Main Difference Between QPSK and 4-PSK
Understanding how Quadrature PSK and 4-Phase PSK relate in digital modulation.
Definition
| Term | Meaning |
|---|---|
| 4-PSK | A general term for a phase shift keying (PSK) scheme that uses four distinct phase states to represent data. |
| QPSK (Quadrature PSK) | A specific implementation of 4-PSK where the four phases are spaced 90° apart (quadrature). |
In essence, QPSK = 4-PSK — both use four phase shifts (0°, 90°, 180°, 270°) to encode two bits per symbol.
Bits per Symbol
| Modulation | Number of Phases | Bits per Symbol | Example Phase Angles |
|---|---|---|---|
| BPSK | 2 | 1 | 0°, 180° |
| QPSK / 4-PSK | 4 | 2 | 0°, 90°, 180°, 270° |
In both QPSK and 4-PSK, each symbol carries 2 bits.
Representation Difference
QPSK is often implemented using two orthogonal carriers (I and Q channels):
s(t) = I(t)cos(2Ï€fct) + Q(t)sin(2Ï€fct)Here, I(t) and Q(t) each carry one bit.
4-PSK, in theory, just refers to any modulation with four distinct phase states — it doesn’t specify how they’re implemented. Hence, QPSK is a practical implementation of 4-PSK using in-phase and quadrature carriers.
Constellation Diagram
Both QPSK and 4-PSK have identical constellation diagrams — four equally spaced points on a circle, 90° apart:
01 (0 + j.1)
*
|
|
11 *---------+---------* 00 (1 + j.0)
|
|
*
10 (0 - j.0)
Baseband and Passband QPSK
The constellation points of Quadrature Phase Shift Keying (QPSK) can be represented as
1 + j0, 0 + j1, −1 + j0, and 0 − j1,
or simply as {1, j, −1, −j}. Since each symbol is separated by a phase difference of
90 degrees (Ï€/2 radians), the QPSK signal can be expressed in its
quadrature baseband form as:
I(t) + jQ(t)
Here, I(t) and Q(t) represent the in-phase and quadrature components of the signal, respectively. This decomposition into two orthogonal carriers is why it is called Quadrature Phase Shift Keying.
The corresponding passband representation of the QPSK signal is given by:
I(t) · cos(2Ï€fct) − Q(t) · sin(2Ï€fct)
where fc is the carrier frequency. The first term represents the in-phase component modulating the cosine carrier, and the second term represents the quadrature component modulating the sine carrier.
QPSK Constellation and Phase Relationship
| Bits | Symbol | Ik | Qk | Complex Symbol (Baseband) | Equivalent Phase (radians) |
|---|---|---|---|---|---|
| 00 | ( 1 ) | +1 | 0 | ( +1 + j0 ) | ( 0 ) |
| 01 | ( j ) | 0 | +1 | ( 0 + j1 ) | (Ï€/2) |
| 11 | ( -1 ) | –1 | 0 | ( -1 + j0 ) | (Ï€) |
| 10 | ( -j ) | 0 | –1 | ( 0 - j1 ) | ( 3Ï€/2 ) or ( –Ï€/2 ) |
Each QPSK symbol corresponds to a unique phase shift on the unit circle, separated by Ï€/2 radians (90°). These phase differences define the quadrature nature of QPSK modulation.
For example, if the input bitstream is 110111,
the corresponding baseband QPSK symbols will be {-1, j, -1}, and the passband signal will appear as shown below:
