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CORDIS: A Scalable Coordinated Resource Allocation Framework for Distributed Cell-Free ISAC

Mehdi Zafari, Björn Ottersten, A. Lee Swindlehurst

arXiv:2609.12195v1eess.SPcs.SYeess.SY

TL;DR

Distributed cell-free ISAC requires beamforming and power coordination, but directly optimizing sensing performance is difficult because its clutter-dependent denominator couples APs and can make optimization costly. CORDIS offers split and decentralized ADMM schemes; simulations show CORDIS-ADMM approaches the centralized sensing bound while retaining scalable local computation and exchange.

Abstract

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Integrated Sensing and Communication (ISAC) is envisioned as a key technology for 6G wireless networks, enabling the joint use of spectrum and hardware for sensing and communication. In multi-static cell-free architectures, coordinating beamforming and power resources across distributed access points (APs) is critical in order to mitigate severe communication-sensing interference. Most existing ISAC resource allocation solutions rely on centralized architectures with full network knowledge, which limits their scalability and practicality in distributed cell-free deployments with imperfect channel state information (CSI). In this paper, we introduce a framework for COordinated Resource allocation for Distributed ISAC Systems (CORDIS) that optimizes network sensing while suppressing clutter and maintaining per-user communication performance constraints. Two algorithms are developed: CORDIS-Split, a low-overhead scheme that pairs fixed local beamformers with centralized power allocation, and CORDIS-ADMM, which jointly optimizes beamforming and power through the consensus Alternating Direction Method of Multipliers (ADMM). By localizing high-dimensional matrix operations, both algorithms ensure fronthaul overhead and per-AP computation remain independent of antenna and AP counts. Simulations demonstrate that CORDIS-ADMM approaches the centralized performance bound and degrades gracefully under CSI estimation error, remaining effective even with locally rank-deficient channels, while CORDIS-Split offers a minimal-overhead alternative. These results confirm that CORDIS is a scalable and communication-efficient foundation for robust ISAC in decentralized wireless networks.

I. INTRODUCTION

The introduction frames distributed cell-free ISAC as a resource-coordination problem: beamforming and power must jointly support communication QoS and sensing under fronthaul and computation limits. CORDIS addresses this with complementary low-overhead and fully decentralized algorithms.

I. INTRODUCTION

  • Cell-free APs offer multistatic sensing diversity, but coordinating beamforming and power while meeting communication QoS, sensing, fronthaul, and computation constraints remains a central challenge.The coordination must scale without exchanging high-dimensional CSI or beamforming vectors.Source: §I · p. 1

A. Background and Related Work

  • Prior resource-allocation approaches provide only parts of the required capability: many centralize processing and global CSI, while edge-focused designs leave joint beamforming and power allocation unresolved.Centralized designs often assume perfect CSI and neglect clutter; decentralized examples may omit target echoes, clutter, detection, or joint allocation.Source: A. Background and Related Work · p. 2

B. Research Gap and Contributions

  • CORDIS-Split fixes robust local MMSE communication precoders with target nulling and uses centralized convex power allocation, exchanging only a few real scalars per user.This decouples beamforming from power allocation.Source: B. Research Gap and Contributions · p. 3
  • CORDIS-ADMM jointly optimizes beamforming and power through decentralized consensus ADMM, with per-round exchange and per-AP computation independent of array size and AP count.The algorithm remains effective for rank-deficient channels.Source: B. Research Gap and Contributions · p. 3
  • The evaluation examines communication-sensing trade-offs, clutter suppression, CSI robustness, and low-rank scalability, reporting that CORDIS-ADMM approaches the centralized performance bound.The evaluations include clutter and imperfect CSI.Source: B. Research Gap and Contributions · p. 3

II. SYSTEM MODEL

  • The system model uses distributed transmit and receive AP sets connected to a CPU, with block-fading channels and TDD phases for training, uplink data, and downlink ISAC.The CPU determines AP clustering and target scheduling and communicates those decisions to APs.Source: §II · p. 3

A. Communication Channel Model

The communication channel model combines LoS and spatially correlated fading components, while the sensing model represents target reflections alongside spatially and temporally correlated clutter. The sensing statistics are treated as known and constant over a coherence block.

