Can Multi-Satellite Cooperation Always Improve Electromagnetic Stealth?

Electromagnetic stealth prevents signals from being detected, identified, and located, which is typically achieved by covert communication technologies, and has become a critical capability for satellite communications. Recently, multi-satellite cooperation has been extensively studied for covert communications, yet whether it can effectively enhance covert transmission performance remains to be verified. This paper investigates the precise conditions for achieving the optimal covert performance of multi-satellite cooperation with respect to the number of deployed satellites. We first introduce a new metric termed the covert radius, which integrates covertness and transmission reliability. Using hierarchical optimization, we derive its closed-form expression through a joint analysis of the time, frequency, spatial, and energy domains. Building on this framework, we theoretically determine the optimal number of cooperative satellites that minimizes the covert radius by employing an asymptotic expansion of implicit functions. The main results reveal that indiscriminately increasing the number of cooperative satellites does not continuously improve covert communication performance. Simulations validate the correctness of the theoretical closed-form solution and provide intuitive results for the covert radius and the optimal number of satellites under typical system parameters.