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A Survey on Fundamental Limits of Integrated Sensing and Communication

An Liu, Zhe Huang, Min Li, Yubo Wan, Wenrui Li, Tony Xiao Han, Chenchen Liu, Rui Du, Danny Tan Kai Pin, Jianmin Lu, Yuan Shen, Fabiola Colone, Kevin Chetty

arXiv:2104.09954v2cs.ITeess.SP

TL;DR

ISAC research needs unified theoretical frameworks and characterization of fundamental performance limits for sensing and communication. This survey classifies traditional sensing and ISAC systems within a unified framework and synthesizes their performance bounds, key insights, open problems, and future directions.

  • Problem

    Important ISAC problems remain open, including unified theoretical frameworks and fundamental limits for sensing distortion, channel capacity, and capacity-distortion tradeoffs.

  • Method

    The survey classifies traditional radio sensing and ISAC technologies into four major categories, then presents system models, performance bounds, and insights for each case.

  • Results

    The survey summarizes research progress on fundamental limits across traditional sensing and ISAC systems and presents typical ISAC channel topologies as abstracted models.

  • Takeaways & Limitations

    Fundamental limits provide performance bounds for practical ISAC technologies and reveal gaps between current technologies and optimal solutions.

Abstract

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The integrated sensing and communication (ISAC), in which the sensing and communication share the same frequency band and hardware, has emerged as a key technology in future wireless systems. Early works on ISAC have been focused on the design, analysis and optimization of practical ISAC technologies for various ISAC systems. While this line of works are necessary, it is equally important to study the fundamental limits of ISAC in order to understand the gap between the current state-of-the-art technologies and the performance limits, and provide useful insights and guidance for the development of better ISAC technologies that can approach the performance limits. In this paper, we aim to provide a comprehensive survey for the current research progress on the fundamental limits of ISAC. Particularly, we first propose a systematic classification method for both traditional radio sensing (such as radar sensing and wireless localization) and ISAC so that they can be naturally incorporated into a unified framework. Then we summarize the major performance metrics and bounds used in sensing, communications and ISAC, respectively. After that, we present the current research progresses on fundamental limits of each class of the traditional sensing and ISAC systems. Finally, the open problems and future research directions are discussed.

I. INTRODUCTION

ISAC research seeks to share frequency bands and hardware for sensing and communication while characterizing the fundamental limits that guide practical system design. This survey introduces a unified classification of radio sensing and ISAC, reviews performance bounds, and identifies open challenges.

  • Motivation: Future wireless systems can use high-resolution communication signals for sensing applications including indoor localization, WiFi sensing, and radar sensing.Millimeter-wave and massive-MIMO technologies provide high resolution in time and angle, motivating joint sensing and communication design.
  • Motivation: Fundamental ISAC limits include sensing distortion bounds, channel capacity, and capacity-distortion tradeoffs.These limits can bound practical technologies and reveal gaps between current systems and optimal solutions.
  • Survey scope: The survey proposes a systematic classification of traditional radio sensing and ISAC within a unified framework.The classification covers radar sensing, wireless localization, and related integrated systems.
  • Classification: Traditional radio sensing and ISAC are divided into device-free and device-based categories according to whether sensing targets transmit or receive signals.Radar sensing is a typical device-free example, whereas wireless localization of mobile devices is device-based.
  • Classification: The survey organizes ISAC research around four categories: device-free sensing, device-based sensing, device-free ISAC, and device-based ISAC.Each category is further divided into different cases and analyzed through system models, performance bounds, and key insights.
  • Radar architectures: Radar sensing is classified into phased-array, MIMO, and phased-MIMO architectures, with further subdivisions based on system structure and characteristics.The survey discusses colocated and distributed arrangements, including phased-array radar classes.

4) Other Device-free Sensing Scenarios:

The paper surveys device-based localization and device-free ISAC scenarios beyond the main classes, emphasizing cooperative localization and representative multiple-access configurations.

