Sensing as a Service in 6G Perceptive Networks: A Unified Framework for ISAC Resource Allocation

I. INTRODUCTION

• Sensing QoS remains less explored than communication QoS despite the need to evaluate both services in perceptive networks.The paper motivates sensing QoS for diverse applications as a foundation for ISAC resource allocation.Source: A. Integrated Sensing and Communication · p. 1
• Detection, localization, and tracking are measured using probability of detection, CRB, and PCRB, respectively.The paper focuses on these three fundamental sensing tasks and leaves imaging and recognition for future research.Source: B. The Definition of Sensing QoS · p. 2
• Limited power and bandwidth create QoS trade-offs among communication users and sensing targets, motivating efficient resource allocation.Different users may require different sensing QoS, so resources should reflect their S&C needs.Source: C. Resource Allocation · p. 2, B. The Definition of Sensing QoS · p. 2
• The framework jointly allocates power and bandwidth in a single-cell MIMO ISAC system providing communication and device-free sensing services.Cooperative multi-cell sensing, including clock synchronization and data fusion, is left for future research.Source: D. Our Contributions · p. 3
• Fairness and comprehensiveness criteria are used to formulate resource-allocation problems, with convex reformulations enabling alternative optimization to decouple power and bandwidth variables.The resulting designs target user-specified sensing and communication QoS demands.Source: D. Our Contributions · p. 3

II. SYSTEM MODEL

• A collocated MIMO base station with Nt transmit and Nr receive antennas serves M objects in a single-cell multibeam setting.The objects are categorized as sensing targets, communication users, or ISAC users.Source: A. The General Framework · p. 3
• ISAC users require both sensing and communication services, whereas communication users require communication only and sensing targets require sensing.Sensing targets may be device-free or device-based.Source: A. The General Framework · p. 3
• Users may request their own state information, such as localization, or state information about other objects, such as beyond-line-of-sight obstacle sensing in V2X.The BS acquires others’ state information through active sensing and transmits it through communication.Source: A. The General Framework · p. 4
• The model assigns radar, ISAC, and communication signals to Q sensing targets, L ISAC users, and K communication users, respectively.The sensing-target and communication-user index sets contain Q + L and L + K elements, respectively.Source: A. The General Framework · p. 4
• The transmit model uses baseband signals and a precoding matrix, while the echo model includes target power, reflection, Doppler, delay, receive beamforming, and AWGN.Communication reception similarly uses receive beamforming and assumes Doppler and delay are perfectly compensated through synchronization.Source: B. Signal Model · p. 4
• Uniform linear arrays with half-wavelength spacing define the transmit and receive steering vectors, and users are assumed spatially well separated.The separation assumption prevents overlap of main lobes toward desired directions.Source: B. Signal Model · p. 4, A. The General Framework · p. 4

• Achievable rate measures communication QoS because it directly depends on wireless resources such as power and bandwidth.Source: C. Communication QoS · p. 5
• Orthogonal frequency bandwidth allocation omits inter-user interference at communication receivers.Source: C. Communication QoS · p. 5
• The achievable sum-rate aggregates the rates of all Mc communication users.Source: C. Communication QoS · p. 5
• The communication allocation vectors contain each user's assigned bandwidth and the corresponding power and bandwidth resources.Source: C. Communication QoS · p. 5
• The unified framework allocates total power and bandwidth among sensing and communication services while satisfying communication QoS requirements.Source: D. A Unified Resource Allocation… · p. 5

• Omnidirectional initial detection is unsuitable for urban perceptive networks because complex surroundings create clutter and many areas lack detection requirements.Source: A. The Detection QoS · p. 5
• Prior angle and reflection-coefficient information enables the base station to tailor beamforming for target detection.Source: A. The Detection QoS · p. 5
• Spatial-temporal matched filtering produces the detection statistic from the received signal in a target's delay-Doppler bin.Source: A. The Detection QoS · p. 5
• Detection distinguishes whether a target exists in a specified delay-Doppler bin through composite binary hypothesis testing.Source: A. The Detection QoS · p. 5
• The detection model accounts for complex-Gaussian channel reflection and matched-filter noise assumptions.Source: A. The Detection QoS · pp. 5–6
• The decision threshold is selected to meet a desired false-alarm rate, after which the probability of detection is determined from the test-statistic distribution.Source: A. The Detection QoS · p. 6

