Flexible Analog Self-Interference Cancellation for Waveform-Robust Monostatic ISAC

I. INTRODUCTION

• Monostatic ISAC must suppress direct leakage and nearby SI, which can be orders of magnitude stronger than sensing echoes, without removing useful delayed echoes.An uncontrolled analog cancellation span can also remove weak static or quasi-static echoes.Source: §I · p. 1
• Prior analog cancelers generally target cancellation depth rather than the delay-span selectivity needed to remove nearby SI while preserving delayed sensing echoes.The paper also notes that waveform design and SIC have largely evolved separately, leaving waveform-statistics effects insufficiently characterized.Source: §I · p. 2
• FASIC digitally generates a cancellation signal for RF-domain subtraction, and WL-NLMS scales adaptation by instantaneous reconstruction-input energy for stability across waveforms.The analysis distinguishes second-order impropriety, accommodated by the widely linear structure, from PAPR-driven high-order moments that govern residual nonlinear SI.Source: §I · p. 2
• Approximately 30–34 dB of stable analog SIC was achieved across four waveform candidates, with low-PAPR waveforms reaching about 3.3 dB deeper SIC.The comparison used a common cancellation architecture, PA model, and passive-suppression level.Source: §I · p. 2

A. Transmit Signal and RF Front-End Model

• The RF-front-end model includes mixer I/Q imbalance and PA nonlinear distortion, while the receiver input also includes sensing echoes, possible uplink communication, and noise.The PA distortion is modeled with a baseband-equivalent parallel Hammerstein model.Source: A. Transmit Signal and RF Front-End… · p. 3

B. Nonlinear SI Model and Basis Expansion

• The self-interference channel applies to the PA output, and the resulting SI is represented through an expanded memory polynomial in the original transmit signal.The effective direct and conjugate responses collect transmitter IQI, PA nonlinearity, and SI-channel effects.Source: B. Nonlinear SI Model and Basis… · p. 3

A. FASIC With WL-NLMS Over the OEMP Basis

• FASIC uses an orthogonal EMP basis and widely linear reconstruction to cancel SI before the receiver front end while configuring the canceled delay range.The orthogonal mapping addresses strong correlation among raw EMP basis functions, which can degrade adaptive-reconstruction conditioning.Source: A. FASIC With WL-NLMS Over the OEMP… · pp. 3–4
• WL-NLMS replaces the fixed step with normalization by instantaneous augmented-regressor energy to address energy variation in high-PAPR waveforms.The normalized step includes a dimensionless adaptation-rate constant and a small regularizer.Source: A. FASIC With WL-NLMS Over the OEMP… · p. 4
• The filter length sets the cancellation span: static echoes within it are suppressed, while echoes beyond it and Doppler-shifted moving-target echoes are preserved.The span should cover the SI channel while remaining shorter than the delay of the nearest static reflector to preserve.Source: A. FASIC With WL-NLMS Over the OEMP… · p. 4

B. Mean Behavior and Stability of the Adaptive Recursion

• Under the stated small-step and disturbance assumptions, the expected weight error follows a recursion governed by the augmented correlation matrix.The disturbance may include receiver noise, far-end signals, finite-basis mismatch, and sensing echoes outside the cancellation subspace.Source: B. Mean Behavior and Stability of the… · p. 5
• The fixed-step mean-stability condition depends on the largest eigenvalue of the augmented correlation matrix, which scales with high-order transmit-envelope moments.Consequently, a step size stable for a low-PAPR waveform can violate the condition for a high-PAPR waveform.Source: B. Mean Behavior and Stability of the… · p. 5
• With finite augmented-regressor energy, the normalized update has a mean-stable step-size range not set by the largest eigenvalue, removing PAPR sensitivity at the mean-stability level.Waveform statistics can still affect convergence through correlation-matrix conditioning, particularly the pseudo-correlation block coupling direct and conjugate branches.Source: B. Mean Behavior and Stability of the… · p. 5
• Second-order properness alone does not eliminate higher-order pseudo-correlation, while perfect non-circularity can make direct and conjugate branches collinear and leave a weight-error direction unidentifiable.When complementary correlation is near zero, the augmented matrix approximately decouples into direct and conjugate covariance blocks.Source: B. Mean Behavior and Stability of the… · pp. 5–6

