Digital Signal Processing Reference
In-Depth Information
Q
01
Q
11
Fig. 6.22
I-Q diagram of (
a
)
BPSK and (
b
) QPSK
3
π
/4
0
1
/4
π
π
I
I
00
10
(a)
(b)
ϕ
QPSK
(
t
)
=
A
c
cos
(ω
c
t
+
φ
n
)
(6.19)
where,
φ
n
=
(
2
n
+
1
)(π/
4
)
,for
n
=
0,1,2,3
For n
=
0, taking
A
c
=
1,
ϕ
QPSK
(
t
)
=
cos
(ω
c
t
+
π/
4
)
ω
c
t
cos
π
4
−
ω
c
t
sin
π
4
=
cos
sin
(6.20)
1
√
2
(
=
cos
ω
c
t
−
sin
ω
c
t
)
From Eq. (
6.20
), cos
ω
c
t
and
−
sin
ω
c
t
are in-phase and quadrature phase carrier
basis, termed as
ξ
I
(
t
) and
ξ
Q
(
t
) respectively. Therefore, Eq. (
6.20
) can be re-written
as
√
2
(
+
) ξ
Q
(
t
)
1
ϕ
QPSK
(
t
)
=
1
) ξ
I
(
t
)
+
(
+
1
(6.21)
The 1st step towards realizing QPSK modulation is partitioning of pulses. The orig-
inal data stream consisting of bipolar pulses, i.e.,
d
k
(
t
)
=+
1or
−
1, representing
...
This pulse stream is partitioned into an in-phase stream
d
I
(
t
), and a quadrature
stream
d
Q
(
t
) taking odd and even bits separately.
=
binary 1 and 0 respectively is expressed as
d
k
(
t
)
d
0
,
d
1
,
d
2
,
d
I
(
t
)
=
d
0
,
d
2
,
d
4
,
...
. (Even bits)
(6.22)
d
Q
(
t
)
=
d
1
,
d
3
,
d
5
,
...
. (Odd bits)
(6.23)
From the Fig.
6.23
, it's clear that, bit rate of
d
I
(
t
) and
d
Q
(
t
) each is actually the half
of the bit rate of
d
k
(
t
).
Therefore, a convenient orthogonal realization [
4
] of the QPSK waveform
is achieved by amplitude modulation by the in-phase and quadric-phase data
partitions into cosine and sine carrier waves, respectively. Hence, the generalized
Search WWH ::
Custom Search