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Joint Communication Sensing Beamforming and Uplink Power Control for Network-Assisted Full-Duplex Cell-Free ISAC Systems

Reza Roshanghias, Seyed Mohammad Karbasi, Reza Saadat

arXiv:2609.06996v1eess.SP

TL;DR

The paper addresses joint beamforming and UL power control for NAFD cell-free ISAC, where target-dependent interference and communication constraints are coupled. It combines target detection with a joint SDR–AO optimization and complementary priority-based beamforming designs. In the considered deployment, MAPRT detection reaches approximately Pd = 0.97 at τs = 10 with false-alarm probability close to 0.05.

  • Problem

    NAFD cell-free ISAC couples target-dependent inter-AP interference with communication and sensing resource allocation, while assuming target-dependent channels are known before target existence is established can be optimistic.

    Source: §I · p. 2

  • Method

    The paper incorporates MAPRT target detection into a four-stage protocol and jointly optimizes DL communication and sensing covariance matrices with UL powers using SDR and alternating optimization.

    Source: §I · p. 2, A. Main Contributions · pp. 2–3

  • Results

    Approximately Pd = 0.97 at τs = 10 with false-alarm probability close to 0.05; reliable target detection and communication QoS were simultaneously maintained in the considered deployment.

    Source: §XIII · p. 19

  • Takeaways & Limitations

    The two priority-based designs provide benchmark operating points for studying the sensing–communication tradeoff in the considered NAFD cell-free deployment.

    Source: §XIII · pp. 18–19

Abstract

from arXiv · show

In this paper, we investigate the problem of designing joint downlink (DL) communication beamformer and uplink (UL) power as well as sensing beamformer in a multi static integrated sensing and communication (ISAC) enabled cell free massive multiple input multiple output (CF mMIMO) system. To this goal, we first consider two priority based beamforming strategies. In the communication prioritized sensing design, we first design the communication beamformers and then the sensing beamformer is projected onto the nullspace of the effective communication channels to suppress its additional interference to both the DL UEs and UL receivers. In the sensing prioritized communication design, we select the sensing beamformer first according to the target direction, while the communication beamformers are subsequently optimized using a max min SINR formulation. In addition to these priority based designs, we formulate a sensing centric joint optimization problem to determine the optimal DL communication beamformers, sensing beamformer, and UL UE transmit powers. Our objective is to maximize the sensing SINR while guaranteeing individual DL and UL SINR requirements and satisfying the per AP and per UE transmitpower constraints. Since the resulting problem is non convex because of the coupled beamforming and UL power variables, the beamforming vectors are lifted into positive semidefinite transmit covariance matrices and semidefinite relaxation (SDR) is applied.

I. INTRODUCTION

The paper studies joint communication, sensing, and interference management in an NAFD cell-free ISAC network, where target detection and resource allocation are coupled. It presents a four-stage protocol, joint SDR–AO optimization, and two priority-based beamforming strategies.

I. INTRODUCTION

  • The network couples DL and UL communication, distributed target sensing, and cross-link interference, while target-dependent channels make detecting target presence before resource allocation important.The framework incorporates imperfect channel estimation, residual DL-to-UL interference, UL-to-DL interference, and target-induced sensing links.Source: §I · p. 2, A. Main Contributions · p. 2

A. Main Contributions

  • A four-stage protocol combines channel estimation, MAPRT-based target detection, target-assisted inter-AP channel estimation, and simultaneous communication–sensing transmission.The APs are partitioned into DL and UL groups that jointly serve users and sense the target.Source: A. Main Contributions · p. 2, §I · p. 2, §II · p. 3
  • The joint design maximizes sensing SINR while meeting individual DL and UL SINR requirements and per-AP and per-UE power limits.The coupled beamforming and UL power problem is handled by lifting beamformers to positive-semidefinite covariance matrices and alternating between SDR beamforming and UL power updates.Source: A. Main Contributions · pp. 2–3
  • Communication-prioritized sensing projects the sensing beam into the nullspace of effective DL and DL-to-UL channels, while sensing-prioritized communication fixes a target-directed sensing beam and optimizes communication by max–min SINR.The two strategies represent opposite communication–sensing priority choices.Source: A. Main Contributions · p. 3
  • MAPRT-based target detection evaluates detection, false-alarm, and misdetection probabilities, and the numerical study compares the joint design with both priority-based strategies.The framework links target detection to subsequent target-aware interference management and resource allocation.Source: A. Main Contributions · p. 3

