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Integrated Sensing and Communication with mmWave Massive MIMO: A Compressed Sampling Perspective

Zhen Gao, Ziwei Wan, Dezhi Zheng, Shufeng Tan, Christos Masouros, Derrick Wing Kwan Ng, Sheng Chen

arXiv:2201.05766v3cs.ITeess.SP

TL;DR

Compressed sampling is presented as a promising solution for ISAC challenges. The framework uses mmWave massive MIMO, an energy-efficient WSA radar receiver, a time-varying frame structure, and CS-based algorithms to support communications and radar sensing, including angular ambiguity and mobility.

  • Problem

    Compressed sampling is presented as a promising solution for challenges in ISAC systems.

  • Method

    The paper develops a CS-based ISAC framework using mmWave massive MIMO, an energy-efficient WSA radar receiver, a time-varying frame structure, and OMP with support refinement.

  • Results

    The proposed OMP-SR algorithm can cope with angular ambiguity and achieve better performance, while the framework supports energy-efficient communications, fast time-varying environments, mobility tracking, and high-mobility users.

  • Takeaways & Limitations

    The framework connects CS-based processing with ISAC architectures and time-varying operation for joint communications and radar sensing.

Abstract

from arXiv · show

Integrated sensing and communication (ISAC) has opened up numerous game-changing opportunities for realizing future wireless systems. In this paper, we propose an ISAC processing framework relying on millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. Specifically, we provide a compressed sampling (CS) perspective to facilitate ISAC processing, which can not only recover the high-dimensional channel state information or/and radar imaging information, but also significantly reduce pilot overhead. First, an energy-efficient widely spaced array (WSA) architecture is tailored for the radar receiver, which enhances the angular resolution of radar sensing at the cost of angular ambiguity. Then, we propose an ISAC frame structure for time-varying ISAC systems considering different timescales. The pilot waveforms are judiciously designed by taking into account both CS theories and hardware constraints induced by hybrid beamforming (HBF) architecture. Next, we design the dedicated dictionary for WSA that serves as a building block for formulating the ISAC processing as sparse signal recovery problems. The orthogonal matching pursuit with support refinement (OMP-SR) algorithm is proposed to effectively solve the problems in the existence of the angular ambiguity. We also provide a framework for estimating the Doppler frequencies during payload data transmission to guarantee communication performances. Simulation results demonstrate the good performances of both communications and radar sensing under the proposed ISAC framework.

I. INTRODUCTION

ISAC combines communications and radar sensing to share resources and support applications requiring resilient connectivity and precise environmental awareness. This paper studies mmWave massive MIMO and compressed sampling to reduce processing and pilot-overhead challenges while recovering channel or imaging information.

  • Motivation: ISAC combines communication and radar systems to share scarce spectrum and expensive hardware resources.It targets scenarios such as autonomous driving, Wi-Fi sensing, and extended reality that require both resilient communications and high-precision environment sensing.
  • Motivation: mmWave massive MIMO supports radar imaging by exploiting high angular resolution to identify target shapes from echoes arriving from different directions.The paper aims to integrate radar sensing into mmWave channel estimation.
  • Challenges: Massive antenna counts create substantial signal-processing burdens, especially when radar must recover high-dimensional imaging information rather than only a few target parameters.Time-varying channel estimation also requires low pilot overhead to reliably serve high-mobility users.
  • Compressed sampling: Compressed sampling is promising because it recovers signals from reduced measurements by leveraging intrinsic sparsity, but its application to ISAC requires further study.Prior CS-based channel-estimation methods exploit sparsity in angular, delay, or combined domains, while existing approaches are generally communication-specific.
  • Prior work and limitations: Widely spaced arrays can enhance radar angular resolution but introduce spatial aliasing and angular ambiguity, complicating beamforming and ISAC processing.Hybrid beamforming reduces received-signal dimensionality and imposes hardware constraints; earlier orthogonal-waveform designs also incur unaffordable pilot overhead.

B. Our Contributions

The paper develops a compressed-sampling ISAC framework for mmWave massive MIMO, combining hardware-aware communication and radar designs for time-varying, high-mobility scenarios.

