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Resource Allocation for Cloud Radar Networks with Communication Constraints

Christian Eckrich, Abdelhak M. Zoubir, Vahid Jamali

arXiv:2608.28173v1eess.SP

TL;DR

Capacity-constrained cloud radar networks must transmit enough distributed measurements to support accurate joint estimation without overwhelming fronthaul and backhaul links. The paper combines buffered access, local spectral windowing, and joint sensor-resource optimization, solved with Big-M and SCA, and reports improved performance over static or equal-resource allocation, especially under tight capacities.

  • Problem

    Capacity-limited communication can bottleneck the joint fusion of distributed radar measurements needed to resolve occlusions and improve target-parameter estimation.

  • Method

    The paper uses a buffered two-hop protocol with local spectral windowing and formulates joint sensor selection and time-frequency allocation as a mixed-integer optimization solved iteratively with Big-M and SCA.

  • Results

    The proposed framework significantly outperforms static or equal-resource baselines under tight capacity constraints by dynamically prioritizing informative sensors.

  • Takeaways & Limitations

    Informative sensor selection and resource allocation can preserve high-fidelity distributed radar sensing within stringent communication budgets.

Abstract

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Distributed radar sensing exploits spatial diversity to resolve occlusions and improve estimation accuracy. Realizing these gains, however, relies on the transmission of high-dimensional radar data to a Fusion Center (FC). This imposes significant demands on the wireless network, especially in dense, dynamic, and interference-prone environments like factories, where resilience and latency are critical. This paper studies the resource allocation problem in a capacity-constrained two-hop cloud radar network. We propose a buffered access protocol where sensors perform local spectral windowing to reduce data rates before transmitting measurements to the FC via intermediate Edge Servers (ESs). The resource allocation is formulated as a mixed-integer optimization problem aimed at minimizing the aggregate Cramer-Rao Lower Bound (CRLB) of the target parameters subject to fronthaul and backhaul capacity constraints. We develop an iterative solution algorithm based on Big-M formulation and Successive Convex Approximation (SCA). The proposed framework efficiently identifies the most informative sensor subsets and optimizes time-frequency resource assignments, ensuring high-fidelity sensing within stringent communication budgets.

I. INTRODUCTION

Distributed radar networks improve coverage, estimation accuracy, and resilience by combining complementary views, but capacity-limited communication requires prioritizing informative measurements. This paper addresses that challenge with a two-hop cloud architecture, buffered transmission, local spectral compression, and joint sensor-resource optimization.

  • Motivation: Distributed radars resolve ambiguities and occlusions through complementary viewpoints, improving coverage, estimation accuracy, and resilience to sensor failures or local blockages.These benefits require joint fusion of measurements at a processing unit rather than independent local estimation.
  • Motivation: Capacity-limited communication creates a bottleneck, so the network must prioritize transmissions from sensors providing the most informative target views.
  • Contributions: The proposed formulation jointly optimizes sensor selection and time-frequency allocation to minimize aggregate CRLB under fronthaul and backhaul capacity constraints.
  • Contributions: Sensors use local spectral windowing to compress measurements before transmitting them through intermediate Edge Servers to the Fusion Center.The architecture uses capacity-limited fronthaul links from sensors to Edge Servers and capacity-limited backhaul links from Edge Servers to the Fusion Center.
  • Contributions: An iterative Big-M and successive convex approximation algorithm addresses the non-convex mixed-integer problem and prioritizes informative sensors under tight capacities.Simulations are reported to show significant improvement over equal-resource baselines, particularly when capacity constraints are tight.
  • System Architecture: The two-hop network connects distributed radar sensors to the Fusion Center through intermediate Edge Servers, while communication resources are scheduled over time-frequency resource blocks.

B. Local Radar Processing

DFTs expose target peaks in a range-Doppler-angle spectrum, after which local windows around candidate detections are transmitted instead of the full data cube. The resulting measurement vectors reduce communication data while introducing truncation and quantization considerations.