  • Device-based Sensing: Wireless localization estimates target locations from reference signals exchanged between anchor nodes and agent nodes.The paper focuses mainly on agents estimating their own positions from wireless reference signals, though anchor-based estimation is also possible.
  • Non-Cooperative Localization: Non-cooperative localization uses signals from neighboring anchors only, with position inferred from TOA, TDOA, AOA, AOD, or RSS measurements.TOA requires synchronization, AOA can localize an agent with two anchors in a 2-D plane theoretically, and RSS avoids synchronization but may be inaccurate in harsh environments.
  • Cooperative Localization: Cooperative localization supplements anchor measurements with signals from other agents and can improve coverage and accuracy with the same number of anchors.Agents may use spatial cooperation with other agents and temporal cooperation with their own previous localization results.
  • Device-free ISAC: Device-free ISAC integrates sensing of targets that do not transmit or receive sensing signals with communication channel topologies such as multiple-access and broadcast channels.The considered scenarios include one base station, K targets, and U users, with mono-static or bi-static radar structures.
  • Device-free ISAC: In mono-static multiple-access ISAC with base-station sensing, the base station estimates target parameters and decodes uplink messages despite collisions between uplink signals and radar echoes.The collision creates a joint estimation and decoding problem.

4) Broadcast Channel with Bi-static Sensing:

The paper organizes integrated sensing and communication by channel topology and sensing arrangement, then introduces estimation-theoretic metrics and bounds for evaluating its fundamental limits.

  • Broadcast Channel with Bi-static Sensing: Broadcast channels with bi-static sensing use separate radar transmitter and receiver roles, with either the base station or mobile users serving as radar sensors.The mobile-sensing case has the base station transmit radar and communication signals while users receive both.
  • Broadcast Channel with Bi-static Sensing: In bi-static mobile sensing, users jointly estimate target parameters and decode downlink messages because downlink signals and radar echoes are coupled.This coupling creates a joint estimation and decoding challenge at each user.
  • Device-based and Device-free ISAC: Device-based ISAC performs sensing through targets capable of transmitting or receiving sensing signals, whereas device-free ISAC senses targets without that capability.Wireless-based localization is the paper’s representative device-based sensing example.
  • Device-based ISAC: For device-based broadcast channels with non-cooperative localization, users independently remove interference and extract localization information from a shared waveform.Joint waveform design at the base station strongly affects both localization and communication performance.
  • Performance Metrics: The paper characterizes sensing performance using parameter-estimation metrics such as MSE and lower bounds including CRB, WWB, and ZZB.CRB is easier to compute but performs poorly at low SNR, while WWB and ZZB improve over CRB across a wider SNR range at higher evaluation complexity.

2) Equivalent Fisher’s Information Matrix (EFIM):

The equivalent Fisher information matrix condenses the information relevant to parameters of interest while accounting for nuisance parameters.

  • Equivalent Fisher’s Information Matrix (EFIM): The parameter vector is partitioned into a parameter of interest θ1 and nuisance parameters θ2.The Fisher information matrix is correspondingly divided into submatrices for the two subvectors and their cross-information.
  • Equivalent Fisher’s Information Matrix (EFIM): The CRB for θ1 can be obtained either from the upper-left block of the inverse full FIM or directly through the EFIM.The direct EFIM approach is more efficient than inverting the entire FIM.
  • Equivalent Fisher’s Information Matrix (EFIM): Ie(θ1) = I(θ1, θ1) − I(θ1, θ2)I(θ2, θ2)^−1I(θ1, θ2)^T.This Schur-complement form removes the information contribution associated with nuisance parameters.
  • Equivalent Fisher’s Information Matrix (EFIM): The EFIM retains all information needed to derive the information inequality and MSE lower bound for θ1.Thus, the reduced matrix is sufficient for evaluating the parameter of interest.

3) Other Performance Metrics:

Beyond MSE bounds and channel capacity, the paper reviews resolution, detection, radar-capacity, and fading-channel metrics for describing sensing and communication limits.

