QPSK (quadrature phase shift keying)

Quadrature Phase Shift Keying (QPSK) is a modulation scheme used in digital communication systems to transmit data over a carrier wave. It is a form of phase modulation where the information is encoded by varying the phase of the carrier wave.

QPSK uses a constellation diagram to represent the modulation scheme. The constellation diagram is a two-dimensional plot with I (In-phase) and Q (Quadrature) axes. Each point in the constellation diagram represents a specific phase and amplitude combination of the carrier wave.

In QPSK, the information is encoded by dividing the input data stream into groups of two bits. Each group of two bits is mapped to a specific phase shift in the constellation diagram. There are four possible phase shifts in QPSK, representing the four possible combinations of the two bits. These phase shifts are 0°, 90°, 180°, and 270°.

To understand how the mapping is done, let's assume we have an input data stream and we want to transmit the binary sequence 10101100 using QPSK modulation.

1. The input binary sequence is divided into groups of two bits: 10, 10, 11, and 00.
2. Each group of two bits is mapped to a specific phase shift:

• 10 is mapped to 0° phase shift.
• 11 is mapped to 90° phase shift.
• 00 is mapped to 180° phase shift.
• 10 is mapped to 270° phase shift.

1. The resulting constellation points for each group of two bits are plotted on the constellation diagram. In this case, the constellation points would be (0°, 1), (90°, 1), (180°, -1), and (270°, 1), where the first value represents the phase shift and the second value represents the amplitude.
2. The carrier wave is modulated by the phase shifts obtained from the constellation points. Each phase shift is maintained for the duration of one symbol period.
3. The modulated carrier wave is transmitted through the channel.

At the receiver, the received signal is demodulated to extract the phase information. This is done by comparing the phase of the received signal with the reference phase values for each symbol. Based on the phase values, the original binary data is reconstructed.

QPSK is widely used in various communication systems, especially in applications where bandwidth efficiency is crucial. It provides twice the data rate compared to binary phase shift keying (BPSK) for the same bandwidth. However, QPSK is more susceptible to errors caused by noise and channel impairments due to the closer spacing between constellation points compared to BPSK. To mitigate these issues, error correction coding and modulation techniques such as differential QPSK (DQPSK) are often used in practical implementations.