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OFDM Synthetic Aperture Radar Imaging with Sufficient Cyclic Prefix

Tian-Xian Zhang, Xiang-Gen Xia

arXiv:1306.3604v2cs.ITmath.IT

TL;DR

Existing LFM and random-noise SAR methods retain IRCI from ambiguity-function sidelobes. This paper uses OFDM pulses with a sufficient cyclic prefix and a corresponding SAR imaging algorithm; simulations report better imaging performance than LFM and random-noise SAR.

  • Problem

    Sidelobes in existing coded-pulse SAR leave IRCI between range cells, a concern for high-range-resolution imaging.

    Source: §I · p. 3

  • Method

    The paper proposes OFDM SAR imaging with a sufficient CP on each pulse and an algorithm that uses OFDM processing to recover range-cell responses.

    Source: §I · p. 4, A. OFDM SAR signal model · p. 7, §IV · p. 21

  • Results

    Simulations show that CP-based OFDM SAR imaging performs better than LFM SAR and random-noise SAR imaging.

    Source: §IV · p. 21

  • Takeaways & Limitations

    With sufficient CP, the proposed method provides an IRCI-free, high-range-resolution SAR image when N ≥ M.

    Source: §I · p. 4, §IV · p. 21

    With PN weights, the OFDM time-domain signal may have high PAPR, an unresolved design problem for radar applications.

    Source: C. Discussion on the design of weights… · pp. 14–15

Abstract

from arXiv · show

The existing linear frequency modulated (LFM) (or step frequency) and random noise synthetic aperture radar (SAR) systems may correspond to the frequency hopping (FH) and direct sequence (DS) spread spectrum systems in the past second and third generation wireless communications. Similar to the current and future wireless communications generations, in this paper, we propose OFDM SAR imaging, where a sufficient cyclic prefix (CP) is added to each OFDM pulse. The sufficient CP insertion converts an inter-symbol interference (ISI) channel from multipaths into multiple ISI-free subchannels as the key in a wireless communications system, and analogously, it provides an inter-range-cell interference (IRCI) free (high range resolution) SAR image in a SAR system. The sufficient CP insertion along with our newly proposed SAR imaging algorithm particularly for the OFDM signals also differentiates this paper from all the existing studies in the literature on OFDM radar signal processing. Simulation results are presented to illustrate the high range resolution performance of our proposed CP based OFDM SAR imaging algorithm.

I. INTRODUCTION

Existing SAR methods use coded pulses and pulse compression, but sidelobes leave inter-range-cell interference (IRCI). The paper proposes sufficient-CP OFDM SAR to use OFDM’s ISI-free subchannels for high-range-resolution imaging.

I. INTRODUCTION

  • Sidelobes of existing coded signals leave IRCI between range cells, which can degrade SAR imaging, especially as the number of cells grows.LFM and random-noise SAR are identified as established approaches that retain this interference.Source: §I · p. 3
  • The paper treats range-cell returns as analogous to communication multipaths, which cause IRCI in SAR and ISI in communications.It connects LFM or step-frequency and random-noise SAR with frequency-hopping and direct-sequence spread-spectrum systems, respectively.Source: §I · p. 3
  • The paper adapts OFDM’s sufficient-cyclic-prefix ability to turn multipath ISI into ISI-free subchannels for SAR range cells.It proposes a new OFDM SAR imaging algorithm, changing both transmission and reception relative to existing SAR methods.Source: §I · pp. 2, 4
  • Known platform velocity and scene range make Doppler shifts available for cross-range formation, range-migration correction, and compensation within a cross range.The paper also outlines an algorithm section, simulation section, and conclusion.Source: §I · p. 4

II. SYSTEM MODEL AND CP BASED OFDM SAR IMAGING

The section introduces the OFDM SAR signal model and then presents the corresponding imaging algorithm.

II. SYSTEM MODEL AND CP BASED OFDM SAR IMAGING

  • The section first describes the OFDM SAR signal model and then proposes the corresponding SAR imaging algorithm.Source: §II · p. 4

A. OFDM SAR signal model

The signal model represents an OFDM pulse with a cyclic prefix and models range-cell returns as multipath contributions. A CP of length M −1 is used for M range cells, with N ≥ M assumed.

