lecture q am
TRANSCRIPT
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Quadrature Amplitude Modulation (QAM) PAM signals occupy twice the bandwidth required
for the baseband
Transmit two PAM signals using carriers of thesame frequency but in phase and quadrature
Demodulation:
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QAM Transmitter Implementation QAM is widely used method for transmitting digital
data over bandpass channels
A basic QAM transmitter
Using complex notation
Serial to
Parallel
Map toConstellation
Point
Impulse
Modulator
Impulse
Modulator
Pulse
Shaping
Filter
Pulse
ShapingFilter
J1
dn
a
n
bn
a*(t)
b*(t)
gT(t)
gT(t)
a(t)
b(t)
Inphase component
quadrature component
s(t)sin wct
cos wct
( )
( ) ( )cos ( ) sin ( ) { ( )} which is the preenvelope of QAM
( ) ( ) ( ) ( ) ( ) ( )c c c
c c
jw t jw kT jw t kT
k k T k T
s t a t w t b t w t s t s t
s t a jb g t kT e s t c e g t kT e
+
+ +
= =
= + =
-
+
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Complex Symbols Quadriphase-Shift Keying (QPSK)
4-QAM
Transmitted signal is contained in the phase
real
imaginary
real
imaginary
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M-ary PSK QPSK is a special case of M-ary PSK, where
the phase of the carrier takes on one of M
possible values
real
imaginary
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Pulse Shaping Filters The real pulse shaping
filter response
Let
where
This filter is a bandpass
filter with the frequency
response
( )T
g t
( ) ( ) ( ) ( )cjw tT I Qh t g t e h t jh t = = +
( ) ( ) cos
( ) ( )sin
I T c
Q T c
h t g t w t
h t g t w t
=
=
( ) ( )T cH w G w w=
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Transmitted Sequences Modulated sequences before passband shaping
Using these definitions
Advantage: computational savings
'
'{ } cos sin{ } sin cos
c
c
jw kT
k k k c k c
jw kT
k k k c k c
a c e a w kT b w kT b c e a w kT b w kT
= = = = +
' '( ) { ( )} ( ) ( )k I k Qk
s t s t a h t kT b h t kT
+ =
= =
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Ideal QAM Demodulation Exact knowledge of the carrier and symbol clock
phases and frequencies
Apply the Hilbert Transform of the received signal togenerate the pre-envelope s+(t)
If gT(t) has no intersymbol interference, we get
exactly the transmitted symbol
( ) ( ) ( ) ( )cjw t
k k T
k
s t s t e a jb g t kT
+=
= = +
( ) n ns nT a jb= +
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QAM Demodulation QAM demodulator using the complex envelope
Receive
Filter
HilbertTransform
Filter
e-jwct
s(t)
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Second Method Based on a pair of DSBSC-AM coherent
demodulators
In DSP implementations, Hilbert transform method is
popular because It only requires single filter
2wc terms are automatically cancelled
LPF
LPF
s(t)2coswct
-2sinwct
a(t)
b(t)
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QAM Front-End Subsystems Automatic gain control
Full scale usage of A/D and avoid clipping
No need to implement AGC in your project The Carrier detect subsystem
Determine if a QAM signal is present at the receiver
This power estimate can be easily formed by averagingthe squared ADC output samples r(n):
You can select cas a number slightly less than 1, i.e, 0.9. When the power estimate p(n) exceeds a predetermined
threshold for a period of time, a received QAM signal isdeclared to be present.
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Carrier Detect Determine a threshold value by inspecting your
power estimate.
The following figure shows the portion of receivedQAM signal and the power estimate average.
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Frame Synchronization
Assume that the receiver knows markersymbols (say, 10 complex symbols, m(n))
Assume that s(k) is the output of your QAMdemodulator. Note that s(k) and m(n) arecomplex.
Of course, in DSP you define complex
numbers by keeping real and imaginary partsin different buffers.
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Frame Synchronization
Correlation,
Peak=
Peakindex=max(abs(Peak))
Note that Peak is complex quantity
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Initial Phase Correction
Defining ej=peak/abs(peak),
then, the phase shift on s(n) which is the
output of QAM demodulator can be correctedas
x(k)=s(index+k-1)e-j
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Switch to QAM Modulation
You can proceed with hilbert transformfiltering and complex downconversion by
setting your receiver pointer to the beginningof your input buffer.
First the receiver is on and transmitter is off
Transmitter starts with marker and PN
sequence, both complex
When transmitter starts, carrier detect willswitch to QAM downconversion
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Carrier Offset Impairment for QAM
Received QAM signal
After Hilbert transform, we can form
Complex demodulator ej2fct+j)
Obtain m1(t) as the real part
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Carrier Offset Impairment for QAM
For PAM signaling carrier offset causesscaling with cosine of the phase offset
For QAM signaling carrier offset causesrotation of the constellation by the carrieroffset
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