This document discusses different digital modulation techniques, focusing on phase-shift keying (PSK). It describes three types of PSK: QPSK, OQPSK, and π/4-QPSK. QPSK uses four phases shifts of 0, 90, 180, and 270 degrees to represent binary data. OQPSK and π/4-QPSK are variants that prevent abrupt 180 degree phase transitions to reduce spectral regrowth and allow use of non-linear amplifiers. OQPSK introduces a time offset between the in-phase and quadrature channels, while π/4-QPSK rotates alternating symbols by 45 degrees.

1. DIGITAL MODULATION TECHNIQES
Phase-Shift keying
NOVEMBER 23, 2020
Supervised by: -
Dr. Samy S. Soliman
Prepared by: -
Mohamed Sewailam

2. Modulation
Modulation is some sort of operations to convert (Map) the baseband signal
(Information) to be transmitted over transmission Media channel (Radio channel).
There are three major types of digital modulation techniques used for transmission
of digitally represented data:
 Amplitude-shift keying (ASK)
 Frequency-shift keying (FSK)
 Phase-shift keying (PSK)
The key difference between modulation techniques is how to represent the digital
signal (Baseband) in proper way on carrier signal amplitude, frequency or Phase to
be transmitted over define communication channel as show in below graph.
Baseband signal can be represented by carrier Amplitude, frequency or Phase or
combination of them to trade of between many elements or attributes (the highest
bite rate, the least bite error rate, the signal immunity to noise (SNR),
transmitter/Receiver complexity, ….).
Here will talk about the Phase-Shift Keying technique and specially compare about
three types of PSK which are QPSK, OQPSK and π/4-QPSK.

3. Phase-shift keying (PSK)
Phase Shift Keying (PSK) is the digital modulation technique in which the phase
of the carrier signal is changed by varying the sine and cosine inputs at a particular
time. As the phase of the output signal gets shifted depending upon the input.
These are mainly of two types, namely BPSK and QPSK, according to the number of
phase shifts it define the type of PSK as the Binary PSK is only two change in phase
and for QPSK there are four changes in Phase. As show in below graph (Constellation
Diagrams).
Quadrature phase-shift keying (QPSK)
This is PSK technique, in which the sine or cosine wave carrier takes four phases
reversals such as 0°, 90°, 180°, and 270° Or 45°, 135°, 225°, and 315°….
Each Phase of the four ones (Symbol) represents two Bits. The following figure
represents the QPSK waveform for two bits input, which shows the modulated result
for different instances of binary inputs.

4. QPSK signal envelopes are the most severely affected by filtering. At the 180° phase
transitions the signal envelope goes through zero amplitude as show in Constellation
Diagrams). In QPSK these transitions occur when both the in-phase and quadrature (I
and Q) channels change phase simultaneously. Such variation requires linear Power
Amplifier to avoid spectral regrowth (side lobes).
In order to eliminate the possibility of a 180° phase transition in the QPSK case, must ensure
that the phase can only change a maximum of 90 or less than 180° at any given transition.
When this is done the maximum envelope variation of the filtered signal will be 3dB.So
OQPSK and pi/4 QPSK are variants of the basic QPSK modulation schemes.
Offset quadrature phase-shift keying (OQPSK)
Offset quadrature phase-shift keying (OQPSK) is a variant of phase-shift keying modulation
using four different values of the phase to transmit. It is sometimes called staggered
quadrature phase-shift keying (SQPSK).
In OQPSK, after splitting the bit stream into odd and even (I and Q bits), one-bit stream is
made offset by half a symbol period (one-bit period) with respect to the other. This ensures
that both bits don’t change state at the same time, thus limiting the maximum phase change
to 90 degrees and preventing any spurious high frequency components.

5. As shown above in the constellation diagram OQPSK prevents phase transition from the
origin by shifting one stream by a bit period and allowing only one bit to change between the
transitions.

6. π/4 quadrature phase-shift keying (π/4 QPSK)
In π/4 QPSK we achieve the same objective (avoid passing through origin) by rotating every
other symbol by 45°. After splitting the bit stream into odd and even (I and Q bits), one-bit
stream is made offset by 1/4 a symbol period (half of bit period) with respect to the other.
Note in the transitions from any one symbol to the next, as shown in the diagram below, that
it is not possible to go through the origin.
Dual constellation diagram for π/4-QPSK. This shows the two separate constellations with
identical Gray coding but rotated by 45° with respect to each other.

7. The modulated signal is shown above for a short segment of a random binary data-stream.
The construction is the same as above for ordinary QPSK. Successive symbols are taken
from the two constellations shown in the diagram. Thus, the first symbol (1 1) is taken from
the "blue" constellation and the second symbol (0 0) is taken from the "green" constellation.
Note that magnitudes of the two component waves change as they switch between
constellations, but the total signal's magnitude remains constant (constant envelope). The
phase-shifts are between those of the two previous timing-diagrams.
The table below summarizes
QPSK, OQPSK and pi/4 QPSK modulation types.
QPSK OQPSK π/4 QPSK
phase changes +/- 90 and +/-180
degrees
phase changes +/- 90 Maximum phase changes +/-45 and
+/-135
There is no offset between I&Q
Bits
There is Tb Offset between I&Q Bits There is Tb/2 Offset between I&Q
Bits
Requirements of linear amplifier
as nonlinear amplifier cause
spectral regrowth because of
abrupt +/-180 degree transitions
of the both bits change the phase
at the same time.
less demands of linear amplifiers,
efficient nonlinear amplifier can be
employed and they do not cause much
spectral regrowth, as one of the bits
changes the phase at a time and occurs
twice during the symbol period with
half the intensity of QPSK
Phase transitions avoid zero crossing.
This will remove design constraints
on the amplifier, nonlinear amplifier
can be employed

8. Index
ASK Amplitude Shift Keying
FSK Frequency Shift Keying
PSK Phase Shift Keying
QPSK Quadrature Phase Shift Keying
OQPSK Offset Quadrature Phase Shift Keying
References
https://en.wikipedia.org/wiki/Phase-shift_keying
https://www.rfwireless-world.com/Terminology/QPSK-vs-OQPSK-vs-pi-4QPSK.html
https://dsp.stackexchange.com/questions/41130/envelope-behavior-difference-between-
qpsk-oqpsk-and-pi-4-qpsk
https://www.slideshare.net/mansournch/oqpsk
https://www.slideshare.net/naveenjakhar12/phase-shift-keying-4-quadrature-phase-shift-
keying
Thank you