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5
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! 78 193
(
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& 5
5
% % ( , 5 & , % % ) ; & + $
ß & ß & ß % & ' ß
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<=> %) % %) $ ) & + 5 % % ) 4 *
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3
1
3
1A3
& ' ) # @ 1@3 ! - + % ) %) & ' ß
& 6
, -
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+5B
+ @ ) α=10−4
Phase estimate
1
0.04
0.5
0.03
0
−0.5
0.02
0.01
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
4
x 10
Estimated step
0.03
0
0.5
1
−5
1.5
2
2.5
α=10
5
x 10
0.04
Estimated stepsize
0.02
0.03
0.01
0.02
optimum stepsize
0
0.01
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
4
x 10
1
Phase error
0
The asymptotic MSE decreases as the estimated
stepsize goes to its optimum value.
0.5
0
0
0.5
1
α=10−6
1.5
2
2.5
5
x 10
0.04
0.03
0
−0.5
0.02
0.01
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
4
x 10
0
0
0.5
1
1.5
2
2.5
5
+ @ +A
::+ & :::+ & +:
&
) ) C * %
% =?
163 ! 6
) 4 D 4 % ! E (
0 (
% * ) & ' ' -% 4 F
* x 10
6 @ +A &
::+ & :::+ & +:
+:
+:
1G3
& '
'+
ß
%
& ' ' ß
& ' ß
,
!
' * ) ) @ 1G3 H<=>
I %)
E % * ) ) (
H % ) 1+3 % =? -
½ '1
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9 ! !
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!
­ ´¾µ ! $! / 5!!
)
$ & & ' ß & + 5 ß ' ' ß
& ß & ' ' ß
5
! @ H ) ! E Phase error
1
0
−0.5
0
0.5
1
1.5
2
2.5
4
x 10
Slope
0.015
0.005
0
0.5
1
1.5
2
2.5
4
x 10
0.15
γ
0.1
0.05
0
#
$ %
$& ''
163 K H # K ,
=% =
=%
?
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1@3 H 7 < <
!
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= L
+99:
153 H #
L K H ? # K #$
%
& '
(
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(((& * +G:+GG +99A
1G3 K H +
+
$ #
0.01
0
1+3 <J K H ? + ($$ 6+ $6 0.5
−1
0
0.5
1
1.5
2
2.5
4
x 10
@ = 5 +A &
::+ & :::+ & ::+ & +:
&
+:
" % <=>
%
) H C % E
6GA ,-& ../
1A3 EK > K M !
!
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1B3 K0 0 <J < $ , +
+99B
123 % # K ( -! ((( 56
6G@+6G@@ +995
193 ? = < # #* <
0 .
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