Joint Optimization of Topology and Frequency Increments with Distributed Frequency Diverse Array for Target Localization

This paper develops a novel optimization framework for target localization in a distributed Frequency Diverse Array (FDA) system. A general signal model is firstly established, where widely dispersed nodes each employ a colocated FDA Multiple-Input Multiple-Output radar exploiting intra-node frequency diversity. Closed-form Cramér-Rao Bound (CRB) expression for distributed FDA is derived, revealing that the overall CRB decouples into a sum of per-node contributions, where the node-specific CRB formulation separates into a geometric factor dependent solely on node coordinates and a ratio of quadratic forms capturing the frequency increment dependence. Based on this structure, a joint optimization problem is formulated to minimize the node-specific CRBs subject to circular position constraints and bounded frequency allocations. To tackle this nonconvex problem, a nested Minorization-Maximization (MM)-Maximum Block Improvement (MBI) algorithm is developed. The outer loop greedily selects the node yielding the greatest overall CRB reduction, while the inner loop optimizes the chosen node’s variables via block-wise updates. In particular, a Coordinate Descent -Projection method leverages the simple algebraic form of the geometric factor for topology optimization, and the MM framework constructs a tight minorant for frequency increments. The MBI strategy updates only the block providing the maximum decrease in the objective. Convergence analysis establishes that every cluster point of the iterates satisfies the Karush-Kuhn-Tucker conditions. Numerical results demonstrate significant CRB reduction and validate the effectiveness of the joint optimization through comparisons with Alternating Optimization and simpler MBI-based counterparts.