  • Sensing Metrics: Radar range resolution is commonly estimated as ΔR = c/(2B), linking separability in range to propagation speed and bandwidth.Ambiguity functions further characterize tradeoffs among range, angle, and Doppler resolution.
  • Sensing Metrics: Detection probability measures detecting an existing target, while false alarm probability measures declaring a target when none exists.These metrics evaluate complementary target-detection errors.
  • Sensing Metrics: Radar capacity treats each independent resolution cell as a binary storage unit and applies a Hartley capacity measure.The number of resolution cells depends on range, angular, pulse-repetition, and Doppler resolutions.
  • Estimation Bounds: WWB and ZZB improve upon CRB over a wide SNR range, while CRB is easier to compute and WWB and ZZB are generally harder to evaluate.The bounds are complementary to radar-resolution metrics for characterizing sensing limits.
  • Communication Metrics: For fast fading, ergodic capacity applies when codewords span many coherence intervals; for slow fading, outage capacity applies when coding spans roughly one coherence interval.The definitions extend to multiuser capacity and outage-capacity regions.

3) Summary:

The paper reviews unified capacity-distortion metrics for ISAC and CRB-based fundamental limits for phased-array radar. These analyses relate communication and sensing performance to information rates, SNR, bandwidth, antenna configuration, and beamforming.

  • ISAC performance metrics: Capacity-distortion performance metrics characterize communication rate under sensing distortion constraints for ISAC.The capacity measures communication performance while distortion measures sensing performance.
  • ISAC performance metrics: Estimation information rate converts MSE distortion into an information-rate quantity, placing communication and sensing rates in the same unit.The lower bound uses the estimation information rate to represent sensing performance.
  • ISAC performance metrics: Current unified capacity-distortion approaches remain limited because their assumptions and information-theoretic models cannot cover many important ISAC scenarios.The survey calls for new frameworks and more general approaches.
  • A. Fundamental Limits of Phased-array Radar: Phased-array radar CRB analyses show that delay and DOA estimation improve with SNR and receive-antenna count, while delay also benefits from effective bandwidth and DOA from normalized spacing.For multi-antenna transmission, transmit beamforming adds a 1/M^2 CRB factor under fixed per-antenna transmit power.

B. Fundamental Limits of MIMO Radar

The survey presents CRB results for colocated MIMO radar, emphasizing how antenna count, pulses, SNR, geometry, and target motion affect sensing accuracy. Compared with phased-array radar, colocated MIMO trades beamforming gain for waveform diversity and broad angular coverage.

  • B. Fundamental Limits of MIMO Radar: Colocated MIMO radar uses independent waveforms from colocated transmitters, producing waveform diversity through independent target observations.This differs fundamentally from phased-array radar, which transmits beamformed signals.
  • B. Fundamental Limits of MIMO Radar: The DOA CRB decreases with M at order 1/M^2 for colocated MIMO radar, versus 1/M^3 for phased-array radar.Phased-array radar obtains an additional O(M) transmit beamforming gain, whereas colocated MIMO radar does not.
  • B. Fundamental Limits of MIMO Radar: Colocated MIMO radar can cover the whole angular space, reducing the initial search time for a target.This broad coverage is identified as an advantage despite the absence of phased-array beamforming gain.
  • B. Fundamental Limits of MIMO Radar: DOA and velocity estimation improve with SNR, pulse count L, antenna product MN, and antenna-position sample variances.Velocity additionally benefits from longer pulse periods and lower radar velocity, while radar motion does not affect DOA estimation.
  • B. Fundamental Limits of MIMO Radar: With time multiplexing, relative radial target motion decreases DOA-estimation accuracy because Doppler induces an unknown baseband phase rotation.The limitation arises specifically in the analyzed time-multiplexed colocated MIMO setting.

2) Colocated MIMO Radar for Multi-Target Sensing:

The survey extends MIMO-radar CRB analysis to multi-target colocated sensing and distributed single- and multi-target sensing. Accuracy depends on target separability, SNR, antenna resources, waveform properties, and spatial diversity.

