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Joint Antenna Positioning and Pilot Power Allocation for Uplink Fluid Antenna-Aided Cell-Free Massive MIMO Systems

Manobendu Sarker, Soumaya Cherkaoui

arXiv:2610.37428v1eess.SYcs.SY

TL;DR

URLLC traffic under finite-blocklength transmission and bursty arrivals requires translating queueing-level QoS requirements into physical-layer targets. The paper maps NMSE to effective SINR and uses alternating optimization for joint antenna positioning and pilot-power allocation, with positioning achieving NMSE reduction comparable to global search at an order-of-magnitude lower cost.

  • Problem

    URLLC delay and reliability requirements need an explicit mapping from physical-layer estimation parameters to queueing-level guarantees, while channel-estimation errors persist as antenna counts grow.

    Source: §I · pp. 1–2

  • Method

    An eigenstructure-based quadratic mapping converts FBL- and MMPP-derived SINR requirements into NMSE thresholds for joint antenna-position and pilot-power optimization.

    Source: §I · p. 2

  • Results

    The position optimizer achieves NMSE reduction comparable to global search at an order-of-magnitude lower cost, while auto-calibrated regularization provides a tunable estimation-quality–energy tradeoff.

    Source: §VI · p. 16

  • Takeaways & Limitations

    The NMSE thresholds decouple physical-layer optimization from queueing-level service specifications in the joint design.

    Source: §I · p. 2

Abstract

from arXiv · show

This paper investigates joint fluid antenna (FA) position optimization and pilot power allocation for uplink cell-free massive MIMO networks supporting ultra-reliable low-latency communication (URLLC) traffic under pilot contamination. By continuously adjusting FA elements within a prescribed aperture, we adapt the spatial correlation structure to the varying propagation environment. We formulate a joint problem to minimize the average normalized mean-squared error (NMSE) subject to QoS constraints governed by finite blocklength and Markov-modulated Poisson process queueing analyses. To ensure tractability, we establish an analytical quadratic relationship between the NMSE and the effective signal-to-interference-plus-noise ratio through eigenstructure alignment factors. This mapping translates complex latency requirements into explicit NMSE thresholds, maintaining a median absolute approximation error below 0.03 dB and less than 10% relative error for over 90% of practical-regime samples. Given the nonconvex nature of the formulation, we propose an alternating optimization framework. Antenna positions are iteratively updated via successive convex approximation using analytical gradients and closed-form Euclidean projections. Pilot powers are allocated through a block coordinate descent scheme that employs safeguarded Newton steps to guarantee monotonic convergence. Furthermore, we introduce an auto-calibrated regularization variant to navigate the Pareto frontier between estimation accuracy and energy consumption. Numerical results show the proposed positioning yields up to 22% NMSE improvement over fixed uniform arrays while operating 7-8x faster than particle swarm optimization. The power allocation achieves within 0.5% of the global optimum at over two orders of magnitude lower computational cost, providing up to 39% pilot energy reduction with negligible estimation penalty.

I. Introduction

The introduction identifies a gap in jointly optimizing fluid-antenna positions and pilot powers for URLLC in cell-free massive MIMO under pilot contamination. It proposes an NMSE–SINR mapping to connect QoS requirements to this joint design, while the network model uses reconfigurable antenna elements and position-dependent spatial correlation.

I. Introduction

  • Prior FA/MA-aided cell-free massive MIMO work mainly targets rate or spectral-efficiency objectives, while pilot-allocation schemes assume fixed array geometries.The introduction describes the resulting gap as the missing joint treatment of AP-side antenna configuration, pilot-power allocation, and estimation-aware URLLC guarantees.Source: §I · pp. 1–2
  • The framework jointly addresses AP-side fluid-antenna optimization, pilot contamination, pilot-power allocation, finite-blocklength transmission, and queueing-level QoS; the authors identify this combination as unaddressed in prior work.Its NMSE–SINR mapping converts FBL- and MMPP-derived SINR requirements into per-UE NMSE thresholds for joint position and pilot-power optimization.Source: §I · p. 2

A. Network Architecture and Fluid Antenna Model

  • Each AP’s N fluid-antenna elements can move within an aperture, subject to a minimum spacing of dmin = λ/2.The position-dependent spatial correlation is shaped by array geometry and propagation conditions, affecting estimation accuracy and interference rejection.Source: §I · p. 1, A. Network Architecture and Fluid… · p. 3

B. Spatially Correlated Channel Model

  • The channel model uses position-dependent spatial correlation; its correlation expression separates deterministic phase shift from decorrelation due to angular dispersion.The paper notes that the correlated-Rayleigh model focuses on NLoS propagation; a complete Rician extension is left for future work.Source: B. Spatially Correlated Channel Model · p. 3

C. UL Pilot Transmission and Channel Estimation

Pilot reuse couples channel estimation across UEs, while the paper’s uplink model carries the resulting estimation and interference effects into SINR and finite-blocklength rate. The achievable rate accounts for short-packet reliability rather than using Shannon capacity as the URLLC benchmark.

