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Multi-Static Target Detection and Power Allocation for Integrated Sensing and Communication in Cell-Free Massive MIMO

Zinat Behdad, Özlem Tuğfe Demir, Ki Won Sung, Emil Björnson, Cicek Cavdar

arXiv:2305.12523v2cs.ITeess.SP

TL;DR

The paper addresses target detection in centralized cell-free massive-MIMO ISAC, where shared resources, clutter, and imperfect CSI complicate simultaneous communication and sensing. It develops centralized clutter-aware detection, sensing-aware power allocation, and a sensing-SE metric for two beam configurations. The proposed integrated algorithms improve detection over communication-centric and orthogonal-sharing approaches, with additional sensing beams supporting lower RCS variances.

  • Problem

    Cell-free ISAC must balance communication and multi-static sensing under shared resources, clutter, and imperfect CSI while detecting targets reliably.

  • Method

    The paper combines a centralized MAPRT detector, sensing-SE metric, and power allocation maximizing sensing SINR under UE SINR and per-AP power constraints, with optional additional sensing beams.

  • Results

    The proposed algorithms significantly improve detection over a fully communication-centric algorithm, while additional sensing beams support lower RCS variances and integrated ISAC exceeds orthogonal resource sharing.

  • Takeaways & Limitations

    Clutter-aware centralized processing and integrated resource use provide effective multi-static sensing in cell-free ISAC, with dedicated sensing resources beneficial when RCS variance is low.

Abstract

from arXiv · show

This paper studies an integrated sensing and communication (ISAC) system within a centralized cell-free massive MIMO (multiple-input multiple-output) network for target detection. ISAC transmit access points serve the user equipments in the downlink and optionally steer a beam toward the target in a multi-static sensing framework. A maximum a posteriori ratio test detector is developed for target detection in the presence of clutter, so-called target-free signals. Additionally, sensing spectral efficiency (SE) is introduced as a key metric, capturing the impact of resource utilization in ISAC. A power allocation algorithm is proposed to maximize the sensing signal-to-interference-plus-noise ratio while ensuring minimum communication requirements. Two ISAC configurations are studied: utilizing existing communication beams for sensing and using additional sensing beams. The proposed algorithm's efficiency is investigated in realistic and idealistic scenarios, corresponding to the presence and absence of the target-free channels, respectively. Despite performance degradation in the presence of target-free channels, the proposed algorithm outperforms the interference-unaware benchmark, leveraging clutter statistics. Comparisons with a fully communication-centric algorithm reveal superior performance in both cluttered and clutter-free environments. The incorporation of an extra sensing beam enhances detection performance for lower radar cross-section variances. Moreover, the results demonstrate the effectiveness of the integrated operation of sensing and communication compared to an orthogonal resource-sharing approach.

I. INTRODUCTION

The paper motivates centralized cell-free massive MIMO as infrastructure for multi-static ISAC, addressing the sensing–communication resource trade-off under clutter and imperfect CSI. It develops a clutter-aware detector, power allocation strategy, sensing-SE metric, and two beam configurations for integrated operation.

  • Motivation: Multi-static sensing offers diversity through multiple uncorrelated observations from distributed transmitters and receivers, while cell-free massive MIMO can provide a synchronized infrastructure.The paper assumes synchronization has already been addressed for communication in cell-free networks and favors centralized phase-coherent processing.
  • Problem: Shared time, frequency, power, and spatial resources create a sensing–communication trade-off that is especially challenging with joint transmission and reception in cell-free ISAC.The paper motivates new processing and resource-allocation schemes that satisfy both requirements.
  • Problem: The work detects a single target under clutter and imperfect CSI, treating unknown transmit–receive channel components as sensing interference while retaining target-reflected communication symbols.Precoding nulls interference toward user equipments rather than target-reflected communication symbols.
  • Approach: The proposed multi-static framework analyzes sensing with existing downlink communication beams alone or with additional dedicated sensing beams.The second configuration allocates resources specifically to sensing to improve sensing performance.
  • Approach: The power allocation strategy optimizes sensing performance while enforcing UE SINR and per-AP transmit-power constraints, and sensing SE accounts for sensing SINR and resource-block usage.The paper compares integrated ISAC operation with orthogonal resource sharing.
  • Approach: A MAPRT detector centrally fuses receive-AP observations across time slots while accounting for clutter, unknown RCS values, and potential directional correlation.The advanced detector is presented as more sophisticated than the earlier clutter-free detector.