  • 2) Colocated MIMO Radar for Multi-Target Sensing: For two colocated-MIMO targets, DOA and velocity CRBs depend on differences in their DOAs and Doppler frequencies.Estimation improves as these differences increase and approaches single-target performance when they are sufficiently large.
  • 3) Distributed MIMO Radar for Single-Target Sensing: Distributed MIMO radar estimates target position and velocity from the time delays and Doppler shifts across transmitter-receiver paths.The antennas are widely separated, enabling observations from different directions.
  • 3) Distributed MIMO Radar for Single-Target Sensing: Distributed-MIMO position and velocity estimation improve with the number of transmit and receive antennas and SNR.Position benefits from squared effective bandwidth and pulse length, while velocity benefits from squared effective pulse length.
  • 3) Distributed MIMO Radar for Single-Target Sensing: For distributed MIMO radar, velocity estimation also improves with SNR and squared effective radar pulse length.This result concerns direct velocity estimation.
  • 3) Distributed MIMO Radar for Multi-Target Sensing: When distributed-MIMO targets are sufficiently separated, their interactions can be ignored and multi-target performance can approach single-target performance.The stated condition is that distances between targets must be large enough.

C. Fundamental Limits of Phased-MIMO Radar

Phased-MIMO radar adapts the ambiguity function through subarray configuration, trading beamforming gain against waveform diversity. Fundamental-limit analyses show how sensing accuracy depends on SNR, array resources, pulse duration, bandwidth, geometry, and target separation.

  • The ambiguity function peaks at the true delay, Doppler, and direction, while a narrower curve indicates better expected estimation performance.
  • Phased-MIMO radar adapts its ambiguity function by changing subarray size and number, unlike MIMO radar with a fixed ambiguity function.LFM improves delay resolution but introduces delay–Doppler coupling.
  • Squared effective bandwidth improves time-delay estimation, while squared effective pulse length improves Doppler-frequency estimation.For the unified CRB orders, the radar-dependent exponent is a = 1 for MIMO radar and a = 2 for phased-array radar.
  • Larger transmit and receive antenna-position variances improve DOA estimation, with exponent a = 1 for MIMO radar and a = 2 for phased-array radar.
  • SNR, transmit and receive antenna counts, and CPI pulse count commonly improve estimation of delay, DOA, and Doppler.Bandwidth, antenna-position variance, and effective pulse length additionally determine delay, DOA, and Doppler estimation, respectively.
  • When targets are sufficiently separated, multiple-target sensing can approach single-target performance because target parameters can be estimated independently.

2) AOA-based Localization:

AOA-based localization infers position from line-of-sight arrival angles, using phase-based beam steering for narrowband signals and time-delay steering for wideband signals. Its limits depend on bandwidth, carrier frequency, SNR, array dimensions, and propagation regime.

  • AOA-based localization infers agent position from arrival angles of line-of-sight paths received from anchors.
  • Narrowband arrays represent inter-antenna arrival-time differences as phase shifts, whereas wideband arrays use time-delayed lines for beam steering.
  • The AOA-localization EFIM combines range and direction information from individual anchors, so diverse anchor directions improve localization performance.
  • In wideband array localization, carrier phases cannot provide TOA information because unknown initial phase prevents phase-based delay measurement.In narrowband systems, phase differences can eliminate the unknown initial phase and provide extra AOA information.
  • Massive arrays reduce narrowband AOA-localization CRB by a factor of MN relative to the single-antenna CRB κ0.M represents beam-steering SNR enhancement, while N is the agent’s antenna count.
  • The narrowband single-antenna CRB κ0 depends on receive SNR, effective bandwidth β, and carrier frequency fc.

3) RSS-based Localization:

RSS-based localization models received-strength measurements through channel attenuation and estimates position using their spatial pattern. Its accuracy depends strongly on path-loss and shadowing parameters, with NLOS effects incorporated implicitly.