  • DFTs along fast-time, slow-time, and spatial dimensions transform the data cube into a range-Doppler-angle spectrum where targets appear as peaks.
  • Local detection extracts a spectral window around each candidate peak for joint detection and processing at the Fusion Center.The window is centered at kp = (kr,p, kd,p, ka,p).
  • The window dimensions are controlled by ∆r, ∆d, and ∆a in the range, Doppler, and angle dimensions.
  • Truncation error arises from discarded Dirichlet-kernel sidelobes and decays inversely with the window size in each dimension.The range-tail contribution is bounded by N^2/(2∆r), with analogous Doppler and angle bounds.
  • Quantized coefficients within each window are assumed to use the radar front-end ADC resolution, making quantization noise dominated by the sensor noise floor.
  • Window coefficients are stacked into yp and transmitted with peak-index information, determining each sensor’s flow rate Ri.The transmission rate depends on whether sensor i sends measurements for target p through vi,p.

C. Communication Model

The protocol separates sensing, fronthaul, and backhaul into dedicated bands while buffering radar measurements locally. Previously acquired batches are relayed as new batches are collected, with fronthaul and backhaul scheduled over orthogonal resource blocks.

  • Sensing and communication use dedicated sensing, fronthaul, and backhaul bands after channel estimation.
  • Radar measurements are acquired in batches and buffered locally while previously acquired batches are relayed upward through the network.
  • Fronthaul and backhaul transmissions are scheduled over K orthogonal time-frequency resource blocks.

1) Fronthaul Phase:

During fronthaul, sensors send buffered measurements to associated Edge Servers over assigned resource blocks. Link capacities and assignments determine whether each sensor’s generated flow rate can be accommodated.

  • During the fronthaul phase, radar sensors transmit buffered measurements to their associated Edge Servers.
  • The estimated capacity of sensor–Edge Server link i,j on resource block k is denoted by C(k)i,j.
  • Binary variable a(k)i,j indicates whether resource block k is assigned to sensor i and Edge Server j.
  • Each resource block can have at most one sensor–Edge Server assignment.This is imposed by the constraint ∑i,j a(k)i,j ≤ 1 for every k.
  • The effective fronthaul capacity available to sensor i must be sufficient to accommodate its generated flow rate Ri.

2) Backhaul Phase:

The backhaul phase forwards aggregated sensor data from ESs to the FC under resource-allocation constraints, supporting joint target estimation. The resulting optimization selects informative sensors while accounting for computational and non-convexity challenges.

  • 2) Backhaul Phase:: ESs forward aggregated measurements to the FC using backhaul resource blocks assigned through binary allocation variables.Each backhaul resource block can be assigned to at most one ES.
  • 2) Backhaul Phase:: The constrained fronthaul-backhaul protocol improves resource utilization, preserves causality, and reduces end-to-end latency within one channel coherence interval.Small measurement batches are transmitted through the two-hop architecture during that interval.
  • 2) Backhaul Phase:: The FC maps local measurement vectors to a common reference frame before fusing them for scene estimation.Standard approaches include sparse reconstruction and maximum likelihood estimation.
  • 2) Backhaul Phase:: The objective minimizes the aggregate CRLB of target parameters using the Fisher information aggregated across sensors.The formulation models received measurements, sensing channels, aggregate noise, and spatially uncorrelated noise variances.
  • 2) Backhaul Phase:: Sensor selection favors measurements with high SNR and ensures every target is observed because an unobserved target has infinite CRLB.The objective therefore couples sensing informativeness with target coverage.
  • 2) Backhaul Phase:: The resulting optimization is a non-convex mixed-integer problem whose binary variables make computation challenging.The paper identifies the general problem as NP-hard and notes that the non-convex objective complicates globally optimal solution methods.

A. Problem Reformulation

The non-convex mixed-integer formulation is made tractable by linearizing the objective, relaxing integer constraints, and applying SCA to encourage binary solutions.

  • A. Problem Reformulation: Big-M formulation linearizes the objective function to obtain a tractable optimization formulation.The reformulation addresses the original non-convex mixed-integer structure.
  • A. Problem Reformulation: The integer constraints are relaxed before successive convex approximation is applied.This creates a continuous optimization stage for the relaxed variables.
  • A. Problem Reformulation: SCA promotes binary solutions while solving the reformulated problem iteratively.The method combines constraint relaxation with successive convex approximation.

1) Objective Linearization:

The objective linearization replaces the inverse Fisher-information contribution with an upper-bounding variable and uses Big-M constraints to remove the remaining binary-continuous product.

