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Radio Imaging and Resource Allocation in Frugal Multistatic D-MIMO ISAC Systems

Sauradeep Dey, Musa Furkan Keskin, Dario Tagliaferri, Gonzalo Seco-Granados, Henk Wymeersch

arXiv:2608.27041v1eess.SP

TL;DR

Radio imaging in frugal D-MIMO ISAC is constrained by hardware complexity and sensing-communication interference. The paper uses orthogonal subcarriers and two-timescale resource allocation to minimize image entropy under communication SE constraints, and reports better trade-offs than superposed coding while examining synchronization-dependent receiver performance.

  • Problem

    Radio imaging needs richer environmental reflectivity maps, but many distributed approaches rely on multi-antenna APs or large arrays, while sensing and communication can interfere.

  • Method

    The framework separates sensing and communication onto orthogonal subcarriers and jointly optimizes AP modes, sensing-subcarrier allocation, and power splitting using long- and short-timescale procedures.

  • Results

    The orthogonal design consistently outperforms superposed coding in sensing-communication trade-offs, with lower entropy and improved localization, while receiver performance depends on synchronization.

  • Takeaways & Limitations

    Interleaved subcarrier allocation improves sensing over clustered allocation, and coherent or non-coherent imaging is preferable in different synchronization regimes.

Abstract

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Emerging integrated sensing and communication (ISAC) systems based on distributed MIMO (D-MIMO) enable radio imaging by exploiting spatial diversity across multiple access points (APs). However, joint sensing and communication introduce mutual interference between communication and sensing signals. In this paper, we propose a downlink D-MIMO ISAC framework that allocates orthogonal subcarriers to sensing and communication to eliminate inter-function interference. We consider a phase-coherent architecture in which single-antenna APs serve communication user equipment (UEs) while constructing a reflectivity image of the environment. We develop a two-timescale resource allocation framework that minimizes reconstructed-image entropy subject to a communication spectral-efficiency (SE) constraint. The proposed design follows a communication-centric policy, where imaging uses the resources left after satisfying the communication requirement. The long-timescale optimization (LTO) determines AP modes and subcarrier assignment, including the partitioning between communication and sensing and the allocation of sensing subcarriers among transmit APs, using synthetic scenarios with random UE and target distributions. The short-timescale optimization (STO) adapts the communication-sensing power-splitting factor to preserve the SE constraint in the current scenario. Numerical results show that the proposed orthogonal subcarrier allocation achieves a superior sensing-communication trade-off compared with conventional superposition, where sensing and communication share the same subcarriers. Finally, we evaluate coherent and non-coherent imaging receivers and identify the synchronization regimes in which each approach provides better imaging and localization performance.

I. INTRODUCTION

The paper develops a frugal phase-coherent D-MIMO ISAC framework using single-antenna APs and orthogonal subcarriers for communication and radio imaging. It combines entropy-based image evaluation with two-timescale resource allocation and examines sensing-communication trade-offs and system modeling choices.

  • Motivation: D-MIMO uses geographically distributed, phase-coherent APs as a virtual antenna array for communication gains and high-resolution sensing from multiple viewpoints.The distributed geometry also supports radio imaging of environmental reflectivity maps for applications including digital twins, autonomous systems, and extended reality.
  • Limitations of prior work: Existing imaging approaches often rely on multi-antenna APs or large arrays, while compressed sensing, message passing, and covariance methods can increase hardware or computational demands.Covariance-based methods additionally require multiple temporal snapshots, making them less suitable for dynamic environments; backprojection offers a linear, single-step alternative.
  • Proposed framework: The proposed frugal architecture assigns disjoint subcarriers to sensing and communication, eliminating inter-function interference while distributing sensing subcarriers across transmit APs.Orthogonal sensing allocation makes AP-specific echoes separable at receive APs and supports image reconstruction for multiple point targets.
  • Sensing evaluation: Image entropy evaluates spatial concentration without prior target locations, addressing limitations of SNR-, detection-probability-, and CRLB-based sensing metrics in unknown multi-target environments.The paper also notes that prior work often models communication with stochastic fading and sensing with LoS-only channels, overlooking their physical coupling.
  • Resource allocation: A two-timescale optimizer selects AP transmit/receive modes, subcarrier allocations, and sensing-communication power splitting while minimizing expected image entropy under communication sum-SE constraints.The long-timescale design uses scenario statistics, while the short-timescale procedure adapts the power split online to instantaneous channel conditions.
  • Results: The framework numerically achieves a superior sensing-communication trade-off to superposed coding, with lower image entropy over communication sum-SE budgets and improved GOSPA localization accuracy.Interleaved sensing-subcarrier allocation also provides better sensing performance than clustered allocation, and coherent and non-coherent receivers are evaluated under imperfect synchronization.

