Binary Phase-Shift Keying (BPSK)

Principle of BPSK

BPSK is the binary form of Phase-Shift Keying (PSK). The term "Binary" indicates that it uses only two distinct states to represent the two binary digits: '0' and '1'. This makes it a one-to-one encoding scheme, where one symbol corresponds to exactly one bit of information.

BPSK uses two phase states of a constant-frequency carrier wave to represent data. The two states are antipodal and separated by 180 degrees $(\pi \text{ radians})$, which maximizes their Euclidean separation for a fixed symbol energy.

Encoding '0's and '1's

A 180° phase shift changes the sign of the carrier. A common mapping is:

• Binary '1' is encoded with a phase of 0°. The carrier wave continues without any change.
• Binary '0' is encoded with a phase of 180°. The carrier wave is inverted at the start of the bit's duration.

The choice of mapping (e.g., '1' to $0^{\circ}$ and '0' to $180^{\circ}$, or vice versa) is arbitrary, as long as both the transmitter and receiver agree on the same convention.

The BPSK Constellation Diagram

A standard way to visualize digital modulation schemes is with a constellation diagram. It plots the symbols on a two-dimensional map defined by In-phase (I) and Quadrature (Q) axes.

• Two Points: Since BPSK has only two symbols, its constellation consists of just two points.
• Constant Amplitude: Both symbols have the same amplitude and symbol energy, so they lie at the same distance from the origin (the center of the plot).
• Location on I-axis:As the phases used are 0° and 180°, both points lie on the horizontal I-axis. The symbol for a 0° phase (e.g., bit '1') is on the positive side, and the symbol for 180° (e.g., bit '0') is on the negative side. There is no Q-component.

BPSK: Noise Performance and Applications

Error Resilience

For an I-axis BPSK constellation, coherent detection decides from the sign of the I component. The decision boundary is the vertical Q-axis at I = 0. The two antipodal points have the largest separation for a fixed symbol energy, which limits the effect of additive noise. With equiprobable bits, two-sided AWGN power spectral density $N_0/2$, bit energy $E_b$, and ideal timing and carrier synchronization, the BER is $P_b = Q(\sqrt{2E_b/N_0}) = \frac{1}{2}\operatorname{erfc}(\sqrt{E_b/N_0})$. For a noiseless symbol, a static phase offset satisfying $|\phi| < 90^{\circ}$ preserves the decision sign, while synchronization errors and fading change this result. The formula shows how the ratio $E_b/N_0$ controls the Bit Error Rate (BER).

Spectral Efficiency and Use Cases

This noise performance has a bandwidth trade-off: BPSK has lower spectral efficiency. Since each symbol carries one bit, BPSK is less suitable for high-speed data transmission than higher-order schemes. Its reliability suits links where data integrity has priority over throughput.

Common Applications include:

• Satellite Communication: Used in systems where signal power is limited and the channel is noisy.
• Deep-Space Probes: NASA deep-space telemetry uses phase modulation, including residual-carrier BPSK, for low-data-rate spacecraft links such as Voyager.
• Contactless Interfaces: Some systems, including ISO/IEC 14443 Type B, use BPSK on a subcarrier.
• Basis for Complex Modulations: QPSK can be implemented with two independent BPSK branches on the in-phase and quadrature components.