A. OFDM SAR signal model

  • An OFDM pulse uses N subcarriers over bandwidth B, with a cyclic prefix formed by repeating the waveform’s tail at its beginning.The pulse duration excluding the CP is T, and the guard-interval duration is TGI.Source: A. OFDM SAR signal model · pp. 5, 9
  • The CP length is set to M −1 for M range cells, so the range-cell paths can be separated without IRCI under this model.The CP is added at the start of the pulse, with guard-interval duration TGI = (M −1)Ts.Source: A. OFDM SAR signal model · p. 7
  • The model assumes N ≥ M and a PRI long enough for all range cells in the swath to fall within the receive window.N < M leads to IRCI, while the monostatic SAR transmitter and receiver are separated in time.Source: A. OFDM SAR signal model · p. 8

B. Range compression

The range-compression procedure uses OFDM processing to recover range-cell coefficients without IRCI when N ≥ M. Its analysis also describes the failure for N < M and compares the method’s SNR gain with LFM range compression.

B. Range compression

  • After removing the first and last M −1 received samples, the receiver forms an N-sample vector for OFDM processing.The tail samples do not contain the full set of M range-cell coefficients.Source: B. Range compression · p. 9
  • The receiver applies an FFT-based OFDM demodulation and an IFFT to estimate the range-cell RCS coefficients without IRCI from other cells.The DFT diagonalizes the circulant channel matrix, and the recovered coefficients determine the corresponding RCS values.Source: B. Range compression · pp. 10–11
  • In the SWMP case, N = M, and a longer CP yields less IRCI and a better high-range-resolution image.The paper identifies this as a special case with no zeros in the vector γ.Source: B. Range compression · pp. 12–13
  • When N < M, the recovered coefficients superpose contributions from several range cells, so IRCI occurs.This is the stated reason for requiring N ≥ M.Source: B. Range compression · p. 13
  • The range-compressed signal incorporates target range migration, while its azimuth phase remains unaffected by range compression.Source: B. Range compression · p. 13
  • The OFDM range-compression SNR gain is N, compared with N + M −1 for an equal-energy LFM pulse of duration (N + M −1)Ts.The paper states that LFM’s gain is larger, but less than 2N.Source: B. Range compression · p. 13
  • With N ≥ M, the OFDM method can ideally detect and image all M scatterers without IRCI, unlike LFM or random-noise SAR sidelobes that can bury targets when M is roughly more than N.The proposed OFDM sidelobes are ideally zero.Source: B. Range compression · p. 14

C. Discussion on the design of weights Sk

The weight discussion balances constant-modulus subcarrier weights against pulse duration, implementation, and PAPR considerations. It also notes that OFDM weights can represent other radar waveforms through their FFTs.

C. Discussion on the design of weights Sk

  • Constant-modulus weights are optimal for avoiding noise enhancement when estimating weighting RCS coefficients, because dividing by small Sk can enhance noise.The constant-weight special case is distinct from the broader constant-modulus condition.Source: C. Discussion on the design of weights… · p. 14
  • Constant weights produce a delta transmit sequence, but the resulting short pulse with power N may be difficult to implement when high range resolution requires many range cells.High resolution requires large bandwidth and, across a swath, a large number of range cells M and correspondingly large N.Source: C. Discussion on the design of weights… · p. 14
  • I.i.d. weights give constant mean signal power over time, spreading energy across a bandwidth comparable to a short pulse over an N-times-longer duration, which is easier to generate and implement.The comparison is between an OFDM signal and a short pulse of comparable bandwidth.Source: C. Discussion on the design of weights… · p. 14
  • PAPR ranges from N in the worst case to 1 in the best mean case; deterministic PN weights may still produce high PAPR, while Zadoff-Chu weights yield discrete PAPR 1.The paper identifies PAPR reduction for radar OFDM as future research; the Zadoff-Chu result applies to finite discrete-time signal values.Source: C. Discussion on the design of weights… · pp. 14–15
  • Any radar waveform’s sampled sequence can be represented by its N-point FFT weights, and the resulting OFDM waveform can approach that radar waveform as N grows.The passage gives LFM and random-noise radar as examples.Source: C. Discussion on the design of weights… · p. 15

D. Insufficient CP case

With an insufficient CP, the paper’s radar timing avoids inter-block interference, but inter-carrier interference produces IRCI. Shorter CPs involve more range cells in that interference and strengthen it.