A. Communication Channel Model

  • Communication channels contain a deterministic LoS array response with random phase and a spatially correlated NLoS component.The model also describes cross-user spatial correlation through an AP-specific shared subspace of dimension r much smaller than the antenna count.Source: A. Communication Channel Model · p. 3

B. Sensing and Clutter Channel Model

  • The sensing channel combines a rank-one LoS target-reflection path with aggregate clutter returns that exhibit Doppler-dependent temporal correlation.The model uses separable space-time clutter correlation, with spatial correlation matrices for transmit and receive APs.Source: B. Sensing and Clutter Channel Model · p. 4
  • The sensing and clutter correlation statistics are assumed known and constant over the coherence block.The clutter scattering component is modeled as a zero-mean, circularly symmetric complex Gaussian stationary process.Source: B. Sensing and Clutter Channel Model · p. 4

C. Uplink Channel Estimation

The uplink estimation model accounts for pilot reuse and contamination, then uses each AP’s pilot observation to obtain channel-estimation statistics and an LMMSE channel estimate.

C. Uplink Channel Estimation

  • When users outnumber available pilot sequences, some users share pilots, causing pilot contamination.The set of users sharing a pilot with user k includes user k itself.Source: C. Uplink Channel Estimation · p. 4
  • Each AP projects its received pilot matrix onto a user’s pilot sequence to obtain a sufficient statistic for estimating that user’s channel.Transmit APs are assumed to know the second-order channel statistics.Source: C. Uplink Channel Estimation · p. 4
  • The channel estimate is formed using a linear MMSE estimator, with the estimate’s mean and covariance specified in the model.The pilot observation also defines the covariance and cross-covariance quantities used for estimation.Source: C. Uplink Channel Estimation · p. 4

III. DOWNLINK ISAC TRANSMISSION

The downlink model describes simultaneous user-data transmission and target illumination, then derives communication and multistatic sensing metrics. For sensing, it uses STAP processing and an average SCNR expression that incorporates clutter and noise.

III. DOWNLINK ISAC TRANSMISSION

  • Each transmit AP serves users and illuminates assigned targets during downlink ISAC, while receive APs collect echoes for their assigned targets.The AP clustering and target scheduling are determined centrally at the CPU.Source: §III · p. 5, B. Multi-Static Sensing Model · p. 5

A. Downlink Communication Model

  • The AP precoding matrix stacks the user-data and sensing-symbol precoders, and each transmit AP must satisfy an average power constraint.User SINR is conditioned on the collective channel estimate and accounts for channel-estimation error.Source: A. Downlink Communication Model · p. 5

B. Multi-Static Sensing Model

  • The multistatic sensing model stacks receive snapshots and uses a space-time steering vector to form a matched STAP filter and normalized spatial-Doppler spectrum.The average SCNR derivation assumes perfect knowledge of the target’s true angle and Doppler to establish a performance upper bound.Source: B. Multi-Static Sensing Model · p. 6
  • For white communication symbols, the space-time clutter-plus-noise covariance is block diagonal with zero slow-time Doppler correlation, and expected STAP SCNR separates into temporal and spatial processing gains.The average SCNR is the sensing metric used in the subsequent CORDIS analysis and optimization.Source: B. Multi-Static Sensing Model · p. 6

IV. CORDIS-SPLIT ALGORITHM

CORDIS-Split separates beamforming from power allocation: APs construct beamformers locally, while the CPU optimizes power variables centrally. Its ideal interference-free transformation relies on full-rank local channels and appropriately designed beamformers.