C. Problem Statement

The problem is to jointly support downlink communication and environmental sensing when resources and AP modes couple the two functions. The paper formulates image-entropy minimization under communication-quality constraints for reconstructing and interpreting multi-target scenes.

  • The system reconstructs a coverage-area image from received sensing signals and detects image peaks to estimate target locations.
  • Image entropy quantifies reconstructed-image quality without requiring prior target locations, making it applicable to complex multi-target scenarios.
  • Joint optimization is required because sensing and communication share transmit power and bandwidth and depend on AP transmit/receive mode selection.The design optimizes AP modes, sensing and communication subcarrier allocation, and the power factor α while satisfying communication quality requirements.

III. RECEIVER-SIDE PROCESSING: IMAGING AND TARGET LOCALIZATION

The receiver reconstructs coverage-area reflectivity images with backprojection, using coherent or non-coherent combination across distributed AP pairs, then detects and refines target locations.

  • Imaging of the Environment: Backprojection reconstructs the coverage-area reflectivity image on a uniformly spaced grid with 0.025 m inter-pixel spacing.It provides a linear imaging benchmark with lower complexity than nonlinear alternatives.
  • Imaging of the Environment: Each transmit-receive AP pair forms a matched image by phase-matching echoes to candidate propagation paths and combining assigned sensing subcarriers.Pairwise images are subsequently combined across AP pairs.
  • Coherent Imaging: Coherent imaging adds pairwise images coherently, producing constructive target peaks and low-amplitude backgrounds that improve detection and localization accuracy.The gain is especially important in the POSE regime, where each transmit AP uses one sensing subcarrier.
  • Non-coherent Imaging: Non-coherent imaging combines pairwise-image magnitudes without phase synchronization across AP pairs.In the POSE regime, one sensing subcarrier per transmit AP removes intra-pair frequency diversity, making non-coherent imaging ineffective.
  • Target Localization: Target localization detects image peaks with CFAR and refines their positions beyond grid resolution using gradient ascent on continuously evaluated BP intensity.The final estimates are obtained after refining coarse discretized-grid locations.

IV. TRANSMITTER-SIDE PROCESSING: TWO-TIMESCALE RESOURCE ALLOCATION

The transmitter-side design jointly selects AP modes, sensing subcarriers, and power splitting to minimize image entropy under a sum-SE constraint, while separating slow combinatorial decisions from fast power adaptation.

  • Problem Formulation: The resource-allocation problem selects AP transmit/receive modes, sensing and communication subcarriers, and power factor α to maximize sensing performance under communication requirements.The formulation minimizes image entropy subject to a communication sum-SE constraint.
  • Performance Metrics: Image entropy measures spatial concentration of reconstructed energy, while sum-SE measures communication performance across UEs and communication subcarriers.Lower entropy indicates sharper, more localized target responses.
  • Caveat: Low image entropy does not necessarily imply accurate target reconstruction, so localization performance must also be evaluated with metrics such as GOSPA.Image energy can concentrate around incorrect target locations.
  • Problem Formulation: The joint optimization is mixed-integer and non-convex, with exponentially growing exhaustive-search complexity and substantial coordination overhead for snapshot-level updates.The scalar power factor α can instead be updated rapidly using instantaneous channel conditions.
  • Two-Timescale Optimization: A two-timescale framework performs offline LTO for AP modes and subcarrier allocation, then uses STO to adapt the power split while preserving the current communication constraint.The LTO stores optimized mode and allocation pairs as codebook entries for online initialization.

C. Long-Timescale Optimization (LTO)

The LTO jointly optimizes long-term AP modes, sensing subcarrier assignments, and power splitting over synthetic UE-target scenarios to minimize expected image entropy while enforcing communication performance.

  • Scenario Generation: LTO uses synthetic scenarios with randomly distributed UEs and point targets, generating and pre-computing their communication and sensing channel realizations.The scenarios provide the offline channel data used for optimization.
  • LTO Objective: The LTO jointly optimizes b, S, and α over the synthetic scenarios to solve the offline resource-allocation problem.These variables represent AP modes, sensing-subcarrier assignments, and the power-splitting factor.
  • Synthetic Evaluation: For each scenario, synthetic sensing observations are generated from the channel model and used to compute image intensity for candidate resource allocations.The image intensity is decomposed into signal-dependent and noise-dependent components.
  • Synthetic Evaluation: Disjoint sensing subcarrier sets and independent noise across subcarriers and receive APs yield a zero-mean noise component with a scenario-dependent variance.This supports evaluation of expected image intensity and entropy.
  • LTO Objective: The expected entropy for each synthetic scenario supplies the LTO sensing objective, while scenario sum-SE values enforce the communication requirement.The resulting joint optimization determines the long-timescale resource configuration.