  • RSS-based localization is especially used in fingerprinting-based and proximity-based schemes.
  • For narrowband signals, received-strength attenuation reflects path loss, log-normal shadowing, and multipath fading.Time averaging is commonly used to estimate mean received signal strength.
  • RSS localization accuracy depends heavily on the path-loss exponent α and shadowing variances η², and is inversely proportional to α².NLOS propagation effects are implicitly included in the RSS signal model.

4) Hybrid Scheme:

Hybrid localization schemes combine multiple signal metrics, while cooperative extensions model how anchor and agent information contributes to position estimation. The resulting bounds expose dependencies on waveform, geometry, cooperation, and multipath structure.

  • Hybrid Scheme: Hybrid DOA-TOA localization derives position CRBs from separate TOA and DOA bounds through the chain rule.The location-coordinate bounds combine CRBθ and CRBτ with geometry-dependent factors involving delay and angle.
  • Hybrid Scheme: TOA accuracy is mainly governed by effective bandwidth, whereas DOA accuracy is mainly affected by antenna number and element separation.The analysis also defines β2 as the squared effective bandwidth and relates DOA performance to array configuration.
  • Hybrid Scheme: Localization accuracy depends on SNR, array configuration, effective bandwidth, and anchor-agent geometry, with large distance magnifying DOA-error effects.The relative distance cτ strengthens the destructive impact of DOA estimation errors on localization.
  • Spatial Cooperation: Spatial cooperation produces highly interrelated agent information, whereas anchor-derived localization information is represented independently across agents.The corresponding EFIM structure is block-diagonal for anchor information and non-block-diagonal for agent cooperation.
  • Spatio-Temporal Cooperation: Spatio-temporal cooperation decomposes the position EFIM into spatial and temporal components, with temporal information coupling consecutive agent positions.The spatial component is block-diagonal, while intra-node measurements create a non-block-diagonal temporal component.
  • Summary and Insights: Multipath couples delay-estimation bounds through the relative delay between paths, while AOA accuracy depends on geometry and can become unbounded for collinear configurations.Perfect transmit beamforming toward the agent can reduce the stated CRBs by an additional factor of M.

VI. INFORMATION-THEORETIC LIMITS OF ISAC

Information-theoretic models represent device-free ISAC sensing through generalized feedback and characterize communication–sensing tradeoffs for point-to-point and multiple-access channels. Joint transmission generally improves these tradeoffs over separation or resource sharing, although multiple-access results may remain bounded rather than fully characterized.

  • Device-free ISAC: Generalized output feedback models radar echoes while ISAC transmitters communicate and estimate channel states simultaneously.The section considers device-free ISAC building blocks with mono-static sensing.
  • Point-to-point channels: For point-to-point channels, the capacity-distortion tradeoff is optimized over input distributions and estimators satisfying an average distortion constraint.The estimator minimizes expected distortion for a given input distribution, constraining the optimal signaling distribution.
  • Point-to-point channels: At P = 10 dB, zero distortion still permits C(D = 0) = 0.733 bcu, while D = 1 recovers unconstrained capacity.The joint design outperforms communication–sensing separation in the illustrated fading-channel example.
  • Multiple-access channels: For multiple-access ISAC, inner and outer capacity-distortion bounds use feedback-induced cooperation, block Markov encoding, and backward decoding.The achievable construction introduces auxiliary variables U, V1, and V2 under specified Markov constraints.
  • Multiple-access channels: When D1 = D2 = D and ps = 0.7, the multiple-access inner bound has a gap from the outer bound, but approaches optimality at small distortion.The joint transmission design outperforms communication–sensing resource sharing.

3) Device-free ISAC over Memoryless Broadcast Channels:

The section extends information-theoretic ISAC analysis to broadcast channels and receiver-side state estimation. Physically degraded broadcast tradeoffs are fully characterized, while Gaussian state-dependent channels show that stringent estimation requirements can eliminate positive communication rate.