IV. CORDIS-SPLIT ALGORITHM

  • CORDIS-Split decouples beamforming design from power allocation by pairing AP-local beamformers with CPU-centralized power optimization.This reduces fronthaul overhead, but applicability is constrained by the rank and conditioning of each AP's local channel matrix.Source: §IV · p. 6
  • The aggregate noise-free downlink signals received by all users at symbol time τ are denoted yDL[τ].The section introduces this received-signal representation before describing the local design.Source: §IV · p. 7
  • For full-rank local channels and appropriately designed beamformers, the ideal transformation gives each user its intended stream without MUI or S2CI.The target transformation is F* = [I_Nue | 0].Source: §IV · p. 7

A. Distributed Robust Beamforming at APs

The APs construct communication and sensing beamformers locally, using channel-aware communication precoding and null-space sensing projections. Priority-weighted allocation distributes sensing power across targets, while residual S2CI from CSI errors is left for the CPU's power-allocation stage.

A. Distributed Robust Beamforming at APs

  • CORDIS-Split decomposes the global ideal transformation into local reference matrices for individual transmit APs.Communication beamformers are locally weighted according to channel quality, with weights normalized across APs.Source: A. Distributed Robust Beamforming at APs · p. 7
  • Local robust MMSE precoding incorporates channel-estimation error covariance to suppress transmission in spatial directions with high channel uncertainty.The method is named local robust MMSE (LR-MMSE).Source: A. Distributed Robust Beamforming at APs · p. 7
  • For sensing, each AP projects target steering vectors onto the null space of its estimated communication channel and uses null-space conjugate beamforming.The projection uses a regularization term chosen to ensure invertibility.Source: A. Distributed Robust Beamforming at APs · p. 7
  • Residual S2CI caused by CSI estimation errors is managed during CPU power allocation rather than suppressed heuristically by local beamforming.The local strategy avoids compromising sensing gain through such heuristic suppression.Source: A. Distributed Robust Beamforming at APs · p. 7
  • The priority-aware projection allocation assigns target power fractions proportional to target priority and the squared norm of each null-space projection.This spatial water-filling mechanism avoids forcing sensing power toward targets whose signatures strongly align with the estimated communication subspace.Source: A. Distributed Robust Beamforming at APs · p. 7

B. Centralized Power Allocation at the CPU

After local beamformer design, the CPU optimizes AP power-splitting ratios under communication QoS constraints. APs send compressed scalar quantities, and the CPU uses a clutter-aware linear sensing surrogate in a convex optimization problem.

B. Centralized Power Allocation at the CPU

  • The CPU optimizes the AP power-splitting ratios to maximize sensing performance subject to communication QoS constraints based on conditional SINR.The implementation sends the optimized ratios back to the APs.Source: B. Centralized Power Allocation at the… · pp. 7–8
  • Each AP forwards only three real-valued scalars per user to the CPU to preserve low fronthaul overhead.The forwarded quantities include channel-related terms and sensing information.Source: B. Centralized Power Allocation at the… · p. 7
  • Because exact SCNR maximization over the power ratios is highly non-convex, the CPU uses a linear surrogate that rewards priority-weighted target echo power and penalizes total transmit clutter illumination.The surrogate exploits the separable Kronecker structure of the clutter model.Source: B. Centralized Power Allocation at the… · p. 7
  • Non-negative slack variables accommodate restrictive QoS constraints, and the resulting convex problem is solvable with standard interior-point methods.The formulation lower-bounds a strictly concave function by an affine constraint.Source: B. Centralized Power Allocation at the… · p. 8

V. CORDIS-ADMM ALGORITHM

CORDIS-ADMM jointly optimizes beamforming and power through iterative consensus using local imperfect CSI and limited information exchange. Its global sensing objective is difficult to optimize directly, so the method uses a clutter-aware linear surrogate with local AP utilities.

