Editing Phase-shift keying (section)

===Implementation===
The implementation of QPSK is more general than that of BPSK and also indicates the implementation of higher-order PSK. Writing the symbols in the constellation diagram in terms of the sine and cosine waves used to transmit them:

:<math>s_n(t) = \sqrt{\frac{2E_s}{T_s}} \cos \left(2 \pi f_c t + (2n - 1)\frac{\pi}{4}\right),\quad n = 1, 2, 3, 4.</math>

This yields the four phases π/4, 3π/4, 5π/4 and 7π/4 as needed.

This results in a two-dimensional signal space with unit [[basis functions]]

:<math>\begin{align}
  \phi_1(t) &= \sqrt{\frac{2}{T_s}} \cos\left(2\pi f_c t\right) \\
  \phi_2(t) &= \sqrt{\frac{2}{T_s}} \sin\left(2\pi f_c t\right)
\end{align}</math>

The first basis function is used as the in-phase component of the signal and the second as the quadrature component of the signal.

Hence, the signal constellation consists of the signal-space 4 points

:<math>\begin{pmatrix} \pm\sqrt{\frac{E_s}{2}} & \pm\sqrt{\frac{E_s}{2}} \end{pmatrix}.</math>

The factors of 1/2 indicate that the total power is split equally between the two carriers.

Comparing these basis functions with that for BPSK shows clearly how QPSK can be viewed as two independent BPSK signals. Note that the signal-space points for BPSK do not need to split the symbol (bit) energy over the two carriers in the scheme shown in the BPSK constellation diagram.

QPSK systems can be implemented in a number of ways. An illustration of the major components of the transmitter and receiver structure are shown below.

[[File:Transmisor QPSK 2.png|thumb|600px|center|Conceptual transmitter structure for QPSK. The binary data stream is split into the in-phase and quadrature-phase components. These are then separately modulated onto two orthogonal basis functions. In this implementation, two sinusoids are used. Afterwards, the two signals are superimposed, and the resulting signal is the QPSK signal. Note the use of polar [[non-return-to-zero]] encoding. These encoders can be placed before for binary data source, but have been placed after to illustrate the conceptual difference between digital and analog signals involved with digital modulation.]]

[[File:Receiver QPSK.PNG|thumb|600px|center|Receiver structure for QPSK. The matched filters can be replaced with correlators. Each detection device uses a reference threshold value to determine whether a 1 or 0 is detected.]]