Source-linked AI summary
Pilot-Based Sensing With OFDM and AFDM: A Resource-Matched Performance Comparison
Siyi Tang, Yin Xu, Aimin Tang, Dazhi He, Wenjun Zhang
TL;DR
A systematic pilot-based sensing comparison of OFDM and AFDM under matched resources is lacking. This paper compares pilot placements and receiver processing through ambiguity analyses and target-detection experiments. Structured pilots improve weak-target detection over OFDM-random, while AFDM-DAFT can detect integer Doppler beyond the conventional slow-time unambiguous-velocity limit at increased search complexity.
Problem
Existing studies do not establish a fair pilot-based OFDM–AFDM sensing comparison under the same pilot resources and consistent sensing conditions.
Source: §I · p. 1Method
The paper matches bandwidth, frame duration, pilot energy, and reserved-resource overhead while comparing OFDM pilot patterns and guarded AFDM pilots through ambiguity analyses and target-detection experiments.
Source: §I · pp. 1–2Results
Structured OFDM and AFDM pilot placements outperform OFDM-random in weak-target detection, and AFDM-DAFT maintains high detection probability beyond the conventional maximum unambiguous velocity at increased search complexity.
Source: B. Target Sensing in Low-Mobility… · p. 5, §V · p. 6Takeaways & Limitations
Pilot placement and receiver processing distinguish sensing outcomes: structured pilots support weak-target detection, while exploiting AFDM’s DAFT structure extends high-mobility Doppler sensing in the tested setting.
Source: B. Target Sensing in Low-Mobility… · p. 5, §V · p. 6
Abstract
from arXiv · showhide
As a waveform candidate for next-generation wireless systems, affine frequency division multiplexing (AFDM) has often been compared with orthogonal frequency division multiplexing (OFDM) under different configurations, while a systematic comparison of their pilot-based sensing performance remains lacking. This paper establishes a comparison with the same bandwidth, frame duration, pilot energy, and reserved-resource overhead. OFDM-random, OFDM-fixed-comb, and OFDM-shifted-comb pilots are compared with AFDM pilots surrounded by guard resources using aperiodic ambiguity functions without cyclic prefix/chirp-periodic prefix (CP/CPP) and cyclic ambiguity functions with CP/CPP, followed by target detection experiments. The results show that OFDM-fixed-comb exhibits low range sidelobes but periodic range ambiguity peaks, while AFDM and OFDM-shifted-comb effectively suppress zero-Doppler range ambiguities. Within the common unambiguous region, all pilot configurations for both waveforms exhibit similar detection thresholds in strong-target detection, while structured OFDM and AFDM pilot placements outperform OFDM-random in weak-target detection. At high mobility, the AFDM receiver using the discrete affine Fourier transform (DAFT) can resolve integer Doppler beyond the conventional slow-time maximum unambiguous velocity, outperforming the tested conventional OFDM and AFDM receivers at the increased search complexity. These results separate the effects of waveform, pilot placement, and receiver processing, providing a basis for AFDM and OFDM pilot-based sensing design.
I. INTRODUCTION
The introduction motivates pilot-based sensing and identifies the lack of a resource-matched OFDM–AFDM comparison that separates waveform, pilot-placement, and receiver effects. It introduces OFDM and AFDM signal models, including the contrasting effects of high Doppler on OFDM and AFDM’s DAFT-domain structure.
I. INTRODUCTION
- OFDM’s mature architecture and FFT-based range–Doppler processing make it a practical ISAC baseline, but high Doppler causes inter-carrier interference through loss of subcarrier orthogonality.Pilot placement and resource allocation also affect sensing performance when pilot resources are limited.Source: §I · p. 1
A. OFDM and AFDM Signal Models
- AFDM uses a DAFT chirp basis with channel-adaptable parameters, producing a controllable affine-domain channel structure that can separate paths by delay and Doppler.The paper notes that single DAFT-domain pilots with guards have been used for AFDM channel estimation and sensing.Source: §I · p. 1
I. INTRODUCTION
- The paper identifies a lack of fair pilot-based OFDM–AFDM comparisons under consistent pilot resources and processing, limiting assessment of their relative performance across scenarios.It frames separating waveform, pilot placement, and receiver design effects as necessary for the comparison.Source: §I · p. 1
- The study matches bandwidth, frame duration, total pilot energy, and reserved-resource overhead, then compares pilot ambiguity functions and target detection across receiver designs.It also includes high-mobility sensing and computational-complexity comparisons.Source: §I · pp. 1–2
A. OFDM and AFDM Signal Models
- The signal model assumes target delays remain within the prefix duration, excluding inter-symbol interference, and retains within-symbol Doppler variation and its resulting ICI.The prefix is a cyclic prefix for OFDM or a chirp-periodic prefix for AFDM.Source: A. OFDM and AFDM Signal Models · p. 2
- For OFDM, small normalized Doppler yields an approximately diagonal effective channel, whereas high Doppler introduces off-diagonal terms and ICI.With suitable AFDM chirp parameters, delay and integer Doppler produce a localized DAFT-domain shift; fractional Doppler spreads energy around it.Source: A. OFDM and AFDM Signal Models · p. 2
B. Pilot Placement Schemes
The paper defines random and structured OFDM pilot placements alongside AFDM’s single-pilot-with-guards configuration. The configurations differ in pilot-grid structure and in how the AFDM pilot uses DAFT-domain chirp signaling.