A. Stage Arrangement of the Proposed Interference Management Mechanism

The interference-management protocol divides each coherence interval into four stages, using target detection to inform inter-AP channel estimation and whether sensing accompanies communication. The channel model includes target-free and target-reflected inter-AP components.

A. Stage Arrangement of the Proposed Interference Management Mechanism

1) Uplink Pilot Training Stage:

  • During UL pilot training, UEs transmit pilots and the CPU estimates UE–AP CSI for later UL reception and DL transmission.The channels are modeled as quasi-static within each coherence interval and frequency-flat over the considered bandwidth.Source: 1) Uplink Pilot Training Stage · p. 4, B. Channel Model · p. 4

2) Target Detection Stage:

  • For target detection, DL APs transmit sensing signals and UL APs cooperatively process them to estimate target presence before target-dependent inter-AP channel estimation.The target indicator determines whether the inter-AP channel includes a target-reflected component.Source: 2) Target Detection Stage · p. 4

3) Downlink Pilot Training Stage:

  • During DL pilot training, UL APs jointly receive DL AP pilots, and the CPU uses the target-presence estimate to estimate effective inter-AP CSI.This allows the estimate to account for target-reflected propagation when a target is detected.Source: 3) Downlink Pilot Training Stage · p. 4

4) Data Transmission and Target Sensing Stage:

  • In the final stage, the CPU coordinates UL and DL communication and, when a target is detected, concurrent sensing and interference suppression.Without a detected target, the system operates in communication-only mode.Source: 4) Data Transmission and Target… · p. 4

B. Channel Model

  • The channel model represents UE–AP channels with spatial covariance matrices that account for average channel power and large-scale propagation effects.The target-free inter-AP channel also incorporates average propagation gain and spatial characteristics.Source: B. Channel Model · p. 5

1) Target-Reflected Channel:

  • Target-reflected propagation is modeled as a bistatic link from a DL AP through the target to a UL AP, with AP-to-target links assumed LoS.The target is assumed to move slowly enough that its RCS remains approximately constant over sensing symbols in consecutive coherence intervals.Source: 1) Target-Reflected Channel · p. 5

III. CHANNEL ESTIMATION IN THE UPLINK PILOT TRAINING STAGE

The paper describes uplink pilot-based MMSE channel estimation and a target-detection stage that uses dedicated sensing transmissions. The DL sensing precoder is directed toward the predicted target location.

III. CHANNEL ESTIMATION IN THE UPLINK PILOT TRAINING STAGE

  • UE pilot sequences are used to form received pilot signals, which are correlated with the assigned sequence to obtain MMSE channel estimates.The estimation error is statistically independent of the estimate and has an associated error covariance matrix.Source: §III · pp. 5–6

IV. TARGET DETECTION STAGE

  • During target detection, DL APs transmit independent sensing waveforms and UL APs process the received signals; conjugate beamforming toward the predicted target location concentrates power toward the target.The sensing precoder is selected for target-presence detection, with the predicted direction and each AP's maximum transmit power informing its design.Source: §IV · p. 6

A. Vectorized Cooperative Sensing Model

The section vectorizes the cooperative sensing observations and models target-free and target-reflected channels under channel uncertainty. It then uses a MAPRT to decide whether the target is present from signals collected over the sensing symbols.

