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Phase-shift keying

Phase-shift keying is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Phase-shift keying rather than just read about it. In short: Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency carrier wave. The modulation is accomplished by varying the sine and cosine inputs at a precise time.

Phase-shift keying — main illustration
Phase-shift keying — illustration

Key takeaways

  • Phase-shift keying belongs to science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Phase-shift keying to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Phase-shift keying from memory before moving on to harder problems.

Reference excerpt

Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency carrier wave. The modulation is accomplished by varying the sine and cosine inputs at a precise time. It is widely used for wireless LANs, RFID and Bluetooth communication. Any digital modulation scheme uses a finite number of distinct signals to represent digital data. PSK uses a finite number of phases, each assigned a unique pattern of binary digits. Usually, each phase encodes an equal number of bits. Each pattern of bits forms the symbol that is represented by the particular phase. The demodulator, which is designed specifically for the symbol-set used by the modulator, determines the phase of the received signal and maps it back to the symbol it represents, thus recovering the original data. This requires the receiver to be able to compare the phase of the received signal to a reference signal – such a system is termed coherent (and referred to as CPSK). CPSK requires a complicated demodulator, because it must extract the reference wave from the received signal and keep track of it, to compare each sample to. Alternatively, the phase shift of each symbol sent can be measured with respect to the phase of the previous symbol sent. Because the symbols are encoded in the difference in phase between successive samples, this is called differential phase-shift keying (DPSK). DPSK can be significantly simpler to implement than ordinary PSK, as it is a 'non-coherent' scheme, i.e. there is no need for the demodulator to keep track of a reference wave. A trade-off is that it has more demodulation errors.

Introduction There are three major classes of digital modulation techniques used for transmission of digitally represented data:

Amplitude-shift keying (ASK) Frequency-shift keying (FSK) Phase-shift keying (PSK) All convey data by changing some aspect of a base signal, the carrier wave (usually a sinusoid), in response to a data signal. In the case of PSK, the phase is changed to represent the data signal. There are two fundamental ways of utilizing the phase of a signal in this way:

By viewing the phase itself as conveying the information, in which case the demodulator must have a reference signal to compare the received signal's phase against; or By viewing the change in the phase as conveying information – differential schemes, some of which do not need a reference carrier (to a certain extent). A convenient method to represent M-ary transmission PSK schemes is on a constellation diagram. This shows the points in the complex plane where, in this context, the real and imaginary axes are termed the in-phase and quadrature axes respectively due to their 90° separation. Such a representation on perpendicular axes lends itself to straightforward implementation. The amplitude of each point along the in-phase axis is used to modulate a cosine (or sine) wave and the amplitude along the quadrature axis to modulate a sine (or cosine) wave. By convention, in-phase modulates cosine and quadrature modulates sine. In PSK, the constellation points chosen are usually positioned with uniform angular spacing around a circle. This gives maximum phase-separation between adjacent points and thus the best immunity to corruption. They are positioned on a circle so that they can all be transmitted with the same energy. In this way, the moduli of the complex numbers they represent will be the same and thus so will the amplitudes needed for the cosine and sine waves. Two common examples are "binary phase-shift keying" (BPSK) which uses two phases, and "quadrature phase-shift keying" (QPSK) which uses four phases, although any number of phases may be used. Since the data to be conveyed are usually binary, the PSK scheme is usually designed with the number of constellation points being a power of two.

Definitions For determining error-rates mathematically, some definitions will be needed:

E b {\displaystyle E_{b}} , energy per bit

E s = n E b {\displaystyle E_{s}=nE_{b}} , energy per symbol with n bits

T b {\displaystyle T_{b}} , bit duration

T s {\displaystyle T_{s}} , symbol duration

1 2 N 0 {\displaystyle {\frac {1}{2}}N_{0}} , noise power spectral density (W/Hz)

P b {\displaystyle P_{b}} , probability of bit-error

P s {\displaystyle P_{s}} , probability of symbol-error

Q ( x ) {\displaystyle Q(x)} will give the probability that a single sample taken from a random process with zero-mean and unit-variance Gaussian probability density function will be greater or equal to x {\displaystyle x} . It is a scaled form of the complementary Gaussian error function:

… excerpt ends here. Continue reading the full article.

Illustrations

Phase-shift keying: Constellation diagram example for BPSK
Constellation diagram example for BPSK
Phase-shift keying: Constellation diagram for QPSK with Gray coding. Each adjacent symbol only differs by one bit.
Constellation diagram for QPSK with Gray coding. Each adjacent symbol only differs by one bit.
Phase-shift keying: 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.
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.
Phase-shift keying: 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.
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.
Phase-shift keying: Timing diagram for QPSK. The binary data stream is shown beneath the time axis. The two signal components with their bit assignments are shown at the top, and the total combined signal at the bottom. Note the abrupt changes in phase at some of the bit-period boundaries.
Timing diagram for QPSK. The binary data stream is shown beneath the time axis. The two signal components with their bit assignments are shown at the top, and the total combined signal at the bottom. Note the abrupt changes in phase at some of the bit-period boundaries.

Worked examples

Example 1 — a first encounter with Phase-shift keying

Start with the simplest possible case. Write down what Phase-shift keying claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Phase-shift keying before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Phase-shift keying ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Phase-shift keying

In research
Phase-shift keying appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Phase-shift keying in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Phase-shift keying is common in secondary-school and first-year university syllabi. It links to neighbouring topics Data transmission, Quantized radio modulation modes, so understanding it makes those chapters shorter.
In everyday life
Look for Phase-shift keying outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Phase-shift keying in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Phase-shift keying means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Phase-shift keying out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Phase-shift keying in simple terms?

Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency carrier wave. The modulation is accomplished by varying the sine and cosine inputs at a precise time.

Why does Phase-shift keying matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Phase-shift keying?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Phase-shift keying.

Tags

  • Data transmission
  • Quantized radio modulation modes

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