V. CORDIS-ADMM ALGORITHM

  • CORDIS-ADMM jointly optimizes beamforming and power through iterative consensus ADMM using local imperfect CSI and limited information exchange.It is intended for settings such as rank-deficient local AP channels or stronger coordination needs.Source: §V · p. 8

A. Global Optimization Problem

  • The global objective is a highly non-convex sum of fractions because its SCNR denominator depends on clutter illumination coupled across APs.Decoupling that denominator with auxiliary variables would require a computationally prohibitive triple loop and can induce gradient blindness that removes the explicit clutter penalty.Source: A. Global Optimization Problem · p. 8
  • CORDIS-ADMM instead uses a clutter-aware linear sensing surrogate that combines priority-weighted target echo power with a regularized penalty on total transmit clutter illumination.The formulation defines local sensing utilities that can be optimized at each AP.Source: A. Global Optimization Problem · p. 8

B. SCA-SOCP Convex Relaxation

The section turns the non-convex sensing and QoS design into tractable SCA and SOC subproblems, then coordinates AP-local decisions through consensus ADMM. The CPU enforces per-user constraints with low-dimensional projections while APs solve local problems.

B. SCA-SOCP Convex Relaxation

  • Successive convex approximation addresses the non-convex sensing problem, while the fractional QoS constraint is transformed into a second-order cone constraint.The QoS transformation takes the square root of both sides and represents interference power with an ℓ2 norm.Source: B. SCA-SOCP Convex Relaxation · pp. 8–9

C. Local Problems and Consensus ADMM

B. SCA-SOCP Convex Relaxation

  • The first-order Taylor expansion minorizes the convex echo power, is tight at the current beamformer, and yields a concave surrogate that monotonically improves the true utility as it is refreshed.The expansion point is refreshed each round.Source: C. Local Problems and Consensus ADMM · p. 10

C. Local Problems and Consensus ADMM

  • The ALM/MM procedure combines a sensing surrogate with augmented-Lagrangian enforcement of coupled SOC QoS constraints, split into per-AP QCQPs and central consensus projections.The outer loop refreshes the sensing surrogate and consensus; its only inner loop is the per-user SOC projection.Source: C. Local Problems and Consensus ADMM · pp. 9–10
  • CORDIS-ADMM fixes the penalty and warm-starts from CORDIS-Split; its per-round fronthaul and AP computation are designed to remain independent of AP and array counts.The method normalizes contribution vectors and uses a common threshold for primal and dual residuals.Source: C. Local Problems and Consensus ADMM · p. 10

VI. SIMULATION RESULTS

The simulations evaluate CORDIS in a distributed cell-free ISAC setting, compare it with centralized and simpler precoding baselines, and assess communication and sensing quality.

Simulation setup

  • The simulated network places transmit APs on a 650 m-radius circle and users and targets within a 1 km-radius disc, using spatially correlated Rician channels and MMSE channel estimates.The channels use 3GPP urban-microcell street-canyon parameters.Source: §VI · p. 10

Baselines

  • CORDIS-Split and CORDIS-ADMM are benchmarked against a centralized upper bound, local robust-MMSE precoding, and global zero-forcing and maximum-ratio precoding.The centralized baseline uses aggregated network CSI without consensus splitting.Source: §VI · p. 10

Metrics

  • Evaluation reports worst-case per-user SINR, minimum per-target SCNR, outage probability, communication coverage, and priority-weighted sum SCNR.The stated metrics include both communication and sensing performance.Source: §VI · p. 10

A. Convergence of CORDIS-ADMM

CORDIS-ADMM converges faster with a fixed penalty than with residual balancing in the displayed realization. As the QoS slack falls, the realized worst-user SINR reaches its required floor.

