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Imaging-Communication Trade-off in VLEO ISAC-SAR Using CP-OFDM

In-Hyeok Lee, Kawon Han

arXiv:2609.18301v2eess.SP

TL;DR

The paper examines how random payloads, platform Doppler, and range-dependent CP deficit jointly affect VLEO ISAC-SAR imaging and communication. It develops an analytical framework and ENESZ for their image-domain effects. Its analysis and end-to-end simulations show that the sufficient-CP duration does not generally coincide with the imaging-optimal duration.

  • Problem

    A unified characterization is needed for how payload randomness, platform-induced Doppler ICI, and range-dependent CP-deficit ICI/ISI propagate through two-dimensional spaceborne SAR imaging.

    Source: §I · p. 2

  • Method

    The paper models the joint impairments in data-bearing CP-OFDM ISAC-SAR, derives image-domain statistics, and formulates ENESZ on a common backscatter-equivalent scale.

    Source: §I · p. 2, §VI · p. 12

  • Results

    The sufficient-CP duration does not generally coincide with the imaging-optimal CP duration, which also depends on receive filter and communication constellation.

    Source: §VI · p. 12

  • Takeaways & Limitations

    CP duration balances delay-interference suppression against coherent processing gain and communication throughput, so sufficient swath coverage need not minimize image ENESZ.

    Source: §V · p. 11, §VI · p. 12

Abstract

from arXiv · show

This paper investigates the imaging--communication trade-off in very-low-Earth-orbit (VLEO) integrated sensing and communication synthetic aperture radar (ISAC-SAR) using cyclic-prefix orthogonal frequency-division multiplexing (CP-OFDM) as the shared waveform. We develop a unified analytical framework that jointly accounts for random communication payloads, range-dependent CP deficit across the swath, and slow-time-varying platform Doppler over the synthetic aperture. The resulting signal model separates the coherently retained component from inter-carrier interference (ICI) and inter-symbol interference (ISI) through common subcarrier-coupling coefficients. By propagating these effects through receive filtering, range compression, and azimuth focusing, we derive image-domain statistics for matched- and reciprocal-filter receivers. Based on the derived statistics, an effective noise-equivalent sigma zero (ENESZ) is formulated to characterize data-dependent sidelobes, ICI/ISI, and noise enhancement on a common backscatter-equivalent scale. The analysis reveals that the CP duration acts as a system-level design parameter bringing scalable trade-off. Increasing the CP improves coherent retention and suppresses range-dependent interference, but simultaneously reduces coherent processing gain and communication payload throughput. Accordingly, the sufficient-CP duration does not generally coincide with the imaging-optimal CP duration. End-to-end simulations for a representative VLEO scenario validate the derived image-domain statistics and demonstrate the resulting trade-off between ENESZ and communication throughput as a function of CP duration.

I. Introduction

The paper addresses the underexplored interaction of random payloads, platform Doppler, and range-dependent CP deficit in coherent spaceborne SAR imaging. It develops a VLEO ISAC-SAR framework that models these effects and their imaging and communication trade-offs using shared CP-OFDM signals.

I. Introduction

  • VLEO is considered for dual-function sensing and communication because reduced slant range can improve radar sensitivity and alleviate communication path loss under platform size, weight, and power constraints.The system reuses data-bearing CP-OFDM communication signals for active SAR imaging.Source: §I · p. 1, A. VLEO ISAC-SAR Geometry and CP-OFDM… · p. 2
  • Data-bearing CP-OFDM spaceborne SAR combines random payloads, aperture-varying Doppler, and range-dependent CP deficit, whose joint image-domain effects remain largely unexplored.Prior work generally studied these impairments separately or used predetermined subcarrier coefficients rather than independently varying communication payloads.Source: §I · pp. 1–2
  • The framework models payload randomness, range-dependent CP deficit, and platform-induced Doppler, then derives image-domain statistics and ENESZ for SAR imaging and communication trade-off analysis.It separates coherent response, ICI/ISI, data-dependent sidelobes, and thermal noise in its analysis.Source: §I · p. 2

A. VLEO ISAC-SAR Geometry and CP-OFDM Signal Model

  • The differential two-way propagation delay across the illuminated swath, Tw = 2∆R/c, sets the echo-window span relevant to the CP requirement.This swath delay differs from the absolute satellite-to-ground round-trip delay.Source: A. VLEO ISAC-SAR Geometry and CP-OFDM… · p. 3
  • The model treats each CP-OFDM symbol as one SAR pulse and stacks the M symbols across the coherent processing interval as raw-data columns.The CP increases symbol period Ts = T + Tcp, reducing the number of symbols M within a fixed CPI as it lengthens.Source: A. VLEO ISAC-SAR Geometry and CP-OFDM… · p. 3, Figure 2 · p. 3

B. Swath-Dependent CP Deficit and Platform-Induced Doppler

The section describes how swath delay and platform motion affect the symbol capture and Doppler conditions across SAR data. CP deficit changes symbol capture across range, while Doppler varies over slow time and produces ICI.