C. Notations

The system uses centralized, synchronized cell-free massive MIMO with distributed transmit and receive APs for downlink communication and multi-static sensing. Communication and optional sensing signals share resources under centralized precoding and per-AP power limits.

  • Each AP either transmits ISAC signals or receives sensing signals, with M antennas arranged as a horizontal ULA.
  • Communication and optional sensing symbols are transmitted over shared waveform and time-frequency resources, with sensing beams directed toward known target locations.
  • The independent unit-power sensing signal could instead combine UE data signals, but analyzing that option is left for future work.
  • Centralized processing jointly selects UE and target precoders from CSI across all NtxM distributed transmit antennas.
  • A common power-control coefficient is assigned to each UE and the target, while every transmit AP must satisfy Pk ≤ Ptx.
  • The model includes communication, target-related sensing, and target-free interference channels, with correlated Rayleigh fading and imperfect CSI estimated using MMSE.

B. Sensing Channel Modeling

The sensing model represents target reflections and target-free propagation between distributed transmit and receive APs. LOS target paths, bistatic RCS uncertainty, clutter, and centralized RZF-based precoding determine the sensing signal and interference structure.

  • The target is modeled through LOS paths from transmit and receive APs, using half-wavelength-spaced ULA responses parameterized by azimuth and elevation angles.
  • Each receive AP observes reflected target signals alongside undesired signals independent of target presence, including clutter and LOS transmit-to-receive paths.
  • Target-free channels represent unknown NLOS paths caused by temporary obstacles and are modeled with correlated Rayleigh fading using a Kronecker structure.
  • RZF precoding uses estimated UE channels, while the sensing precoder projects the target channel onto the nullspace of the UE-channel subspace.

IV. DOWNLINK COMMUNICATION AND COMMUNICATION SPECTRAL EFFICIENCY FOR ISAC

The downlink model combines centrally precoded communication and sensing signals across coherence blocks, while the sensing receiver aggregates target, interference, and noise components from multiple receive APs.

  • Downlink communication model: The UE downlink signal contains desired transmission, multiuser and self-interference terms, sensing-signal interference, and receiver noise.
  • Downlink communication model: Communication spectral efficiency uses a coherence-block pre-log factor, with τp pilot symbols and the remaining symbols carrying downlink data.
  • Multi-static sensing model: The sensing model allows multiple sensing blocks per coherence block or longer blocks spanning coherence blocks, with τs ≤ τc in the considered case.
  • Multi-static sensing model: The received sensing signal combines known target-reflected components, unknown target-free interference channels, and receiver noise.
  • Multi-static sensing model: Each receive AP forwards its sensing signal to the edge cloud, where signals from all Nrx receivers are concatenated for centralized processing.
  • Multi-static sensing model: Unknown sensing channels and interference terms are concatenated across transmitters and receivers, with independent AP links producing block-diagonal correlation structure.

VI. SENSING PERFORMANCE METRICS

Sensing performance is characterized by detection and false-alarm probabilities, mutual information, and a sensing spectral-efficiency metric that accounts for sensing resource usage.

  • Detection probability Pd measures correct target detection, while false-alarm probability Pfa measures incorrect detection when no target is present.
  • Sensing mutual information measures information shared between the target response and reflected signals from an information-theoretic perspective.
  • Sensing spectral efficiency accounts for the symbols allocated to sensing within the communication interval, unlike an ASE expression that omits sensing resource usage.
  • The sensing SE uses a pre-log factor based on total sensing symbols per coherence block and log2(1 + SINRs), where SINRs is the sensing SINR.