B. Problem Formulation

• Detection QoS optimization can maximize the detection parameter ρq because probability of detection increases monotonically with ρq = pqςq.Source: B. Problem Formulation · p. 6
• The fairness criterion maximizes the minimum detection probability across sensing targets.Source: B. Problem Formulation · p. 6
• The fairness power-allocation problem enforces total power, communication sum-rate, and bounds preventing extremely large or small allocations.Source: B. Problem Formulation · p. 6
• The comprehensiveness criterion maximizes the sum of detection probabilities across all targets.Source: B. Problem Formulation · p. 6
• Proportional rate constraints can encode different target importance levels and reduce to max-min allocation when all importance weights are equal.Source: B. Problem Formulation · p. 6

IV. TARGET LOCALIZATION

• Localization estimates range and azimuth, with lower QoS suitable for nearby large targets and more resources preferred for important targets.Source: §IV · p. 6

A. The Localization QoS

• CRB provides a tractable lower-bound metric for localization estimation variance when mean squared error is difficult to characterize.Source: A. The Localization QoS · pp. 6–7
• Localization CRB depends on receive beam width, effective time duration, and effective bandwidth derived from the waveform spectrum.Source: A. The Localization QoS · p. 7

• Power affects sensing and communication similarly, whereas bandwidth affects radar and communication differently through interference and resource sharing.Source: B. Motivation on Bandwidth Allocation · p. 7
• Within one beam, communication users can receive orthogonal bands, but sensing targets reflect signals across all frequency bands and share the beam's bandwidth.Source: B. Motivation on Bandwidth Allocation · p. 7
• Inter-beam interference arises from power leakage between beams and can be reduced by matched filtering with orthogonal bandwidth.Source: B. Motivation on Bandwidth Allocation · p. 7
• The range-estimation CRB is inversely proportional to received SINR multiplied by bandwidth, linking sensing accuracy and communication sum-rate through the SBP.Source: B. Motivation on Bandwidth Allocation · p. 7
• The SBP ratio compares maximum-bandwidth and orthogonal-bandwidth schemes using allocated bandwidth and interference-related factors.Source: B. Motivation on Bandwidth Allocation · pp. 7–8
• As antenna count increases, the SBP ratio increases; maximum bandwidth is favored for massive MIMO, whereas orthogonal allocation is necessary for small-scale MIMO at high SNR.Source: B. Motivation on Bandwidth Allocation · p. 8
• The analysis ultimately allocates non-overlapped bandwidth to all sensing and communication users to avoid interference.Source: B. Motivation on Bandwidth Allocation · p. 8
• ISAC signals remove communication interference from sensing echoes, but dedicated radar and communication signals are expected to perform better at higher spectral-resource consumption.Source: B. Motivation on Bandwidth Allocation · p. 8

C. Problem Formulation

• Localization minimizes distance and AoA CRBs while guaranteeing communication QoS.Source: C. Problem Formulation · p. 8
• The comprehensiveness formulation uses normalized factors to combine distance and AoA objectives.Source: C. Problem Formulation · p. 8
• Power and bandwidth vectors are constrained by per-object minimum and maximum allocations.Source: C. Problem Formulation · p. 8
• The comprehensiveness formulation imposes proportional sensing-QoS factors, while the fairness formulation becomes a corresponding max-min problem.Source: C. Problem Formulation · p. 8
• Power and bandwidth are coupled in the localization objective and constraints, making the optimization non-convex.Source: C. Problem Formulation · p. 8
• Alternating optimization decouples power and bandwidth by solving successive sub-problems with one allocation fixed at each step.Source: C. Problem Formulation · p. 8, §3 · p. 9, §5 · p. 9
• The algorithm alternates until convergence to obtain a sub-optimal solution.Source: C. Problem Formulation · p. 9, §5 · p. 9
• An initial bandwidth-selection method addresses infeasibility that can arise from inappropriate initialization under large communication thresholds.Source: §5 · p. 9

V. TARGET TRACKING

• Tracking extends localization by estimating moving-target states and predicting their future values.Source: §V · p. 9, A. The tracking QoS · p. 9
• The state model uses Cartesian position and velocity components for constant-velocity targets.Source: A. The tracking QoS · p. 9
• The nonlinear measurement model transforms Cartesian target states into polar radar parameters.Source: A. The tracking QoS · p. 9
• Measurement noise is modeled as independent zero-mean additive white Gaussian noise with a covariance matrix.Source: A. The tracking QoS · p. 9
• The measurement covariance depends on power and bandwidth through the CRBs of range, velocity, and AoA estimation.Source: A. The tracking QoS · p. 9
• The PCRB combines prior and data Fisher information, with the prior information recursively updated across epochs.Source: A. The tracking QoS · pp. 9–10
• The epoch-specific Fisher information depends on predicted state information and allocated power and bandwidth resources.Source: A. The tracking QoS · p. 10
• The predicted PCRB provides the tracking-quality bound for the target state.Source: A. The tracking QoS · p. 10