B. Pilot Placement Schemes
- The modulation-domain frame S is partitioned into known pilots P and unknown data Ddata with disjoint support.The paper uses pilot-only sensing and assumes data are zero for simplicity.Source: B. Pilot Placement Schemes · p. 2
- OFDM-random selects a fixed number of pilot positions randomly over the frequency–time grid, while OFDM-fixed-comb places pilots at regularly spaced subcarrier and symbol indices.The comb spacings are Df subcarriers and Dt symbols.Source: B. Pilot Placement Schemes · p. 2
- OFDM-shifted-comb changes the subcarrier positions using an integer comb shift while preserving the pilot-bearing symbol indices.The shift changes the range–Doppler ambiguity pattern.Source: B. Pilot Placement Schemes · p. 3
- AFDM uses one DAFT-domain pilot per symbol surrounded by zero-valued guards, with the inverse DAFT generating a chirp waveform for sensing.The guards are reserved to mitigate interference from unknown data.Source: B. Pilot Placement Schemes · p. 3
A. Ambiguity Function
Pilot-based sensing uses known pilot samples and defines total useful-sample pilot energy per frame.
A. Ambiguity Function
- For pilot-based sensing, the paper uses known pilot waveforms and defines total useful-sample pilot energy per frame as Ep.The setup assumes data are zero for simplicity.Source: A. Ambiguity Function · p. 3
1) Aperiodic Ambiguity Functions without CP/CPP:
The section defines an aperiodic ambiguity function for sensing and relates delay and Doppler to range and velocity. It describes how pilot placement shapes unambiguous regions and ambiguity backgrounds.
1) Aperiodic Ambiguity Functions without CP/CPP:
- The normalized aperiodic ambiguity function evaluates the concatenated useful symbols across integer delay and Doppler frequency.Range and velocity are R = cℓ/(2B) and v = cf/(2fc).Source: 1) Aperiodic Ambiguity Functions… · p. 3
- For OFDM-fixed-comb, the delay response repeats every N/Df samples, setting a maximum unambiguous range.The full-frequency-grid reference is Ru = c/(2∆f); these range limits do not determine aperiodic peak heights.Source: 1) Aperiodic Ambiguity Functions… · p. 3
- Pilots every Dt symbols define a conventional slow-time maximum unambiguous velocity with principal interval |v| < vu.Here, T is the useful-symbol duration.Source: 1) Aperiodic Ambiguity Functions… · p. 3
- Irregular pilot placement generally produces a distributed ambiguity background instead of regular peaks.Source: 1) Aperiodic Ambiguity Functions… · p. 3
2) Cyclic Ambiguity Functions with CP/CPP:
With CP/CPP, the section describes cyclic ambiguity processing and a CPP-based AFDM pilot construction. For integer delays, the cyclic zero-Doppler response has zero sidelobes under stated processing conditions.
2) Cyclic Ambiguity Functions with CP/CPP:
- With prefix-inclusive symbol duration Tsym, the maximum unambiguous velocity is vu = c/(4fcDtTsym).Source: T CPP · p. 3
- Table I is identified as containing the common simulation parameters.Source: Table I · p. 3
T CPP
- The AFDM pilot is a chirp generated by inverse DAFT at a fixed DAFT index, with a complex coefficient and CPP shift.The coefficient is zero in symbols without pilots.Source: T CPP · p. 3
- For integer q coprime to N, the cyclic zero-Doppler response is zero at delays 1 through N−1.The zeros require integer delays and correct CPP processing; they do not imply zero sidelobes at fractional delays or nonzero Doppler.Source: T CPP · p. 3
B. Typical Case Study
Under matched pilot resources, the schemes show distinct range–Doppler ambiguity patterns, while structured pilots concentrate sidelobe energy more effectively than OFDM-random. Fixed-comb has periodic range peaks, whereas shifted-comb and AFDM suppress zero-Doppler range ambiguities.