VII. MAPRT DETECTOR FOR SENSING

The paper develops a MAPRT detector for multi-static target detection in cell-free ISAC with clutter and unknown channel gains. It centrally fuses receive-AP signals and tests target absence against presence using estimated target and target-free components.

  • The MAPRT detector extends prior single-transmitter, single-antenna formulations to the paper’s cell-free multi-static sensing system.The transmitted signals are known through the C-RAN architecture, while direction-dependent MIMO target paths create more complex received-signal relationships.
  • The resulting test statistic specifies how signals from multiple receive APs are centrally fused in the edge cloud for target detection.Detection uses τs received sensing symbols for a particular target location.
  • The detector compares H0, no target, with H1, target present, using received sensing symbols modeled as target-free channels plus noise, with the target contribution added under H1.The unknown channel-gain vectors represent target RCS and target-free channels.
  • The MAPRT forms a likelihood ratio by maximizing joint probability densities over unknown channel parameters separately under H1 and H0.The detection threshold λd is selected to achieve a desired false alarm probability.
  • The derivation assumes independent complex-Gaussian target-free channels and target RCS vectors with covariance matrices R and Rrcs, respectively.The correlated RCS covariance is retained in the detector model.

VIII. POWER ALLOCATION ALGORITHMS

The proposed ISAC power-allocation algorithms maximize sensing SINR while satisfying communication and per-AP power constraints. A concave-convex procedure iteratively solves convexified subproblems and outputs transmit power coefficients.

  • The proposed algorithms optimize sensing SINR while supporting downlink communication and optionally using dedicated additional sensing symbols.They are evaluated against communication-centric and orthogonal-sharing benchmarks.
  • The optimization enforces minimum UE SINR thresholds and maximum transmit power per AP alongside the sensing objective.The communication threshold is denoted γc and the per-AP power limit Ptx.
  • A first-order Taylor approximation lower-bounds the objective at each iteration, producing a linearized objective for the next convex subproblem.The procedure updates the power variables and auxiliary variable around the previous iterate.
  • The sensing objective is represented through real-valued quadratic forms using the real parts of Hermitian matrices Ar and Br.The resulting formulation defines the objective as f(ρ,t) = ρT Arρ.
  • The concave-convex procedure iterates until the change in t falls below ε and then outputs the transmit power coefficients ρ(c).Under mild conditions, the algorithm is guaranteed to converge to a stationary point.

B. Communication-Centric Algorithm

The communication-centric benchmark performs simultaneous sensing and downlink communication but allocates power solely to minimize communication transmit power. It ignores sensing requirements during optimization.

  • The communication-centric algorithm optimizes transmit power using only communication constraints while sensing occurs simultaneously with downlink transmission.Its formulation includes UE SINR requirements and per-AP transmit-power limits.

C. Orthogonal Sharing Algorithm

The orthogonal-sharing benchmark separates sensing and communication resources within each coherence block and optimizes their power coefficients independently. Its evaluation uses the paper’s cell-free simulation setup and compares sensing-communication spectral-efficiency regions.

  • C. Orthogonal Sharing Algorithm: Orthogonal sharing divides coherence-block symbols between sensing and communication, so the two functions use separately optimized power coefficients.Communication follows the communication-centric optimization, while sensing maximizes sensing SINR under per-AP power limits.
  • C. Orthogonal Sharing Algorithm: Communication symbols do not contribute to sensing performance in the orthogonal-sharing configuration.The sensing receiver therefore processes a separately allocated sensing signal.
  • IX. Numerical Results: The simulations use a 500 m × 500 m area, 16 transmit APs, 2 sensing receivers, and 8 UEs, with receivers selected as the closest APs to the sensing hotspot.The target is placed within a 15 m × 15 m central hotspot.
  • IX. Numerical Results: The channel model scales target-free channel gains by s, where larger s represents stronger clutter power.The setup uses the 3GPP Urban Microcell model for communication and target-free channels.
  • IX. Numerical Results: Orthogonal sharing exhibits a sensing-communication SE trade-off because dividing symbols changes the sensing and communication pre-log factors.The ISAC configurations are compared against this trade-off in the sensing-communication SE region.
  • IX. Numerical Results: The comparison includes communication-centric, ISAC without additional sensing symbols, ISAC with dedicated sensing symbols, and orthogonal sharing.Detection probability is averaged over random UE locations, channel realizations, and RCS realizations.

