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Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). Any digital modulation scheme uses a finite number of distinct signals to represent digital data. Phase-shift keying (PSK) is a method of digital communication in which the phase of a transmitted signal is varied to convey information. Phase shift keying is a technique which shifts the period of a wave.

This is the same wave as the first, but its phase has been shifted. Notice that the period starts at the wave’s highest point. So what’s the point? It just so happens that we have shifted this wave by one quarter of the wave’s full period. We can shift it another quarter, if we wanted to, so the original wave would be shifted by half it’s period. And we could do it one more time, so that it would be shifted three quarters of it’s original period. This means we have 4 separate waves. So why not let each wave stand for some binary value? Since there are 4, we can let each wave signify 2 bits (00, 01, 10, 11):

This technique of letting each shift of a wave represent some bit value is phase shift keying. But the real key is to shift each wave relative to the wave that came before it. Above is an example. Please note that I just randomly chose binary vales for each wave, and that the values shown are not correct!. The correct pattern should be: 00 00 10 00 10 00.

There are several methods that can be used to accomplish PSK. More sophisticated forms of PSK exist. It is multiple phase-shift keying (MPSK), there are more than two phases, usually four (0, +90, -90, and 180 degrees) or eight (0, +45, -45, +90, -90, +135, -135, and 180 degrees). If there are four phases (m = 4), the  MPSK mode is called quadrature phase-shift keying or quaternary phase-shift keying (QPSK), and each phase shift represents two signal elements. If there are eight phases (m = 8), the MPSK mode is known as octal phase-shift keying (OPSK), and each phase shift represents three signal elements. In MPSK, data can be transmitted at a faster rate, relative to the number of phase changes per unit time, than is the case in BPSK.

The most common digital modulation techniques are :

•  Phase-shift keying (PSK):
•  Binary PSK (BPSK), using M=2 symbols
•  Quadrature PSK (QPSK), using M=4 symbols
•  8PSK, using M=8 symbols
•  16PSK, using M=16 symbols
•  Differential PSK (DPSK)
•  Differential QPSK (DQPSK)
•  Offset QPSK (OQPSK)
•  ð/4-QPSK

Quadrature phase-shift keying (QPSK) Constellation diagram for QPSK with Gray coding. Each adjacent symbol only differs by one bit. Sometimes known as quaternary or quadriphase PSK, 4-PSK, or 4- QAM[6], QPSK uses four points on the constellation diagram, equispaced around a circle. With four phases, QPSK can encode two bits per symbol, shown in the diagram with Gray coding to minimize the BER — twice the rate of BPSK. Analysis shows that this may be used either to double the data rate compared to a BPSK system while maintaining the bandwidth of the signal or to maintain the data-rate of BPSK but halve the bandwidth needed.As with BPSK, there are phase ambiguity problems at the receiver and differentially encoded QPSK is used more often in practice.

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:

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

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

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.

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 in next page.

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.

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.

Bit error rate

Although QPSK can be viewed as a quaternary modulation, it is easier to see it as two independently modulated quadrature carriers. With this interpretation, the even (or odd) bits are used to modulate the in-phase component of the carrier, while the odd (or even) bits are used to modulate the quadrature-phase component of the carrier. BPSK is used on both carriers and they can be independently demodulated.

As a result, the probability of bit-error for QPSK is the same as for BPSK :

However, in order to achieve the same bit-error probability as BPSK, QPSK uses twice the power (since two bits are transmitted simultaneously).

The symbol error rate is given by:

If the signal-to-noise ratio is high (as is necessary for practical QPSK systems) the probability of symbol error may be approximated :

QPSK signal in the time domain

The modulated signal is shown below for a short segment of a random binary data-stream. The two carrier waves are a cosine wave and a sine wave, as indicated by the signalspace analysis above. Here, the odd-numbered bits have been assigned to the in-phase component and the evennumbered bits to the quadrature component (taking the first bit as number 1). The total signal — the sum of the two components — is shown at the bottom. Jumps in phase can be seen as the PSK changes the phase on each component at the start of each bit-period. The topmost waveform alone matches the description given for BPSK above.

Timing diagram for QPSK. The binary data stream is shown beneath the time axis. The two signal components with their bit assignments are shown the top and the total, combined signal at the bottom. Note the abrupt changes in phase at some of the bit-period boundaries.

The binary data that is conveyed by this waveform is: 1 1 0 0 0 1 1 0.