A. Convergence of CORDIS-ADMM

  • About 150 iterations with fixed ρ versus about 250 with adaptive ρ are needed to reach the residual tolerance in the displayed realization.The adaptive update does not accelerate convergence in this setting, so subsequent experiments use fixed ρ.Source: A. Convergence of CORDIS-ADMM · p. 10, Figure 1 · p. 11
  • The maximum per-user SOC slack decreases by several orders of magnitude, and its decay certifies that the per-user SINR guarantee is met at convergence.The slack is the only mechanism by which the per-user SINR constraint can be violated.Source: Figure 1 · p. 11, A. Convergence of CORDIS-ADMM · p. 11
  • As slack shrinks, the realized worst-user SINR reaches the 5 dB floor, indicating that CORDIS-ADMM spends the communication power needed for QoS and reinvests the remainder into sensing.The figure plots SOC slack against realized worst-user SINR.Source: A. Convergence of CORDIS-ADMM · p. 11, Figure 1 · p. 11

B. Communication-Sensing Trade-off and Operating Point

CORDIS-ADMM approaches centralized sensing performance while remaining effective under imperfect CSI and locally rank-deficient channels. The experiments characterize its communication-sensing trade-offs, robustness, scalability, and coordination overhead.

B. Communication-Sensing Trade-off and Operating Point

  • CORDIS-ADMM sustains weighted-sum SCNR of ≈52 dB, within about 1 dB of the centralized ceiling and roughly 6 dB above CORDIS-Split; γ⋆=5 dB is selected as a balanced operating point.Across the SINR-target sweep, ADMM stays near the required user floor rather than over-serving users, while reallocating resources to sensing.Source: B. Communication-Sensing Trade-off and… · p. 11

C. Operating-Point Performance Distributions

  • At γ⋆=5 dB, CORDIS-ADMM's SCNR distribution is statistically indistinguishable from centralized performance and several dB above CORDIS-Split, while its realized outage is ≈25%.CORDIS-Split has ≈4% outage; communication-oriented baselines lose roughly 10 dB in SCNR.Source: C. Operating-Point Performance… · p. 11, Figure 3 · p. 11

D. Clutter Suppression

  • As κ increases, joint-scheme worst-case SCNR rises and then saturates, while worst-case SINR is insensitive; κ⋆=0.08 lies at the SCNR curve's knee.The gain requires at least partial angular separation between clutter support and target directions; coincident directions also attenuate target returns.Source: Figure 4 · p. 11, D. Clutter Suppression · p. 12

E. Robustness to Imperfect CSI

  • With poor channel estimates, CORDIS-ADMM's worst-case SCNR remains within about 1 dB of its best value, and robust-MMSE designs degrade more gracefully in communication as pilot power falls.The paper attributes communication robustness to incorporating estimation-error covariance into the precoder and SINR model.Source: E. Robustness to Imperfect CSI · p. 12, Figure 5 · p. 12

F. Scalability in the Locally Low-Rank Regime

  • When user load exceeds the per-AP antenna count, CORDIS-ADMM keeps outage ≈0.27 at the heaviest load and SCNR within about 1 dB of centralized, while fixed-beamformer schemes degrade.In this locally low-rank regime, CORDIS-Split outage climbs past 0.5 and Global MRT approaches 0.8.Source: F. Scalability in the Locally Low-Rank… · p. 12, Figure 6 · p. 12

G. Fronthaul and Computational Overhead

  • CORDIS-Split exchanges three compressed scalars per user, while CORDIS-ADMM exchanges 104 scalars per round over ≈92 rounds; both schemes' message sizes are independent of array size.CORDIS-ADMM's per-AP computation is independent of AP count; centralized payload instead grows from 320 real scalars at M=16 to 1280 at M=64 and with AP count.Source: G. Fronthaul and Computational Overhead · pp. 12–13, Figure 7 · p. 12, Table III · p. 13

VII. CONCLUSION

  • Within about 1 dB of the centralized sensing bound, CORDIS-ADMM preserves per-user QoS and target SCNR in the locally low-rank regime where CORDIS-Split saturates.The conclusion reports this outcome over a 3GPP UMi correlated-Rician channel with clutter and imperfect CSI.Source: §VII · p. 13
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