M-ary Phase-Shift Keying (M-PSK)

Generalizing PSK to M phases to encode log2(M) bits per symbol.

From Binary to M-ary: Increasing Data Rate

The fundamental goal of advanced modulation is to increase . Instead of encoding just one bit at a time, we can encode groups of bits into a single signal state, or "symbol." M-PSK is a direct generalization of this idea.

BPSK (2-PSK): Uses 2 phase states ( $0^{\circ}$ , $180^{\circ}$ ) to represent $2^1 = 2$ symbols, encoding $N=1$ bit per symbol.
QPSK (4-PSK): Uses 4 phase states (e.g., $45^{\circ}$ , $135^{\circ}$ , $225^{\circ}$ , $315^{\circ}$ ) to represent $2^2 = 4$ symbols, encoding $N=2$ bits per symbol.

M-PSK, or M-ary Phase Shift Keying, extends this principle to any number of states $M$ , where $M$ is typically a power of 2. Each symbol can then represent $N = \log_2(M)$ bits.

How M-PSK Works: The Constellation Diagram

The operation of M-PSK is best visualized using a . In M-PSK, all symbols have the same amplitude (power), so they lie on a circle. The M points are spaced equally around this circle.

The angular separation between any two adjacent symbols is given by the simple formula: $\text{Phase Separation} = \frac{360^{\circ}}{M}$ .

Example: 8-PSK

8-PSK is a common implementation used when a higher data rate than QPSK is needed.

Number of states: $M = 8$ .
Bits per symbol: $N = \log_2(8) = 3$ bits. (e.g., '000', '001', ...)
Phase separation: $\frac{360^{\circ}}{8} = 45^{\circ}$ .
The possible phases are: $0^{\circ}$ , $45^{\circ}$ , $90^{\circ}$ , $135^{\circ}$ , $180^{\circ}$ , $225^{\circ}$ , $270^{\circ}$ , and $315^{\circ}$ .

The Price of Efficiency: Practical Limitations and BER

While increasing $M$ boosts data rate, it comes at a significant cost: noise immunity. As we cram more points onto the constellation circle, the distance between them shrinks dramatically.

In any real communication channel, the signal is corrupted by noise, which causes the received symbol to be slightly offset from its ideal position. If the noise is strong enough, or the symbols are too close together, the receiver might misinterpret one symbol for its neighbor. This is known as a symbol error, which increases the .

For $M > 8$ (e.g., 16-PSK), the points become so close that the system is extremely sensitive to phase noise and other channel impairments. This leads to a high BER, making such high-order PSK schemes impractical for most applications. For this reason, 8-PSK is often considered the highest practical order of PSK in common use.

Interactive M-PSK – Constellation and Time Waveform

Order M

Mapping

Params

Carrier frequency fc (Hz): 40 Hz

Bit rate (bit/s): 6 bit/s

Amplitude A: 1.0

Data

Bit sequence

SNR for simulation (dB): 20 dB

M-PSK modulated signal

Constellation diagram (M-PSK)

The Alternative for Higher Data Rates: QAM

To achieve higher bit rates while maintaining better noise immunity than high-order M-PSK, a different technique is used: . QAM allows symbols to have different amplitudes in addition to different phases. This frees the symbols from the constraint of a single circle and allows them to be arranged in a grid, which maximizes the distance between adjacent points for a given average power.