Quadrature phase shift keying

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The quadrature phase shift keying or four phase modulation (English Quadrature Phase Shift Keying or Quaternary Phase Shift Keying , QPSK ) is a digital modulation method in telecommunications and a form of phase shift keying (PSK) . With QPSK, two bits can be transmitted per symbol . This doubles the utilization of the available bandwidth ( spectral efficiency ) compared to binary phase shift keying (PSK ).


Constellation diagram QPSK (also known as 4- QAM )
Spectrum of a QPSK signal

An essential property is that the four symbol points drawn in the complex plane in the adjacent constellation diagram are exactly the same distance from the zero point in terms of amount. This means that the amplitude does not carry any information, only the phase . The name of this modulation technique is derived from this. Each information point is a carrier of two information bits. The QPSK gives the same results as a 4- QAM . With a QAM, however, two mutually orthogonal carriers of the same frequency are modulated in their amplitude. The resultant of both carriers again has amplitude and phase, which is then linked to a symbol - in terms of transmission technology, however, there is no phase modulation with QAM, but rather a QDSB (AM with suppressed carrier).

The following pictures show two DVB-S signals. In the case of the weaker signal, it can be seen that with a large number of points a clear assignment to the constellation diagram shown on the right is no longer possible, which leads to almost 8% of the data being lost. Thanks to forward error correction , the channel can at least be viewed with strong artifact formation , while all errors can be corrected with a medium-strong signal and an error-free image can be reproduced.


The serial data stream of an NRZ signal is first split into two parallel paths using a demultiplexer . Now two bits, so-called dibits , can be processed. The function of a complex symbol with real and imaginary parts is assigned to these dibits. Two sinusoidal signals of the same frequency are used as carriers , one of which is phase-shifted by 90 ° (cosine signal). The QPSK signal is the addition of two PSK signals. The reception process works in reverse.

QPSK is used for signal transmission in digital satellite channels (e.g. DVB-S ), for terrestrial broadcasting of digital signals and also for wired transmission methods.


π / 4-QPSK

Sets of constellation points shown in two colors that are rotated by π / 4 to each other

A major extension of QPSK is π / 4-QPSK. With conventional QPSK there is the problem that the transition between two diagonal transmission symbol points in the complex plane leads through the zero point. In the transition between these diagonal transmission symbols, this means that the amplitude, the so-called envelope, is reduced to practically zero. On the receiver side, it makes the necessary synchronization more difficult and, due to non-linearities in the transmission path, promotes signal distortion and undesired intermodulation .

Timing diagram for a π / 4 QPSK signal

One remedy is π / 4-QPSK. Independent of the user data, an additional phase jump of π / 4 (45 °) and changing direction is made after each transmission symbol. This results in two alternating constellation diagrams as shown in the adjacent figure by the two colors. This ensures that the transition between two symbols never goes through the origin, i.e. H. a sufficiently large carrier amplitude is always sent. In addition, the clock synchronization on the receiver side is made easier because, regardless of the useful data and its coding, there are always regular phase jumps in the received signal.


With offset QPSK, each half step lies on a constellation point
Time diagram for an offset QPSK signal

Another possibility of avoiding the passage through the zero point, i.e. a reduction in the amplitude, is offered by the offset QPSK. The real part and the imaginary part of the complex symbol are sent offset by half a symbol duration so that the maximum change with a half step is only 90 ° instead of 180 ° as with the conventional QPSK. One can clearly imagine that the course of the state transitions follows the shape of the square delimited by the four states and can no longer take the diagonal path through the zero point. Conversely, the constellation point on which the signal is located changes at twice the rate of the symbol duration. If only the I or Q component is considered, only a rate of change equal to the symbol duration is shown.

Differential QPSK (DQPSK)

With differential QPSK, an upstream differential coding is used to avoid the ambiguity of the phase points at the receiver. With differential QPSK, the information is not assigned to the individual symbols in the constellation diagram, but is transmitted in the relative change in phase position in relation to the previous symbol. This results in four possible relative phase rotations of 0 (0 °), π / 2 (90 °), π (180 °) and 3π / 2 (270 °) to the previous symbol, which means that the information of two bits per symbol can be transmitted . The advantage of the unnecessary synchronization of the phase position between transmitter and receiver is bought by increasing the bit error rate and reducing the performance of any forward error correction that may be present , since every reception error can affect two symbols with a total of four bits.


Fax machines : A well-known application in which a QPSK signal can also be overheard is the transmission of black and white images ( facsimiles ) over the telephone network. Unmodulated, the carrier would sound like a pure sine tone. The modulation makes the signal more broadband. The carrier, which is keyed quickly and continuously, then sounds like a noise.

This type of modulation is now also used in HSDPA technology in UMTS networks. Here the data rate is increased from 384 kbit / s to approx. 2 Mbit / s.