Swarm Antenna Arrays: From Deterministic to Stochastic Modeling

Swarm antenna arrays, composed of spatially distributed antennas mounted on unmanned agents, offer unprecedented flexibility and adaptability for wireless sensing and communication. However, their reconfigurable architecture, susceptibility to collisions, and inherently stochastic nature present significant challenges to realizing collaborative gain. It remains unclear how spatial coordination, positional perturbations, and large-scale topological configurations affect coherent signal aggregation and overall system performance. This paper investigates the feasibility of achieving coherent beamforming in such systems from both deterministic and stochastic perspectives. First, we develop a rigorous theoretical framework that characterizes the necessary and sufficient conditions for the emergence of grating lobes in multiple linear configurations. Notably, we show that for dual linear arrays, the classical half-wavelength spacing constraint can be safely relaxed without introducing spatial aliasing. This result challenges traditional array design principles and enables more flexible, collision-aware topologies. Second, we present a theoretical analysis, supported by empirical validation, demonstrating that coherent gain can be approximately preserved under realistic positional perturbations. Our results reveal that spatial perturbations introduce measurable degradation in the main lobe, an effect that cannot be mitigated merely by increasing the number of antennas. Instead, the primary benefit of scaling lies in reducing the variance of perturbation-induced fluctuations.