B. Problem Formulation

• Tracking optimization maximizes tracking QoS while satisfying communication QoS demands.Source: B. Problem Formulation · p. 10
• The comprehensiveness formulation uses proportional tracking-QoS factors across sensing services.Source: B. Problem Formulation · p. 10
• Power and bandwidth allocations are defined per epoch, with a communication QoS threshold that can also vary by epoch.Source: B. Problem Formulation · p. 10
• Alternating optimization decouples power and bandwidth, and each sub-problem is made convex by linearizing the nonlinear equality constraint.Source: B. Problem Formulation · p. 10
• The predicted PCRB depends on predicted state information from the motion model and the previous epoch’s state.Source: B. Problem Formulation · p. 10
• An extended Kalman filter updates tracking information so resources for the next epoch can be optimized.Source: B. Problem Formulation · p. 10

1) State Prediction:

• The updated MSE matrix in the Kalman iteration equals the predicted PCRB from the preceding tracking step.Source: 2) MSE Matrix Prediction · p. 10
• Resources are allocated by solving the tracking-QoS resource-allocation problem at each epoch.Source: 3) Resource Allocation · p. 10
• The base station simultaneously provides communication and sensing by iteratively performing prediction and tracking with resource allocation.Source: 6) MSE Matrix Update · p. 10
• Figure 7 reports sensing PD versus communication threshold for comprehensiveness, while Figures 6 and 8 report fairness trade-offs and power allocations.Source: Figure 7 · p. 11, Figure 6 · p. 11, Figure 8 · p. 11
• The simulations use distances [100m, 120m, 120m, 110m, 100m] and evaluate theoretical and simulated PD under perfect beamforming.Source: §VI · p. 11, A. Target Detection · p. 11
• The fairness scheme exhibits three PD stages as the communication threshold increases: constant, decreasing, then bifurcating above 4.68 bps/Hz.Source: A. Target Detection · p. 11
• In the comprehensiveness scheme, sensing-target PDs follow the preset proportion γ = [1, 0.95, 0.9], while the ISAC user receives the best detection QoS.Source: A. Target Detection · p. 11

Target Localization

• 7.68 bps/Hz is achievable with the initialized power and bandwidth allocation, whereas equal bandwidth allocation becomes infeasible when Γc > 5.88 bps/Hz.The initialization process uses steps 2 and 3 of Algorithm 1.Source: B. Target Localization · p. 12
• Localization CRBs increase as the communication threshold Γc rises until the allocation problem becomes infeasible.More resources are devoted to communication, leaving relatively fewer resources for localization accuracy.Source: B. Target Localization · p. 12
• For Γc < 7.05 bps/Hz, allocated power remains constant while bandwidth is adjusted; beyond that threshold, sensing-target power begins to decrease.This occurs after sensing-target bandwidth reaches its minimum value at Γc = 7.05 bps/Hz.Source: B. Target Localization · p. 12

Target Tracking

• For an ISAC user moving from 141m to 100m from the BS, its MSE decreases and more resources are allocated to it.The allocation changes as the user’s communication channel improves during movement.Source: C. Target Tracking · p. 13
• When the ISAC user passes across the BS, MSE first decreases and then increases, reaching its minimum at the closest distance with θ = −90°.The corresponding power and bandwidth allocation trends follow the MSE variation.Source: C. Target Tracking · p. 13
• Lower communication QoS requirements yield a higher probability of achieving smaller MSE, while sensing MSE remains above a fixed value when communication constraints are inactive.The CDF comparison covers all sensing targets and reflects the sensing–communication trade-off.Source: C. Target Tracking · p. 13

APPENDIX

• For fixed bandwidth bq, eigenvalue decomposition rewrites the objective using positive coefficients derived from positive-definite matrices.The resulting expression establishes convexity with respect to the power variable pq.Source: APPENDIX · pp. 13–14
• The resulting objective term is convex because it is a linear combination of convex functions.This conclusion follows after the matrix-based reformulation for fixed bq.Source: APPENDIX · p. 14
• For fixed power pq, the corresponding reformulation has the same structure as the fixed-bandwidth case, so convexity follows by the same process.The appendix applies the analogous matrix argument to the bandwidth variable.Source: APPENDIX · p. 14