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MIMO-OFDM Joint Radar-Communications: Is ICI Friend or Foe?

Musa Furkan Keskin, Henk Wymeersch, Visa Koivunen

arXiv:2103.15694v1eess.SPcs.IT

TL;DR

High-mobility ICI degrades OFDM JRC sensing and complicates multi-target detection with arbitrary communication symbols. The paper proposes an ICI-aware MIMO-OFDM algorithm based on angle estimation, joint CFO/channel estimation, and GLRT-based detection; simulations show improved performance over conventional methods and resolution of targets sharing delay-Doppler-angle cells.

  • Problem

    High-mobility ICI degrades OFDM radar and creates a need for multi-target sensing that preserves arbitrary transmit data symbols while exploiting MIMO information.

  • Method

    The method estimates angles with MUSIC, reformulates delay-Doppler sensing as joint CFO/channel estimation using APES-like filtering, and applies iterative GLRT-based interference-canceling detection.

  • Results

    The proposed approach substantially improves detection and range-velocity estimation over conventional FFT methods, approaches ICI-free performance, and resolves targets sharing a delay-Doppler-angle cell.

  • Takeaways & Limitations

    ICI can supply velocity information and an additional CFO dimension for target resolvability rather than serving only as an impairment.

Abstract

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Inter-carrier interference (ICI) poses a significant challenge for OFDM joint radar-communications (JRC) systems in high-mobility scenarios. In this paper, we propose a novel ICI-aware sensing algorithm for MIMO-OFDM JRC systems to detect the presence of multiple targets and estimate their delay-Doppler-angle parameters. First, leveraging the observation that spatial covariance matrix is independent of target delays and Dopplers, we perform angle estimation via the MUSIC algorithm. For each estimated angle, we next formulate the radar delay-Doppler estimation as a joint carrier frequency offset (CFO) and channel estimation problem via an APES (amplitude and phase estimation) spatial filtering approach by transforming the delay-Doppler parameterized radar channel into an unstructured form. To account for the presence of multiple targets at a given angle, we devise an iterative interference cancellation based orthogonal matching pursuit (OMP) procedure, where at each iteration the generalized likelihood ratio test (GLRT) detector is employed to form decision statistics, providing as by-products the maximum likelihood estimates (MLEs) of radar channels and CFOs. In the final step, target detection is performed in delay-Doppler domain using target-specific, ICI-decontaminated channel estimates over time and frequency, where CFO estimates are utilized to resolve Doppler ambiguities, thereby turning ICI from foe to friend. The proposed algorithm can further exploit the ICI effect to introduce an additional dimension (namely, CFO) for target resolvability, which enables resolving targets located at the same delay-Doppler-angle cell. Simulation results illustrate the ICI exploitation capability of the proposed approach and showcase its superior detection and estimation performance in high-mobility scenarios over conventional methods.

I. INTRODUCTION

The paper develops ICI-aware sensing for multi-target MIMO-OFDM JRC systems while retaining arbitrary communication data symbols. It reformulates delay-Doppler estimation through joint CFO and channel estimation, then exploits CFO information for improved target resolvability and detection.

  • Motivation: High-mobility Doppler-induced ICI raises OFDM radar sidelobes, reduces dynamic range, and can mask weak targets.These effects arise because Doppler shifts destroy subcarrier orthogonality at the receiver.
  • Research gap: Prior ICI compensation methods restrict transmit symbols, often address single targets or assume prior detection, and have largely studied SISO radar.Such restrictions can reduce communication data rate and impede dual-functional operation.
  • Objective: The paper targets generic multi-target MIMO-OFDM sensing with arbitrary transmit symbols, jointly mitigating and exploiting ICI without hampering OFDM communication.The proposed formulation is designed for high-mobility vehicular JRC applications.
  • Method: Radar delay-Doppler estimation is recast as joint channel and CFO estimation through an APES-like spatial filtering formulation.This formulation transforms the Doppler-parameterized radar channel into an unstructured form and supports ICI-decontaminated target-specific channels.
  • Method: The three-step detector estimates angles with MUSIC, estimates CFOs and channels per angle, and applies GLRT-based multi-target detection with interference cancellation.The method is presented for MIMO-OFDM DFRC sensing with multiple targets.
  • Findings: CFO estimates provide unambiguous velocity information and add a fourth resolvability dimension, while simulations show performance close to ICI-free observations and above conventional FFT methods.The additional CFO dimension can distinguish targets sharing a delay-Doppler-angle cell.

