Digital Signal Processing Reference
In-Depth Information
Notice further that the regularity conditions for the CRBs hold:
∂
ln
p
( )
()
x
;
θ
E
=
∂
ln
p
()
x
;
θ
θ
o
BP
∂
E
∂
θ
∂∂
ln
p
( )
()
x
θ
;
E
s
BP
∂
θ
N
∑
() ()
−−⋅
BP
BP
E
1
xn
[]
θ θ
D
o
s
i
2
σ
i
=
1
=
=0
N
∑
−−⋅ ⋅
()
BP
()
BP
E
1
xn
[]
θ θ
DD
o
s
i
i
2
σ
i
=
1
Consequently, using the results in (13.22), node B can be synchronized to node P.
Likewise, all the other nodes in the checked region in
Figure 13.1
can be simultane-
ously synchronized to the parent node, node P, without any additional timing message
transmissions, thus saving a significant amount of energy. Besides, there is no loss of
synchronization accuracy when compared with other approaches [19].
13.3.3
Receiver-Receiver Synchronization
Receiver-receiver synchronization is an approach to synchronize a set of children nodes
who receive the beacon messages from a common sender (a reference or parent node).
Consider a parent (reference) node P and arbitrary nodes A and B, which locate within
the communication range of the parent node in Figure 13.4. Suppose, in
Figure 13.5
both node A and node B receive the
i
t h
beacon from node P at time instants
T
2,
i
(B)
of their local clocks, respectively. Nodes A and B record the arrival time of the broadcast
packet according to their own timescales and then exchange their time stamps. Suppose
(A)
and
T
2,
i
Receiver-Receiver
synchronization
B
P
A
Parent node
Beacons
FIgure 13.4
Receiver-receiver synchronization.
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