Lecture q Am

7/28/2019 Lecture q Am

1/17

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:


2/17

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

+

+ +

= =

= + =

-

+


3/17

Complex Symbols Quadriphase-Shift Keying (QPSK)

4-QAM

Transmitted signal is contained in the phase

real

imaginary

real

imaginary


4/17

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


5/17

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=


6/17

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

+ =

= =


7/17

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)


9/17

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)


10/17

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.


11/17

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.


12/17

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.


13/17

Frame Synchronization

Correlation,

Peak=

Peakindex=max(abs(Peak))

Note that Peak is complex quantity


14/17

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


15/17

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


16/17

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


17/17

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

-

Lecture q Am

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