  • Architecture: The proposed DFRC architecture uses a communication unit with CSA-HBF and a radar unit with a WSA and low-resolution ADCs.The CU handles communication, while the RU receives radar echoes.
  • Architecture: The WSA provides energy-efficient communications and high angular resolution for radar sensing, at the cost of angular ambiguity.Its larger spatial aperture improves angular resolution, while wider antenna spacing introduces ambiguity.
  • Frame and waveform design: The ISAC frame structure and pilot waveform design integrate radar sensing with communication channel estimation under HBF hardware constraints.The design accounts for different timescales and CS requirements while satisfying HBF constraints.
  • Frame and waveform design: The resulting frame structure supports tracking high-mobility targets and serving high-mobility users in fast time-varying environments.Small pilot blocks are inserted between adjacent data frames to estimate target and user Doppler frequencies for demodulation.
  • CS-based sensing: OMP-SR uses spatial consistency to resolve WSA angular ambiguity by combining coarse angle estimates with refined sensing-matrix supports.The CU and RU observe targets from the same directions, enabling ambiguity elimination during each iteration.

B. Time-Varying Communications and Radar Channel Models

The paper models time-varying communication and radar channels for mmWave massive MIMO, representing propagation through angular, delay, path, and target-cluster parameters.

  • Communication channel: The communication channel uses a Rician model with one LoS path and clustered NLoS paths.Each path is characterized by time-varying delays, channel coefficients, and angular parameters.
  • Communication channel: Angles of arrival and departure contain azimuth and elevation components for the modeled communication paths.Azimuth ranges over [0, 2π), while elevation ranges over [0, π/2).
  • Radar channel: The radar channel models echoes from multiple targets, each producing multiple resolvable paths with time-varying delays and propagation coefficients.The path coefficient accounts for free-space loss and target radar cross section.
  • Radar channel: Spatial consistency makes the communication and radar arrays observe targets at the same propagation directions.The arrays are co-located and parallel, linking their angular observations.
  • Radar channel: Modeling targets as clusters with multiple paths enables angular-domain estimation of target shape and radar imaging information.The paper states that such imaging can remain available when visible-light and laser signals are blocked.

III. FRAME STRUCTURE AND WAVEFORM DESIGN

The paper designs a timescale-aware ISAC frame and CS-compatible pilot waveforms that satisfy hybrid-beamforming hardware constraints while supporting channel estimation and radar sensing.

  • Frame structure: The proposed frame structure accounts for small, moderate, and large timescales in time-varying ISAC channels.Small-timescale channels are treated as time-invariant, while delays, angles, and Doppler frequencies are assumed stable over moderate timescales; large changes trigger new estimation and sensing.
  • Frame structure: During the initial joint CE and radar sensing stage, shared pilot signals support communication channel estimation and radar sensing before beamformer design.The CU transmits ISAC pilots, while the UT and RU use received pilots and echoes, respectively, to obtain the information used for subsequent beamforming.
  • Frame structure: Short pilot signals inserted between payload blocks estimate Doppler components while guard intervals reduce inter-frame interference and allow RF-circuit reconfiguration.The guard interval is sufficiently long to separate pilots and payload data and provide time for reconfiguring RF circuits.
  • Signal model: The resulting received-pilot models form noisy linear systems that can be solved as compressed-sensing problems using sparse channel structure and underdetermined measurements.The UT formulation is represented as y = Φ vec(HSD) + n, while low-resolution ADC quantization is modeled at the RU and ignored at the high-resolution-ADC UT.
  • Waveform design: The pilot waveform is designed using both CS theory and HBF hardware constraints rather than conventional orthogonal-waveform design for underdetermined estimation.The design considers measurement-matrix structure, constant-modulus phase shifters, and non-negligible reconfiguration time between analog precoders or combiners.
  • Waveform design: Pilot symbols are divided into sub-frames that share analog precoders, with zero baseband signals during RF switching intervals and invalid measurements removed.This preserves pilot diversity while reserving idle time for hardware reconfiguration; larger sub-frame counts require more zero pilot signals.

IV. COMPRESSIVE SENSING FOR ISAC AND DOPPLER ESTIMATION

The paper formulates communication estimation and radar sensing as sparse signal-recovery problems using WSA dictionaries, then introduces CS-based processing and Doppler estimation for time-varying ISAC.

  • CS formulation: Communication estimation and radar sensing are formulated as sparse signal-recovery problems with dictionaries designed for the widely spaced array.The proposed algorithm exploits spatial consistency to address angular ambiguity and improve angular resolution.
  • Doppler estimation: The framework also provides a method for estimating Doppler frequencies of served users and targets during payload transmission.These estimates support communication performance in time-varying ISAC operation.

