Joint jammer selection and power optimization in covert communications against a warden with uncertain locations

In covert communications, joint jammer selection and power optimization are important to improve performance. However, existing schemes usually assume a warden with a known location and perfect Channel State Information (CSI), which is difficult to achieve in practice. To be more practical, it is important to investigate covert communications against a warden with uncertain locations and imperfect CSI, which makes it difficult for legitimate transceivers to estimate the detection probability of the warden. First, the uncertainty caused by the unknown warden location must be removed, and the Optimal Detection Position (OPTDP) of the warden is derived which can provide the best detection performance (i.e., the worst case for a covert communication). Then, to further avoid the impractical assumption of perfect CSI, the covert throughput is maximized using only the channel distribution information. Given this OPTDP based worst case for covert communications, the jammer selection, the jamming power, the transmission power, and the transmission rate are jointly optimized to maximize the covert throughput (OPTDP-JP). To solve this coupling problem, a Heuristic algorithm based on Maximum Distance Ratio (H-MAXDR) is proposed to provide a sub-optimal solution. First, according to the analysis of the covert throughput, the node with the maximum distance ratio (i.e., the ratio of the distances from the jammer to the receiver and that to the warden) is selected as the friendly jammer (MAXDR). Then, the optimal transmission and jamming power can be derived, followed by the optimal transmission rate obtained via the bisection method. In numerical and simulation results, it is shown that although the location of the warden is unknown, by assuming the OPTDP of the warden, the proposed OPTDP-JP can always satisfy the covertness constraint. In addition, with an uncertain warden and imperfect CSI, the covert throughput provided by OPTDP-JP is 80% higher than the existing schemes when the covertness constraint is 0.9, showing the effectiveness of OPTDP-JP.