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MIMO-OFDM ISAC Waveform Design for Range-Doppler Sidelobe Suppression

Peishi Li, Ming Li, Rang Liu, Qian Liu, A. Lee Swindlehurst

arXiv:2406.17218v1eess.SP

TL;DR

Random information symbols in dual-functional MIMO-OFDM ISAC waveforms create range-Doppler sidelobes that can mask weak targets. The paper designs an SLP waveform to reduce integrated sidelobe level under sensing and communication constraints, reporting lower sidelobes than communication-only waveforms and detection and estimation close to radar-only designs.

  • Problem

    Communication-signal randomness creates high ambiguity-function sidelobes that can mask weak targets and increase ghost-target false alarms, while existing designs do not effectively address this range-Doppler sensing impact.

    Source: §I · p. 2

  • Method

    The paper designs an SLP-based MIMO-OFDM waveform to minimize range-Doppler ISL under target illumination, multi-user QoS, and constant-modulus constraints, using an MM-ADMM algorithm.

    Source: §I · p. 2

  • Results

    More than 45dB lower normalized range-Doppler ISL than communication-only waveforms, with target detection and estimation close to radar-only waveforms.

    Source: §I · p. 2

  • Takeaways & Limitations

    The simulations support SLP-based ISAC as a dual-function design that combines user QoS constraints with improved radar sensing performance.

    Source: §I · p. 2

Abstract

from arXiv · show

Integrated sensing and communication (ISAC) is a key enabling technique for future wireless networks owing to its efficient hardware and spectrum utilization. In this paper, we focus on dual-functional waveform design for a multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) ISAC system, which is considered to be a promising solution for practical deployment. Since the dual-functional waveform carries communication information, its random nature leads to high range-Doppler sidelobes in the ambiguity function, which in turn degrades radar sensing performance. To suppress range-Doppler sidelobes, we propose a novel symbol-level precoding (SLP) based waveform design for MIMO-OFDM ISAC systems by fully exploiting the temporal degrees of freedom (DoFs). Our goal is to minimize the range-Doppler integrated sidelobe level (ISL) while satisfying the constraints of target illumination power, multi-user communication quality of service (QoS), and constant-modulus transmission. To solve the resulting non-convex waveform design problem, we develop an efficient algorithm using the majorization-minimization (MM) and alternative direction method of multipliers (ADMM) methods. Simulation results show that the proposed waveform has significantly reduced range-Doppler sidelobes compared with signals designed only for communications and other baselines. In addition, the proposed waveform design achieves target detection and estimation performance close to that achievable by waveforms designed only for radar, which demonstrates the superiority of the proposed SLP-based ISAC approach.

I. INTRODUCTION

Random communication symbols raise range-Doppler sidelobes, a sensing challenge for MIMO-OFDM ISAC. The paper proposes SLP waveform design to reduce those sidelobes while meeting sensing, communication, and transmission constraints.

I. INTRODUCTION

  • Prior beamforming designs focus on spatial signal statistics, while this work investigates SLP waveform design that uses temporal and spatial degrees of freedom.The paper describes this as the first investigation of SLP-based range-Doppler sidelobe suppression for MIMO-OFDM ISAC.Source: §I · pp. 1–2
  • Random communication signals produce high ambiguity-function sidelobes that can mask weak targets and increase false alarms for ghost targets.Earlier approaches include reciprocal filtering, which can enhance noise, and combining communication symbols with radar probes, which may leave interference when users and targets are near.Source: §I · p. 2
  • The design minimizes ambiguity-function range-Doppler ISL subject to target illumination power, multi-user QoS, and constant-modulus constraints, using an MM-ADMM algorithm.The discrete periodic ambiguity function provides a quantitative basis for evaluating radar sensing performance and waveform designs.Source: §I · p. 2
  • More than 45dB lower normalized range-Doppler ISL than communication-only waveforms, with target detection and estimation close to radar-only waveforms.The paper attributes the sensing performance to sidelobe suppression.Source: §I · p. 2

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • The modeled dual-function base station uses MIMO-OFDM to serve K single-antenna users and sense targets from echoes for range and velocity estimation.It has Nt transmit and Nr receive antennas, Nc subcarriers, and Ns OFDM symbols.Source: §II · p. 3

A. Transmit Signal Model

  • The base station precodes each subcarrier's information symbols at each time slot, using SLP to exploit both symbol values and their temporal properties.The resulting precoded sequences are OFDM-modulated into a baseband signal.Source: A. Transmit Signal Model · p. 3

B. Radar Echo Signal Model and Signal Processing

The section models the target echo and explains how the base station processes it to form a range-Doppler map. Delay and Doppler phase variations support range and velocity estimation, while waveform randomness can raise sidelobes.

Radar Echo Signal Model and Signal Processing

  • The echo model assumes constant target radar cross section over the OFDM signal duration and expresses round-trip delay and Doppler shift through target range and velocity.It also assumes the target azimuth is known and focuses estimation on range and velocity.Source: B. Radar Echo Signal Model and Signal… · pp. 3–4
  • Delay-induced phase across subcarriers supports range estimation, while slow-time Doppler phase supports velocity estimation.Randomness across subcarriers and slow time produces high range and Doppler sidelobes, respectively.Source: B. Radar Echo Signal Model and Signal… · p. 4
  • The base station samples and transforms the received echo, then applies matched filtering and Fourier transforms to form a range-Doppler map for peak-based target detection and estimation.The target azimuth is assumed known, so spatial filtering uses its steering vector before range and velocity estimation.Source: B. Radar Echo Signal Model and Signal… · p. 4

C. Radar Performance Metric

The ambiguity function characterizes the transmit waveform's range-Doppler sidelobes, which affect sensing quality. The section uses integrated sidelobe level (ISL) to quantify them and includes target illumination power as a proxy for receive SNR.

Radar Performance Metric

  • The ambiguity function's sidelobes matter because low range-Doppler sidelobes make radar less prone to false alarms or detection errors.The ambiguity function is the time-frequency composite autocorrelation of the transmitted signal.Source: C. Radar Performance Metric · pp. 4–5
  • The desired ambiguity function has a narrow peak at zero range and Doppler offset and low sidelobes elsewhere, but embedded communication data can raise sidelobes unless controlled.The section identifies ghost peaks and weak-target detection as reasons to control data-induced sidelobes.Source: C. Radar Performance Metric · p. 5
  • The design uses ISL to quantify sidelobes and target illumination power as a proxy for receive SNR, whose direct measurement is difficult without target RCS and noise-power information.Increasing transmission power toward the target proportionally improves receive SNR.Source: C. Radar Performance Metric · p. 5

D. Communication Model and Performance Metric

The base station sends information-bearing waveforms to single-antenna users over frequency-selective channels. The section defines symbol-level precoding through constructive interference and imposes a safety margin to express communication QoS.

Communication Model and Performance Metric

  • The communication receiver down-converts, digitizes, removes the cyclic prefix, and applies a DFT before obtaining each user's subcarrier signal.The model assumes frequency-selective fading channels.Source: D. Communication Model and Performance… · p. 5
  • The base station uses symbol-level precoding rather than block-level precoding to design each precoded signal, assuming PSK symbols for the formulation.The paper states that the formulation can extend to other constellations, including higher-order QAM, with more involved mathematics.Source: D. Communication Model and Performance… · p. 6
  • For QPSK, a symbol is correctly detected when its received signal lies in its constructive-interference region, and precoding places the noise-free signal away from decision boundaries for robustness.For the illustrated symbol, the positive halves of the x and y axes are decision boundaries and the first quadrant is the detection region.Source: D. Communication Model and Performance… · p. 6
  • The buffer Γk is a safety margin between the constructive-interference region and decision boundaries, chosen to guarantee a minimum user QoS in SNR or symbol error rate.The resulting constructive-interference constraints are used as the multi-user communication performance metric.Source: D. Communication Model and Performance… · p. 6

E. Problem Formulation

The waveform design minimizes range-Doppler ISL while meeting target illumination, communication QoS, and constant-modulus requirements. The resulting problem is non-convex because of its quartic objective and non-convex constraints.

Problem Formulation

  • Constant-modulus transmission is imposed to avoid power-amplifier nonlinear distortion and enhance amplifier efficiency.The time-domain transmit vector is constrained to have constant-amplitude elements.Source: E. Problem Formulation · p. 6
  • The design minimizes range-Doppler ISL subject to target illumination power, multi-user communication QoS, and constant-modulus waveform constraints.The QoS is measured by the gap between the constructive-interference region and symbol decision boundaries.Source: E. Problem Formulation · p. 6
  • The formulation is difficult because its objective is a non-convex quartic function and its illumination-power and constant-modulus constraints are non-convex.The target illumination constraint specifies a required minimum power P0.Source: E. Problem Formulation · p. 6

III. SLP-BASED ISAC WAVEFORM DESIGN FOR RANGE-DOPPLER SIDELOBE SUPPRESSION

The section recasts the waveform-design problem for algorithm development, including a compact expression for range-Doppler ISL and a convex reformulation of the illumination-power constraint.

III. SLP-BASED ISAC WAVEFORM DESIGN FOR RANGE-DOPPLER SIDELOBE SUPPRESSION

  • The MM-ADMM algorithm addresses the non-convex waveform-design problem by reformulating illumination power, applying MM, and using ADMM for the constant-modulus constraint.The algorithm alternates between solving the resulting subproblems.Source: §III · p. 7

A. Problem Reformulation

  • The illumination-power constraint is converted into a convex form using the positive-semidefinite property of the relevant matrix.The reformulation defines the bound as P̄0 = NtPT − P0.Source: A. Problem Reformulation · p. 7
  • The range-Doppler ISL is equivalently rewritten in a compact form with respect to the transmit waveform.The derivation uses matrix manipulations and the definitions of the matrices in the formulation.Source: A. Problem Reformulation · p. 7

B. MM Transformation

The MM transformation builds tractable surrogate objectives around the current waveform iterate. It majorizes the quartic and quadratic terms to obtain a convex upper bound, while the constant-modulus constraint remains non-convex for ADMM.

B. MM Transformation

  • MM replaces the objective in (36a) with a locally approximating surrogate upper bound, minimized at each iteration.This transforms the original problem into a series of more tractable subproblems.Source: B. MM Transformation · p. 7
  • The range-Doppler ISL objective contains a quartic term f1(x) and a quadratic term f2(x), which are further majorized to form a favorable convex upper bound.The quadratic term is handled using a surrogate derived from a Hermitian matrix and its largest eigenvalue.Source: B. MM Transformation · p. 8
  • The resulting subproblem remains non-convex because of the constant-modulus constraint, which the method assigns to ADMM.The objective and illumination-power constraint are described as convex.Source: B. MM Transformation · p. 9

C. ADMM Transformation

The ADMM transformation separates the non-convex constant-modulus constraint from the other constraints using an auxiliary variable, then expresses the problem through a feasibility indicator and augmented Lagrangian.

C. ADMM Transformation

  • An auxiliary variable z = eF^H x and an equality constraint are introduced to decouple the constant-modulus constraint from the other convex constraints.Source: C. ADMM Transformation · p. 9
  • The feasible region for the inequality constraints is represented by an indicator function incorporated into the objective.Source: C. ADMM Transformation · p. 9
  • The augmented Lagrangian uses dual variables λ and μ and penalty parameter ρ, and is minimized by alternating updates of x, z, λ, and μ.Source: C. ADMM Transformation · p. 9

D. Block Update

The block-update procedure alternates optimization over x and z with gradient updates of the dual variables. The algorithm repeats these updates and returns the waveform when its stated stopping condition is met.

