A Survey on Fundamental Limits of Integrated Sensing and Communication

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.Source: §I · p. 1
• 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.Source: §I · p. 2

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.Source: §I · p. 2

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.Source: §II · pp. 2–3
• 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.Source: §II · p. 3

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.Source: A. Device-free Sensing · p. 3, 3) Phased-MIMO Radar · p. 4

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.Source: B. Device-based Sensing · p. 5

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.Source: 1) Non-Cooperative Localization · pp. 5–6

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.Source: 1) Non-Cooperative Localization · p. 6, 2) Cooperative Localization · p. 6

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.Source: C. Device-free ISAC · pp. 6–7, 1) Multiple Access Channel with… · p. 7, 2) Multiple Access Channel with… · p. 7
• 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.Source: 1) Multiple Access Channel with… · p. 7

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.Source: 4) Broadcast Channel with Bi-static… · p. 8
• 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.Source: 4) Broadcast Channel with Bi-static… · p. 8

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.Source: D. Device-based ISAC · p. 8

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.Source: 2) Broadcast Channel with… · p. 8

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.Source: A. Estimation-Theoretic Metrics for… · p. 9, 1) Mean-Square-Error and Relevant… · p. 9

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.Source: 2) Equivalent Fisher’s Information… · p. 10
• 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.Source: 2) Equivalent Fisher’s Information… · p. 10
• 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.Source: 2) Equivalent Fisher’s Information… · p. 10
• 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.Source: 2) Equivalent Fisher’s Information… · p. 10

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.Source: 3) Other Performance Metrics · pp. 10–11
• 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.Source: 3) Other Performance Metrics · p. 11
• 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.Source: 3) Other Performance Metrics · p. 11

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.Source: 4) Summary · p. 11

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.Source: 2) Ergodic and outage capacity of a… · pp. 11–12

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.Source: C. Performance Metrics for ISAC · p. 12, 3) Capacity-Distortion Function… · p. 13
• 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.Source: 1) Estimation-Information-Rate Induced… · p. 12
• 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.Source: 4) Summary · p. 13

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.Source: A. Fundamental Limits of Phased-array… · pp. 13–14

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.Source: 1) Colocated MIMO Radar for… · p. 14
• 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.Source: 1) Colocated MIMO Radar for… · p. 14
• 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.Source: 1) Colocated MIMO Radar for… · pp. 14–15
• 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.Source: 1) Colocated MIMO Radar for… · p. 15
• 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.Source: 1) Colocated MIMO Radar for… · p. 15

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.Source: 2) Colocated MIMO Radar for… · p. 15

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.Source: 3) Distributed MIMO Radar for… · p. 15
• 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.Source: 3) Distributed MIMO Radar for… · p. 16
• For distributed MIMO radar, velocity estimation also improves with SNR and squared effective radar pulse length.This result concerns direct velocity estimation.Source: 3) Distributed MIMO Radar for… · p. 16

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.Source: 4) Distributed MIMO Radar for… · p. 16

• The ambiguity function peaks at the true delay, Doppler, and direction, while a narrower curve indicates better expected estimation performance.Source: C. Fundamental Limits of Phased-MIMO… · p. 17
• 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.Source: C. Fundamental Limits of Phased-MIMO… · p. 17
• 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.Source: D. Summary and Insights · p. 17
• Larger transmit and receive antenna-position variances improve DOA estimation, with exponent a = 1 for MIMO radar and a = 2 for phased-array radar.Source: D. Summary and Insights · p. 17
• 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.Source: D. Summary and Insights · p. 17
• When targets are sufficiently separated, multiple-target sensing can approach single-target performance because target parameters can be estimated independently.Source: D. Summary and Insights · p. 18

• AOA-based localization infers agent position from arrival angles of line-of-sight paths received from anchors.Source: 2) AOA-based Localization · p. 19
• Narrowband arrays represent inter-antenna arrival-time differences as phase shifts, whereas wideband arrays use time-delayed lines for beam steering.Source: 2) AOA-based Localization · p. 19
• The AOA-localization EFIM combines range and direction information from individual anchors, so diverse anchor directions improve localization performance.Source: 2) AOA-based Localization · p. 20
• 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.Source: 2) AOA-based Localization · p. 20
• 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.Source: 2) AOA-based Localization · p. 20
• The narrowband single-antenna CRB κ0 depends on receive SNR, effective bandwidth β, and carrier frequency fc.Source: 2) AOA-based Localization · p. 20

• RSS-based localization is especially used in fingerprinting-based and proximity-based schemes.Source: 3) RSS-based Localization · p. 21
• 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.Source: 3) RSS-based Localization · p. 21
• 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.Source: 3) RSS-based Localization · p. 21

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.Source: 4) Hybrid Scheme · p. 21
• 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.Source: 4) Hybrid Scheme · p. 21
• 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.Source: 4) Hybrid Scheme · p. 21

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.Source: 1) Spatial cooperation · p. 22

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.Source: 2) Spatio-Temporal Cooperation · p. 22

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.Source: C. Summary and Insights · pp. 22–23

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.Source: A. Capacity-distortion tradeoff for… · p. 23, 1) Device-free ISAC over Memoryless… · p. 23

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.Source: 1) Device-free ISAC over Memoryless… · p. 23
• 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.Source: 1) Device-free ISAC over Memoryless… · p. 24, Figure 29 · p. 24

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.Source: 2) Device-free ISAC over Memoryless… · p. 24
• 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.Source: 2) Device-free ISAC over Memoryless… · p. 24, Figure 31 · p. 25

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.Source: 3) Device-free ISAC over Memoryless… · p. 25, Figure 32 · p. 25
• 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.Source: 3) Device-free ISAC over Memoryless… · p. 25
• 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.Source: 3) Device-free ISAC over Memoryless… · p. 25

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.Source: B. Capacity-Distortion Tradeoff for… · p. 25
• 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.Source: B. Capacity-Distortion Tradeoff for… · p. 25

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.Source: 1) Application of MAC with Mono-Static… · p. 26, Figure 34 · p. 26

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.Source: 2) Application of Point-to-Point… · p. 27
• 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.Source: 1) Performance Analysis for Point to… · p. 27

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.Source: 2) Performance Analysis and… · pp. 27–28
• 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.Source: 2) Performance Analysis and… · p. 28, Figure 37 · p. 28, Figure 36 · p. 28

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.Source: §VIII · pp. 28–29
• 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.Source: 1) Tight Bounds for Memoryless ISAC… · p. 29
• 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.Source: 2) Information-Theoretical Bounds for… · p. 29

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.Source: 1) More Complicated ISAC Network… · p. 29, 2) Intelligent reflecting surface… · pp. 29–30
• 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.Source: 3) Environment Side Information aided… · p. 30, 1) Channel Estimation Error · p. 30, 2) Frequency Offset and Timing… · p. 30

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.Source: §IX · p. 30