QPSK Online Simulator

Simulator for QPSK Modulation Quadrature (4-PSK)

Bitstream (Even length)

Carrier Freq (Hz)

Samples Per Symbol

The Math Behind QPSK

Quadrature Phase Shift Keying (QPSK) is a form of digital modulation that transmits two bits per symbol by changing the phase of a carrier wave.

s(t) = A cos(2πf_ct + θ_n)

• Phase (θ_n): Each pair of bits (dibit) corresponds to a specific phase shift. In Gray coding, we use:
  "00" → π/4 (45°)

  "01" → 3π/4 (135°)

  "11" → 5π/4 (225°)

  "10" → 7π/4 (315°)
• Efficiency: Since 4 phases are used, QPSK carries double the data of BPSK in the same bandwidth.

Simulation Workflow

1. Bit Grouping (Dibits)

The input bitstream is split into pairs. A stream of "1,0,1,1" becomes [1,0] and [1,1].

2. Phase Mapping

Each pair is mapped to one of the four quadrature phases using Gray Coding to minimize bit errors.

3. Waveform Synthesis

For every symbol, a carrier wave segment is generated: y = cos(2π * fc * t + phase).

4. Continuous Visualization

The segments are stitched together and plotted using Plotly.js to show the final phase-modulated signal.