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Adaptive Virtual Waveform Design for Millimeter-Wave Joint Communication-Radar

Preeti Kumari, Sergiy A. Vorobyov, Robert W. Heath

arXiv:1904.05516v1eess.SPcs.IT

TL;DR

Limited velocity estimation motivates an adaptive mmWave JCR design using a few non-uniform preambles to create virtual preambles. The paper evaluates radar CRB and communication DMMSE trade-offs with MMSE-based optimizations, finding that non-uniform waveforms generally outperform uniform ones, especially at low SNR and high target density.

  • Problem

    Prior mmWave JCR systems had limited velocity estimation, while increasing preamble duration to improve accuracy degrades communication data rate.

  • Method

    The paper uses a few non-uniform preambles in a CPI to construct virtual preambles, then optimizes waveform placement using radar CRB and communication DMMSE.

  • Results

    Non-uniform waveforms generally perform much better than uniform waveforms, especially at low SNR and high target density.

  • Takeaways & Limitations

    Virtual waveforms can improve velocity-estimation accuracy without much reduction in communication data rate while enabling quantitative radar–communication trade-off design.

Abstract

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Joint communication and radar (JCR) waveforms with fully digital baseband generation and processing can now be realized at the millimeter-wave (mmWave) band. Prior work has proposed a mmWave wireless local area network (WLAN)-based JCR that exploits the WLAN preamble for radars. The performance of target velocity estimation, however, was limited. In this paper, we propose a virtual waveform design for an adaptive mmWave JCR. The proposed system transmits a few non-uniformly placed preambles to construct several receive virtual preambles for enhancing velocity estimation accuracy, at the cost of only a small reduction in the communication data rate. We evaluate JCR performance trade-offs using the Cramer-Rao Bound (CRB) metric for radar estimation and a novel distortion minimum mean square error (MMSE) metric for data communication. Additionally, we develop three different MMSE-based optimization problems for the adaptive JCR waveform design. Simulations show that an optimal virtual (non-uniform) waveform achieves a significant performance improvement as compared to a uniform waveform. For a radar CRB constrained optimization, the optimal radar range of operation and the optimal communication distortion MMSE (DMMSE) are improved. For a communication DMMSE constrained optimization with a high DMMSE constraint, the optimal radar CRB is enhanced. For a weighted MMSE average optimization, the advantage of the virtual waveform over the uniform waveform is increased with decreased communication weighting. Comparison of MMSE-based optimization with traditional virtual preamble count-based optimization indicated that the conventional solution converges to the MMSE-based one only for a small number of targets and a high signal-to-noise ratio.

I. INTRODUCTION

The paper develops an adaptive mmWave JCR waveform that uses a few non-uniformly placed preambles to improve velocity estimation while preserving communication performance. It quantifies the radar–communication trade-off with CRB and DMMSE metrics and optimizes virtual waveforms against uniform designs.

  • Motivation: Prior mmWave JCR approaches using WLAN preambles had poor velocity estimation because their probing preambles or signal durations were short.The control-PHY approach also supported at most 27.5 Mbps with a low update rate.
  • Motivation: Using multiple preambles at constant spacing improves velocity estimation but requires longer total preamble duration, degrading communication data rate.The proposed design targets this communication–radar trade-off through sparse time-domain sensing.
  • Virtual waveform design: The proposed waveform places a few preambles non-uniformly within a CPI and uses their differences to construct several uniform virtual preambles.The resulting virtual increase in radar pulse integration time enhances velocity estimation while relaxing the communication-rate trade-off.
  • Optimization framework: An MMSE-based optimization quantifies the trade-off between radar CRB and communication DMMSE and formulates three adaptive waveform-design problems.The problems constrain radar CRB, constrain communication DMMSE, or optimize a weighted average of both metrics.
  • Evaluation: The study compares uniform and virtual waveforms through simulations varying SNR, preamble count, and target count under automotive and IEEE 802.11ad-based settings.Closed-form waveform configurations such as nested and Wichmann virtual waveforms reduce the computational complexity of finding an optimal design.
  • Results: Virtual waveforms are especially desirable at high SNR with low target density and at low SNR with high communication DMMSE.Traditional preamble-count optimization converges to MMSE-based optimization only at low target density and high SNR.

II. SYSTEM MODEL

The system uses an adaptive single-carrier mmWave waveform for communication and radar, with variable-length frames and preambles placed according to Doppler sampling requirements. Frame parameters can be optimized for joint communication-radar performance.

