Quadrature Phase Shift Keying (QPSK)

📊Modulations 🧪Simulations 💻MATLAB

🚀 Try QPSK Simulation Tool

Run MATLAB-based and online QPSK simulations instantly.

Open Simulator

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(2πfct) + Q(t)sin(2πfct)

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

             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}.

I(t) + jQ(t)

I(t) · cos(2πfct) − Q(t) · sin(2πfct)

QPSK Constellation and Phase Relationship

Bits	Symbol	I	Q	Complex Symbol	Phase
00	(1)	+1	0	(+1 + j0)	0
01	(j)	0	+1	(0 + j1)	π/2
11	(-1)	-1	0	(-1 + j0)	π
10	(-j)	0	-1	(0 - j1)	3π/2

For example, if the input bitstream is 110111, the corresponding baseband QPSK symbols will be {-1, j, -1}.

Passband QPSK signal representation

Further Reading

1. Quadrature Multiplexing
2. MATLAB Code for QPSK Modulation and Demodulation
3. MATLAB code for Constellation Diagram of QPSK
4. MATLAB Code for BER performance of QPSK with BPSK, 4-QAM, 16-QAM, 64-QAM, 256-QAM, etc