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Resource allocation in Distributed ISAC Systems: A Location Sensitive Mode Selection and Task Assignment Framework
Kwadwo Mensah Obeng Afrane, André B. J. Kokkeler, Yang Miao
TL;DR
Location-dependent sensing requirements motivate resource allocation that accounts for a target’s proximity to a region of interest. RAMSTA uses a sigmoid-based proximity parameter in a weighted sum-rate and position-PCRLB optimization, solved with a penalized convex-concave procedure. The paper reports that ROI sensitivity thresholds adapt the communication-sensing trade-off relative to the target’s predicted location and predefined ROI.
Problem
Sensing requirements can vary by target location, motivating resource allocation that accounts for stricter accuracy needs in particular regions.
Source: §I · p. 1Method
RAMSTA jointly selects AP modes and tasks using a sigmoid-based ROI proximity parameter in a weighted sum-rate and position-PCRLB minimization, solved by penalized convex-concave procedure.
Source: §I · p. 1Results
ROI sensitivity thresholds allow adaptive variation of the communication-sensing trade-off with respect to predicted target location and a predefined ROI.
Source: §V · p. 6Takeaways & Limitations
The framework’s ROI sensitivity thresholds tune the communication-sensing trade-off according to the target’s predicted location relative to the ROI.
Source: §V · p. 6
Abstract
from arXiv · showhide
In this work we propose a region of interest (ROI)-aware mode selection and task assignment (RAMSTA) framework for distributed integrated sensing and communication (ISAC) systems. In realistic ISAC use-cases, the sensing performance requirement can be location dependent. Vehicular targets at a traffic intersection, unmanned aerial vehicle approaching a restricted airspace or a sparsely populated areas may require different levels of detection or localization accuracy. This warrants the design of location sensitive resource allocation to account for the varying sensing performance requirements. Thus, we design a sigmoid-based ROI proximity parameter to tune the communication-sensing trade-off in a weighted sum rate and position posterior Cram\'er-Rao lower bound minimization problem. The resulting mixed-integer non-linear program is solved by applying a penalized convex-concave procedure. We show that the ROI sensitivity thresholds allows the adaptive variation of the communication-sensing trade-off with respect to the predicted location of the target and relative to a predefined ROI.
I. INTRODUCTION
The introduction motivates ROI-aware resource allocation because sensing requirements can become stricter in particular regions along a target’s trajectory. RAMSTA adapts the communication-sensing trade-off through joint AP mode selection and task assignment, while the system model defines the distributed AP, UE, and ROI setting.
I. INTRODUCTION
- Prior mode-selection and resource-allocation work does not account for ROI-aware design, although sensing requirements may be stricter in hazardous or restricted regions along a target’s trajectory.Examples include dangerous road intersections and restricted airspace near airports.Source: §I · p. 1
- RAMSTA uses a sigmoid-based ROI proximity parameter to adapt the communication-sensing trade-off while assigning AP operating modes and communication, sensing, or ISAC tasks.The framework also employs ROI-aware heuristic subcarrier allocation and non-uniform power allocation.Source: §I · p. 1
- The optimization minimizes a weighted sum of position PCRLB and sum rate, with mode selection and task assignment as variables.The resulting mixed-integer nonlinear program is solved using a penalized convex-concave procedure.Source: §I · p. 1
II. SYSTEM MODEL
- The system model considers distributed APs serving single-antenna downlink UEs while tracking one target, with higher sensing quality required inside a spherical ROI.The ROI is specified by a known center and radius.Source: §II · p. 1
A. Sensing Model
The sensing model describes cooperative probing and echo reception across distributed APs, along with the signal and array components used to represent the bistatic link.
1) Signal Model:
- The model distinguishes communication and sensing transmit powers, subcarrier allocations, beamformers, and baseband symbols.The communication variables are associated with each downlink UE; the sensing variables are associated with each AP and subcarrier.Source: 1) Signal Model · p. 2
- Downlink APs transmit probing signals toward the target, while uplink APs receive reflected echoes for processing at the CPU.The received signal is indexed by subcarrier, OFDM symbol, and the receiving and transmitting APs.Source: 1) Signal Model · p. 2
- The bistatic signal description includes a radar channel, AP-to-AP channel-estimation error, and noise.Its listed link parameters include attenuation, Doppler shift, delay, and subcarrier spacing.Source: 1) Signal Model · p. 2
- Transmit and receive steering vectors represent the target’s horizontal and vertical angles of departure and arrival.The array description also specifies wavelength and antenna spacing along the x and z axes.Source: 1) Signal Model · p. 2
- The sensing beamformer is chosen as a conjugate beamformer in the target’s predicted angle-of-departure direction.The model states this choice is made for simplicity.Source: 1) Signal Model · p. 2
2) Target Tracking Model:
The tracking model propagates a target state under nearly constant velocity and uses a recursively computed Fisher information matrix to define a predicted-position PCRLB sensing objective.