D. Insufficient CP case

  • An insufficient CP causes inter-carrier interference that leads to IRCI, although radar’s receive-wait interval prevents inter-block interference between consecutive OFDM pulses.The no-IBI condition follows from waiting for the first pulse’s radar returns before transmitting the second pulse.Source: D. Insufficient CP case · p. 15
  • A shorter insufficient CP brings more range cells into the IRCI term ξm, making the interference stronger.ξm depends on neighboring-cell reflectivities and the transmitted signal.Source: D. Insufficient CP case · p. 16

III. SIMULATIONS AND PERFORMANCE DISCUSSIONS

Simulations compare CP-based OFDM SAR with LFM, conventional OFDM, and random-noise approaches, finding improved range sidelobes and tank-image definition with sufficient CP. Shortening the CP degrades reconstruction, while residual MSE at sufficient length is attributed to fixed-reference-range processing and increases with swath width.

III. SIMULATIONS AND PERFORMANCE DISCUSSIONS

  • The compared imaging methods use different range-compression procedures but identical range-cell migration correction and azimuth compression.The simulations use a fixed reference range cell at the swath center for range-cell migration correction and azimuth compression.Source: §III · p. 17
  • CP-based OFDM produces much lower range-profile sidelobes than the other signals, while all four signals have the same 3 dB mainlobe width.The comparison is for a point target at the range-swath center without additive noise.Source: §III · p. 18, Figure 6 · p. 19
  • Azimuth point-spread profiles are similar for LFM, CP-based OFDM, conventional OFDM, and random-noise signals.The comparison covers the four signals used in the simulations.Source: §III · p. 18, Figure 7 · p. 19
  • The tank boundaries are less blurred with CP-based OFDM SAR than with the other three signals, while zero CP causes significant imaging degradation.The authors attribute the zero-CP degradation to their receiver range-reconstruction method and state that sufficient CP is needed for IRCI-free range reconstruction.Source: §III · pp. 18–20
  • With 96 range cells, CP length 95 gives precise imaging, whereas shorter CPs increase IRCI and can submerge targets.The authors report that empty-cell amplitudes at CP length 95 are below −300 dB due to computer numerical errors; CP lengths 95 and 80 outperform conventional OFDM, but zero CP performs worse.Source: §III · p. 20
  • MSE degradation occurs when CP length is below M − 1; residual error at sufficient length is attributed to fixed-reference-range processing, and wider swaths increase it.The reported MSE averages 1,000 independent Monte Carlo simulations; it is expected to be zero at CP length M − 1 absent the fixed-reference-range processing error.Source: §III · pp. 20–21

IV. CONCLUSION

The conclusion presents sufficient-CP OFDM SAR as an IRCI-free, high-range-resolution method and reports better simulated imaging than LFM and random-noise SAR. It also identifies CP length as necessary and notes unresolved OFDM-specific issues.

IV. CONCLUSION

  • The proposed algorithm models OFDM SAR with sufficient CP and achieves zero IRCI for each cross range.The conclusion says the paper establishes the system model and derives the imaging algorithm.Source: §IV · p. 21
  • The sufficient CP length is M −1, determined by the number of range cells in the swath, which is directly related to range resolution.Source: §IV · p. 21
  • The optimal OFDM pulse duration is To = (2N −1)Ts with CP length N −1, and the proposed system's minimum range equals its maximal swath width.Source: §IV · p. 21
  • Simulations found CP-based OFDM SAR imaging better than LFM and random-noise SAR, with ideally zero range sidelobes.The conclusion presents zero IRCI as the method's ideal property.Source: §IV · p. 21
  • Imaging performance degrades and IRCI increases when the CP length is insufficient.The sufficient length is M −1 samples for M range cells within a swath.Source: §IV · p. 21
  • Future work includes addressing OFDM's high PAPR, sensitivity to unknown Doppler shifts that may cause ICI, and performance for distributed targets.The authors identify these as unresolved research problems.Source: §IV · pp. 21–22
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