B. Swath-Dependent CP Deficit and Platform-Induced Doppler

  • The receiver uses a T-duration DFT window matched to reference delay τg; the ISI-free interval is [τg, τg + Tcp] and the adopted gate centers it within [0, Tw].The gate placement may be selected according to desired swath coverage.Source: B. Swath-Dependent CP Deficit and… · p. 3
  • Outside that interval, the desired symbol is partially captured, with late and early scatterers introducing adjacent symbols at opposite ends of the DFT window.The capture factor β is the fraction of the window occupied by the desired symbol; under Tw < T, at most one adjacent symbol enters a window.Source: B. Swath-Dependent CP Deficit and… · p. 3
  • When Tcp ≥ Tw, a gate placement can keep every scatterer in the ISI-free interval with capture factor β = 1; when Tcp < Tw, some scatterers fall outside it.For the latter case, an adjacent symbol with an independent payload occupies the uncaptured fraction, substituting interference for part of the desired echo.Source: B. Swath-Dependent CP Deficit and… · pp. 3–4, Figure 3 · p. 4
  • Platform-induced normalized Doppler evolves continuously over the synthetic aperture, producing ICI, while CP deficit varies across the swath according to scatterer range and CP duration.The impairments therefore act predominantly along different raw-data axes: slow time for Doppler and range for CP deficit.Source: B. Swath-Dependent CP Deficit and… · p. 4, Figure 4 · p. 4

C. Received-Signal Model under ISI/ICI Effects

The received-signal model projects each range-gated symbol window onto the subcarrier basis, separating the intended component from ICI and ISI through shared coupling coefficients. CP deficit and Doppler redistribute energy differently: the former produces both ICI and ISI, while the latter produces ICI.

C. Received-Signal Model under ISI/ICI Effects

  • The intended-cell coefficient has squared magnitude β² sinc²(βεm), representing the coherent fraction retained under joint CP deficit and platform-induced Doppler.Remaining energy enters ICI through ˜Ik̸=0 and ISI through Jk.Source: C. Received-Signal Model under ISI/ICI… · p. 5
  • The model jointly represents range-dependent capture β and slow-time Doppler offset εm in common coupling kernels, separating the retained signal, ICI, and ISI.Each receiver window discards the CP and takes a T-duration DFT; a distributed scene superposes contributions with their own β and channel coefficient.Source: C. Received-Signal Model under ISI/ICI… · pp. 4–5
  • With CP deficit alone, intended, ICI, and ISI energies are β², β(1 −β), and 1 −β; with Doppler alone, intended energy is sinc²(εm) and the remainder is ICI.Thus CP deficit redistributes energy into both ICI and ISI, whereas Doppler redistributes it into ICI only.Source: Figure 5 · p. 5, C. Received-Signal Model under ISI/ICI… · p. 6
  • In frequency terms, Doppler shifts subcarrier sampling away from response zeros, while partial capture broadens the own-symbol response and adds an adjacent-symbol response responsible for ISI.At full capture with εm = 0, subcarrier orthogonality is recovered.Source: Figure 6 · p. 5, C. Received-Signal Model under ISI/ICI… · p. 6

A. Receive Filtering and Range Compression

The receiver compensates for the known communication data before range compression, using matched or reciprocal filtering. The reciprocal filter removes the matched filter’s data-dependent sidelobe but scales ICI, ISI, and noise contributions, creating a receiver trade-off.

A. Receive Filtering and Range Compression

  • The matched filter uses ρn,m = s∗n,m/pn,m, whereas the reciprocal filter uses ρn,m = 1/sn,m.The receiver first compensates for the known transmitted communication data through receive filtering.Source: A. Receive Filtering and Range… · p. 6
  • Range compression applies an inverse DFT across subcarriers, and the intended component remains coherent while filtering fluctuation, ICI, and ISI contribute a zero-mean incoherent floor.Under the assumed data independence and four-fold rotational symmetry, the second-order cross terms vanish.Source: A. Receive Filtering and Range… · p. 6
  • The reciprocal filter eliminates the matched filter’s data-dependent sidelobe proportional to µ4 −1, but scales ICI, ISI, and thermal-noise contributions by ν.Choosing between the filters trades suppression of the data-dependent pedestal sidelobe against robustness to interference and noise.Source: A. Receive Filtering and Range… · p. 6

B. Azimuth Focusing and Image Floor-to-Peak Ratio

Backprojection coherently accumulates the target response across slow time, while the pedestal, ICI, ISI, and thermal noise remain mutually incoherent. The resulting aperture integration reduces the image floor-to-peak ratio by a factor of M.

