Principle of Phase-Shift Keying

Phase-Shift Keying (PSK) is a robust digital modulation method where information is encoded in discrete changes to the phase of a high-frequency carrier wave. Imagine a clock hand: to send information, we can instantly jump the hand to specific positions (phases) on the clock face. For the entire duration of the transmission, the length of the hand (the amplitude) and the speed at which it rotates (the frequency) remain constant.

This focus on phase makes PSK schemes inherently resilient to amplitude-based noise and distortions, which are common issues in many transmission channels.

Visualizing PSK: Constellation Diagrams

The most intuitive way to visualize a PSK scheme is through a Constellation Diagram. Each unique phase used by the modulation is represented as a point. Because PSK keeps the amplitude constant, all points lie on a circle centered at the origin.

The Simplest Form: Binary PSK (BPSK)

BPSK is the most basic form of PSK. It uses two phases to represent the two binary states: '0' and '1'.

• Phases: The two phases are chosen to be maximally separated for the best noise immunity. This means they are $180^\circ$ ($\pi$ radians) apart. For example:
  • Bit '0' → 180° phase
  • Bit '1' → 0° phase
• Data Rate: Since each symbol represents one state, BPSK encodes 1 bit per symbol.
• Noise Immunity: BPSK is extremely robust. An error can only occur if noise in the channel shifts the signal's phase by more than $\pm 90^\circ$, which requires a significant amount of noise power.

BPSK Constellation Diagram

The BPSK constellation consists of just two points. With a 0°/180° phase separation, these points lie on the horizontal (I) axis at equal distances from the origin.

Doubling the Speed: Quadrature PSK (QPSK)

QPSK (also called 4-PSK) is the next step up, using four distinct phases. This allows it to transmit twice as much data as BPSK without increasing the required bandwidth.

• Phases: The four phases are typically spread evenly around the circle, $90^\circ$ apart (e.g., 45°, 135°, 225°, 315°).
• Data Rate: With four states ($2^2 = 4$), QPSK can encode 2 bits per symbol. Each symbol represents a unique two-bit sequence, called a dibit (e.g., '00', '01', '11', '10').
• Gray Coding: To minimize errors, dibits are assigned to phases using Gray Coding. This means adjacent points in the constellation differ by only one bit. If noise causes the receiver to mistake '01' for its neighbor '11', only one bit is wrong, not two.

Generalization: M-ary PSK (M-PSK)

The principle of PSK can be extended to use $M$ different phases, where $M$ is a power of 2. This is called M-ary PSK.

• An M-PSK scheme encodes $N = \log_2(M)$ bits per symbol.
• Examples include BPSK ($M=2$), QPSK ($M=4$), and 8-PSK ($M=8$, which encodes 3 bits per symbol).
• The Trade-off: While increasing $M$ improves spectral efficiency (more bits/s per Hz), it comes at a significant cost. As $M$ grows, the points on the constellation move closer together. This reduces the separation between phases, making the system much more susceptible to noise and phase distortions.
• Practical Limits: Due to this diminishing noise immunity, 8-PSK is often considered the highest practical order of PSK in common use. For higher efficiency, schemes like QAM, which also vary the amplitude, are preferred.

A Practical Solution: Differential PSK (DPSK)

A significant challenge for standard PSK is coherent detection. The receiver needs a perfectly stable phase reference to correctly determine the phase of the incoming signal. DPSK cleverly bypasses this problem.

In DPSK, information is not encoded in the absolute phase of a symbol, but in the change of phase between consecutive symbols.

• Example (DBPSK):
  • To send a '1', the phase is changed by 180°.
  • To send a '0', the phase is kept the same (0° change).
• Advantages: The receiver is much simpler, as it only needs to compare the phase of the current symbol with the previous one. This makes it robust against slow phase drifts introduced by the transmission channel.
• Disadvantages: DPSK can be slightly more prone to errors than an ideal coherent system. An error in detecting one symbol can cause a subsequent error, a phenomenon known as error propagation.

Pushing the Limits: Dual-Polarization QPSK (DP-QPSK)

DP-QPSK is an advanced modulation technique used in modern high-capacity systems (like fiber optics) to dramatically increase throughput. It exploits another property of electromagnetic waves: polarization.

The principle is to transmit two independent QPSK signals simultaneously on the same carrier frequency, but using two different, orthogonal polarizations (e.g., vertical and horizontal).

This effectively doubles the spectral efficiency. Since each QPSK signal carries 2 bits/symbol, DP-QPSK achieves an effective rate of 4 bits per symbol without using any additional frequency bandwidth. It offers a similar capacity to 16-QAM but can have better performance against certain channel impairments.

Interactive QPSK – Constellation and Time Waveform

QPSK modulated signal

Constellation diagram