B. Typical Case Study
- OFDM-fixed-comb produces periodic range ambiguity peaks, while OFDM-shifted-comb suppresses them on the zero-Doppler cut but moves them to coupled delay–Doppler positions.AFDM achieves range compression through chirp matching without comb-induced range ambiguity peaks.Source: B. Typical Case Study · p. 3, Figure 2 · p. 4
- OFDM-fixed-comb, OFDM-shifted-comb, and AFDM share symbol spacing Dt = 4, producing periodic Doppler ambiguities from sparse slow-time sampling.Each scheme reserves 512 resources, with equal total pilot energy and constant-modulus QPSK pilots.Source: B. Typical Case Study · pp. 3–4
- OFDM-fixed-comb has low sidelobes between its strong periodic range peaks; shifted-comb suppresses those peaks, while AFDM has residual chirp sidelobes.OFDM-random instead produces a higher distributed sidelobe background.Source: B. Typical Case Study · p. 4, Figure 3 · p. 4
- Without CP/CPP, OFDM-fixed-comb and OFDM-shifted-comb achieve higher range PSLRs than AFDM within the comparison windows.With CP/CPP, structured schemes reach the numerical floor for sampled range sidelobes, but their 2D PSLRs remain near 13.30 dB; OFDM-random has approximately 10 dB higher ISLR.Source: B. Typical Case Study · p. 4, Table II · p. 4
- Structured OFDM and AFDM have similar 2D PSLR and ISLR, while OFDM-random has approximately 10 dB higher ISLR from distributed residual correlations.The distributed background may mask weak echoes; structured placement concentrates more energy within the mainlobe.Source: B. Typical Case Study · p. 4, Table II · p. 4
IV. TARGET DETECTION RESULTS
The section describes conventional OFDM and AFDM time-domain matched-filter processing alongside an AFDM-DAFT receiver adapted for high mobility. The AFDM-DAFT approach searches delay and affine-shift branches to resolve integer Doppler beyond the conventional slow-time limit, at increased search cost.
A. Signal Processing and Complexity
- Conventional OFDM forms range-Doppler power maps with pilot multiplication, a subcarrier IFFT, and a slow-time FFT; AFDM time-domain matched filtering uses circular correlation and a slow-time FFT.Both conventional paths use FFT/IFFT-based processing.Source: A. Signal Processing and Complexity · p. 5
- AFDM-DAFT matches pilot responses over candidate delays and affine-shift branches, then uses slow-time FFTs to resolve integer Doppler beyond the conventional maximum unambiguous velocity.The receiver adapts the AFT–Doppler method in to pilot sensing.Source: A. Signal Processing and Complexity · p. 5
- AFDM-DAFT searches an ALM-cell detection grid rather than the LM grid used by conventional processing, increasing detection search costs.A = 2αmax + 1 counts affine branches, and L counts delay hypotheses.Source: A. Signal Processing and Complexity · p. 5
- Detection uses two-dimensional CA-CFAR and local-maximum extraction, with integer-bin estimates and no interpolation.Detection probability counts trials with a candidate inside the association gate; multi-target matching is one-to-one.Source: A. Signal Processing and Complexity · p. 5
B. Target Sensing in Low-Mobility Scenarios
In the representative three-target scene, structured OFDM and AFDM pilot placements detect the weak target more reliably than OFDM-random as weak-target SNR rises. The results also connect weak-target detection to distributed sidelobe interference from stronger targets.
B. Target Sensing in Low-Mobility Scenarios
- All structured placements reach weak-target detection probability 1 by −20 dB, while OFDM-random remains between 0.076 and 0.116 from −20 to 0 dB.All schemes detect the strong target every trial; at −30 dB, medium-target detection is 0.778 for OFDM-random and approximately 0.98 for structured schemes.Source: B. Target Sensing in Low-Mobility… · p. 5
- Structured pilot placement improves weak-target detection in this scene, whereas OFDM-random’s distributed background masks the weak echo.The comparison is reported for a representative three-target scenario with relative target powers of 16, 8, and 0 dB.Source: B. Target Sensing in Low-Mobility… · p. 5
- With fixed target power ratios, reducing noise leaves relative strong-target interference unchanged, so detection can remain interference-limited at high SNR.Sidelobes at target locations are therefore a key pilot-design criterion.Source: B. Target Sensing in Low-Mobility… · p. 5
C. Target Sensing in High-Mobility Scenarios
AFDM-DAFT resolves integer Doppler beyond the conventional slow-time velocity limit, while conventional receivers alias or fail at high mobility. Its extended detection range comes with a larger search grid.
C. Target Sensing in High-Mobility Scenarios
- AFDM-DAFT maintains PD = 1 through 467.532 m/s, while conventional receivers fail beyond their unambiguous-velocity limit.At ν = 1.5, conventional receivers have zero correct detections across SNRs; AFDM-DAFT reaches PD = 1 from −20 dB onward.Source: C. Target Sensing in High-Mobility… · pp. 5–6, Figure 5 · p. 6
- AFDM-DAFT exploits DAFT-domain structure to resolve integer Doppler beyond the slow-time limit, at the cost of increased search complexity.The high-mobility detection grid has ALM cells versus LM for conventional processing.Source: C. Target Sensing in High-Mobility… · p. 6
V. CONCLUSION
- Without interference cancellation, structured sparse OFDM and AFDM pilots reliably detect the weak target from −20 dB onward, unlike OFDM-random.In the common unambiguous region, the compared schemes have similar detection probability for strong-target detection.Source: §V · p. 6