C. UL Pilot Transmission and Channel Estimation

  • When K > τp, UEs reuse pilot sequences, and the pilot-sharing set identifies the UEs whose transmissions contaminate a given UE’s pilot observation.The LMMSE observation covariance depends on co-pilot UEs’ correlation matrices, coupling their estimation quality.Source: C. UL Pilot Transmission and Channel… · pp. 3–4

E. UL SINR and FBL Rate

  • The effective uplink SINR accounts for desired signal power, channel-estimation uncertainty, non-coherent interference, coherent interference from pilot-sharing UEs, and effective noise.The CPU uses channel estimates as maximum-ratio-combining vectors in centralized detection.Source: E. UL SINR and FBL Rate · p. 4
  • For URLLC short packets, the paper adopts a finite-blocklength achievable-rate approximation because Shannon capacity is an optimistic benchmark.The approximation accounts for the rate penalty associated with limited coding blocklength.Source: E. UL SINR and FBL Rate · p. 4

F. URLLC Traffic Model and QoS Requirements

The traffic model represents each UE’s bursty packet arrivals with a two-state MMPP and its service as an MMPP/M/1 queue. Delay-violation requirements are converted to minimum service-rate, rate, and ultimately SINR requirements.

F. URLLC Traffic Model and QoS Requirements

  • Bursty arrivals are modeled by a two-state MMPP, with OFF-to-ON and ON-to-OFF transitions and an ON-state arrival rate.The average arrival rate is λavg,k = νkλON,k/(ξk + νk).Source: F. URLLC Traffic Model and QoS… · p. 4
  • Each UE is modeled as an MMPP/M/1 queue with exponential service time and service rate µk = Rk/Lk; stability requires λavg,k < µk.The queueing delay distribution is used to express the URLLC delay-violation requirement.Source: F. URLLC Traffic Model and QoS… · pp. 4–5
  • The delay-violation constraint yields a numerically obtained minimum service rate, which determines a minimum rate and then an SINR target through the finite-blocklength rate expression.The service-rate constraint does not admit a closed-form inversion.Source: F. URLLC Traffic Model and QoS… · p. 5

III. Problem Formulation

This passage introduces the channel-estimation quality parameter before formulating the joint optimization of antenna positions and pilot-power allocation.

III. Problem Formulation

  • The channel-estimation quality parameter is defined as a precursor to the joint optimization problem for fluid-antenna positions and pilot-power allocation.Source: §III · p. 5

A. Channel Estimation Quality Metric

The paper uses NMSE to quantify channel-estimation quality at individual AP links and across a UE’s serving cluster. Antenna positions affect this metric through the estimate covariance and spatial correlation matrix.

A. Channel Estimation Quality Metric

  • The per-link NMSE is defined for the UE–AP link, with its expression obtained by substituting the error covariance.The resulting quantity depends on the link’s position-dependent covariance terms.Source: A. Channel Estimation Quality Metric · p. 5
  • Antenna positions enter per-link NMSE through the estimate covariance Φk,m and spatial correlation matrix Rk,m, making spatial reshaping relevant to estimation quality and resulting SINR.Adjusting element locations reshapes spatial correlation and can enhance channel-estimation accuracy.Source: A. Channel Estimation Quality Metric · p. 5
  • For a UE served by multiple APs, effective NMSE is a weighted average of link NMSE across its serving cluster.The weights βk,m tr(Rk,m) emphasize estimation quality on stronger links.Source: A. Channel Estimation Quality Metric · p. 5

B. SINR-NMSE Relationship via Eigenstructure Approximation

The paper approximates the SINR–NMSE relationship using factors that capture covariance eigenstructure alignment, yielding a reduced quadratic-fractional surrogate. The approximation relies on per-AP NMSE uniformity for the reduced mapping and is reported to be accurate in practical regimes.

