Time Synchronization for Wireless Sensor Networks - Adaptive Signal Processing in Wireless Communications - page 371

Ct

i ()=+⋅+,

θθ
o

te (13.1)

s

where the parameters θ o and θ s are called clock offset (phase difference) and clock skew
(frequency difference), respectively, and e stands for random noise.
Assuming the effect of random noise e is negligible, from (13.1), the clock relationship
between two nodes, say node 1 and node 2, can be represented by

() ()
=+⋅ ,

12 12

Ct () θθ

o

Ct ()

1 s 2

where θ (12) and θ s (12) are the relative clock offset and skew between node 1 and node 2,
respectively. Thus, θ (12) = 0 and θ s (12) = 1 when the two clocks are perfectly synchronized.
Suppose there are L nodes in the network, then the global network-wide synchroniza-
tion is achieved when C i ( t ) = C j ( t ) for all i , j = 1, … , L .
Time synchronization in wireless sensor networks is a complicated problem due to
the following reasons. First, every single oscillator has unique clock parameters regard-
less of its type. For instance, according to the data sheet of a typical crystal-quartz oscil-
lator commonly used in sensor networks, the frequency of a clock varies up to 40 ppm,
which means clocks of different nodes can lose as much as 40 ms in a second. In other
words, every single oscillator might assume a different skew parameter ranging from
-20 to 20 ppm.
Notice that in general, the clock skew θ s is a time-dependent random variable (RV)
and there are two concepts used often in clock terminology regarding the nature of
time-dependent randomness present in clock parameters. These concepts are referred to
as short-term and long-term stabilities, respectively. For the oscillators currently used in
sensor networks, all these parameters are almost constant for short-term time intervals
[10]. Besides, the total power of the noise process is too small to be effective in short time
spans [11]. Therefore, the parameters of a clock are assumed to be constants for the time
period of interest.
As far as the long-term stability is concerned, the clock parameters are subject to
change due to environmental or other external effects such as temperature, atmospheric
pressure, voltage changes, and hardware aging [10]. Hence, in general, the relative clock
offset keeps changing with time, which means that the network has to perform periodic
time resynchronization to adjust the clock parameters.

13.2.2 Design Considerations

Time synchronization for conventional wired networks has been thoroughly studied
and a plethora of synchronization protocols have been developed as surveyed in [1]. For
wireless sensor networks, there are a number of unique and important factors to be con-
sidered when designing time synchronization protocols as listed below.

• Energy consumption : Energy consumption is momentous in wireless sensor

networks due to their limited and generally nonrechargeable power resources.
Hence, the design of wireless sensor networks should be subjected to maintain-
ing minimal energy expenditure in each sensor node. Various types of power