Heterogeneous Joint Radar Communications

• Heterogeneously-distributed JRC systems are multi-node networks that share spectrum between diverse radar and communications nodes for flexible, interference-managed operations.
• They integrate a variety of radar types and multi-tier communications infrastructures, enabling multi-target tracking and high-throughput data links for 6G and future networks.
• Advanced signal processing techniques, including dual-blind deconvolution and convex optimization, ensure near-perfect parameter recovery amid complex resource allocation trade-offs.

Heterogeneously-distributed joint radar communications (JRC) systems are multi-node, functionally and geographically diverse networks in which radar and wireless communications nodes share spectral resources without strict waveform, spatial, or synchronization constraints. These architectures provide key enablers for spectrum sharing in 6G and beyond, supporting multi-target tracking, high-throughput communications, and distributed sensing. The foundational aspect of these systems is their ability to flexibly coordinate resource allocation, manage interference, and jointly process signals arising from heterogeneous radar types and multi-tier communications infrastructures (Vargas et al., 2021, Wu et al., 2021, Leyva et al., 2021, Jacome et al., 2022, Wu et al., 2021).

1. System Architectures and Operational Models

Heterogeneously-distributed JRC systems are characterized by both structural and functional heterogeneity:

• Radar Diversity: Node types may include colocated MIMO radars (MMRs), phased array radars (PARs), mechanical-scan radars (MSRs), as well as passive/multistatic sensors exploiting illuminators of opportunity. Each operates with distinct power, dwell-time, and beam patterns, resulting in non-uniform coverage and measurement asynchrony (Wu et al., 2021, Wu et al., 2021).
• Communications Hierarchies: Typical architectures encompass macro cellular base stations, small-cell or micro-tier nodes, and a panoply of user endpoints. These systems employ OFDMA-based bandwidth partitioning and maintain connections under variable interference profiles.
• Shared Resource Space: The full communication–radar spectrum is partitioned into subchannels, with some reserved for fixed radar transmissions and the rest dynamically assigned to macro/micro users' communications (Wu et al., 2021).

System configuration is specified by a node- and subchannel-indexed set of allocations, interference coupling coefficients governing cross-system interactions, and constraints enforcing spectral, power, and latency budgets.

2. Signal, Channel, and Measurement Models

Received signals at any node are modeled as the superposition of:

• Radar Returns: Echoes from multiple targets, each parameterized by delay, Doppler, and—in multi-antenna receivers—angle-of-arrival. When transmit waveforms are unknown (e.g., in passive or opportunistic radar), processing is necessarily "dual-blind."
• Communications Signals: Multi-carrier OFDM or block-modulated signals subjected to multipath and Doppler, with potentially unknown channel characteristics due to rapidly-varying environmental conditions (Vargas et al., 2021, Jacome et al., 2022).
• Noise and Interference: Both thermal noise and structured interference, with cross-coupling terms α{j,i}^r, α{i,j}^c capturing radar-to-communications and communications-to-radar impacts, respectively.

Target motion is typically modeled via linear dynamical systems (e.g., coordinated constant velocity, with process noise), and radar measurements are functionally linked to position, velocity, and bearing (Wu et al., 2021, Wu et al., 2021).

3. Joint Processing and Blind Recovery Methodologies

The dual-blind deconvolution (DBD) framework underpins parameter estimation in the most challenging JRC scenarios:

• Problem Structure: The receiver must jointly recover unknown radar target parameters, communications channel/paths, and both unknown waveforms from mixed, overlapped observations (Vargas et al., 2021, Jacome et al., 2022).
• Atomic Norm Minimization (ANM): Both radar and communications contributions are modeled via mixtures of continuous-parameter atoms (steering vectors in delay, Doppler, and, for arrays, angle domains). Recovery proceeds via convex optimization of atomic norms (Vargas et al., 2021).
• Convex Formulation: The estimation reduces to a semidefinite program (SDP) enforcing data fidelity and atomic norm penalization, with theoretical guarantees of exact recovery under minimum-separation and sparsity conditions.
• Distributed and Multi-dimensional Extension: In networked settings, each node contributes local measurements; fusion is performed across nodes either centrally or via distributed consensus mechanisms, with measurement models calibrated for asynchrony and local clock skews (Jacome et al., 2022).

This methodology achieves perfect or near-perfect continuous-valued recovery of target and channel parameters—subject to trivial scaling ambiguities—given sufficient measurement redundancy and SNR.

