|AM · SSB · FM · PM · QAM · SM|
|OOK · FSK · ASK · PSK · QAM|
MSK · CPM · PPM · TCM · OFDM
|FHSS · DSSS|
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). In Telecommunications, modulation is the process of varying a periodic Waveform, i In Telecommunications, modulation is the process of varying a periodic Waveform, i Amplitude modulation ( AM) is a technique used in electronic communication most commonly for transmitting information via a Radio Carrier wave Single-sideband modulation ( SSB) is a refinement of Amplitude modulation that more efficiently uses electrical power and bandwidth. Phase modulation (PM is a form of Modulation that represents information as variations in the instantaneous phase of a Carrier wave. Space modulation is a radio Amplitude Modulation technique used in Instrument Landing Systems that incorporates the use of multiple antennas fed with various radio In Telecommunications, modulation is the process of varying a periodic Waveform, i On-off keying ( OOK) is a type of Modulation that represents Digital Data as the presence or absence of a Carrier wave. Frequency-shift keying (FSK is a Frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a Carrier wave Amplitude-shift keying ( ASK) is a form of Modulation that represents Digital Data as variations in the Amplitude of a Carrier In Digital modulation, Minimum-shift keying (MSK is a type of continuous phase Frequency-shift keying that was developed in the late 1960s Continuous phase modulation ( CPM) is a method for modulation of data commonly used in Wireless modems In contrast to other coherent digital Phase Pulse-position modulation is a form of signal Modulation in which M message bits are encoded by transmitting asingle pulse in one of 2^M possible time-shifts In Telecommunication, trellis modulation (also known as trellis coded modulation, or simply TCM) is a modulation scheme which allows highly efficient Orthogonal frequency-division multiplexing ( OFDM) — essentially identical to Coded OFDM ( COFDM) and Discrete multi-tone modulation ( Spread-spectrum techniques are methods by which Energy generated in a particular bandwidth is deliberately spread in the Frequency domain, resulting Frequency-hopping spread spectrum ( FHSS) is a method of transmitting radio signals by rapidly switching a carrier among many frequency channels, using In Telecommunications direct-sequence spread spectrum ( DSSS) is a Modulation technique A digital system uses discrete (discontinuous values usually but not always Symbolized Numerically (hence called "digital" to represent information for In Telecommunications, modulation is the process of varying a periodic Waveform, i Debt AIDS Trade in Africa (or DATA) is a Multinational non-government organization founded in January 2002 in London by U2 's The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0 In the fields of communications, Signal processing, and in Electrical engineering more generally a signal is any time-varying or spatial-varying quantity In Telecommunications, a carrier wave, or carrier is a Waveform (usually Sinusoidal) that is modulated (modified with an input signal
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 bits. The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 0 and 1. A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication 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).
Alternatively, instead of using the bit patterns to set the phase of the wave, it can instead be used to change it by a specified amount. The demodulator then determines the changes in the phase of the received signal rather than the phase itself. Since this scheme depends on the difference between successive phases, it is termed differential phase-shift keying (DPSK). DPSK can be significantly simpler to implement than ordinary PSK since there is no need for the demodulator to have a copy of the reference signal to determine the exact phase of the received signal (it is a non-coherent scheme). In exchange, it produces more erroneous demodulations. The exact requirements of the particular scenario under consideration determine which scheme is used.
All convey data by changing some aspect of a base signal, the carrier wave, (usually a sinusoid) in response to a data signal. In Telecommunications, modulation is the process of varying a periodic Waveform, i A digital system uses discrete (discontinuous values usually but not always Symbolized Numerically (hence called "digital" to represent information for Amplitude-shift keying ( ASK) is a form of Modulation that represents Digital Data as variations in the Amplitude of a Carrier Frequency-shift keying (FSK is a Frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a Carrier wave In Telecommunications, a carrier wave, or carrier is a Waveform (usually Sinusoidal) that is modulated (modified with an input 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:
A convenient way to represent PSK schemes is on a constellation diagram. A constellation diagram is a representation of a signal modulated by a digital Modulation scheme such as Quadrature amplitude modulation or Phase-shift keying This shows the points in the Argand plane where, in this context, the real and imaginary axes are termed the in-phase and quadrature axes respectively due to their 90° separation. In Mathematics, the complex plane is a geometric representation of the Complex numbers established by the real axis and the orthogonal imaginary axis In Mathematics, the real numbers may be described informally in several different ways Geometric interpretation Geometrically imaginary numbers are found on the vertical axis of the complex number plane 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.
