing limitations persist in real-time high-dynamic range adaptation, environmental non-stationarity, joint SOI/SI estimation, and scalable hardware realization. State-of-the-art systems routinely achieve $>$90 dB total SI cancellation, but realization at GHz bandwidths and in dense multipath continues to challenge both analog and digital SIC techniques (Han et al., 2021, Kristensen et al., 2019, Kim et al., 2023, Kurzo et al., 2020, Anttila et al., 2014, Kurt et al., 2024, Korpi et al., 2014).