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Figure 5 Signaling of master synchronization in WSN.

Figure 6 Diagram of master synchronization in WSN.

The limited feedbacks of two-step scheme illuminates the feasibility of proposed pulse master synchronization in WSNs. Figure 9 Average acquisition time with respect to in forward channel.

Numerical results are presented in Section 6, and conclusions are drawn in Section 7. The master synchronization presented in this paper aims at the synchronization problem when a master sends commands or messages to tag nodes.

The search process is the same as the pulse master synchronization described in Section 2. Thus, the search period in the first step is, and acquisition precision is.

In Section 3, the stability of these distributed feedback control methods are analyzed, and a stable acquisition is proposed in Section 4. The performance of the single-step pulse master synchronization is also deduced in Section 4. In Section 5, a two-step master synchronization is given to reduce the acquisition time, and its performance is analyzed either.

In master synchronization, is regarded as the phase of local oscillator in the tag receiver, and as adjustable phase of transmitter.

The intuitive reason of instability in master synchronization is that the feedback control error departs from the right phase in master node due to the large delay.

Sawtooth-waveform- and sine-waveform- (SPLL-) based master synchronization are also compared in the figure for their high convergence rate.

If the master synchronization requires a precision in the interval of, the searching stepsize requires to be less than.

In this view, we propose a two-step acquisition scheme to limit acquisition time and feedback times in master synchronization, while guaranteeing the precision.