3) Problem Formulation for LTO:

The LTO jointly selects AP modes, sensing subcarrier allocation, and power splitting to minimize worst-case expected image entropy while meeting average sum-SE constraints across synthetic scenarios.

  • Problem formulation: LTO jointly optimizes AP modes, subcarrier allocation, and power factor α against image entropy and average sum-SE constraints.The optimized AP configuration and sensing allocation are selected across synthetic scenarios, while α is optimized during LTO.
  • Problem formulation: The objective minimizes the maximum expected image entropy across all synthetic scenarios.
  • Problem formulation: Optimizing α during LTO ensures AP modes and subcarrier allocation are evaluated under the best possible power allocation.Only the optimized pair (b∗, S∗) is stored as the codebook entry for a given budget β.
  • Problem formulation: The average sum-SE constraint is evaluated across K synthetic scenarios.The threshold is defined relative to the communication budget β and scenario-wise maximum achievable sum-SE.
  • Solution approach: A greedy-search-based technique solves P2 by first studying AP mode selection, sensing subcarrier allocation, and power-factor optimization individually.Insights from these subproblems are combined into a joint LTO strategy.

4) AP Mode Selection:

AP mode selection uses greedy single-AP changes, retaining feasible candidates and selecting the one with the lowest maximum image entropy across synthetic scenarios. Sensing subcarriers are structured equally and maximally interleaved across transmit APs.

  • AP mode selection: Algorithm 1 initializes with G−1 transmit APs and one receive AP closest to the coverage-area center.The search begins from a communication-favorable configuration.
  • AP mode selection: Each iteration flips one AP mode, then optimizes the candidate’s sensing allocation and power factor.Candidates violating the average sum-SE constraint are discarded.
  • AP mode selection: Among feasible candidates, the mode vector minimizing maximum image entropy across synthetic scenarios is selected until no single-AP change improves it.
  • Sensing subcarrier allocation: The structured sensing allocation assigns every transmit AP the same κ sensing subcarriers, leaving S−κN subcarriers for communication.Thus, the total number of sensing subcarriers is Ssen=κN.
  • Sensing subcarrier allocation: Maximally interleaved allocation gives transmit AP n the subcarriers {n, n+N, ..., n+(κ−1)N}.Each AP receives uniformly spaced subcarriers spanning effective bandwidth κNΔf.
  • Sensing subcarrier allocation: For each feasible κ, the sensing allocation is constructed and α is chosen as the minimum value satisfying the average sum-SE constraint.The feasible range ends at the largest κ preserving feasibility with α=1.

6) Power Factor Selection:

The power factor α is selected by exploiting the monotonic increase of average sum-SE with α, using bisection over the interval [0,1].

  • Power factor selection: Optimal α∗ is obtained by bisection search over [0,1] because average sum-SE increases monotonically with α.

7) Joint LTO Framework:

The joint framework initializes a communication-favorable LTO configuration, then adapts it online through STO to satisfy instantaneous sum-SE constraints. STO first adjusts sensing subcarriers, then AP modes, while preserving imaging diversity where possible.

  • Joint LTO framework: LTO initializes with G−1 transmit APs, one receive AP, and κ=1 sensing subcarrier per transmit AP.This uses G−1 sensing subcarriers and S−(G−1) communication subcarriers.
  • Short-timescale optimization: STO starts from the LTO AP modes and subcarrier allocation and evaluates the current channels using the communication threshold γ=βRmax.The LTO power factor is discarded before the short-timescale update.
  • Joint LTO framework: Figure 2 summarizes the offline LTO and online STO interaction, covering AP mode selection, subcarrier allocation, and power-factor allocation.
  • Short-timescale optimization: If full communication power satisfies the instantaneous constraint, STO sets α to the minimum value meeting the sum-SE threshold.Because R increases monotonically with α, bisection over [0,1] determines α∗.
  • Short-timescale optimization: If infeasible at α=1, STO decrements κ to release N sensing subcarriers per iteration while preserving AP topology and spatial imaging diversity.The largest κ restoring feasibility at α=1 is retained.
  • Short-timescale optimization: If κ=1 remains infeasible, receive APs are converted iteratively into transmit APs until the communication constraint is satisfied.At each iteration, the receive AP closest to the weakest-SE UE is switched to transmit mode.

E. Convergence Analysis

The framework’s LTO and STO stages use finite, monotonic searches and bisection to obtain feasible resource configurations and communication power factors. The numerical evaluation uses synthetic network realizations and evaluates sum-SE, image entropy, and GOSPA.