  • 1) Objective Linearization:: The inverse Fisher information for target p is upper bounded by t_p, whose minimization represents the original CRLB objective.The formulation uses the sensor contribution to the Fisher information for each target.
  • 1) Objective Linearization:: The product t_p v_i,p creates a bilinear non-convex constraint involving the CRLB bound and sensor-selection variable.Here v_i,p indicates whether sensor i contributes measurements for target p.
  • 1) Objective Linearization:: Big-M introduces t′_i,p = t_p v_i,p and replaces the bilinear term with an equivalent set of linear constraints.The constant t_p,max is chosen empirically to upper-bound the worst-case CRLB.

2) Binary Relaxation and Penalization:

The algorithm relaxes selected variables, retains binary backhaul decisions, penalizes fractional values, and applies iterative SCA updates until convergence.

  • 2) Binary Relaxation and Penalization:: Sensor-selection and fronthaul-allocation variables are relaxed to continuous values in [0, 1], while backhaul-allocation variables remain binary.The smaller number of backhaul variables makes direct integer optimization more manageable.
  • 2) Binary Relaxation and Penalization:: Keeping backhaul variables binary avoids an overly loose relaxation that could produce suboptimal solutions.The choice is motivated by both computational tractability and solution quality.
  • 2) Binary Relaxation and Penalization:: A regularization term penalizes fractional relaxed solutions and promotes binary decisions.Its quadratic terms are concave, making the resulting objective a difference of convex functions.
  • 2) Binary Relaxation and Penalization:: SCA replaces the concave penalty with a first-order Taylor expansion around the current solution and updates the linearization point iteratively.The resulting problem is solved repeatedly as the reference point changes.
  • 2) Binary Relaxation and Penalization:: Algorithm 1 initializes variables and penalties, solves a MILP each iteration, checks fractional violations, and updates penalties when violations exceed 0.1.The process terminates when convergence is reached or the maximum iteration count is met.

B. Proposed Algorithm & Complexity Analysis

The proposed algorithm addresses the non-convex mixed-integer allocation problem through nested Big-M and SCA iterations, with complexity driven mainly by binary variables, sensors, and SCA iterations. Allocation updates can be reused when network conditions remain stable.

  • Proposed Algorithm: The algorithm uses nested loops that linearize concave penalties, adaptively update penalty parameters, and round relaxed variables after convergence.Binary violations exceeding a threshold increase their corresponding penalties in subsequent iterations.
  • Complexity Analysis: The computational complexity is dominated by iterative MILP solutions, whose branch-and-bound cost is generally exponential in the number of binary variables.Each branch requires solving a linear program, which is polynomial-time solvable using interior point methods.
  • Complexity Analysis: The largest complexity impact comes from the number of sensors, while total cost also scales with the number of binary variables and SCA iterations.The stated sensor-dependent terms include I + J + 2K + 3IP + KIJ + KJ.
  • Implementation: Allocation updates need only occur when sensing geometry or network conditions change significantly, enabling reuse across buffered measurement batches.This reduces the need to repeatedly perform the computationally demanding allocation update under stable conditions.

IV. SIMULATION RESULTS AND DISCUSSION

Simulations compare dynamic resource allocation with equal allocation across sensors under varying capacity-to-load ratios. The proposed method remains effective under constrained capacity, while both methods converge to the aggregated-data accuracy limit at high capacity.

  • Simulation Setup: The simulation uses two Edge Servers, one Fusion Center, distributed sensors, four random targets, and 50 Monte Carlo trials with randomized placements and channel realizations.Sensors use M = 8 antenna elements, L = 256 chirps, N = 256 samples, and a 50 ms frame duration.
  • Simulation Setup: The proposed dynamic method is compared against a static baseline that allocates resources equally across all sensors.Performance is measured using the sum of normalized CRLBs for all targets versus capacity normalized by total sensor flow rate.
  • Results: Under tight capacity constraints, the baseline degrades and eventually breaks down, whereas the proposed method maintains reasonable performance by prioritizing informative sensors.The comparison evaluates resilience as the network capacity per sensor becomes insufficient to cover all targets.
  • Results: For ρ > 2, both methods converge to the maximum achievable estimation accuracy based on aggregated data across all sensors.The high-capacity limit is indicated by the black solid and dashed horizontal lines in Fig. 4.
  • Results: Adding sensors improves the proposed framework through Sensor Gain but can degrade the baseline through Dilution Loss from fixed resource allocation.The proposed method gains additional informative views, while equal allocation spreads limited resources more thinly.
  • Conclusion: The conclusion reports that dynamic prioritization significantly outperforms static allocation, especially under tight capacity constraints.The paper attributes this outcome to selecting the most informative sensors within the capacity-constrained network.
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