  • Broadcast channels: A two-user broadcast ISAC transmitter sends separate messages while estimating channel states through output feedback.The model uses memoryless channels with i.i.d. state sequences and receivers that know their own states.
  • Broadcast channels: The capacity-distortion region is fully characterized for physically degraded ISAC broadcast channels, with inner and outer bounds for general channels.A multiplicative-binary-state example depicts the tradeoff region for γ = 0.5 and q = 0.6.
  • Broadcast channels: Joint transmission generally outperforms resource sharing that splits resources between sensing and communication.This conclusion is stated for the broadcast example and the broader device-free ISAC models discussed in the section.
  • Device-based ISAC: For device-based ISAC, receiver-side state estimation yields capacity-distortion characterizations for point-to-point and two-user multiple-access channels with i.i.d. states.The point-to-point model assumes the state is unknown to the transmitter.
  • Device-based ISAC: In the state-dependent Gaussian channel, positive communication rate requires estimation distortion above QN/(Q+N), demonstrating a cost for finer receiver estimation.The channel assumes Si ∼ CN(0, Q), Zi ∼ CN(0, N), and average input power P.

C. Summary

Application studies use estimation-information rate, equivalent MSE, CRB, and position error bound to analyze practical sensing–communication tradeoffs. Flexible resource allocation and training overhead create measurable compromises between communication performance and sensing accuracy.

  • MAC with mono-static BS sensing: Mono-static base-station radar and uplink communication form a multiple-access setting whose tradeoff is evaluated using communication and estimation information rates.Water-filling generally gives the strongest inner bound through flexible sub-band partitioning and optimized power allocation.
  • Point-to-point communication with localization: In vehicular mono-static sensing, the data–preamble fraction α jointly controls communication spectral efficiency and velocity or range CRBs.The resulting α optimization targets a weighted tradeoff between communication and radar performance.
  • Point-to-point communication with localization: Positioning waveform design trades localization accuracy against communication because edge-concentrated power enlarges bandwidth, whereas communication favors central spectral concentration.Power partitioning likewise improves rate coverage at the expense of localization accuracy.
  • Multiple access communication with localization: Multi-user millimeter-wave localization allocates training and data resources under a fixed frame, quantifying communication with effective data rate and localization with PEB.Exhaustive beam alignment contributes Fisher information across the codebook beams.
  • Multiple access communication with localization: More beam-training time improves alignment and localization accuracy but reduces data-transmission time, producing an optimal training overhead.The optimum balances effective achievable sum rate against localization performance.

3) Other Performance Analysis:

The survey identifies substantial gaps beyond the analyzed memoryless and simplified ISAC models. Open directions include richer channel dynamics, additional network topologies, environmental information, and practical impairments such as imperfect CSI and synchronization errors.

  • Other performance analysis: Fundamental limits for many ISAC scenarios remain open, including complete capacity-distortion characterization for non-i.i.d. point-to-point mono-static sensing.The survey also calls for analysis under imperfect CSI, frequency offset, timing errors, and mobility.
  • Other performance analysis: For memoryless ISAC channels, inner and outer bounds often do not coincide, leaving only part of the capacity-distortion region determined.Existing results commonly assume i.i.d. and ergodic channel and sensing states over a codeword.
  • Other performance analysis: Block-varying ISAC channels require accounting for state-sensing and CSIT-acquisition overhead together with imperfect CSIT.Under imperfect CSIT, Shannon capacity may not be well defined, complicating capacity-distortion analysis.
  • Future directions: Future studies should examine merged sensing and communication network topologies, including mono-static interference networks and IRS-aided ISAC.IRS passive beamforming changes the communication and sensing channel, making its fundamental-limit analysis different from conventional ISAC.
  • Future directions: Practical analyses should incorporate environment side information, channel-estimation errors, CSI feedback delay, quantization, frequency offset, timing errors, and mobility dynamics.The survey proposes new information-theoretic frameworks and tracking-limit analyses for these settings.
  • Summary: The survey organizes ISAC into device-free sensing, device-based sensing, device-free ISAC, and device-based ISAC, then reviews models, bounds, insights, and open problems.It emphasizes that ISAC fundamental limits cannot be obtained by trivially combining separate sensing and communication bounds.
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