• EMSE measures the residual penalty from finite-step-size adaptation and therefore determines the attainable SIC floor.Source: C. Steady-State EMSE and Covariance… · p. 6
• The covariance recursion uses a circular-Gaussian reference closure, omitting an augmented-regressor complementary term that is O(µ2) and dropped in the first-order analysis.Source: C. Steady-State EMSE and Covariance… · p. 6
• Steady-state energy conservation also recovers the first-order floor without requiring a Gaussian regressor model.The derivation balances mean weight-error energy before and after an update.Source: C. Steady-State EMSE and Covariance… · p. 6
• Fourth-order regressor statistics enter only an O(µ2) term, whose neglect recovers the first-order result independently of the Gaussian approximation.Source: C. Steady-State EMSE and Covariance… · p. 6
• Under A4, replacing the instantaneous data-dependent step with an effective step approximates WL-NLMS by a fixed-step recursion to first order.The effective step slightly underestimates the mean instantaneous step, especially for heavy-tailed high-PAPR regressors.Source: C. Steady-State EMSE and Covariance… · p. 7
• The WL-NLMS first-order steady-state floor is waveform-independent, depending on the dimensionless step size and uncancelable disturbance; waveform statistics affect conditioning and convergence speed.Source: C. Steady-State EMSE and Covariance… · p. 7

D. Amplitude Moments and Nonlinear SI Power

• Low-PAPR envelopes have γp < 1 at high orders, near-Gaussian high-PAPR waveforms have γp ≈ 1, and their moment separation grows with p.For the Gamma envelope-power model, m = 1 gives γp = 1; larger m produces more concentrated, lower-PAPR envelopes, with separation exceeding an order of magnitude by the fifth order.Source: D. Amplitude Moments and Nonlinear SI… · p. 7, Figure 2 · p. 7
• The highest retained moment γP is the most sensitive indicator of waveform-dependent nonlinear SI under finite-order, finite-tap reconstruction.The normalized amplitude moment γp provides an order-resolved measure of how envelope distribution feeds nonlinear PA orders.Source: D. Amplitude Moments and Nonlinear SI… · p. 7
• The waveform-dependent factor γp also dominates the diagonal energy of the raw basis Gram matrix under common pulse shaping and power normalization.Each raw component of order p has magnitude |x[n]|^p, so its power is governed by E{|x[n]|2p}.Source: D. Amplitude Moments and Nonlinear SI… · p. 7
• Under common power normalization, γ1 = 1 leaves linear SI unchanged, while nonlinear-order power and basis energy vary with the corresponding γp moments.The raw basis branches of order p share the same envelope moment; the dominant scaling omits cross-terms between memory taps and basis branches.Source: D. Amplitude Moments and Nonlinear SI… · pp. 7–8

IV. WAVEFORM CANDIDATES AND THEIR SUITABILITY FOR SIC

• Four candidate waveforms are studied under a common bandwidth and average-power normalization.Source: §IV · p. 8
• The assessment focuses on waveform suitability for analog SIC.Source: §IV · p. 8
• Complementary correlation and high-order amplitude moments are identified as the waveform statistics most relevant to analog SIC.Source: §IV · p. 8

A. Candidate Waveforms

• SC directly pulse-shapes QPSK symbols, and its envelope variation makes it the low-PAPR reference.Its envelope variation is mainly determined by RRC pulse shaping and oversampling.Source: A. Candidate Waveforms · p. 8
• OFDM applies an inverse DFT to data symbols; as active subcarriers increase, its samples approach a circular complex Gaussian distribution associated with high PAPR.Source: A. Candidate Waveforms · p. 8
• The considered CP-OTFS implementation maps delay-Doppler symbols through time-frequency processing and CP-OFDM, giving it multicarrier-like envelope statistics.Source: A. Candidate Waveforms · p. 8
• Chirped DFT-s-OFDM uses DFT spreading to reduce PAPR relative to OFDM, while its unit-modulus chirp changes phase without changing the instantaneous envelope.Source: A. Candidate Waveforms · p. 8

B. Properness of the Candidate Waveforms

• For a zero-mean complex variable, κ(z) = |E{z2}|/E{|z|2}, with κ(z) = 0 denoting second-order properness.Source: B. Properness of the Candidate Waveforms · p. 8
• Deterministic linear transforms preserve the properness condition E{xxT} = 0 for a proper data vector.The described transforms include those used in OFDM, OTFS, and chirped DFT-s-OFDM; SC satisfies the condition through linear pulse shaping.Source: B. Properness of the Candidate Waveforms · p. 8
• All four candidate waveforms share second-order properness, which therefore does not distinguish their expected SIC behavior.Source: B. Properness of the Candidate Waveforms · p. 8

