2PSK

2PSK, commonly known as binary phase-shift keying (BPSK), is a binary phase modulation scheme used in digital communications. It encodes one bit per symbol by selecting one of two carrier phases separated by 180 degrees. The constellation consists of two points on the unit circle, opposite each other; the two phases are typically 0 and π radians. As a member of the PSK family, 2PSK features a constant envelope, offering robustness to amplitude variations and simplicity for coherent receivers.

The transmitted signal is typically represented in the passband as s(t) = sqrt(2P) cos(ωc t + θk), where θk ∈ {0, π} and P is the symbol energy. Each symbol carries one bit, so the symbol rate matches the bit rate for binary encoding. At the receiver, coherent detection uses a locally generated carrier with a phase reference to demodulate the signal. The decision rule assigns the bit 0 to θ = 0 and bit 1 to θ = π, based on the sign of the correlator output. Noncoherent detection is possible with differential encoding (DPSK), but standard 2PSK relies on carrier phase synchronization.

Performance in additive white Gaussian noise shows a symbol error rate and bit error rate characterized by P_e = Q(√(2 Eb/N0)), where Eb is the energy per bit and Q is the tail probability of the Gaussian. Because of its constant envelope, 2PSK is bandwidth-efficient relative to some other schemes but generally less spectrally efficient than higher-order PSK constellations. It remains widely used in systems requiring reliable performance with simple hardware, such as GPS C/A code modulation and various low-rate digital links.