Time Synchronization for Wireless Sensor Networks - Adaptive Signal Processing in Wireless Communications - page 400

nodes participating in a particular multihop data transmission synchronize with each
other, is a better choice.
In order to determine whether aO or SI mode is to be used, the following network
parameters are introduced in AMTS:

• : Number of branches (edges) in a spanning tree of the network. It can be
obtained after the level discovery phase.
τ

B

• : Resynchronization period, i.e., the time between resynchronizations.
h • - : Average of hops per unit time. In every sensing event, the destination node

accumulates the number of hops that have occurred in that particular trans-
mission to its storage. During the synchronization phase, the reference node
collects the information about the total number of hops occurred in the last
synchronization period and determines the average number of hops per unit
time ( - ) in the network. This information indicates how busy the network traf-
fic is and can be included in timing messages with a small overhead.
δ

• : Latency factor (0 ≤ δ ≤ 1) reflecting the amount of allowed delay in data
transmission. Higher latency factor means less concern for network delays. For
example, δ is set to be 0 for sensor networks requiring network synchroni-
zation all the time. On the other extreme, for delay-independent networks, δ
should be close to 1.
N • : Number of timing message exchanges per pairwise synchronization.

In the aO mode, the number of timing messages per unit time is given by - = 2 BN /τ,
while in the SI mode, - = 2 - N . To minimize the number of timing messages per unit
time - , the synchronization mode should be selected as follows:

aO

2 BN δ

2 hN , (13. 39)

≶
SI

τ

or equivalently,

aO B
h

δ

τ . (13.4 0)

≶
SI

From (13.40), the synchronization mode changes from aO to SI when τ is smaller than
B δ/ - and vice versa. In the SI mode, the reference node periodically inquires about the
number of hops that occurred during the past time interval, and then it makes a deci-
sion whether or not to switch to the aO mode. Notice that AMTS is an iterative process,
and the resynchronization period parameter in the mode selection will be from the last
iteration of AMTS.

13.5.3.2 Determination of Resynchronization Period
As the resynchronization period τ increases, the network becomes more power efficient.
Thus, τ should be chosen as large as possible. However, a too large value of τ induces a
critical synchronization problem since the clock difference (offset) between nodes keeps