  • The proposed adaptive single-carrier waveform serves communication and radar systems simultaneously.
  • The CPI contains a fraction µ of communication symbols and a fraction (1 − µ) of preamble symbols.
  • Each JCR frame contains a fixed preamble, variable-length data segment, and constant-duration inter-frame space.
  • Frame locations are integer multiples of the Doppler Nyquist sampling interval TD, with TD ≤ λ/(4vmax).
  • The generic waveform parameters, including each frame’s location and size, can be optimized for desirable JCR performance.

B. Receive signal models

The receive models describe frequency-selective communication and radar channels under block-fading assumptions. Radar echoes combine delayed, Doppler-shifted target reflections with noise, while perfect data-interference cancellation is assumed during training.

  • The communication link is modeled as highly directional mmWave line-of-sight transmission with path loss determined by distance, antenna gains, and the path-loss exponent.
  • The received communication signal consists of delayed, attenuated copies of transmitted signals plus additive white Gaussian noise.
  • Each virtual radar scattering center is characterized by range, delay, velocity, Doppler shift, and radar cross-section.
  • The radar received signal contains attenuated, delayed, Doppler-shifted matched-filter echoes and additive white Gaussian noise.
  • Training sequences are used for radar estimation, but data can interfere with training because the two-way radar channel has a larger delay spread.
  • The model assumes perfect cancellation of the data part during received training, while developing interference-cancellation algorithms is left for future work.

III. PROPOSED RADAR PROCESSING

The radar processor estimates target velocities from channel observations across multiple preambles or frames. It uses correlation-based channel estimation followed by subspace methods, especially MUSIC, to exploit virtual waveform structure.

  • The method estimates target velocities using channel observations collected from proposed JCR frames of equal or varying lengths.
  • Correlation processing estimates the channel from training sequences, after which super-resolution velocity algorithms calculate target velocities.
  • For a selected range bin, the channel vector across M frames is modeled using target amplitudes, Doppler vectors, and noise.
  • The study focuses on MUSIC-class subspace methods, whose velocity resolution is not constrained by CPI duration as in FFT-based processing.
  • Multiple preambles enable sample-covariance processing, with target powers represented in a diagonal covariance matrix.

IV. PERFORMANCE METRICS

The paper evaluates communication with effective spectral efficiency and DMMSE, radar with CRB, and their joint trade-off through scalar MMSE-based metrics. The formulation supports optimization while avoiding limitations of radar estimation-rate measures.

  • A. Communication performance metric: Effective communication data rate is defined as Ceff = µC, reflecting the fraction of communication symbols transmitted in the CPI.
  • B. Radar performance metric: The CRB provides a lower bound on the variance of an unbiased estimator and is used as the radar performance metric.
  • B. Radar performance metric: The CRB formulation accommodates multiple velocity parameters through derivatives of the channel Doppler and co-waveform Doppler matrices.
  • C. Joint communication-radar performance metric: The proposed communication DMMSE is an MMSE-based scalar metric analogous to distortion in rate-distortion theory.
  • C. Joint communication-radar performance metric: Radar estimation-rate metrics are limited because radar parameters are not drawn from countable symbol distributions and extensions to other parameters require simplifications.
  • C. Joint communication-radar performance metric: Trace is selected for the MMSE-based metric because it sums all eigenvalues, while determinant and largest eigenvalue provide alternative summaries.
  • C. Joint communication-radar performance metric: Log-scale quantities are used to achieve proportional fairness because communication DMMSE and radar CRB values are usually substantially different.

V. ADAPTIVE WAVEFORM DESIGN PROBLEM FORMULATION

The paper formulates adaptive JCR waveform design as a multi-objective optimization balancing radar velocity CRB and communication DMMSE. It considers weighted, radar-constrained, and communication-constrained formulations, then develops tractable uniform and virtual waveform solutions.

  • Problem formulation: The JCR design jointly minimizes radar velocity CRB and effective communication DMMSE through scalarized convex performance metrics.The radar and communication objectives are represented by ϕr(CRB) and ϕc(DMMSEeff), with weighting factors assigning task priorities.
  • Problem formulation: The unconstrained weighted-average formulation combines convex-hull radar and communication metrics to obtain a Pareto-optimal design.
  • Problem formulation: Adaptive weights ωr and ωc can reflect scenario requirements, including varying radar SNR.
  • Problem formulation: The radar CRB-constrained problem minimizes communication distortion while enforcing a required radar CRB threshold Υr.For a fixed sparse pulse configuration, the formulation can reduce to finding the minimum frame count meeting the radar requirement.
  • Problem formulation: The communication DMMSE-constrained problem minimizes radar performance subject to a required communication DMMSE threshold Υc.With a predefined frame count and sufficiently large CPI, the optimization reduces to selecting frame locations.
  • Adaptive waveform design solutions: The unrestricted placement problem is generally combinatorial, so the paper uses specific preamble configurations with favorable ambiguity functions to obtain polynomial-complexity solutions.These configurations reduce the optimization to a few variables and support adaptive single-carrier designs.
  • Adaptive waveform design solutions: Uniform designs place preambles at the Doppler Nyquist rate 1/TD, whereas virtual designs place them non-uniformly at sub-Nyquist rates 1/(qmTD) with integer qm > 1.The virtual-waveform examples include uniform and coprime configurations.