A. Dictionary Design

The dictionary design maps spatial channels into angular-domain sparse representations for WSA and CSA arrays, balancing finer WSA resolution against angular ambiguity.

  • Angular ambiguity: For WSA spacing d > 0.5λ, multiple angular points can maximize the correlation function, so direct maximization cannot identify the actual angle and may cause missed detections or false alarms.This is the principal sensing trade-off introduced by widely spaced sampling.
  • Angular resolution: WSA provides higher angular resolution and lower sidelobes than CSA in the non-ambiguity region, producing sparser angular-domain channels and suppressing power leakage.The improved resolution facilitates sparse signal recovery, provided that angular ambiguity is eliminated.
  • Dictionary construction: Angular-domain dictionaries quantize channel angles into predefined samples, transforming spatial-domain channels into angular-domain representations.Azimuth and elevation dictionaries are combined to represent the overall WSA channel.
  • Dictionary construction: The WSA dictionary uses more angular samples to improve approximation of real channel angles, whereas unitary sampling offers uniqueness but limited resolution.Increasing the number of angular samples creates a redundant dictionary that can represent real angles more accurately.
  • WSA versus CSA: Unlike the CSA dictionary, the WSA dictionary covers a smaller angular range for each channel-angle component, creating angular ambiguity.False angles are related to real angles through integer spatial-period offsets.
  • Sparse representation: The WSA dictionary is tailored to radar sensing while preserving sparse angular-delay channel representations arising from dual sparsity in angle and delay.The resulting dictionaries serve as the basis for formulating the channel and radar sensing problems.

B. The Proposed CS-Based Algorithms

The paper develops OMP-SR for WSA-based radar sensing and a low-complexity UT estimator, using spatial consistency to resolve ambiguity and support beamforming.

  • Radar sensing: OMP-SR solves the radar sparse-recovery problem by exploiting spatial consistency and the mixed angular resolutions of WSA and CSA.The algorithm refines selected supports and reconstructs the radar channel from estimated delays and angles.
  • Radar sensing: OMP-SR combines coarse and finer angle estimates, adjusts the finer estimate by an integer spatial-period term, and replaces the sensing-matrix atom with a refined steering vector.The refined matrix is then used for subspace projection and residual updates.
  • Radar sensing: The radar procedure estimates target delays, azimuth angles, and elevation angles, while the reconstructed spatial-delay channel can retain target information beyond point identification.The text notes that radar imaging may use channel information such as target shapes and types, but that feature extraction is outside this paper's scope.
  • Algorithm control: The residual-energy stopping threshold is difficult to choose in high-dynamic ISAC scenarios because unsuitable values can increase computation or reduce precision.The paper instead adopts a maximum-iteration criterion obtained experimentally to make runtime and performance predictable.
  • Communication estimation: At the UT, one correlation step identifies the strongest LoS atom and estimates LoS angles and delay offset with low computational complexity.This design reflects the UT's limited measurements and computational capability; the full channel can be recovered at higher complexity if needed.
  • Communication estimation: The UT feeds its estimates back to the CU, after which the UT and CU perform beamforming based on the estimated channel-angle information.The stated purpose is to support reliable data transmission.

C. Doppler Estimation Framework

The framework estimates Doppler frequencies from impulse pilots inserted between payload data frames, using scheduled, well-separated terminals to suppress inter-user interference. The same framework extends directly to radar-target speed estimation and can operate communications and sensing in time division.

  • Pilot-based Doppler estimation: Scheduling at most NRF well-separated terminals enables user-wise Doppler estimation by treating residual inter-user interference as noise.Users are separated in either the angular or delay domain, so interference terms are significantly suppressed after beamforming.
  • Pilot-based Doppler estimation: Impulse pilots are inserted between data frames, with zero-padding on both sides to eliminate inter-frame interference.Each user equipment emits an uplink impulse pilot between every two data frames.
  • Communication channel model: Only LoS components are retained for communication-oriented estimation because strong LoS paths and beam steering make NLoS contributions negligible after beamforming.The analysis assumes a high mmWave Rician factor and treats the remaining NLoS influence as noise.
  • Doppler extraction: Successive impulse-pilot observations form noisy uniformly spaced samples of a single-tone sinusoid whose frequency is the user’s Doppler frequency.The sampling interval is Δ = (2L + ND)Ts, and the framework uses WNALP for Doppler estimation.
  • Radar extension: The Doppler framework applies directly to radar-target speed estimation by repeating impulse pilots during tracking and aligning beams toward targets.Communication and radar Doppler estimation can be scheduled in time division to avoid cross-interference.