B. Receive Signal Model

The signal model represents a multi-target OFDM radar frame across antenna, fast-time, and slow-time dimensions while explicitly modeling Doppler-induced ICI. It defines the target parameters, operating assumptions, and the resulting sensing objective.

  • Receive Signal Model: Each far-field target is characterized by channel gain, azimuth angle, round-trip delay, and normalized Doppler shift.The normalized Doppler shift is ν = 2v/c and produces the time-varying delay τ(t) = τ − νt.
  • Assumptions: The model assumes CP duration exceeds the furthest target delay, Doppler shifts satisfy |ν| ≪ 1/N, and the wideband effect is negligible.The small-surveillance-volume assumption supports the delay approximation used in the model.
  • Signal representation: After CP removal, sampling produces fast-time observations within each OFDM symbol that are organized with slow-time samples across symbols.The frame contains M OFDM symbols, each with N subcarriers and total duration T_sym = T_cp + T.
  • ICI representation: The diagonal phase rotation matrix D(ν) captures Doppler-dependent fast-time phase shifts that create ICI, analogous to CFO effects in OFDM communications.The paper therefore refers to ν as CFO when emphasizing its fast-time phase-rotation effect.
  • Sensing objective: The sensing task is to detect possibly multiple targets and estimate their channel gains and delay-Doppler-angle parameters from the received antenna data cube.The received frame aggregates multiple targets and additive noise in a fast-time/slow-time matrix representation.

III. ICI-AWARE PARAMETER ESTIMATION VIA APES SPATIAL FILTERING

The method first estimates target angles with MUSIC by exploiting a spatial covariance structure that is independent of target delays and Dopplers. This provides angle estimates for subsequent spatial filtering.

  • Algorithm Overview: The algorithm treats this angle-estimation stage as the first step of an ICI-aware delay-Doppler-angle estimation procedure.The section assumes at most one target per azimuth cell before extending the method to multiple targets.
  • Angle Estimation via MUSIC: MUSIC is used to obtain high-resolution angle estimates from the spatial covariance matrix, including when only a small number of antennas is available.The estimated angles correspond to peaks of the MUSIC spatial spectrum.
  • Angle Estimation via MUSIC: The spatial covariance matrix is modeled as a low-rank signal covariance plus scaled diagonal noise under sufficiently large dimensions and non-overlapping targets in delay or Doppler.The approximation supports applying standard MUSIC despite ICI.

B. Step 2: Angle-Constrained Joint CFO and Unstructured Channel Estimation via APES Beamforming

For each estimated angle, the method reformulates radar delay-Doppler estimation as joint CFO and unstructured time-domain channel estimation. An APES spatial beamformer produces angle-specific channel and CFO estimates while treating other target components as interference.

  • Radar-Communications Duality: The formulation exploits a duality between ICI-aware OFDM radar sensing and joint channel/CFO estimation in OFDM communications.Radar targets are interpreted as uncooperative users, while probing symbols act as communication data or pilots.
  • Joint CFO and Channel Estimation: For each estimated angle, the method jointly estimates CFO and unstructured time-domain channels using an APES spatial beamforming formulation.The unstructured representation replaces the original delay-Doppler-parameterized radar channel during this stage.
  • APES Beamforming: The APES beamformer is designed so its output approximates the noiseless received signal for the selected angle.The spatial beamforming vector is constrained by the estimated angle.
  • Step 2 Outputs: The outputs of Step 2 are CFO estimates and unstructured single-target channel estimates collected over OFDM symbols.The channel representation uses time-domain channels with a number of taps constrained by the cyclic-prefix requirement.

C. Step 3: Angle-Constrained Delay-Doppler Recovery from Unstructured Channel Estimates

The third step recovers delay, Doppler, and gain from the unstructured channel estimates. It then uses the CFO estimate to resolve Doppler ambiguity before naming the resulting method APES-UML.

  • Delay-Doppler Recovery: Delay and Doppler are estimated from the unstructured channel estimates using a least-squares formulation that exploits the channel structure.On the specified uniform grid, the delay and Doppler estimates can be obtained by a 2-D FFT.
  • Delay-Doppler Recovery: Channel gain is estimated from the recovered delay-Doppler parameters and the unstructured channel estimates.The gain estimate follows the delay-Doppler recovery step.
  • Doppler Ambiguity Resolution: The CFO estimate is used to resolve ambiguity in the Doppler estimate obtained from slow-time phase rotations.CFO is estimated from fast-time phase rotations, providing complementary ambiguity information.
  • Three-Step Procedure: The complete single-target procedure estimates delay-Doppler-gain parameters after first estimating angles, CFOs, and time-domain channels.Algorithm 1 lists the three stages and names the resulting procedure APES-UML.