A. Uniform waveform design

Uniform waveforms use equally spaced preambles at the Doppler Nyquist rate, making radar CRB behavior depend strongly on target count, SNR, and frame count. Their increasing preamble duration can severely reduce communication spectral efficiency.

  • Uniform waveform design: Uniform waveform designs place MU frames at constant spacing TD throughout a CPI, with frame locations qm = m and MU = {1, 2, · · · , MU}.
  • Uniform waveform design: The uniform-waveform CRB exists when the target count K is smaller than the number of preambles MU and approaches zero as SNR increases.MUSIC is used for velocity estimation under K < MU.
  • Uniform waveform design: As target distance ρ decreases, uniform-waveform optimal solutions improve continuously because the radar CRB decreases with increasing SNR.
  • Uniform waveform design: Increasing target count K degrades the CRB and causes uniform optimization solutions to deteriorate rapidly.The CRB’s existence depends on MU, while the optimal frame-count behavior changes across the constrained formulations.
  • Uniform waveform design: Nyquist-rate placement of multiple frames increases physical preamble duration and can substantially reduce communication spectral efficiency.This limits the feasibility and optimality of uniform adaptive designs.
  • Virtual waveform design: Non-uniform designs use sparse preamble placements and hole-free difference co-waveforms, enabling MUSIC-like processing over a contiguous virtual aperture.Their CRB expression requires 2K ≤ |CV|.
  • Virtual waveform design: For K << MU and equal physical frame counts, non-uniform waveforms reduce CRB faster than uniform waveforms and can identify O(MV^2) sources.Their feasible optimization set expands because they may require fewer frames for a radar CRB while maintaining validity constraints.
  • Virtual waveform design: Non-uniform designs reduce the radar–communication trade-off at low target density, but their advantage decreases under high-SNR saturation and small radar distances.Lower sparse-set cardinality also reduces communication spectral-efficiency overhead.

VII. SIMULATION RESULTS

The simulations evaluate uniform and non-uniform virtual waveform designs under IEEE 802.11ad-based mmWave automotive parameters. They examine radar–communication trade-off curves across target counts, distances, and SNR conditions.

  • Simulation setup: The simulations compare radar RCRB and communication DMMSE trade-offs for uniform, nested, and Wichmann waveforms.

A. Performance trade-off

Virtual waveforms relax the radar–communication trade-off relative to uniform waveforms, especially in sparse or multi-target settings with low communication DMMSE. However, non-uniform designs show saturation and their practical achievability depends on snapshots and estimator choice.

  • Performance trade-off: Wichmann, nested, and uniform waveforms are compared using radar RCRB and communication DMMSE across target counts, distances, and SNRs.
  • Performance trade-off: The Wichmann virtual waveform has the most relaxed radar–communication trade-off, followed by nested and uniform waveforms.
  • Performance trade-off: Virtual waveforms provide greater advantage over uniform waveforms as communication DMMSE worsens in the single-target case.
  • Performance trade-off: For multiple targets, uniform-waveform radar CRBs exist only when M > K, whereas virtual-waveform CRBs can exist with M < K.
  • Performance trade-off: At low communication DMMSE, virtual-waveform radar CRBs saturate at high SNR and large K/M ratios.
  • Convex-hull trade-off: Trade-off curves are approximately convex for K = 1 but deviate farther from convexity as target distance decreases for K = 30.The uniform curve is more visibly convex than non-uniform curves.
  • Convex-hull trade-off: Using the convex hull discards non-beneficial points and can produce a more relaxed RCRB–DMMSE trade-off through time-sharing or probabilistic occurrence.
  • Velocity estimation: Direct-MUSIC reaches the RCRB more efficiently than DA-MUSIC at high SNR, while DA-MUSIC is more efficient at low SNR.Small-snapshot algorithms reach the RCRB at high SNR, whereas low SNR requires more snapshots.

