Multi-Antenna Covert Communications with a BPP Field of Wardens

This paper considers a multi-antenna jamming to facilitate covert communications with multiple wardens. Specifically, the jammer generates artificial noise (AN) with random power to deliberately create interference to prevent a communication being detected by an adversarial warden (Willie), where Warden's location is modeled as a uniform binomial point process (BPP). The detection performance for each warden is analyzed under line-of-sight (LoS) channels i.e., the expressions for the false alarm (P-FA) and miss detection (P-MD) probabilities are analytically derived. Then, the communication performance of the covert communication in terms of the channel capacity is optimized following a stochastic spatial geometry framework. Numerical results show that the average detection error probability (i.e., P-FA + P-MD) decreases with the number of Willies and also decreases as the the jammer gradually parallel to the receiver's position relative to the transmitter, which leads to the reduction in the covert throughput.