In PSK, the constellation points chosen are usually positioned with uniform angular spacing around a circle. A constellation diagram is a representation of a signal modulated by a digital Modulation scheme such as Quadrature amplitude modulation or Phase-shift keying In Geometry and Trigonometry, an angle (in full plane angle) is the figure formed by two rays sharing a common Endpoint, called Circles are simple Shapes of Euclidean geometry consisting of those points in a plane which are at a constant Distance, called the 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 2.
For determining error-rates mathematically, some definitions will be needed:
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. A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication In Telecommunications and Computing, bitrate (sometimes written bit rate, data rate or as a Variable R or f b In Digital communications, symbol rate, also known as baud or modulation rate is the number of symbol changes (signalling events made to the transmission medium per second In Science, and especially in Physics and Telecommunication, noise is fluctuations in and the addition of external factors to the stream of target In Statistical signal processing and Physics, the spectral density, power spectral density ( PSD) or energy spectral density ( The watt (symbol W) is the SI derived unit of power, equal to one Joule of energy per Second. The hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second. Probability is the likelihood or chance that something is the case or will happen The normal distribution, also called the Gaussian distribution, is an important family of Continuous probability distributions applicable in many fields It is a scaled form of the complementary Gaussian error function:
The error-rates quoted here are those in additive white Gaussian noise (AWGN). Explanation In communications, the additive white Gaussian noise ( AWGN) channel model is one in which the only impairment is the linear addition of White noise is a random signal (or process with a flat Power spectral density. Gaussian noise is noise that has a Probability density function (abbreviated pdf of the Normal distribution (also known as Gaussian distribution Explanation In communications, the additive white Gaussian noise ( AWGN) channel model is one in which the only impairment is the linear addition of These error rates are lower than those computed in fading channels, hence, are a good theoretical benchmark to compare with. This is about the phenomenon of loss of signal in telecommunications
Owing to PSK's simplicity, particularly when compared with its competitor quadrature amplitude modulation, it is widely used in existing technologies.
The wireless LAN standard, IEEE 802.11b, uses a variety of different PSKs depending on the data-rate required. A wireless LAN or WLAN is a Wireless Local area network, which is the linking of two or more computers or devices without using wires IEEE 80211b-1999 or 80211b, is an amendment to the IEEE 80211 specification that extended throughput to up to 11 Mbit/s using the same 2 At the basic-rate of 1 Mbit/s, it uses DBPSK. A megabit is a unit of Information or computer storage abbreviated Mbit (or Mb) To provide the extended-rate of 2 Mbit/s, DQPSK is used. In reaching 5. 5 Mbit/s and the full-rate of 11 Mbit/s, QPSK is employed, but has to be coupled with complementary code keying. Complementary Code Keying (CCK is a Modulation scheme used with Wireless networks (WLANs that employ the IEEE 802 The higher-speed wireless LAN standard, IEEE 802.11g has eight data rates: 6, 9, 12, 18, 24, 36, 48 and 54 Mbit/s. IEEE 80211g-2003 or 80211g, is an amendment to the IEEE 80211 specification that extended throughput to up to 54 Mbit/s using the same 2 The 6 and 9 Mbit/s modes use BPSK. The 12 and 18 Mbit/s modes use QPSK. The fastest four modes use forms of quadrature amplitude modulation.
Because of its simplicity BPSK is appropriate for low-cost passive transmitters, and is used in RFID standards such as ISO 14443 which has been adopted for biometric passports, credit cards such as American Express's ExpressPay, and many other applications. Radio-frequency identification ( RFID) is an automatic identification method relying on storing and remotely retrieving data using devices called RFID tags or ISO/IEC 14443 defines a Proximity card used for Identification that usually uses the standard Credit card Form factor defined by ISO/IEC See also Passport A biometric passport is a combined paper and electronic identity document that uses Biometrics to authenticate the identity of travelers American Express ( sometimes known as " AmEx " or " Amex " is a diversified global Financial services company headquartered in Newer American Express Credit cards come with a feature known as ExpressPay.
Bluetooth 2 will use π / 4-DQPSK at its lower rate (2 Mbit/s) and 8-DPSK at its higher rate (3 Mbit/s) when the link between the two devices is sufficiently robust. Bluetooth is a wireless protocol utilizing short-range communications technology facilitating data transmission over short distances from fixed and/or mobile devices creating wireless Bluetooth 1 modulates with Gaussian minimum-shift keying, a binary scheme, so either modulation choice in version 2 will yield a higher data-rate. A similar technology, IEEE 802.15.4 (the wireless standard used by ZigBee) also relies on PSK. ZigBee is the name of a specification for a suite of high level communication protocols using small IEEE 802. 15. 4 allows the use of two frequency bands: 868–915 MHz using BPSK and at 2. The hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second. 4 GHz using OQPSK. The hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second.