B. SINR-NMSE Relationship via Eigenstructure Approximation

  • Eigenstructure-alignment factors make the trace-product-dependent SINR tractable as a reduced quadratic-fractional function of NMSE.The trace products depend on covariance eigenstructure alignment, which otherwise precludes a closed-form NMSE dependence.Source: B. SINR-NMSE Relationship via… · pp. 5–6
  • The delay-violation probability is a queueing-level reliability metric, distinct from the decoding error probability in the finite-blocklength rate expression.Source: B. SINR-NMSE Relationship via… · p. 5
  • The self-alignment factor captures eigenvalue concentration, while the cross-alignment factor measures spatial overlap between UE covariance structures.Both are computable from statistical CSI and vary with antenna positions through inter-element spacings.Source: B. SINR-NMSE Relationship via… · p. 5
  • The approximation error vanishes as effective pilot SNR ρk,m grows or condition number κk,m approaches 1, and is reported accurate near 10 dB and κk,m ≤ 10.The stated practical regime includes moderate angular spread; under pilot contamination, the passage indicates that ρk,m is replaced, but does not specify the replacement here.Source: B. SINR-NMSE Relationship via… · p. 5
  • Per-AP NMSE uniformity is assumed only for the reduced SINR mapping; the channel model, LMMSE covariance, and per-AP NMSE evaluation remain link-specific.The sensitivity analysis reports median absolute SINR deviations of 0.017 dB for the assumption.Source: B. SINR-NMSE Relationship via… · p. 5
  • In the reduced surrogate, Ck is evaluated at current antenna positions and pilot powers for local SINR prediction and threshold inversion.The coefficients are recomputed when thresholds are updated.Source: B. SINR-NMSE Relationship via… · p. 6

C. NMSE Threshold for QoS Guarantee

Under Assumption 1, the paper converts a per-UE SINR requirement into an equivalent NMSE threshold. This threshold lets the design express URLLC QoS as an estimation-quality constraint.

C. NMSE Threshold for QoS Guarantee

D. Joint Optimization Problem

The paper formulates joint fluid-antenna positioning and pilot-power allocation to minimize average effective NMSE while guaranteeing URLLC QoS for every UE. The design uses statistical CSI and imposes physical position and pilot-power constraints.

D. Joint Optimization Problem

  • The joint problem minimizes average NMSE while guaranteeing URLLC QoS for all UEs using large-scale fading and spatial-correlation statistics that vary more slowly than small-scale fading.Source: D. Joint Optimization Problem · p. 6
  • Position constraints enforce minimum element spacing and implicit ordering, while pilot powers are bounded by hardware and interference considerations.Source: D. Joint Optimization Problem · p. 6
  • The formulation is challenging because position-dependent correlation is transcendental and the NMSE constraint couples achieved NMSE with a variable-dependent threshold.These features motivate the alternating-optimization framework developed next.Source: D. Joint Optimization Problem · p. 6

IV. Proposed Solution

The proposed alternating-optimization approach cycles between antenna-position optimization and pilot-power allocation; because each subproblem reduces the shared objective, the objective is non-increasing across iterations and converges to a stationary point.

IV. Proposed Solution

  • Alternating optimization cycles between antenna-position optimization and pilot-power allocation, with each subproblem reducing the shared objective and making it non-increasing across iterations.The passage states that this guarantees convergence to a stationary point.Source: §IV · p. 6

A. Antenna Position Optimization

This section presents an SCA framework for antenna-position optimization under nonlinear NMSE and QoS constraints, using frozen thresholds, penalty-based constraint handling, and projection onto a convex feasible set. It also describes extensions to discretized hardware and coupling-aware covariance models under stated conditions, with operation assuming slowly evolving spatial covariance.

A. Antenna Position Optimization

  • The SCA update linearizes a frozen-threshold objective, adds proximal regularization, and projects onto the convex feasible polytope of antenna positions.The QoS threshold and reduced SINR coefficients are recomputed at the current position iterate; a candidate is accepted only if the true penalized objective decreases.Source: A. Antenna Position Optimization · p. 7
  • Projection onto Xm exploits isotonic-regression structure for O(N) complexity; with minimum-gap ordered positions, projection reduces to pool-adjacent-violators followed by boundary clipping, versus O(N3) for general quadratic programming.Source: A. Antenna Position Optimization · p. 7
  • For fixed penalty parameter µ, accepted antenna-position iterates produce a monotonically non-increasing penalized objective; asymptotically regular sequences have stationary accumulation points.Stationarity is for the limiting frozen-threshold objective with thresholds evaluated at the accumulation point.Source: A. Antenna Position Optimization · p. 8

