In Phase I the ES nodes act in a distributed manner to determine which ES will become the master ES. The master ES collects position information, determines the optimum ES interconnections, and distributes the results back to the ES nodes. The ES nodes determine the master ES by broadcasting MYCALL packets and collecting MYCALL packets until the MYCALL Timer expires with a prespecified time, T. The MYCALL packets contain the callsign and boot-time of each ES. The ES with oldest boot-time is designated as the master. T should be chosen as the smallest value which allows enough time for all MYCALL packets to be received. This would be approximately 0.492 * (N-1) seconds, where N is the total number of ES nodes. NEWSWITCH packets take on the order of 0.439 seconds to transfer, and therefore, it will take 0.439 * (N-1) seconds to send these packets. The ES nodes will respond with SWITCHPOS packets which will take another 0.679 * (N-1) seconds. These events occur after each MYCALL packet has been received, and can occur before the MYCALL Timer has expired.
The next step in Phase I is to run the topology algorithm which is based on a consistent labeling algorithm . This algorithm generates all fully connected topologies given ES node locations and constraints on the antenna beams such that beams do not interfere with one another. The information required by the topology module is the GPS location of all ES nodes, transmit and receive beam widths, transmit radius, the number of non-interfering frequency pairs, and an interference multiplier. An interference multiplier of 1.0 assumes adaptive power control, in which case it is assumed that beam power control will be adjusted to exactly match the link distance. The interference multiplier multiplied by a link's actual length will determine the range of interference created by the link. This takes on the order of seconds where L is the number of available frequency pair combinations with the addition of 1 for no link. Assigning distinct frequencies allows beams to overlap without interference. R is the number of constrained links and is a constant. The constraints are based on maximum beam length, beam widths, and number of frequencies which can be supported.
The final step in Phase I is to distribute the topology information to all ES nodes in TOPOLOGY packets. This takes approximately 0.664 + (0.1 * (N-1)) seconds.
The time for Phase I to complete as a function of N is shown in Equation 1.