Clustering is an effective method for improving the performance of large scale mobile ad hoc networks. However, when the moving speed is very fast, the topology changes quickly, which leads to frequent cluster topology updates. The drastically increasing control overheads severely threaten the throughput of the network. SCBCS (Signal Characteristic Based Cluster Scheme) is proposed as a method to potentially reduce the control overheads caused by cluster formation and maintenance in aeronautical ad hoc networks. Each node periodically broadcasts Hello packets. The Hello packets can be replaced by data packets, which preserve bandwidth. The characteristics of the received packets, such as the Doppler shift and the power of two successive Hello packets, help to calculate the relative speed and direction of motion. Then, the link connection lifetime is estimated by the relative speed and direction of motion. In the clustering formation procedure, the node with the longest estimated link connection time to its one-hop neighbors is chosen as the cluster head. In the cluster maintenance procedure, re-affiliation and re-clustering schemes are designed to keep the clusters more stable. The re-clustering phenomenon is reduced by limiting the ripple effect. Simulations have shown that SCBCS prolongs the link connection lifetime and the cluster lifetime, which can reduce the topology update overheads in highly dynamic aeronautical ad hoc networks.