D. Computational Complexity Analysis

The complexity analysis decomposes OMP-SR and summarizes the costs of channel estimation and Doppler estimation. The Doppler framework has complexity O(UPD).

  • OMP-SR: OMP-SR comprises correlation, support refinement, subspace projection, and residual-update stages with iteration-dependent computational costs.The analysis identifies these four operations as the algorithm’s major complexity components.
  • Channel estimation: The low-complexity channel-estimation scheme has an overall complexity expressed in terms of Nvalid, the dimension of yvalid.The supplied complexity statement specifies Nvalid as the relevant received-vector dimension.
  • Doppler estimation: The proposed Doppler estimation framework has computational complexity O(UPD).The cost scales with the number of users, impulse pilots, and the associated processing dimension.

V. SIMULATION RESULTS

Simulations evaluate the proposed ISAC scheme in a vehicular DFRC network under practical channel, array, pilot, and ADC settings. Results show that support refinement, pilot diversity, and suitable WSA design improve radar sensing.

  • Radar sensing performance: OMP-SR NMSE decreases rapidly initially but worsens after the minimum as excessive iterations fail to match the actual CIR sparsity.More iterations are appropriate for terrestrial scenes with more targets or scatters than for extremely sparse aerial or satellite scenarios.
  • Radar sensing performance: Larger dictionary dimension and WSA element spacing improve radar NMSE by providing finer angular resolution, but increase CS dimension or antenna-array size.The paper therefore recommends choosing these parameters to balance sensing performance and hardware complexity.
  • Radar sensing performance: OMP-SR significantly outperforms original OMP and block-OMP across downlink transmit powers and quantization resolutions.With practical 5-bit ADCs, sensing performance approaches that of ideal infinite-resolution ADCs.
  • Radar sensing performance: OMP-SR accurately estimates all target angles and delays, whereas OMP without support refinement exhibits severe angular blurring from WSA ambiguity.The blurring can cause missed detections or false alarms, motivating support refinement for WSA sensing.

2) Communication performance:

Communication simulations evaluate ASE, Doppler estimation, and downlink BER under hybrid-beamforming constraints. Redundant dictionaries and pilot diversity improve ASE, while Doppler compensation preserves BER performance in time-varying channels.

  • ASE performance: Redundant dictionaries significantly improve ASE at the same pilot overhead, with rdic = 2 and P = 300 approaching perfect-LoS-angle performance.A single analog combiner performs poorly, while increasing the UT codebook size improves ASE.
  • ASE performance: The pilot waveform design is effective and necessary for HBF-aided ISAC systems to obtain pilot diversity under practical hardware constraints.The communication results corroborate the sensing-side dependence on codebook size and pilot diversity.

VI. CONCLUSIONS

The proposed mmWave massive-MIMO ISAC framework combines an energy-efficient WSA receiver, time-varying frame structure, CS-based sparse recovery, and Doppler estimation under HBF constraints. OMP-SR addresses angular ambiguity, while Doppler estimation supports speed measurement and payload-data demodulation.

  • The energy-efficient WSA radar receiver enhances angular resolution, while accepting angular ambiguity as a trade-off.The proposed architecture is designed to provide energy-efficient communications alongside high angular resolution for radar sensing.
  • The time-varying ISAC frame structure facilitates estimation of angles, delays, and Doppler frequencies across different timescales.Its pilot waveforms are designed to satisfy hardware constraints induced by the HBF array.
  • CS-based sparse signal recovery with dedicated dictionaries reduces pilot overhead while exploiting compressive sensing techniques.The formulation targets ISAC processing under the HBF architecture and supports recovery of the relevant parameters.
  • OMP-SR copes with angular ambiguity and achieves better recovery performance than traditional counterparts.The algorithm is proposed specifically for radar sensing with the WSA architecture.
  • The Doppler-frequency estimation framework supports target-speed measurement and payload-data demodulation.The framework estimates Doppler frequencies of users and targets during ISAC operation.
  • Future work includes robust quantized CS, radar-sensing and CE-algorithm interaction, beamforming design, near-field analysis, and proof-of-concept field experiments.
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