IV. ICI-AWARE DETECTOR/ESTIMATOR DESIGN VIA GLRT AND OMP

To handle multiple targets at one angle, the method replaces the single-target steps with an OMP-based iterative interference-cancellation procedure. A GLRT detects the strongest target in each residue and returns CFO and channel estimates as by-products.

  • OMP-Based Detection: The multiple-target extension uses orthogonal matching pursuit with iterative interference cancellation at a fixed azimuth angle.The procedure modifies the single-target algorithm’s Step 2 and Step 3.
  • GLRT Detection: At each iteration, the method tests for a target in the current residue using a GLRT under hypotheses of target absence or presence.The receive beamformer is steered toward the estimated angle.
  • GLRT Detection: The GLRT combines spatial and APES beamforming optimizations to form its detection statistic.The first optimization is a Capon beamforming problem, while the second is the APES beamforming problem used for CFO estimation.
  • Iterative Cancellation: When the GLRT statistic crosses the threshold, the procedure detects the strongest target in the current residue and obtains its CFO estimate as a by-product.The detected target’s effect is then removed from the residue for subsequent iterations.

B. OMP for Iterative Interference Cancellation

The OMP procedure iteratively updates channel estimates for detected targets and computes residuals for subsequent GLRT-based detections, under a sparse-scene assumption.

  • OMP-based channel update: The procedure jointly estimates channels of multiple targets at one angle using their CFO parameters through an APES-based optimization.The formulation generalizes the APES beamforming problem to multiple targets.
  • OMP-based channel update: At each iteration, updated atom sets represent the CFOs of detected targets and support closed-form channel estimation.The current atom set is constructed from the detected targets’ CFO estimates.
  • Sparse-scene assumption: The algorithm assumes that the number of targets at an azimuth cell with distinct CFOs does not exceed N/L.This sparsity condition is motivated by N/L = T/T_cp ≫ 1 for OFDM.
  • Iterative interference cancellation: After updating detected-target channels, the method computes a residual that becomes the input to GLRT detection at the next iteration.The GLRT and OMP updates are combined in Algorithm 2.

C. GLRT for Detection of Multiple Targets at the Same Angle-CFO Cell

The third step detects multiple targets sharing an angle-CFO cell by applying a GLRT-derived delay-Doppler metric to channel estimates and resolving Doppler ambiguity with CFO information.

  • Problem formulation: Multiple targets at the same angle-CFO cell can produce channel estimates that superpose echoes with different delays.The method models this case using the channel estimate and CFO pair output by Algorithm 2.
  • Delay-Doppler detection: Algorithm 3 applies a 2-D FFT to obtain a delay-Doppler spectrum, then uses CFAR detection to identify peaks above a false-alarm threshold.Detected target gains are estimated from the GLRT metric.
  • Delay-Doppler detection: Unlike Algorithm 2, the method detects multiple targets without interference-cancellation iterations by searching the delay-Doppler metric for threshold-exceeding peaks.This procedure is designed for targets sharing the same angle-CFO cell but differing in delay.
  • Doppler ambiguity resolution: CFO estimates resolve Doppler ambiguities after delay-Doppler detections are obtained.The algorithm uses the CFO estimate associated with each channel estimate to perform ambiguity resolution.
  • Resolution trade-off: Poor CFO resolution can permit mutual interference in the CFO domain, whereas delay-Doppler resolution makes such interference unlikely.The stated resolutions are 1/(f_cT) for CFO and 1/(f_cMT_sym) for the delay-Doppler Doppler estimate.

V. NUMERICAL RESULTS

The numerical study evaluates the proposed APES-UML algorithm against standard and ICI-free 2-D FFT benchmarks using randomly generated QPSK symbols and a common CFAR detector.

  • Simulation setup: The evaluation uses an OFDM system configured for low-cost vehicular JRC scenarios with few antennas and low bandwidth.The transmit beamformer points toward −30° and target SNR is defined as |α_k|^2/σ^2.
  • Evaluation protocol: All schemes use an identical CFAR detector with probability of false alarm P_fa = 10^-4.This common detector setting supports comparison across the evaluated processing chains.
  • Evaluation goals: The experiments first illustrate ICI suppression and exploitation, then assess detection and estimation performance against the benchmark schemes.The numerical section therefore covers both mechanism-level behavior and comparative performance.