  • LTO convergence: Algorithm 1 greedily searches AP modes while jointly optimizing sensing allocation and power splitting to minimize worst-case expected image entropy.The search terminates at a local optimum of the restricted problem induced by interleaved equal-subcarrier allocation.
  • STO convergence: For fixed AP modes and sensing allocation, the communication power factor is found by bisection because sum-SE is continuous and non-decreasing in that factor.The method selects the smallest feasible factor in [0, 1].
  • STO convergence: The STO stage first checks sum-SE feasibility and then performs the power-factor bisection search.Feasibility recovery reduces the number of sensing subcarriers per transmit AP when needed.
  • Termination guarantees: Finite search spaces and unidirectional updates guarantee finite-time termination for the feasibility and AP-mode update stages.The AP mode vector has at most 2^G configurations, while the sensing-subcarrier count is bounded and integer-valued.
  • Evaluation setup: The evaluation uses random UE and target locations across independent STO realizations and measures communication with sum-SE and sensing with image entropy and GOSPA.A representative synthetic scenario is used for the computationally tractable LTO search.

B. Imaging Performance Under Different Sum-SE Budgets

Higher normalized communication budgets shift imaging outcomes toward higher entropy and GOSPA, while adaptive AP modes and interleaved sensing subcarriers improve the sensing-communication trade-off. At β = 0.75, the proposed framework consistently outperforms the fixed-mode and alternative subcarrier-allocation baselines on reported localization outcomes.

  • Sum-SE budgets: At β = 0.25, image entropy is 9.43 bits, versus 11.69 bits at β = 0.9, with higher budgets producing stronger sidelobes and secondary peaks.Across 100 STO realizations, increasing β shifts both entropy and GOSPA CDFs toward higher values.
  • Sum-SE budgets: 93%, 67%, and 53% of realizations achieve GOSPA < 10^-3 for β = 0.25, 0.75, and 0.9, respectively.These cases correspond to correct detection and localization of all targets without missed detections or false alarms.
  • Impact of AP Mode Selection: The proposed adaptive AP-mode framework achieves lower average image entropy and higher average sum-SE than the fixed AP-mode benchmark.The benchmark fixes alternating transmit and receive AP modes, whereas the proposed configuration adapts modes during optimization.
  • Impact of AP Mode Selection: At β = 0.75, GOSPA < 10^-4 occurs in 72% of proposed-framework realizations versus 58% for the fixed-mode baseline.Both percentages represent correct detection and localization of all targets without missed detections or false alarms.
  • Impact of Sensing Subcarrier Allocation: Interleaved sensing subcarrier allocation achieves the lowest average entropy across the sum-SE regime and detects and localizes all targets in 72% of β = 0.75 realizations.Each transmit AP spans a large effective bandwidth, improving range resolution relative to clustered allocations.

D. Comparison with Superposition Scheme

The proposed orthogonal allocation improves the sensing–communication trade-off over superposition by eliminating inter-function interference. Its optimization converges, while phase synchronization determines whether coherent or non-coherent imaging is preferable.

  • Scheme comparison: Orthogonal subcarriers eliminate the mutual sensing–communication interference caused by superposing both signals on every subcarrier.The superposition scheme transmits sensing and communication signals over all S subcarriers, whereas the proposed scheme separates them.
  • Scheme comparison: The proposed framework consistently achieves a better sensing–communication trade-off than superposition and POSE across the evaluated sum-SE regimes.Superposition is stronger than POSE at low sum-SE, while POSE performs better at higher sum-SE; the proposed framework remains superior overall.
  • Scheme comparison: 72% of STO realizations correctly detect and localize all targets with the proposed scheme, versus 58% for both superposition and POSE.When all targets are detected, superposition still has larger localization errors because interference distorts reconstructed target peaks.
  • Convergence and complexity: LTO image entropy decreases monotonically and converges within approximately 15 iterations, at a runtime of about 5 × 10^3 s.The sum-SE initially drops to satisfy the prescribed budget and then remains constant.
  • Convergence and complexity: Higher β shifts the STO runtime distribution upward because stricter SE constraints require more restoration iterations and larger communication subcarrier sets increase evaluation cost.The runtime CDF exhibits staircase behavior because feasibility restoration performs a discrete number of resource-allocation updates.
  • Phase synchronization robustness: At ϕmax = π/2 rad, non-coherent imaging produces cleaner target peaks and lower entropy than coherent imaging under phase synchronization errors.The reported entropies are 11.21 bits for non-coherent imaging and 12.09 bits for coherent imaging.
  • Phase synchronization robustness: Coherent imaging has lower entropy for small phase errors, but non-coherent imaging becomes preferable when ϕmax > 1 rad.Non-coherent entropy remains constant as maximum phase error increases, whereas coherent entropy increases.
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