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Baseband and Passband Data 2. Baseband and Passband Data Transmissions (Contin.)

QAM (quadrature amplitude modulation) transmits two independent baseband signals in the same bandwidth. The QAM signal is the sum of the baseband signals multiplied by cosine and sine carriers. At the receiver, each baseband signal is recovered by multiplying the received signal by the appropriate carrier. QAM can transmit m bits per symbol by encoding m bits into one of 2^m possible signal points, where each point has coordinates representing the amplitude of each carrier. This forms a signal constellation with points spaced to allow unique decoding of each symbol.

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110 views7 pages

Baseband and Passband Data 2. Baseband and Passband Data Transmissions (Contin.)

QAM (quadrature amplitude modulation) transmits two independent baseband signals in the same bandwidth. The QAM signal is the sum of the baseband signals multiplied by cosine and sine carriers. At the receiver, each baseband signal is recovered by multiplying the received signal by the appropriate carrier. QAM can transmit m bits per symbol by encoding m bits into one of 2^m possible signal points, where each point has coordinates representing the amplitude of each carrier. This forms a signal constellation with points spaced to allow unique decoding of each symbol.

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2.

Baseband and Passband Data


Transmissions (contin.)
2.10 Quadrature - amplitude modulation (QAM)

In this type of modulation two independent baseband data signal are


transmitted in the same bandwidth.
2.10 QAM (contin.)

The QAM signal is

s (t ) = x (t ) cos ω 0 t + y (t ) sin ω 0 t (2.26)

where x(t) and y(t) are the baseband signals. To obtain, in the receiving
part, the baseband signal x(t), this QAM signal is multiplied by a local carrier
cosω0t:

1
s(t ) cos ω0 t = [x(t ) + x(t ) cos 2ω0t + y(t ) sin 2ω0t ] (2.27)
2

The components x(t)cos2ω0t and y(t)sin2ω0t represent AM signals with their


frequency spectra centred on the twice of the carrier frequency and can be
eliminated using a lowpass filter. In the same way the baseband signal y(t) is
obtained, the received signal s(t) being multiplied by another local carrier, sinω0t.
2.10 QAM (contin.)
To transmit m bits per symbol interval (T), each group of m bits is encoded in
one of the M=2m levels (states) of the modulated carrier, which is considered like
a sum of two in quadrature carriers. To each state corresponds a point in a two -
dimensional space, with coordinates xk, yk, representing the amplitudes of these
two carriers. The graph of all points (xk, yk) representing the possible states of the
modulated carrier is called signal constellation.
yk , Q
“0000” “0001” “0011” “0010”
s1 s2 3d
s3 s4
16-QAM
“1000” “1001” “1011” “1010”
s5 s6 s7 s8
d
Signal constellation -3d -d d 3d
xk , I
for m = 4 (16QAM)
s9 s10 -d
s
11 s12
“1100” “1101” “1111” “1110”

s13 s14 s
-3d 15
s 16
“0100” “0101” “0111” “0110”
2.10 QAM (contin.)
2.10 QAM (contin.)

To each group of m bits from the serial flow of data bits at the coder input will
correspond two values xk and yk at the coder outputs, representing the amplitudes
of rectangular pulses applied at the lowpass filters inputs. The input signals in
these lowpass filters, x(t) and y(t), can be expressed like:

x(t ) = ∑x
k
k g (t − kT ); y (t ) = ∑y
k
k g (t − kT ) (2.28)

where g(t) is the rectangular pulse with unity amplitude and the duration
T, equal with the duration of m bits. If the response of the lowpass filters to the
input g(t) is h(t), then p(t) and q(t), their responses to x(t) and y(t), are:
p(t ) = ∑ x h(t − kT );
k
k q (t ) = ∑ y h(t − kT )
k
k (2.29)
2.10 QAM (contin.)

The QAM signal is:

s (t ) = ∑ x h(t − kT ) cos ω t + ∑ y h(t − kT ) sin ω t


k
k 0
k
k 0 (2.30)

and a pair of coordinates xk, yk is a signal point, called also symbol. The symbol
interval is T, equal with the duration of m bits.

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