A. Vectorized Cooperative Sensing Model

  • Vectorization of the inter-AP channel matrices gives a compact aggregate representation of the sensing signals collected across UL APs.The UL AP signals are forwarded to the CPU and stacked across symbols.Source: A. Vectorized Cooperative Sensing Model · pp. 6–7
  • The aggregate model distinguishes target-free and target-reflected channels, with uncertainty in target location and reflection characteristics represented in the target-reflected channel covariance.The model also specifies a mean target-reflected channel tied to the physical channel model and estimated bistatic RCS.Source: A. Vectorized Cooperative Sensing Model · pp. 6–7

B. MAPRT-Based Target Detection

  • The CPU stacks sensing observations over τ_s symbols and formulates target detection as a binary choice between target absence and presence.The stacked receiver-noise vector is included in the detection formulation.Source: B. MAPRT-Based Target Detection · p. 7
  • Assuming statistical independence of target-free and target-reflected channel components, the MAPRT compares a likelihood ratio with a threshold selected for a desired false-alarm probability or other detection criterion.The decision rule yields the estimated target-presence indicator.Source: B. MAPRT-Based Target Detection · p. 7

V. CHANNEL ESTIMATION IN THE DOWNLINK PILOT TRAINING STAGE

The downlink pilot stage lets UL APs estimate effective inter-AP channels using pilots sent by the DL AP antennas. The channel estimates use MMSE filtering based on channel and pilot-observation statistics.

V. CHANNEL ESTIMATION IN THE DOWNLINK PILOT TRAINING STAGE

  • All DL AP antennas send mutually orthogonal downlink pilots, which UL APs jointly receive to estimate inter-AP channels.The channel model includes the target-reflected component in the effective inter-AP channel.Source: §V · pp. 7–8

A. Received Downlink Pilot Signal

  • Each UL AP correlates its received pilot matrix with the pilot assigned to a DL AP antenna, producing a sufficient statistic for estimating that inter-AP channel.Pilot orthogonality supports the corresponding observation.Source: A. Received Downlink Pilot Signal · p. 8

B. MMSE Estimation of the Inter-AP Channel

  • The MMSE estimate uses the second-order statistics of the effective inter-AP channel and pilot observation, with its conditional mean determined by the target-reflected component.The filtering matrix is defined from those statistics.Source: B. MMSE Estimation of the Inter-AP… · p. 8

C. Target-Detection-Assisted Channel Estimate

The practical inter-AP channel estimate uses the MAPRT target-presence estimate because the true target indicator is unknown to the CPU. In downlink transmission, communication and sensing share time-frequency resources, and sensing is activated only when a target is declared present.

C. Target-Detection-Assisted Channel Estimate

  • Because the true target indicator is unknown to the CPU, the practical inter-AP channel estimate uses the target indicator estimated by the MAPRT detector.The estimate is modeled using the covariance of the effective inter-AP channel and the covariance of its estimate.Source: C. Target-Detection-Assisted Channel… · p. 8

A. Downlink Spectral-Efficiency Analysis

  • DL APs transmit communication and sensing simultaneously over the same time-frequency resources using multi-antenna precoding, with sensing activated only when the target is declared present.The communication signals serve DL UEs while the sensing waveforms illuminate the target.Source: A. Downlink Spectral-Efficiency Analysis · p. 8
  • The DL SINR formulation accounts for multi-user DL interference, channel-estimation-error interference, sensing-induced interference, and UL-to-DL cross-link interference.The received signal is decomposed into its components before the instantaneous DL SINR is written.Source: A. Downlink Spectral-Efficiency Analysis · p. 9

B. Uplink Spectral-Efficiency Analysis

The uplink analysis models simultaneous UL reception and DL communication-sensing transmission, including residual cross-link interference after cancellation. It then combines signals across UL APs and accounts for communication, sensing, estimation-error, and noise terms in the UL SINR.

