BPSK maps binary 0 to a carrier phase of 0 degrees and binary 1 to 180 degrees (or vice versa). The constellation diagram shows two points diametrically opposite on a circle. The receiver multiplies the received signal by a local carrier (coherent detection) and integrates over the symbol period. The sign of the result determines the bit. The maximum phase separation (180 degrees) gives BPSK the best noise performance of any PSK scheme.

The theoretical BER for coherent BPSK in AWGN is: BER = Q(sqrt(2*Eb/N0)) = 0.5*erfc(sqrt(Eb/N0)). At Eb/N0 = 10 dB: BER = 3.9 x 10^-6. This is identical to QPSK (which transmits 2 bits/symbol at the same BER per bit). BPSK requires approximately 10 dB Eb/N0 for BER = 10^-5, about 3 dB less than uncoded 8PSK.

Deep space communications (maximum range, lowest SNR). GPS L1 C/A signal (1575.42 MHz, 1.023 Mcps BPSK spreading). CDMA pilot channels. Low-rate telemetry links. Any application prioritizing reliability over throughput. In modern systems like LTE/5G, BPSK is the fallback modulation at cell edge where SNR is lowest.

Signal Processing

BPSK

BPSK (Binary Phase Shift Keying) is a digital modulation scheme that encodes 1 bit per symbol by shifting the carrier phase between 0° and 180°. The maximum constellation point separation (d = 2√E_b) gives BPSK the best noise immunity of all M-PSK schemes. Theoretical BER = Q(√(2E_b/N₀)), achieving 10⁻⁵ at E_b/N₀ = 9.6 dB. Used in GPS, deep space, CDMA pilots, and LTE/5G cell-edge fallback.

Category: Signal Processing

Bits/Symbol: 1

Understanding BPSK

The BPSK signal can be expressed as s(t) = √(2E_b/T)·cos(2πf_ct + π·d_k), where d_k is 0 or 1. The two constellation points are at +1 and −1 on the real axis. Coherent detection requires carrier phase recovery (Costas loop or squaring loop) because the modulated signal has a suppressed carrier.

BPSK and QPSK have identical BER per bit at the same E_b/N₀. QPSK is more spectrally efficient (2 bits/symbol), so BPSK is used only when maximum robustness or simplest implementation is needed. Differential BPSK (DBPSK) avoids carrier recovery but has approximately 1 dB worse performance.

BPSK BER

BER = Q(√(2E_b/N₀))
= ½·erfc(√(E_b/N₀))

Key points:
E_b/N₀ = 7 dB: BER = 1.2×10⁻³
E_b/N₀ = 10 dB: BER = 3.9×10⁻⁶
E_b/N₀ = 13 dB: BER = 2.3×10⁻⁹

PSK Modulation Comparison

Scheme	Bits/Sym	E_b/N₀ @10⁻⁵	Spectral Eff.
BPSK	1	9.6 dB	1 bps/Hz
QPSK	2	9.6 dB	2 bps/Hz
8PSK	3	13.0 dB	3 bps/Hz
16QAM	4	13.4 dB	4 bps/Hz

Common Questions

Frequently Asked Questions

How it works?

Phase 0°=bit 0, 180°=bit 1. Max separation gives best noise immunity. Coherent detection with carrier recovery.

BER?

Q(√(2Eb/N0)). Same as QPSK per bit. 10⁻⁵ at 9.6 dB. Best of all PSK schemes.

Where used?

GPS L1, deep space, CDMA pilots, LTE/5G cell-edge. Any link prioritizing reliability over throughput.

Related Terms

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Signal Processing

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