B. Azimuth Focusing and Image Floor-to-Peak Ratio

  • The target response grows as M² while the mutually incoherent pedestal, ICI, ISI, and thermal-noise floor grows as M, reducing the floor-to-peak ratio by a factor of M.The residual Doppler-related linear phase shifts azimuth position without changing the chirp rate or focusing.Source: B. Azimuth Focusing and Image… · pp. 6–7
  • The analysis assumes that the variation of |˜I0| over the synthetic aperture is sufficiently small for the stated approximation of aperture-averaged coherent retention.The ratio uses Γ for focused-image floor to peak and SNRm for per-symbol echo-to-noise ratio.Source: B. Azimuth Focusing and Image… · p. 7
  • The image floor-to-peak ratio Γ includes coherent loss from CP deficit and Doppler, ISI excess from symbol-power variation, and the coherent processing gain NM.NM ≃BTa/(1 + Tcp∆f), so its CP overhead matches that of the communication rate.Source: B. Azimuth Focusing and Image… · p. 7

A. Effective Noise-Equivalent Sigma Zero (ENESZ)

ENESZ expresses the total focused-image floor relative to the coherently retained response on a backscatter-equivalent scale. Unlike conventional NESZ, it includes scene-generated waveform floors and can therefore depend on scene backscatter.

A. Effective Noise-Equivalent Sigma Zero (ENESZ)

  • ENESZ expresses the total image floor on a backscatter-equivalent scale relative to the coherently retained response, and can depend on scene backscatter because waveform-induced floor arises from scene returns.Conventional NESZ instead characterizes the backscatter coefficient at which target return equals the thermal-noise floor and is scene independent.Source: A. Effective Noise-Equivalent Sigma… · p. 7
  • Conditioned on a fixed scene realization, data-payload randomness and thermal noise make the focused image a random field whose zero-mean floor components aggregate into the swath-averaged image floor F.These components include data-dependent fluctuations, ICI/ISI, and thermal noise.Source: A. Effective Noise-Equivalent Sigma… · p. 7
  • The focused-image floor combines receive sidelobes and ICI/ISI with the thermal-noise floor after SAR imaging.In this model, sidelobes, ICI, ISI, and thermal noise contribute mutually incoherently to a distributed floor.Source: A. Effective Noise-Equivalent Sigma… · p. 7

B. Communication Throughput

Communication throughput is the nominal data-payload rate under a reliable-link assumption, with CP framing reducing the number of data-bearing OFDM symbols transmitted per unit time.

B. Communication Throughput

  • Increasing T_cp lengthens the OFDM-symbol period and reduces the number of data-bearing symbols transmitted per unit time.With occupied bandwidth, subcarrier count, and average transmit power fixed, this isolates the deterministic throughput overhead of CP framing.Source: B. Communication Throughput · p. 8
  • Each data-bearing subcarrier conveys b_c payload bits per OFDM symbol, so an OFDM symbol carries N b_c payload bits.The number of symbols in one CPI is M = ⌊T_a/(T + T_cp)⌋.Source: B. Communication Throughput · p. 8
  • R_com measures nominal data-payload throughput under a reliable-link assumption, not achievable rate or throughput including SNR or block-error effects.T_cp determines the framing-related reduction, while b_c sets the level for a given communication configuration.Source: B. Communication Throughput · p. 8

C. Imaging-Communication Trade-off Design via CP Length

CP duration jointly affects image ENESZ and communication throughput, so choosing it requires balancing imaging gains against CP overhead and receiver-dependent effects.

C. Imaging-Communication Trade-off Design via CP Length

  • The CP overhead factor 1 + T_cp/T multiplies both ENESZ terms, while increasing T_cp reduces thermal-noise and scene-dependent contributions as the CP deficit shrinks.Imaging gains saturate once the swath is fully captured, but the overhead continues growing; therefore, the imaging-optimal CP need not equal T_w.Source: C. Imaging-Communication Trade-off… · p. 8
  • The matched filter includes constellation-dependent pedestal sidelobes, whereas the reciprocal filter removes that pedestal but scales the thermal and ICI/ISI floor by ν.Which receiver is favored depends jointly on CP duration, mean scene backscatter, and constellation statistics.Source: C. Imaging-Communication Trade-off… · p. 8
  • A weighted sum of normalized throughput and image-quality metrics provides a CP-selection criterion, with priority weight w setting the communication emphasis.Because the objective is not generally concave, the criterion is solved by a one-dimensional search over [0, T_w].Source: C. Imaging-Communication Trade-off… · p. 8
  • Along the trade-off boundary, increasing CP lowers ENESZ at the cost of throughput; beyond T_cp*, both metrics worsen, and the optimum depends on system, scene, and communication configurations.Figure 7 presents the throughput–ENESZ trade-off as a function of guard interval (CP length).Source: C. Imaging-Communication Trade-off… · pp. 8–9, Figure 7 · p. 8

