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

Binary and M-ary PSK

Using more than two phase states allows a symbol to carry several bits and can increase the bit rate for a given symbol rate. spectral efficiency. Instead of encoding one bit at a time, a modulator can map a group of bits to one 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, uses $M$ equally spaced phase states. When $M=2^N$, each symbol maps to $N = \log_2(M)$ bits. For other values of $M$, the mapping must be specified, for example as a block mapping; some states may remain unused or the average bits per symbol may be fractional, depending on the coding scheme.

M-PSK constellation diagram

A constellation diagram represents the possible states of a digital modulation scheme. constellation diagram. In M-PSK, all symbols have the same amplitude and energy, so their points lie on a circle. The M points are equally spaced around this circle.

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

M-PSK distance and BER

At fixed symbol energy, increasing $M$ raises the number of bits per symbol but reduces the angular separation and the minimum distance between adjacent points on the constellation circle.

In a real communication channel, noise can offset the received symbol from its reference position. If the offset crosses a decision boundary, the receiver can interpret one symbol as its neighbor. This is a symbol error, which can increase the Bit Error Rate (BER).

For $M > 8$, such as 16-PSK, adjacent phases are separated by 22.5° instead of 45° in 8-PSK. For a fixed target BER, coherent detection in additive white Gaussian noise generally requires a higher $E_s/N_0$ as $M$ grows. 16-PSK and higher orders remain possible when the link budget, phase tracking, coding, and required throughput permit; 8-PSK is one practical choice in some systems, not a universal limit.

QAM for higher bit rates

QAM provides a different distance and power trade-off for higher bits per symbol. Quadrature Amplitude Modulation (QAM). QAM allows symbols to have different amplitudes and phases. For selected constellation orders and the same average power, a grid can provide a larger minimum distance than a corresponding high-order PSK constellation. Amplitude variation also makes QAM sensitive to amplitude noise and nonlinear amplification.