•  The odd bits, highlighted here, contribute to the in-phase component: 1 1 0 0 0 1 1 0
•  The even bits, highlighted here, contribute to the quadrature-  phase component: 1 1 0 0 0 1 1 0

Variants

Offset QPSK (OQPSK)

Signal doesn’t cross zero, because only one bit of the symbol is changed at a time Offset quadrature phase-shift keying (OQPSK) is a variant of phase-shift keying modulation using 4 different values of the phase to transmit. It is sometimes called Staggered quadrature phase-shift keying (SQPSK).

Difference of the phase between QPSK and OQPSK

Taking four values of the phase (two bits) at a time to construct a QPSK symbol can allow the phase of the signal to jump by as much as 180° at a time. When the signal is lowpass filtered (as is typical in a transmitter), these phaseshifts result in large amplitude fluctuations, an undesirable quality in communication systems. By offsetting the timing of the odd and even bits by one bit-period, or half a symbolperiod, the in-phase and quadrature components will never change at the same time. In the constellation diagram shown on the right, it can be seen that this will limit the phase-shift to no more than 90° at a time. This yields much lower amplitude fluctuations than non-offset QPSK and is sometimes preferred in practice.

The picture on the right shows the difference in the behavior of the phase between ordinary QPSK and OQPSK. It can be seen that in the first plot the phase can change by 180° at once, while in OQPSK the changes are never greater than 90°.

The modulated signal is shown below for a short segment of a random binary data-stream. Note the half symbol-period offset between the two component waves. The sudden phase-shifts occur about twice as often as for QPSK (since the signals no longer change together), but they are less severe. In other words, the magnitude of jumps is smaller in OQPSK when compared to QPSK.

Timing diagram for offset-QPSK. The binary data stream is shown beneath the time axis. The two signal components with their bit assignments are shown the top and the total, combined signal at the bottom. Note the half-period offset between the two signal components.

#/4–QPSK

Dual constellation diagram for ð/4-QPSK. This shows the two separate constellations with identical Gray coding but rotated by 45° with respect to each other.

This final variant of QPSK uses two identical constellations which are rotated by 45° (ð/4 radians, hence the name) with respect to one another. Usually, either the even or odd symbols are used to select points from one of the constellations and the other symbols select points from the other constellation. This also reduces the phase-shifts from a maximum of 180°, but only to a maximum of 135° and so the amplitude fluctuations of ð / 4–QPSK are between OQPSK and non-offset QPSK.

 One property this modulation scheme possesses is that if the modulated signal is represented in the complex domain, it does not have any paths through the origin. In other words, the signal does not pass through the origin. This lowers the dynamical range of fluctuations in the signal which is desirable when engineering communications signals.

On the other hand, π/4–QPSK lends itself to easy demodulation and has been adopted for use in, for example, TDMA cellular telephone systems.

The modulated signal is shown below for a short segment of a random binary data-stream. The construction is the same as above for ordinary QPSK. Successive symbols are taken from the two constellations shown in the diagram. Thus, the first symbol (1 1) is taken from the ‘blue’ constellation and the second symbol (0 0) is taken from the ‘green’ constellation. Note that magnitudes of the two component waves change as they switch between constellations, but the total signal’s magnitude remains constant. The phase-shifts are between those of the two previous timing-diagrams.

Timing diagram for π/4-QPSK. The binary data stream is shown beneath the time axis. The two signal components with their bit assignments are shown the top and the total, combined signal at the bottom. Note that successive symbols are taken alternately from the two constellations, starting with the ‘blue’ one.

SOQPSK

The license-free shaped-offset QPSK (SOQPSK) is interoperable with Feher-patented QPSK (FQPSK), in the sense that an integrate-and-dump offset QPSK detector produces the same output no matter which kind of transmitter is used. These modulations carefully shape the I and Q waveforms such that they change very smoothly, and the signal stays constant-amplitude even during signal transitions. (Rather than traveling instantly from one symbol to another, or even linearly, it travels smoothly around the constant-amplitude circle from one symbol to the next). The standard description of SOQPSK-TG involves ternary symbols.

DPQPSK

Dual-polarization quadrature phase shift keying (DPQPSK) or dual-polarization QPSK

8PSK

8PSK (8 Phase Shift Keying) is a phase modulation algorithm. Phase modulation is a version of frequency modulation where the phase of the carrier wave is modulated to encode bits of digital information in each phase change. The “PSK” in 8PSK refers to the use of Phased Shift Keying. Phased Shift Keying is a form of phase modulation which is accomplished by the use of a discrete number of states. 8PSK refers to PSK with 8 sates. With half that number of states, you will  have QPSK. With twice the number of states as 8PSK, you will have 16PSK.Because QPSK has 8 possible states 8PSK is able to encode three bits per symbol. 8PSK is less tolerant of link degradation than QPSK, but provides more data capacity.