Formation-Dependent Cardinality Concealment of Target Swarms in Multifunction Radar

Recognizing a swarm of unmanned surface vehicles does not guarantee that its physical cardinality can be recovered. This study examines how formation, viewing aspect ψ, defined as the orientation of the formation relative to the radar line of sight (RLOS), and sensing resources affect these two tasks in a multifunction radar. A two-stage simulation framework evaluates group recognition against a single extended target (Stage 1) and cardinality recovery (Stage 2) using regularized linear discriminant analysis, with the aggregate nominal radar cross-section held constant. Certification is assessed using one-sided 95% confidence bounds. At N = 9 and baseline resources, group observability is certified in 12 of 35 formation-aspect conditions. For abreast formations at ψ=60∘ and 90∘, the group selection probability is 0.993, whereas the exact recovery probabilities are 0.108 and 0.067. This cardinality concealment, in which group observability is certified but exact recovery is not, persists over N=6,…,12 for both geometries. Coarse size information nevertheless remains, as 52-56% of estimates over N=3,…,12 lie within one target of the true value, against 28% for uniform guessing. Increasing bandwidth up to tenfold or coherent dwell up to fourfold yields no certified exact recovery. These results are specific to the evaluated simulation model and signal-processing framework and do not establish a general limitation of radar systems.