Switched-port or pixelated FA architectures

  • For switched-port or pixelated arrays, mapping the continuous SCA solution to the nearest feasible port controls implementation loss through port spacing.The mapping must preserve element ordering and minimum spacing; for grid-restricted candidates, accept only those reducing the true penalized objective, since continuous-stationarity does not establish discrete optimality.Source: 4) Discrete and switched-port… · p. 10

Mutual coupling

  • A coupling-aware covariance can replace the standard model while preserving the SCA and BCD structures when it is differentiable and meets the descent argument’s smoothness and boundedness conditions.The minimum spacing dmin = λ/2 mitigates strong coupling, and gradients must include derivatives of the position-dependent coupling matrix.Source: 5) Mutual coupling · p. 10

Mobility and covariance stability

  • The design targets slow covariance evolution; under moderate mobility, periodic statistical-CSI refresh and warm-started re-execution handle drift, while very fast mobility requires predictive tracking or mobility-aware reconfiguration.The broader operating regime treats antenna reconfiguration and pilot power allocation as slow-timescale steps; very fast mobility is left for future work.Source: 6) Mobility and covariance stability · pp. 10–11

Simulation Setup

  • The evaluation models a 200 × 200 m² CF mMIMO network with 16 APs, 8 single-antenna UEs, and four FA elements per AP.Each AP’s aperture is 4λ with minimum spacing λ/2; the setup uses 3.5 GHz carrier frequency, 20 MHz bandwidth, MMPP URLLC traffic, and 100 independent network realizations.Source: A. Simulation Setup · p. 11

B. Validation of Analytical Framework

The analytical approximations are validated across practical and URLLC operating regimes, including scenarios with pilot contamination. The positioning evaluation reports NMSE gains over fixed arrays and a runtime advantage over PSO, with performance depending on array size, aperture, and network load.

2) NMSE Variation Bound and Sensitivity

  • The per-AP NMSE variation bound holds in all 2400 controlled realizations, and its mean falls below 0.05 at average-link pilot SNRs of 15 and 20 dB for 3 and 10 dB spreads, respectively.The bound is less tight at larger spreads when the weakest serving-link pilot SNR remains low; Fig. 3(a) compares empirical variation with the bound.Source: 2) NMSE Variation Bound and Sensitivity · p. 11, Figure 3 · p. 12
  • Among 15095 practical-regime samples, uniform-NMSE substitution yields median and 90th-percentile absolute SINR deviations of 0.017 and 0.286 dB, respectively.For ∆k < 0.3, covering approximately 69% of samples, the 90th-percentile deviation remains below 0.283 dB; larger deviations cluster where per-AP NMSE is strongly nonuniform.Source: 2) NMSE Variation Bound and Sensitivity · p. 11, Figure 3 · p. 12

3) SINR-NMSE Relationship

  • The quadratic SINR-NMSE approximation has median absolute error of 0.02–0.03 dB across operating regimes, with over 96% of samples within 10% error when NMSE < 0.1.The validation compares exact and approximate SINR across 800 UE configurations; Fig. 4 depicts the comparison and relative-error distributions.Source: 3) SINR-NMSE Relationship · pp. 11–12, Figure 4 · p. 12

4) Validation at URLLC Operating Points

  • At URLLC operating points, the approximation’s median relative error is 0.51% for feasible samples versus 3.52% for infeasible samples.The validation uses 400 UE samples; Fig. 5 compares exact and approximate SINR and relative-error distributions for feasible and infeasible samples.Source: 4) Validation at URLLC Operating Points · p. 12

C. Performance of Proposed Antenna Positioning Scheme

  • The proposed SCA scheme improves NMSE by up to 22% over FUA as array size increases, closely matching PSO’s up to 21.4% reduction.All schemes’ QoS feasibility rises from approximately 73% to 92.5% as N grows; Fig. 6 reports NMSE reduction and feasibility versus N.Source: 1) Impact of Array Size · p. 13, Figure 6 · p. 13

2) Impact of Aperture Size

  • For aperture Wm = 4λ, SCA and PSO reduce NMSE relative to FUA by 12.7% and 14.5%, respectively; gains fall to 2.4% and 3.6% at Wm = 8λ.Fig. 7 plots NMSE reduction and feasibility versus aperture; the reported non-monotonicity reflects a larger feasible region without additional elements and spacing beyond decorrelation distance.Source: 2) Impact of Aperture Size · p. 13, Figure 7 · p. 13