D. Block Update

  • For fixed z and dual variables, the x-update is a convex problem that can be solved with existing methods such as an interior-point method.Source: D. Block Update · p. 9
  • The algorithm repeats its inner updates and returns x⋆ when the relative change in ξISL is at most δth.Source: D. Block Update · p. 9
  • Given x and the dual variables, the z-update is non-convex because of an absolute-value operation but has a closed-form solution.Source: D. Block Update · p. 9
  • With x and z fixed, the algorithm updates λ and μ using gradient descent.Source: D. Block Update · p. 9

E. Summary

The proposed MM-ADMM algorithm is summarized as the method for SLP-based ISAC waveform design, and SQUAREM is adopted to expedite convergence. Table I is identified as the source of essential simulation parameters.

E. Summary

  • Algorithm 1 summarizes the proposed MM-ADMM method for SLP-based ISAC waveform design.The convergence threshold is denoted by δth.Source: E. Summary · p. 9
  • Table I lists the simulation parameters.Source: Table I · p. 10
  • SQUAREM is adopted to expedite convergence, and simulations show sufficiently rapid convergence.Source: E. Summary · p. 10

1) Initialization :

The simulation section specifies initialization and computational-complexity considerations, then compares waveform designs. The proposed SLP waveform reduces sidelobes and improves detection and estimation relative to communication-aware baselines, with performance close to radar-only design.

1) Initialization :

  • Initialization maximizes worst-case communication QoS under a power budget, using a relaxed convex power constraint instead of the tight constant-modulus constraint.The resulting initialization problem is convex.Source: 1) Initialization · p. 10

2) Computational Complexity Analysis:

  • The complexity analysis considers iterative updates of x, z, λ, and µ, with interior-point update complexity related to optimization-variable dimension and LMI and SOC constraint counts.The total complexity is estimated across iterations.Source: 2) Computational Complexity Analysis · p. 10

IV. SIMULATION RESULTS

  • The proposed algorithm’s ISL consistently decreases with each iteration and converges within a reasonable number of iterations.Source: Figure 3 · p. 10, §IV · p. 11
  • The proposed SLP waveform suppresses range and Doppler sidelobes by roughly 15 dB more than the combined waveform.Radar-only achieves very low sidelobes but lacks the desired communication capability.Source: §IV · p. 11, Figure 5 · p. 11
  • Across communication QoS requirements, the proposed waveform significantly reduces normalized range-Doppler ISL versus the combined waveform, while ISL rises with stricter QoS and more users.Source: §IV · p. 11, Figure 6 · p. 11
  • In the close-target scenario, communication-only and combined waveforms cannot identify the weak target, whereas the proposed SLP waveform places its mainlobe above the strong target’s sidelobes.This facilitates weak-target detection and estimation amid the strong target.Source: Figure 7 · p. 11, §IV · p. 12
  • At identical RMSE, the SLP waveform requires 5 dB lower SNR gain than reciprocal filtering and approximately 8 dB less than the combined waveform, while nearly matching radar-only RMSE.Source: §IV · p. 12, Figure 9 · p. 12
  • The proposed SLP waveform’s detection ROC is close to radar-only, and both significantly outperform the other benchmarks.The weak target RCS is −3 dBsm for this ROC comparison.Source: §IV · p. 12, Figure 8 · p. 12

V. CONCLUSIONS

The paper proposes an SLP-based waveform design for MIMO-OFDM ISAC that exploits increased spatial and temporal degrees of freedom to reduce range-Doppler sidelobes. Its MM-ADMM algorithm addresses the non-convex design problem, and simulations show performance approaching radar-only design while outperforming communication-aware benchmarks in sidelobes, detection, and estimation.

V. CONCLUSIONS

  • The proposed MIMO-OFDM ISAC waveform design exploits increased spatial and temporal DoFs to reduce range-Doppler sidelobes.Its optimization minimizes range-Doppler ISL subject to target illumination power, multi-user communication QoS, and constant-modulus constraints.Source: §V · p. 12
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