B. Uplink Spectral-Efficiency Analysis

  • After reconstructing DL-to-UL interference from DL transmit signals and estimated inter-AP channels, the CPU subtracts it, leaving a residual signal that reflects channel-estimation error.The actual effective inter-AP channel is decomposed into its estimate and residual error.Source: B. Uplink Spectral-Efficiency Analysis · p. 9
  • The CPU detects each UL UE's data by combining signals received at all UL APs, using MRC receive combiners.The resulting decision statistic is formed before the detected signal is decomposed.Source: B. Uplink Spectral-Efficiency Analysis · p. 9
  • The UL SINR includes multi-user UL interference, UL channel-estimation-error interference, residual DL-to-UL cross-link interference, sensing-waveform interference, and receiver noise.The detected signal is decomposed into desired and interference components before the instantaneous SINR is expressed.Source: B. Uplink Spectral-Efficiency Analysis · p. 10
  • The sensing interference-management mechanism uses CSI and decoded communication symbols to partially reconstruct and suppress UL and DL communication interference.UL interference reconstruction uses estimated UL channels and detected symbols; the symbol-error term decreases as UL SINR increases.Source: B. Uplink Spectral-Efficiency Analysis · p. 10

C. Sensing SINR Analysis

The sensing SINR is evaluated at each uplink AP after receive filtering, with the filter chosen to maximize the output SINR. The section then introduces priority-based beamforming strategies to examine the sensing–communication tradeoff.

C. Sensing SINR Analysis

  • The sensing observation at each UL AP is processed through a receive filter to form a scalar radar observation.The analysis separates the desired target-reflected signal from interference and noise.Source: C. Sensing SINR Analysis · pp. 10–11
  • For fixed transmit precoders, the receive filter is chosen to maximize the sensing SINR, yielding an optimal filter from a generalized Rayleigh quotient.The resulting maximum sensing SINR is the performance metric at each UL AP.Source: C. Sensing SINR Analysis · p. 11

VII. PRIORITY-BASED AND JOINT BEAMFORMING STRATEGIES

  • Two priority-based strategies accompany the joint design: one protects communication first, while the other fixes sensing first and then optimizes communication.The baseline schemes allocate each DL AP’s power between communication and sensing using ρ, the communication-power fraction.Source: §VII · p. 11
  • The sensing-prioritized strategy selects the sensing direction using the dominant sensing direction of the general sensing matrix.The section defines the dominant sensing direction before describing the priority-based strategies.Source: §VII · p. 11

A. Communication-Prioritized Sensing Beamforming

The communication-prioritized design forms communication beams first and projects the sensing beam into the nullspace of effective communication channels. The sensing-prioritized alternative fixes a sensing beam first and then optimizes communication under SINR constraints.

A. Communication-Prioritized Sensing Beamforming

  • CPS designs communication beams first, then constructs a sensing beam that adds no interference to DL UEs or UL communication receivers.It uses the remaining spatial degrees of freedom for target illumination.Source: A. Communication-Prioritized Sensing… · p. 11
  • The CPS sensing beam uses the nullspace projector of the effective communication channels, suppressing direct DL sensing interference and residual DL-to-UL sensing interference after combining.The beam is scaled to satisfy each DL AP’s sensing-power budget.Source: A. Communication-Prioritized Sensing… · p. 11

B. Sensing-Prioritized Communication Beamforming

  • SPC selects its sensing beam first without considering communication channels, then optimizes communication beamformers while holding that sensing beam fixed.The sensing direction is scaled to satisfy the per-AP sensing-power constraints.Source: B. Sensing-Prioritized Communication… · p. 11
  • With the sensing beam and UL powers fixed, SPC maximizes the minimum DL SINR, using bisection over a common SINR target and convex feasibility problems.The DL and UL QoS constraints are converted to SOC constraints for each trial target.Source: B. Sensing-Prioritized Communication… · p. 12
  • For centralized optimization, the sensing SINR accounts for residual DL leakage from inter-AP CSI errors and residual UL-to-sensing interference from decoding and channel-estimation errors.These terms are represented in the effective target and interference quantities.Source: B. Sensing-Prioritized Communication… · p. 12

VIII. VECTOR-FORM JOINT OPTIMIZATION

The joint design maximizes sensing performance while optimizing DL communication beams, the sensing beam, and UL powers. Alternating updates treat receive combiners as fixed during each transmit-variable update and refresh them using estimated CSI.