4. Resource Allocation and Optimization Techniques

Efficient spectrum and power coordination is vital to achieve high-fidelity radar tracking alongside requisite communications throughput:

• Optimization Objective: Core goals are minimization of Bayesian Cramér–Rao bound (CRB) on target state estimation and satisfaction of user throughput requirements, subject to joint power, dwell-time, bandwidth, and discrete subcarrier assignment constraints (Wu et al., 2021, Wu et al., 2021).
• Mixed-integer, Nonconvex Programs: The resource assignment problem incorporates binary subchannel variables, continuous power/dwell splits, and coupled interference structures.
• Alternating Optimization Algorithms: Notable algorithms such as ADAM and ANCHOR employ alternating updates—separately optimizing over discrete assignments and continuous resource profiles—with inner minimax loops leveraging closed-form eigenstructure updates for Fisher information maximization (Wu et al., 2021, Wu et al., 2021).
• Simulated Annealing for Frequency Assignment: Binary OFDMA sub-bands are optimized using neighbor-move exploration, with objective- or constraint-driven acceptance/rejection at each iteration.

These frameworks converge monotonically to stationary points, and practical evaluations demonstrate substantial reductions in tracking mean-square error (MSE) over uniform or random allocation schemes, often providing an order-of-magnitude improvement in RMSE for multi-target tracking (Wu et al., 2021).

5. Performance Metrics and Trade-offs

A variety of performance metrics quantify the operational efficacy of heterogeneously distributed JRC systems:

Metric	Radar Domain	Comms Domain
Bayesian CRB (tracking error)	Position/velocity RMSE	—
Fisher Information Matrix (FIM)	Measurement/information rate	—
Detection probability (P_D)	Neyman–Pearson	—
SINR, Throughput	—	User capacity/bitrate
Interference coupling (α^{r}, α^{c})	Radar-comms, comms-radar links	Radar-comms, comms-radar links

• Trade-offs: Raising radar dwell or power improves tracking, but increases interference and can degrade user link SINR. Resource allocation shifts (e.g., sub-band reassignments or dwell-time reductions elsewhere) balance node- and user-specific constraints.
• Joint Estimation–Information Bound: Multiuser-detection radar (MUDR) theory quantifies fundamental trade-offs via a sum-rate pentagonal bound in (estimation rate, communication rate) space, showing cooperative decoding and SIC strategies outperform classical orthogonalization (Bliss, 2014).

6. Synchronization, Coordination, and Scalability

Network heterogeneity and asynchrony necessitate advanced mechanisms for distributed operation:

• Synchronization: Clock and phase alignment is enforced (at best) via GNSS-referenced hardware or IEEE 1588v2 precision time protocol; performance loss due to residual jitter and drift is theoretically modeled via SNR degradation exponents in the CRLB analysis (Leyva et al., 2021).
• Cooperative Processing: Channel state exchange, distributed control, and resource message passing over the backhaul enable both centralized and partially distributed processing, with trade-offs in backhaul bandwidth, latency, and estimation optimality.
• Computational Scaling: Large-scale convex programs are solved via block Toeplitz structure exploitation, first-order methods (e.g., ADMM, Frank–Wolfe), and, in some contexts, approximate greedy or machine learning-enhanced heuristics (Vargas et al., 2021, Jacome et al., 2022).

Scalability remains a key challenge for real-time and ultra-dense deployments.

7. Practical Outcomes and Future Directions

Empirical studies and simulation-based evaluations establish the practical value of heterogeneous JRC systems:

• Tracking Gains: Coordinated allocation (e.g., via ANCHOR) delivers calibrated RMSE reductions (e.g., ≈ 13 m vs. ≈ 87 m for uniform split) and achieves rapid convergence in multi-target MTT (Wu et al., 2021).
• Communications Guarantees: Resource allocation frameworks maintain communications throughput (with positive QoS margin) while optimizing radar performance (Wu et al., 2021, Wu et al., 2021).
• Extension Readiness: Current frameworks extend to more tiers, moving sensors, and adaptive fusion scheduling, and admit further constraints for operational deployment in emerging 6G/7G architectures.

Limitations persist in computational cost, model mismatch resilience (e.g., nonideal pulses or partial prior knowledge), and integration with low-dynamic-range hardware (Vargas et al., 2021, Jacome et al., 2022). Continued research is targeting greedy/deep-learning-enabled solutions and distributed convex-analytic approaches suited for large, flexible next-generation JRC networks.