A. Sensing-Communication SE Region

The paper evaluates sensing-communication trade-offs and target-detection performance for ISAC power-allocation schemes under varying sensing resources, clutter, detector assumptions, and target reflectivity. Integrated ISAC operation generally outperforms orthogonal or communication-centric alternatives, while additional sensing beams and clutter-aware processing provide specific benefits.

  • Sensing-Communication SE Region: ISAC and ISAC+S operate beyond the sensing-communication SE region of orthogonal sharing, while ISAC+S provides higher sensing SE than ISAC.Orthogonal sharing divides coherence-block symbols between sensing and communication; ISAC uses all available downlink symbols but shares transmit power.
  • Impact of the Sensing Blocklength: Detection probability grows with sensing blocklength and stabilizes after τs = 80 symbols; ISAC and ISAC+S converge to OS performance for τs ≥80.OS performs better below 80 symbols because its power is dedicated to sensing, whereas ISAC schemes face communication constraints.
  • Impact of Target Reflectivity: For RCS variance ≥10 dBsm, ISAC and ISAC+S achieve detection probability close to 1 at false alarm probabilities 0.1 and 0.01.The communication-centric algorithm does not exceed Pd = 0.8 because it neglects sensing requirements.
  • Impact of Target-Free Channels and Target Detector: The advanced processing detector improves realistic-scenario detection by exploiting target-free-channel statistics, creating a substantial gap over simple processing.The scaling parameter s controls unknown target-free-channel interference; lower s reduces interference and improves detection.
  • Impact of Target-Free Channels and Target Detector: When clutter power is low and RCS variance is high, simple processing approaches advanced processing while remaining computationally friendlier.Simple processing forms a lower bound in realistic conditions and can reach high performance at high RCS variance.
  • Overall Detection Performance: Additional sensing beams further support detection at lower RCS variances, while the proposed algorithms outperform the fully communication-centric algorithm with or without them.The conclusion also reports gains in cluttered conditions and effectiveness relative to orthogonal resource sharing.

APPENDIX

The appendix derives likelihood expressions for the MAP ratio test and sensing SINR by conditioning on target-free channels and target hypotheses. It also reduces the relevant optimization terms to quadratic forms and expectation expressions.

  • MAPRT Derivation: Under H0, the received vector is modeled as yτ = hτ + nτ, and minimizing the quadratic objective estimates the target-free channel as ĥ = D^-1b.Substituting this estimate yields the denominator of the likelihood ratio.
  • MAPRT Derivation: Under H1, the received vector includes target, target-free-channel, and noise terms: yτ = gτ + hτ + nτ.The conditional density is formed using the independence of h and α from the hypothesis.
  • MAPRT Derivation: The H1 optimization estimates α and h by setting the derivatives of the objective with respect to α^H and h^H to zero.Inserting the resulting estimates into the objective produces the numerator of the likelihood ratio.
  • Sensing SINR: The sensing SINR is derived by expanding received-signal expectations, using known communication symbols, channel independence, and correlated Rayleigh channel modeling.The derivation treats communication symbols as deterministic at the edge cloud and expresses expectation terms through channel correlation matrices.

APPENDIX C: PROOF OF CONVEXITY OF f (ρ, t)

The appendix proves convexity of f(ρ,t) by deriving its gradient and Hessian, then showing the Hessian is positive semidefinite through a nonnegative quadratic form.

  • Convexity Proof: The proof begins by deriving the gradient vector of f(ρ,t) before analyzing its Hessian.The gradient is used as the first step toward establishing convexity.
  • Convexity Proof: Positive semidefiniteness of the Hessian is established by expressing the relevant term in quadratic form and using the positive semidefiniteness of A_r.The resulting expression is always nonnegative, proving that f(ρ,t) is convex.
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