Quadrature Phase-Shift Keying (QPSK)

QPSK is the abbreviation of Quadrature Phase-Shift Keying, which is the phase modulation method using four phases.

The signal of QPSK can be represented as:

$s(t) = A\cos{(2\pi ft+\phi)}$

where $$A$$ is the amplitude of carrier wave, $$f$$ is the frequency of carrier wave and $$\phi$$ is the phase which changes depending on the signals:

• when 11, $$\phi = \pi/4$$
• when 01, $$\phi = 3\pi/4$$
• when 00, $$\phi = -3\pi/4$$
• when 10, $$\phi = -\pi/4$$

Furthermore, expanding $$s(t)$$,

$\begin{eqnarray}s(t) & = & A\cos{(2\pi ft+\phi)} \& = & A\cos{(2\pi ft)}\cos{(\phi)} – A\sin{(2\pi ft)}\sin{(\phi)} \& = & \frac{I}{\sqrt{2}}A\cos{(2\pi ft)} – \frac{Q}{\sqrt{2}}A\sin{(2\pi ft)} \end{eqnarray}$

where $$I = \sqrt{2}\cos{\phi}$$ and $$Q = \sqrt{2}\sin{\phi}$$ also stasifies the following conditions:

• when 11, $$I = 1, Q = 1$$
• when 01, $$I = -1, Q = 1$$
• when 00, $$I = -1, Q = -1$$
• when 10, $$I = 1, Q = -1$$

Thus, QPSK can be regarded as the superposition of BPSK whose phase shifted for 90 degrees.

In this case, each BPSK signal are called I-channel and Q-channel.

QPSK signal can be plotted as:

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