C. Envelope Statistics and SIC Prediction

• The highest retained moment γP governs the waveform-dependent SIC floor because nonlinear SI outside the finite-order, finite-tap basis remains uncanceled.The residual floor also includes uncancelable disturbance and the WL-NLMS adaptation-induced EMSE floor; the latter is waveform-independent to first order.Source: C. Envelope Statistics and SIC… · p. 9
• Low-PAPR SC and chirped DFT-s-OFDM have smaller high-order moments than OFDM and OTFS, reducing nonlinear SI exposed to finite-basis mismatch.DFT spreading gives chirped DFT-s-OFDM a single-carrier-like envelope, and its unit-modulus chirp preserves that envelope.Source: C. Envelope Statistics and SIC… · pp. 8–9

V. SIMULATION RESULTS

• The evaluation compares SC, OFDM, OTFS, and chirped DFT-s-OFDM using FASIC with WL-NLMS.It examines waveform statistics, analog SIC depth, sensing preservation, and cancellation-span flexibility.Source: §V · p. 9
• All four waveforms use the same analog canceler, hardware impairments, passive suppression, and adaptation parameters.This common configuration is intended to attribute performance differences to waveform statistics rather than waveform-specific tuning.Source: §V · p. 9
• The validation proceeds from waveform statistics to SIC depth, then assesses sensing preservation and cancellation-span flexibility.Source: §V · p. 9

A. Simulation Setup

• The simulations use identical bandwidth and average-power constraints, QPSK, and 50 independent Monte Carlo realizations for averaged SIC depth, PAPR, and normalized amplitude moments.The common canceler uses WL-NLMS with µ = 0.5 and L = 24 half-symbol-spaced taps, with no waveform-specific parameter tuning.Source: A. Simulation Setup · p. 9

B. Waveform Statistics

• SC and chirped DFT-s-OFDM have about 4 dB lower PAPR than OFDM and OTFS at the 99.9% CCDF point, and the two low-PAPR waveforms have nearly the same PAPR.All four candidates are nearly proper after waveform generation; their shared RF front-end raises impropriety to approximately κ ≈ 0.15–0.16, while their high-order moments differ substantially.Source: B. Waveform Statistics · pp. 9–10
• At order five, γ5 ≈ 0.035 for SC and chirped DFT-s-OFDM, about 15 dB below OFDM and OTFS, compared with roughly 4 dB separation in PAPR.The order-resolved moments distinguish waveform envelope statistics more sharply than PAPR, which captures only the envelope tail.Source: Figure 3 · p. 9, B. Waveform Statistics · p. 10

C. SIC Depth

• Approximately 33.9 dB SIC is achieved by SC and chirped DFT-s-OFDM, versus 30.3–30.9 dB for OFDM and OTFS; the low-PAPR group is about 3.3 dB deeper.The single FASIC configuration yields more than 30 dB cancellation beyond passive suppression for all four waveforms, without waveform-specific tuning.Source: C. SIC Depth · p. 10, Table II · p. 10
• The residual SIC gap is attributed to finite-basis mismatch: OFDM and OTFS leave more high-order nonlinear SI outside the adopted basis than SC and chirped DFT-s-OFDM.The dominant waveform-dependent factor is high-order envelope statistics, especially the highest retained moment, rather than waveform family itself.Source: C. SIC Depth · p. 10

D. Sensing Preservation

• After FASIC, the strongest static reflector is recovered in the correct delay bin for every waveform, with zero ToA error at 1.5 m range resolution.CIR peak-to-floor ratios after cancellation are 12.9–21.7 dB; SC and chirped DFT-s-OFDM have the largest margins, 21.7 and 19.9 dB.Source: D. Sensing Preservation · p. 10, Figure 5 · p. 11
• Both moving targets are visible after FASIC for every waveform, with peak-to-background ratios of approximately 10–15 dB.The same cancellation architecture preserves delay and Doppler information across all four candidates.Source: D. Sensing Preservation · p. 11, Figure 4 · p. 11

E. Cancellation-Span Flexibility

• Static reflectors remain visible outside the effective cancellation span; when the span crosses the τ − 2 Ts boundary, their margins fall below the 6 dB visibility threshold.At an intermediate span, the 18 Ts reflector is absorbed while the 24 Ts reflector remains visible; SIC depth degrades only when the span is too short to represent the SI channel.Source: E. Cancellation-Span Flexibility · p. 11, Figure 6 · p. 11
• At the Doppler frequencies tested, moving targets remain visible even when their delays are shorter than the cancellation span.Static echoes inside the selected span are absorbed, while delayed echoes outside it are preserved.Source: E. Cancellation-Span Flexibility · pp. 11–12

VI. CONCLUSION

• The conclusion identifies future work in frequency-selective and time-varying SI channels, richer nonlinear bases, adaptive normalization for high-PAPR waveforms, and hardware prototypes.The reported validation is based on one common hardware and canceler configuration.Source: §VI · p. 12