3) Impact of Network Load

  • As UE load rises, PSO’s NMSE reduction reaches 17.8% and SCA’s comparable gain reaches 13.2%, while feasibility falls from approximately 96% at K = 8 to 31–38% at K = 32.With fixed τp, increasing co-pilot interference masks positioning gains; the results indicate greatest benefit under moderate loads and a need for complementary pilot or bandwidth provisioning at high loads.Source: 3) Impact of Network Load · p. 13, Figure 8 · p. 13

Runtime comparison

  • The proposed SCA scheme runs 7–8× faster than PSO across evaluated network loads while delivering near-optimal NMSE reduction.Fig. 9 compares runtime versus K; the reported complexity is O(ImaxKMN^3) for SCA versus O(PsG · KMN^3) for PSO.Source: 3) Impact of Network Load · pp. 13–14, Figure 9 · p. 14

D. Performance of Proposed Pilot Power Allocation Scheme

The pilot-power evaluation finds that the joint sequential design improves estimation quality across average and upper-tail UEs while reducing pilot energy. Regularization tunes the estimation–energy tradeoff, and repeated outer alternation adds little benefit relative to its cost.

Outer AO Behavior

  • The first additional outer alternation lowers aggregate mean NMSE by only 0.63%, while median cumulative runtime rises to about 3× and QoS feasibility falls by 1.25 percentage points.Across Cycles 2–5, aggregate mean NMSE stays within [0.024915, 0.024952], so the sequential SCA–BCD design is retained.Source: 1) Outer AO Behavior · p. 14

Large-Scale Tail and QoS Performance

  • 24.24%, 31.9%, and 18.5% lower average, 95th-percentile, and maximum NMSE, respectively, than FUA + Full; SCA–BCD also beats position-only and power-only designs.The joint design maintains QoS feasibility while reducing aggregate pilot power in the more bandwidth-limited, pilot-reuse-intensive large-scale setting.Source: Table IV · p. 14, 2) Large-Scale Tail and QoS Performance · p. 14

Estimation Quality–Power Tradeoff

  • 33.5% pilot power reduction with less than 0.1% NMSE degradation is available at η ≤0.05; at η = 0.1, reduction reaches 38.8% with a 0.3% NMSE penalty.At η = 0, Proposed (ω = 0) achieves 30.6% NMSE reduction relative to Full, matching Exhaustive within 0.3 percentage points.Source: Figure 10 · p. 15, 3) Estimation Quality–Power Tradeoff · p. 15

Impact of UE Density

  • At K = 8, Proposed (ω = 0) achieves 30.7% NMSE gain, matching FP at 30.7% and approaching Exhaustive at 31.0%; at K = 20, Proposed (ω > 0) reduces pilot power by 59.5%.The power-aware variant's reduction exceeds FP by 5.0 to 14.7 percentage points across loads, with the gap widening as load increases.Source: 4) Impact of UE Density · p. 15, Figure 11 · p. 16

Computational Cost

  • Up to 3× faster than FP at K/τp ≤2, BCD with ω = 0 contrasts with Exhaustive search, which is over 100× slower than BCD and FP across evaluated loads.BCD and FP remain within sub-second execution scales at higher loads.Source: Figure 12 · p. 16, 4) Impact of UE Density · p. 16

VI. Conclusion

The paper presents alternating optimization for joint fluid-antenna positioning and pilot-power allocation, using an eigenstructure-based NMSE–SINR mapping to connect service requirements with physical-layer targets. Its results show estimation and energy-efficiency gains within the studied cell-free massive MIMO setting, and it identifies extensions for future work.

Conclusion

  • An eigenstructure-based NMSE–SINR mapping translates queueing-level service requirements into estimation targets, enabling antenna-position optimization via SCA and pilot-power allocation via BCD.The joint design addresses FBL rate constraints and MMPP-driven bursty arrivals in cell-free massive MIMO networks.Source: §VI · p. 16
  • The positioning stage achieves NMSE reduction comparable to global search at an order-of-magnitude lower cost, while the power allocator offers a tunable estimation-quality–energy tradeoff.Both stages execute at sub-second-scale runtimes for periodic reconfiguration on the slow-fading timescale.Source: §VI · p. 16
  • Future extensions include joint pilot-sequence assignment, multi-antenna UEs with fluid antennas, and adaptive reconfiguration under mobility.Source: §VI · p. 16

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