V. Simulation Results

End-to-end simulations validate the analytical predictions and show that CP duration trades throughput against ENESZ, with imaging optima depending on receiver and constellation. The simulations also show distinct range-dependent CP-deficit effects and a Doppler penalty that grows with normalized Doppler span.

V. Simulation Results

  • At T_cp = T_w, the coastal-scene image has near-ideal sinc-shaped compression, with corner-reflector 3 dB widths of 2.17 m in ground range and 1.22 m in azimuth.The CP covers the swath delay span, so the image is free of ISI and its floor consists of thermal noise and pedestal sidelobes.Source: §V · p. 10
  • The aggregate image floor comes from thermal noise and scene-wide pedestal sidelobes, setting which targets remain visible above it.Targets whose peaks fall within floor fluctuations are only partially discernible.Source: §V · p. 10
  • With no CP, the far-range capture factor is 0.61 versus 0.98 at swath center; increasing CP from zero to T_w raises the far-range strongest-target peak by about 5 dB.At T_cp = T_w, measured target peaks at both locations closely follow expected levels.Source: §V · p. 10, Figure 10 · p. 10
  • At the operating point, normalized Doppler span ε_max ≃ 0.094 produces ENESZ penalties of approximately 0.1 dB for MF and 0.37 dB for RF.The penalty increases with normalized Doppler span.Source: §V · p. 11, Figure 11 · p. 11
  • Across 16-, 64-, and 1024-QAM, simulated throughput–ENESZ operating points closely follow analytical predictions as CP duration varies.Figure 13 shows the trade-off for matched- and reciprocal-filter receivers, with the optimum varying by receiver and constellation.Source: Figure 13 · p. 11, §V · p. 11
  • For QPSK, the analytical ENESZ closely matches simulation across the CP range, and the imaging optimum is T_cp* = 0.72T_w rather than T_w.Intrinsic imaging ENESZ decreases with CP, but the increasing CP-overhead penalty creates an interior minimum.Source: §V · p. 11, Figure 12 · p. 11
  • For the reciprocal filter, all tested QAM constellations share T_cp* = 0.72T_w; for the matched filter, the optimum falls from 0.30T_w for 16-QAM to 0.26T_w for 64-QAM and 0.25T_w for 1024-QAM.The matched-filter optimum shifts shorter as the constellation-dependent pedestal becomes larger, while the reciprocal-filter constellation factor changes ENESZ level but not the optimum location.Source: §V · pp. 11–12
  • Overall, the CP-dependent imaging–communication optimum depends on receive filter and constellation, while the simulations validate the framework from local target response to swath-averaged ENESZ.The CP deficit causes range-dependent coherent-retention loss, and platform-induced Doppler ICI causes a velocity-dependent penalty.Source: §V · p. 12

VI. Conclusion

The paper develops an end-to-end analytical framework for VLEO CP-OFDM ISAC-SAR and uses it to characterize how CP duration affects imaging and communication. Simulations validate the image-domain statistics and ENESZ predictions, while showing that sufficient CP and imaging-optimal CP generally differ.

VI. Conclusion

  • The unified signal model accounts jointly for random payloads, range-dependent CP deficit, and platform-induced Doppler, then propagates their effects through SAR processing.Image-domain analysis separates coherent response from data-dependent sidelobes, ICI/ISI, and thermal noise to formulate ENESZ on a common backscatter-equivalent scale.Source: §VI · p. 12
  • CP deficit causes range-dependent coherent-retention loss and ICI/ISI, while platform-induced Doppler introduces slow-time-dependent ICI over the synthetic aperture.CP duration also controls coherent processing gain and communication throughput, so sufficient CP does not generally coincide with imaging-optimal CP.Source: §VI · p. 12
  • End-to-end simulations validate the image-domain statistics and ENESZ predictions and confirm a CP-dependent imaging–communication trade-off.The imaging-optimal CP further depends on the receive filter and communication constellation.Source: §VI · p. 12
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