A. Illustrative Example: ICI Suppression and Exploitation Capability of the Proposed Algorithm

The illustrative scenario tests multi-target separation under velocity ambiguity, overlapping range-angle cells, and ICI, showing how MUSIC, iterative CFO processing, and APES-UML recover targets and suppress interference.

  • Scenario: The scenario contains five targets, including three sharing a range-velocity-angle cell and two sharing a velocity-angle cell but having different ranges.Their SNRs are {20, 15, 10, 10, −10} dB, respectively.
  • Angle estimation: MUSIC identifies distinct target angles with few receive antennas, unlike ordinary beamforming.This angle resolution supports the angle-constrained beamforming used in the next processing step.
  • CFO-domain processing: During OMP iterations, interference cancellation creates CFO-spectrum valleys at the velocities of removed strong targets and exposes weaker targets.At θ = −35°, the strongest 20 dB target is detected first; subsequent iterations cancel its contribution and continue detection.
  • ICI exploitation: CFO information resolves Targets 1–3 as separate objects with unambiguous velocities, adding a resolvability dimension beyond standard slow-time processing.The proposed formulation separates velocity estimation in the fast-time and slow-time components.
  • ICI suppression: APES-UML removes ICI from target-specific channels, making masked range peaks visible and producing range profiles close to the ICI-free case.The standard FFT masks Target 5, whereas APES-UML reveals its peak; spatial filtering also limits leakage between different angles.
  • Spatial filtering: MIMO-enabled spatial filtering separates individual target reflections from the mixed received signal in the angular domain.The APES cost function designs beamformers for estimated target angles.

B. Detection and Estimation Performance

Across detection and estimation tests, APES-UML remains close to ICI-free performance while standard FFT degrades as target velocity increases. The proposed method suppresses multi-target ICI and exploits it to resolve Doppler ambiguities.

  • Experimental setup: The evaluation uses 100 independent Monte Carlo noise realizations in a two-target scenario with Target 2 as the reference target.The study varies the reference-target SNR and both target velocities to examine ICI masking from a strong Target 1.
  • Detection: APES-UML significantly outperforms standard FFT detection and stays close to the ICI-free benchmark across target velocities.At 120 m/s, standard 2-D FFT becomes blind within the evaluated SNR range, whereas APES-UML reaches the ICI-free upper bound.
  • Detection: APES-UML achieves false alarm performance close to FFT with ICI-free observations, whereas standard FFT generally fails except at high SNR and low mobility.False discovery rate is defined as FDR = V/(V + S), with V denoting false alarms and S reference-target detections.
  • Range estimation: APES-UML achieves almost the same range RMSE as the ICI-free benchmark and maintains consistent range estimation as velocity increases.FFT-based estimation degrades with ICI and cannot estimate target parameters below a velocity-dependent SNR threshold because of missed detections.
  • Velocity estimation: For 70 m/s and 120 m/s targets, FFT-based methods fail on velocity estimation because their unambiguous velocity is vmax = ±24.41 m/s.Joint CFO/channel estimation enables UML to estimate the true velocity with high accuracy and can outperform the ICI-free benchmark in these ambiguous-velocity cases.
  • Overall findings: The proposed algorithm mitigates ICI from multiple targets and exploits it for Doppler-ambiguity resolution while supporting arbitrary OFDM data symbols.The reported simulations cover probability of detection and range/velocity estimation accuracy in high-mobility MIMO-OFDM DFRC.

SUPPLEMENTARY MATERIAL FOR

The supplementary derivation develops the spatial covariance matrix of OFDM radar observations using large-sample approximations and data-symbol covariance properties. It separates direct, cross-target, noise, and signal-noise terms before completing the covariance result.

  • Spatial covariance derivation: The derivation begins by substituting the radar observation model into the spatial covariance matrix expression.The supplementary section identifies the resulting direct and cross-target contributions.
  • Covariance approximations: The noise covariance is approximated using the law of large numbers when M and/or N is sufficiently large.Signal-noise cross terms are likewise neglected because transmit data symbols and noise are uncorrelated.
  • Direct and cross-target terms: The direct term is simplified using the radar model, unitary DFT properties, and unit-magnitude steering-vector elements.These steps reduce the direct contribution before applying the covariance of the transmit-symbol matrix.
  • Direct and cross-target terms: The cross-term is rewritten with Hadamard-product properties and evaluated through the transmit-data distribution and covariance assumptions.Under assumption (17), the cross-term disappears.
  • Proof completion: The final covariance expression follows by inserting the intermediate direct-term and cross-term results into the preceding covariance equation.The supplementary proof concludes after this substitution.
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