B. Optimal waveform designs

The study evaluates MMSE-based optimal waveform designs across communication weightings, target counts, distances, and SNRs. Non-uniform waveforms generally outperform uniform waveforms, with the advantage depending on weighting and target conditions.

  • Weighted average optimization-based design: The advantage of nested waveforms over uniform waveforms decreases as communication weighting approaches 1.At communication weighting ωc = 1 and K = 1, all tested waveforms converge because the lowest possible M is used.
  • Weighted average optimization-based design: The optimal number of frames M decreases as communication weighting increases, from M = 40 at zero communication weighting to the lowest feasible M satisfying CRB existence.This behavior is reported across the tested waveform designs.
  • Target count and SNR: For most scenarios, nested waveforms perform best and uniform waveforms worst; Wichmann waveforms generally outperform nested waveforms.The non-uniform waveform advantage increases with target count but can reduce with radar SNR at high target count because of saturation.
  • Communication weighting 0.96: At communication weighting 0.96, the optimal M increases with target count in most cases, except for nested waveforms under high-SNR, large-K saturation.The optimal weighted average degrades with target count, while the non-uniform advantage increases with K and can reduce with radar SNR at high K.
  • Target distance: The optimal M increases with distance at low target count but decreases with distance at high target count.The reported explanation combines pathloss-driven radar RCRB degradation at large distances with saturation at small distances for high target count.
  • Target distance and SNR: The optimal weighted average generally improves with decreasing target distance, while saturation effects appear for nested and Wichmann waveforms at K = 30.For non-uniform waveforms, improvement with radar SNR decreases as target count grows, whereas it remains constant for uniform waveforms.

2) Radar CRB constrained optimization-based design:

The radar-CRB-constrained design optimizes communication DMMSE and frame count under radar constraints. Virtual waveforms, especially Wichmann, generally provide better feasible trade-offs than uniform waveforms, with gains varying by target count, distance, SNR, and DMMSE constraint.

  • Radar CRB constrained optimization-based design: For a minimum radar CRB of -18 dB, Wichmann achieves the best optimal DMMSE, followed by nested, while uniform performs worst.The virtual-waveform advantage increases with target count at high SNR and with distance at low target density.
  • Radar CRB constrained optimization-based design: The optimal DMMSE increases with target count and decreasing SNR, while its dependence on target count is weaker in the reported comparison.All three waveforms converge at low target count and small target distance.
  • Radar RCRB feasibility: At ρ = 20 m, the feasibility of the optimal radar-RCRB solution depends on target count and the virtual-preamble count condition 2K ≤ |CV|.The supplied passages identify this condition as the boundary for the reported feasibility analysis.
  • Communication DMMSE constrained optimization-based design: For a given DMMSE constraint, Wichmann has the highest feasibility, uniform the lowest, and Wichmann achieves better optimal RCRB than nested and uniform.This follows from selecting the maximum M satisfying the communication constraint on the convex hull of the JCR trade-off curve.
  • Communication DMMSE constrained optimization-based design: For DMMSE constraints of −31.3 dB and −27.6 dB, the optimal frame counts are M = 6 and M = 40 in most scenarios, respectively.For K = 30 at 80 m and 100 m, nested uses M = 39 at −27.6 dB because the M = 40 radar RCRB is non-decreasing.
  • Communication DMMSE constrained optimization-based design: The optimal radar RCRB worsens with increasing target count and increasing radar distance; Wichmann is usually best and uniform usually worst.At high SNR and high K/M, nested and Wichmann can exhibit saturation, while uniform may be infeasible when K ≥ M.

4) Comparison with VP count optimization-based design:

The adaptive virtual waveform design outperforms uniform waveforms in most cases, while MMSE-based optimization captures communication–radar trade-offs more directly than virtual-preamble-count optimization. The count-based solution is mainly useful as a coarse estimate, with agreement depending on target count and SNR.

  • For K = 1, the VP count-based and CRB-based solutions are close at high SNR, but they diverge as target count and radar SNR increase.
  • The VP count-based design provides a coarse estimate of the CRB-based communication DMMSE-constrained solution, with the optimal-solution gap increasing with target count and decreasing target distance.
  • The proposed design uses a few non-uniform preambles and sparse sensing to improve velocity-estimation accuracy without substantially reducing communication data rate.
  • The radar CRB–communication DMMSE trade-off contains non-convex points caused by non-decreasing CRB values or radar-CRB saturation at high SNR.
  • MMSE-based optimization formulates minimum communication DMMSE, minimum radar CRB, and weighted MMSE-average problems for balancing communication and radar performance.
  • Non-uniform waveforms perform much better than uniform waveforms in most cases, especially at low SNR and high target density.
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