2) Target Tracking Model:
- The target state comprises 3D position and velocity and evolves between tracking intervals under a nearly constant velocity model.The state transition includes process noise.Source: 2) Target Tracking Model · p. 2
- The measurement model is defined for each bistatic AP pair, with measurement-noise covariance derived in Appendix A.The supplied text identifies the measurement function and its noise, but does not give their full expressions.Source: 2) Target Tracking Model · p. 2
- Tracking performance is measured with the PCRLB, whose Fisher information matrix is computed recursively using a data FIM derived from the received signal.The sensing objective is the trace of the predicted-position PCRLB, evaluated at the target’s predicted state.Source: 2) Target Tracking Model · p. 2
B. Communication
The communication model considers cooperative downlink service to selected UEs and introduces their achievable rate in terms of channel and transmission quantities.
B. Communication
- Downlink APs cooperatively serve a selected subset of UEs, with the serving assignments specified by an allocation variable.Source: B. Communication · p. 2
- The model introduces an achievable-rate expression for each downlink UE.Source: B. Communication · p. 2
- The listed rate-expression quantities include the downlink channel gain, maximum-ratio-transmission beamformer, and receiver noise.Source: B. Communication · p. 2
A. ROI-aware tuning parameters
RAMSTA uses a sigmoid-based ROI proximity parameter to adapt the communication–sensing trade-off to the target’s predicted location relative to the ROI.
A. ROI-aware tuning parameters
- The sigmoid-based parameter is defined using the predicted target position’s distance from the ROI center and a normalized proximity margin.Source: A. ROI-aware tuning parameters · p. 3
- The dimensionless proximity parameter decreases monotonically with distance from the ROI center and approaches unity as the target approaches the ROI.The normalized proximity margin contributes to the parameter’s distance dependence.Source: A. ROI-aware tuning parameters · p. 3
- The parameter adaptively tunes the communication–sensing trade-off, with δ_i bounded by ROI sensitivity thresholds δ_min and δ_max.δ_i approaches δ_max near the ROI center and δ_min farther away.Source: A. ROI-aware tuning parameters · p. 3
B. RAMSTA
RAMSTA jointly assigns AP operation modes and communication, sensing, or ISAC tasks. Its non-convex mixed-integer formulation is transformed into a convex form using relaxations, linearizations, and semidefinite programming.
B. RAMSTA
- The formulation constrains task assignment across transmit APs, including a minimum number assigned to sensing and bounds on APs assigned per UE and overall.Power and subcarriers are allocated heuristically and are not optimization variables or constraints.Source: B. RAMSTA · p. 3
- The non-convex MINLP relaxes binary constraints and applies PCCP, replacing concave components with first-order Taylor approximations and penalizing constraint violations.Slack variables are introduced for the resulting constraints.Source: B. RAMSTA · p. 3
- Bilinear terms are reformulated and linearized with McCormick constraints, while the position PCRLB objective is reformulated as a semidefinite program.The convex form can be solved with CVX.Source: B. RAMSTA · p. 3
- Algorithm 1 starts from feasible uniform subcarrier and power allocation and iteratively solves the reformulated problem while updating its penalty coefficient.Source: B. RAMSTA · p. 4
C. Power and Subcarrier Allocation
After mode and task assignment, RAMSTA allocates subcarriers and power using ROI-proximity-sensitive heuristics rather than including them in the optimization.
