Digital Signal Processing Reference
In-Depth Information
The surrounding nodes receive this pulse sequence, and based on the locations of
the observed zero-crossings, the surrounding nodes predict when the next pulse will
be transmitted. Then, these nodes emit pulses at their predicted times and an aggregate
pulse sequence will be generated. It is shown in [35] that although the prediction at indi-
vidual nodes may not be perfect, under certain conditions on the pulse and in asymp-
totically dense networks, the zero-crossings of the aggregate waveform sequence will be
at the same positions as the zero-crossings of the original waveform sequence emitted by
the leader node due to spatial averaging. This aggregate pulse sequence will be heard by
the nodes lying further away from the leader node, and these nodes perform prediction
as described before and emit their pulses at their predicted times. The procedure will be
continued until all the nodes are synchronized.
Notice that the synchronization algorithms discussed in this section only provide a
unified ticking rhythm across sensor nodes, but not the synchronization of clock time.
A good analog is a group of people clapping together to get a rhythm. However, there
exist applications in which a unified rhythm is enough, e.g., in distributed beamform-
ing and reachback channel [36]. As another variation, a joint physical and network layer
time synchronization scheme was proposed to overcome the effects of imperfect physi-
cal layer synchronization due to the nature of common wireless channels [37].
13.5
Adaptive Time Synchronization for WSNs
While all the above protocols in section 13.4 can achieve instantaneous synchronization
among nodes, the timing of different nodes would drift apart as time passes; therefore,
periodic resynchronization is needed to maintain long-term synchronization. Intuitively,
less resynchronization needs less energy but leads to a larger synchronization error, while
more frequent resynchronization leads to a smaller synchronization error but requires
more energy. A natural question is what is the minimum resynchronization frequency
(or equivalently, maximum resynchronization period) that can meet the desired syn-
chronization precision. Therefore, adaptive algorithms are necessary to dynamically
determine the resynchronization period, number of beacons to be used in each round
of synchronization, synchronization accuracy, and so on. In this section, we will review
three existing adaptive time synchronization algorithms proposed in the literature.
13.5.1 Rate-Adaptive Time Synchronization (RATS)
Consider the case where node A sends time-stamped messages to node B periodically
with period τ, and node B records the receiving times of the messages. Based on a num-
ber of data points (
T
i
(A)
,
T
i
(B)
), where
T
i
(A)
and
T
i
(B)
are the time stamps made at node A and
node B respectively, node B wants to determine the largest τ such that the synchroniza-
tion error is smaller than a certain limit. The rate-adaptive time synchronization [38]
is an algorithm that determines the optimal τ adaptively. Its idea can be summarized
using the flowchart shown in
Figure 13.8
.
First, node B calculates the optimal number
of data samples for model parameters (e.g., clock offset and skew) estimation based on
the current value of τ. Next, node B takes the required number of data points (stored
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