VIII. VECTOR-FORM JOINT OPTIMIZATION

  • The joint design optimizes DL communication beams, the sensing beam, and UL powers to maximize sensing performance while holding receive combiners fixed during each transmit-variable update.The receive combiners are refreshed using estimated CSI.Source: §VIII · p. 12
  • The vector-form formulation includes a switch that turns sensing off for communication-only operation or enables the joint communication-and-sensing design.The switch is denoted bδT in the formulation.Source: §VIII · p. 12

IX. MATRIX SDR REFORMULATION

  • The matrix reformulation uses AP antenna-selection matrices and applies semidefinite relaxation by dropping the rank-one constraints.The selection matrix Di extracts the antennas of DL AP i.Source: §IX · p. 13

A. Beamforming Update

  • For fixed UL powers, a trial sensing SINR converts the beamforming update into an SDP feasibility problem with sensing, DL QoS, UL QoS, per-AP power, and PSD constraints.Bisection on the trial sensing SINR yields the beamforming update.Source: A. Beamforming Update · p. 13

B. UL Power Update

  • For fixed covariance matrices, maximizing sensing SINR is equivalent to minimizing residual UL-to-sensing interference.The resulting UL power update is a linear program.Source: B. UL Power Update · p. 13

XI. REMARKS ON THE PROPOSED FORMULATION

The formulation extends the interference-management framework with SDR-based joint optimization and explicit channel-error covariance terms. Simulations report large sensing gains over priority-based schemes while maintaining communication QoS.

XI. REMARKS ON THE PROPOSED FORMULATION

  • The framework extends four-stage interference management with SDR optimization of DL beams, the sensing beam, and UL powers; explicit channel-error covariance terms make QoS constraints conservative under imperfect CSI.The sensing function can be switched on or off according to the detector output.Source: §XI · p. 13

XII. NUMERICAL RESULTS

  • The target-aware SDR-AO procedure estimates channels and error covariances, updates communication and sensing combiners, then alternates an SDP beamforming update with an UL power update.Rank-one beamformers are recovered by principal-eigenvector extraction, with Gaussian randomization if required.Source: §XII · p. 14

A. Simulation Setup

  • The simulated network uses 10 distributed APs, four DL UEs, four UL UEs, and a target; detector thresholds use 300 target-absent realizations and detection probabilities use 300 Monte Carlo trials.The APs and UEs occupy a 200 m square service region, with 10 m minimum AP–UE separation.Source: A. Simulation Setup · p. 14

1) Impact of the Communication–Sensing Power Allocation

  • In the priority-based schemes, increasing ρ improves or preserves communication performance while reducing sensing SINR; CPS falls from approximately 21 dB to 2–3 dB, and SPC from approximately 17 dB to below 0 dB.This comparison shows the explicit communication–sensing power-allocation tradeoff for those schemes.Source: 1) Impact of the Communication–Sensing… · pp. 14–15, Figure 4 · p. 15
  • The Fig. 4 comparison assigns fraction ρ of AP power to communication in CPS and SPC, while SDR-AO jointly optimizes power allocation and achieves approximately 44 dB sensing SINR across the ρ range.The SDR-AO curve is independent of ρ in this comparison because it has no predefined communication–sensing split.Source: 1) Impact of the Communication–Sensing… · pp. 14–15, Figure 4 · p. 15