C. Power and Subcarrier Allocation
- The subcarrier split uses δ_i to divide resources between communication and sensing, then assigns UE subcarriers by average channel gain and sensing subcarriers to sensing transmit APs in an interleaved manner.The procedure follows Algorithm 2.Source: C. Power and Subcarrier Allocation · p. 4
- Each transmit AP receives an equal share of total power, which ISAC APs split between communication and sensing according to δ_i; single-task APs use all their power for that task.Power is then distributed equally across assigned subcarriers.Source: C. Power and Subcarrier Allocation · p. 4
IV. RESULTS
The simulations examine AP topology, ROI-sensitive communication–sensing trade-offs, mode and task assignments, and tracking against benchmarks. RAMSTA maintains strong inside-ROI tracking, with performance varying by topology and ROI sensitivity thresholds.
IV. RESULTS
- The simulation uses 6 APs, 3 UEs, and one target; an EKF at the CPU fuses valid multistatic link measurements via covariance intersection.The target has a 5 dBsm radar cross-section.Source: §IV · p. 4
- Outside the ROI, δmax = 0.8 and δmin = 0.2 yield 278.9 Mbps and 0.0099 m; inside, they yield 91 Mbps and 0.0006 m.At δmax = 0.7 and δmin = 0.3, outside the ROI the sum rate and position PCRLB are 260.9 Mbps and 0.0032 m; inside they are 116.7 Mbps and 0.0007 m.Source: Figure 2 · p. 5, §IV · p. 5
- At i = 4, triangular topology has an inside-ROI position PCRLB of 0.0108 m, versus 0.0312 m for random and 0.0507 m for collinear topology.The authors attribute the gain to APs inside the ROI forming high-SNR multistatic links; APs outside provide diverse observability, and later analyses use the triangular topology.Source: §IV · p. 4, Figure 2 · p. 5
- With δmin = 0.2 and δmax = 0.8, outside-ROI APs favor transmit modes with communication tasks, while inside-ROI assignments balance transmit-ISAC and receive APs.With δmin = δmax = 0.5, communication- and sensing-favorable modes and tasks are balanced across tracking intervals.Source: Figure 3 · p. 5, §IV · p. 5
- At i = 6, RAMSTA’s position PCRLB is 0.0006 m, versus 0.0008 m for RAMSTA-2 and 0.0022 m for RAMSTA-3; ROI-Proximity reaches 0.039 mm at i = 5.The 0.0002 m gain over RAMSTA-2 is attributed to ROI-aware power and subcarrier allocation, but comes with degraded communication and sensing performance inside and outside the ROI, respectively.Source: Figure 4 · p. 5, §IV · p. 6
V. CONCLUSION
The conclusion presents RAMSTA as a way to adapt the communication–sensing trade-off to the target’s predicted location relative to an ROI. It also identifies extensions to resource allocation, beamforming, ROI shape, and proximity prediction.
V. CONCLUSION
- RAMSTA uses a sigmoid-based ROI proximity parameter to tune the communication–sensing trade-off in a weighted position PCRLB and sum-rate minimization problem.Source: §V · p. 6
- The resulting mixed-integer nonlinear program is solved using a penalized convex-concave procedure.Source: §V · p. 6
- ROI sensitivity thresholds adapt the communication–sensing trade-off to the predicted target location relative to a predefined ROI.Future work would address end-to-end resource allocation and beamforming for polyhedron-shaped ROIs, and ROI-proximity prediction errors.Source: §V · p. 6
APPENDIX DERIVATION OF (6)
The appendix derives the FIM formulation from stacked observations and an unknown parameter vector. It identifies position and velocity information blocks, their coupling, and a corresponding measurement-noise covariance.
APPENDIX DERIVATION OF (6)
- The observation vector y stacks measurements over subcarriers and transmit-receiver AP pairs and is modeled as y ∼ CN(µ, σ).The unknown parameter vector γ is composed of φ and α.Source: APPENDIX DERIVATION OF (6) · p. 6
- For indices satisfying r′≠r and j′≠j, the cited passage reports the partial derivative of φr′,j′ as the six-component zero vector [0, 0, 0, 0, 0, 0].Source: APPENDIX DERIVATION OF (6) · p. 6
- The FIM’s position and velocity blocks characterize information for those quantities, while its off-diagonal elements characterize their coupling.Source: APPENDIX DERIVATION OF (6) · p. 6
- The derivation omits the off-diagonal terms of (31) and the derivatives for brevity.Source: APPENDIX DERIVATION OF (6) · p. 6
- The measurement-noise covariance is obtained as Rr,j = ˜J(γ)−1, with φr,j restricted to [fr,j, τr,j, θr, ϕr].Source: APPENDIX DERIVATION OF (6) · p. 6