数字通信课件4

4
Review——Markov state diagramrkov state diagram of delay modulation
S2 s2 t s3 t s1 t S1 s1 t s4 t s4 t S3 s2 t
S4
s3 t
5
Review——State transition matrix
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4.3.3 Nonlinear modulation method with memory
For n 3 / 2
sl ( t ) I n 2 k g ( t ( n 2k )T ) k 0 j g ( t ( n 1)T ) I n I n 2 k 1 g ( t ( n 2 k 1)T ) k 0
The minimum frequency shift (difference) for two frequency modulated signals being orthogonal is (1/2T), where T is the channel symbol duration. The MSK just achieves the minimum shift as its name reveal itself.
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4.3.3 Nonlinear modulation method with memory
d (t )
n
I ( t nT ),
n

where I n { ( M 1), ( M 3), ..., ( M 1)}
denotes the amplitude of nth k-bit blocks.
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Review——Representations of ContinuousPhase Phase trajectory or phase tree Phase trellis Phase cylinder t Phase state trellis q( t ) ( )d Phase state diagram
cos[2 ( fc I n /( 4T )) t n I n / 2 n ] for nT t ( n 1)T
cos[2 cos[2 cos[2 cos[2
f t 0 / 2], cos[2 f t 0 / 2] f t 1 / 2], cos[2 f t 1 / 2] f t 2 / 2], cos[2 f t 2 / 2] f t 3 / 2], cos[2 f t 3 / 2]

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4.3.3 Nonlinear modulation method with memory
(Conventional) QPSK：
I 2 k I 2 k 1 g ( t 2kT )]cos( 2 fc t ) 2 s( t ) I 2 k I 2 k 1 k g ( t 2kT )]sin( 2 fc t )] 2
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4.3.3 Nonlinear modulation method with memory
MSK = sum of two staggered quadraturemodulated BPSK signals, each with a sinusoidal envelope. The corresponding sum of the two quadrature signals becomes a constant amplitude, frequency-modulated signal.
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Review——CPFSK
Obstacle : Abrupt switching from one oscillator to another will result in relatively large spectral side lobes. Solution: A single carrier whose frequency is changed continuously.
Digital Communications Chapter 4 : Characterization of Communication Signals and Systems (4.3.3~4.4)
1
Review——Differential encoding
Advantages with DE for BPSK (under coherent demodulation) The phase or signs of the received waveforms are not important for detection, What is important is the change in signs of successive pulses. The sign changes can be correctly detected even if the demodulating carrier has a sign ambiguity.
4.3.3 Nonlinear modulation method with memory
MSK：
s( t )
k
[I

2k
g ( t 2kT )]cos( 2 fc t ) I 2 k 1 g ( t ( 2k 1)T )]sin( 2 fc t )]
=OQPSK with 1/2 cycle of a sinusoid pulse shape sin( t / 2T ), 0 t 2T g(t ) 0, otherwise Offset QPSK：
DE
1 0 T0 0 1
(For input zero) delay modulation
0 0 T0 1 1 0 0 0 0 0 0 0 0 1 1 0 0
0 1 T1 1 0
(For input one)
( t;I) 2
k
n L
I h q( t kT ), nT t ( n 1)T
k k
k
9
n
( nT ;I) h I k 2 h I n L1q(( L 1)T ) I n1q(T )
Review——Why Minimum-shift？
( t;I)
t nT ( ) , nT t ( n 1)T I I q t nT I k n n n 2 k 2T
n1
n s( t ) cos 2 fi t ( 1) i n , i 1, 2 2 1 Frequency shift 2T
For 0 t 4T and ( I 0 , I1 , I 2 , I 3 ) ( 1, 1, 1, 1)
s( t ) g ( t T ) sin( 2 fc t )
1 1
cos( 2 fc t ) I 2 k g ( t 2kT ) I 0 sin( 2 fc t ) [ I 2 k 1 g ( t ( 2k 1)T )]
1, 0 t 2T g(t ) 0, otherwise
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4.3.3 Nonlinear modulation method with memory
Vectorization of MSK signals
s( t ) cos[2 fc t n I n ( t nT ) /( 2T )] for nT t ( n 1)T

s( t )
1, 0 t 2T =OQPSK with g(t ) 0, otherwise rectangular pulse shape
k
[I

2k
g ( t 2kT )]cos( 2 fc t ) I 2 k 1 g ( t ( 2 k 1)T )]sin( 2 fc t )]
(Quadrature signal component)
s( t ), a constant amplitude, frequency-modulated signal
*Frequency at [ nT , ( n 1)T ] fc (1 /( 4T )) I n
I 0 1 I 1 1 I 2 1 I 3 1
S2
0 0 T1 0 0
1 0 0 0 1 0 1 0 0 0 1 0
0/s1(t) S1 0/s1(t) 0/s4(t) 0/s4(t) S3
(For input zero) (For input one)
S4
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Review——Trellis diagram
For DE
Assume T 1 and fc 1.2
cos( 2 fc t ) g ( t 2kT )
k 0 1
(In-phase signal component)
1 sin( 2 fc t ) g ( t T ) g ( t ( 2k 1)T ) k 0
channelcode bit k input bit k channelcode bit k 1
channelcode bit k channelcode bit k 1 , when input bit k 0 channelcode bit k channelcode bit k 1 , when input bit k 1
2
Review——Delay modulation