2) Performance with Individual Communication QoS Constraints

  • Under CPS-matched individual DL QoS, SDR-AO communication SINR closely follows CPS over most tested distances, though at 40 m CPS reaches approximately 16 dB versus approximately 13 dB for SDR-AO.The optimization targets sensing subject to communication QoS, not communication SINR beyond those requirements.Source: 2) Performance with Individual… · p. 15, Figure 5 · p. 16
  • With individual CPS-matched DL QoS requirements, SDR-AO achieves 50–54 dB sensing SINR across target distances, versus 8–13 dB for CPS and 5–9 dB for SPC.The target–UE distance varies from 5 m to 50 m.Source: 2) Performance with Individual… · pp. 15–16, Figure 5 · p. 16

C. Convergence of the Proposed SDR–AO Algorithm

The proposed SDR–AO procedure produces a non-monotonic sensing-SINR trajectory, while the illustrated network realization satisfies its communication requirements and yields high target-detection probability. The optimized solution also shows distinct UL power use across users and an aggregate sensing pattern shaped by the distributed APs.

C. Convergence of the Proposed SDR–AO Algorithm

  • The sensing SINR rises from approximately 36.1 dB to 43.2 dB after iteration two, peaks near 51.5 dB around iteration nine, and ends at approximately 48.9 dB after 12 iterations.The objective sequence is not strictly monotonic because subsequent beamforming, UL power-allocation, and DL-SINR refinement updates may not preserve the preceding block's value.Source: C. Convergence of the Proposed SDR–AO… · p. 16

D. Communication SINR Performance

  • All four DL UEs achieve approximately 2.1 dB, while UL UEs 1–4 achieve approximately 18.9, 2.8, 18.8, and 25.0 dB, respectively.All users satisfy the original 0 dB minimum SINR requirement; the max–min DL refinement yields nearly identical DL SINRs, unlike the UL allocation.Source: D. Communication SINR Performance · p. 16

E. UL Power-Allocation Evolution

  • All optimized UL powers remain below the 0.1 W maximum; UL UE 1 falls from approximately 3.5×10−3 W to 4 × 10−4 W, while UL UE 3 uses very little power.The considered realization satisfies UL communication constraints without requiring UEs to operate close to their maximum available transmit powers.Source: E. UL Power-Allocation Evolution · pp. 16–17

F. Per-AP Transmit-Power Utilization

  • All five DL APs operate at approximately their 3 W per-AP power constraint.The active constraints are consistent with sensing-SINR maximization, which can use additional feasible DL power for target illumination while meeting communication and interference constraints.Source: F. Per-AP Transmit-Power Utilization · p. 17

G. MAPRT Target-Detection Performance

  • At τs = 8, Pd reaches approximately 0.98; for τs ≥ 8, Pd stays within 0.95–0.98 and Pmd within 0.02–0.05, while empirical Pfa spans 0.04–0.08.The largest detection improvement occurs from τs = 5 to 8, with relatively limited gains beyond that for this simulation setting.Source: G. MAPRT Target-Detection Performance · p. 17

H. Separation of the MAPRT Test Statistic

  • Under H0, the MAPRT statistic centers near −6; under H1, it concentrates around 4–8, with a calibrated threshold near −1.3 and only small overlap around the boundary.The observed distributional separation is consistent with high detection probability and relatively small misdetection.Source: H. Separation of the MAPRT Test… · p. 18

I. Optimized Sensing Beampattern

  • The aggregate sensing beampattern has attenuation regions near −26° and 19°, with normalized gains of approximately −9.5 and −10 dB, respectively.It approaches 0 dB toward the outer angular regions and is approximately −3 dB around broadside; this is an aggregate distributed-AP representation, not a single-ULA pattern.Source: §I · p. 18, Figure 12 · p. 18

XIII. CONCLUSION

  • The MAPRT detector achieved approximately Pd = 0.97 at τs = 10 with false-alarm probability close to 0.05, while communication QoS was maintained.The conclusion reports reliable target detection and communication QoS in the considered NAFD cell-free deployment.Source: §XIII · p. 19
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