Notably absent from these various schemes is 8-PSK. This is because its error-rate performance is close to that of 16-QAM — it is only about 0. 5 dB better — but its data rate is only three-quarters that of 16-QAM. The decibel ( dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power or intensity relative to Thus 8-PSK is often omitted from standards and, as seen above, schemes tend to 'jump' from QPSK to 16-QAM (8-QAM is possible but difficult to implement).
BPSK is the simplest form of PSK. It uses two phases which are separated by 180° and so can also be termed 2-PSK. It does not particularly matter exactly where the constellation points are positioned, and in this figure they are shown on the real axis, at 0° and 180°. This modulation is the most robust of all the PSKs since it takes serious distortion to make the demodulator reach an incorrect decision. It is, however, only able to modulate at 1 bit/symbol (as seen in the figure) and so is unsuitable for high data-rate applications when bandwidth is limited.
Since there is only one bit per symbol, this is also the symbol error rate. In Telecommunication, an error ratio is the Ratio of the number of Bits elements, characters, or blocks incorrectly received Explanation In communications, the additive white Gaussian noise ( AWGN) channel model is one in which the only impairment is the linear addition of
In the presence of an arbitrary phase-shift introduced by the communications channel, the demodulator is unable to tell which constellation point is which. Channel, in communications (sometimes called communications channel) refers to the medium used to convey Information from a As a result, the data is often differentially encoded prior to modulation.
Binary data is often conveyed with the following signals:
where fc is the frequency of the carrier-wave.
Hence, the signal-space can be represented by the single basis function
where 1 is represented by and 0 is represented by . In Mathematics, particularly Numerical analysis, a basis function is an element of the basis for a Function space. This assignment is, of course, arbitrary.
The use of this basis function is shown at the end of the next section in a signal timing diagram. The topmost signal shows PSK modulating a cosine wave, and is the signal that the BPSK modulator would produce. The bit-stream that causes this output is shown above the signal (the other parts of this figure are relevant only to QPSK).
Sometimes known as quaternary or quadriphase PSK or 4-PSK, 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. Name Bell Labs researcher Frank Gray introduced the term reflected binary code in his 1947 patent application remarking that the code had "as 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.
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:
As with BPSK, there are phase ambiguity problems at the receiver and differentially encoded QPSK is more normally used in practice. Signal-to-noise ratio (often abbreviated SNR or S/N) is an Electrical engineering concept also used in other fields (such as scientific Measurements
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 π / 4, 3π / 4, 5π / 4 and 7π / 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. In Mathematics, particularly Numerical analysis, a basis function is an element of the basis for a Function space.
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 below.
The binary data that is conveyed by this waveform is: 1 1 0 0 0 1 1 0.
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).
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. A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication When the signal is low-pass filtered (as is typical in a transmitter), these phase-shifts 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 symbol-period, 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.
This final variant of QPSK uses two identical constellations which are rotated by 45° (π / 4 radians, hence the name) with respect to one another. Usually, either the even or odd data bits are used to select points from one of the constellations and the other bits 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 π / 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. This article is about the medium access technology The name "TDMA" is also commonly used in the United States to refer to D-AMPS, which is a mobile telephone
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.
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. In Telecommunication, a ternary signal is a signal that can assume at any given instant one of three Significant conditions such as power level
Any number of phases may be used to construct a PSK constellation but 8-PSK is usually the highest order PSK constellation deployed. With more than 8 phases, the error-rate becomes too high and there are better, though more complex, modulations available such as quadrature amplitude modulation (QAM). Although any number of phases may be used, the fact that the constellation must usually deal with binary data means that the number of symbols is usually a power of 2 — this allows an equal number of bits-per-symbol.
For the general M-PSK there is no simple expression for the symbol-error probability if M > 4. Unfortunately, it can only be obtained from:
This may be approximated for high M and high Eb / N0 by:
The bit-error probability for M-PSK can only be determined exactly once the bit-mapping is known. However, when Gray coding is used, the most probable error from one symbol to the next produces only a single bit-error and
The graph on the left compares the bit-error rates of BPSK, QPSK (which are the same, as noted above), 8-PSK and 16-PSK. It is seen that higher-order modulations exhibit higher error-rates; in exchange however they deliver a higher raw data-rate.
Bounds on the error rates of various digital modulation schemes can be computed with application of the union bound to the signal constellation. In Probability theory, Boole's inequality, named after George Boole, (also known as the union bound) says that for any finite or Countable
As mentioned for BPSK and QPSK there is an ambiguity of phase if the constellation is rotated by some effect in the communications channel the signal passes through. Channel, in communications (sometimes called communications channel) refers to the medium used to convey Information from a This problem can be overcome by using the data to change rather than set the phase.
For example, in differentially-encoded BPSK a binary '1' may be transmitted by adding 180° to the current phase and a binary '0' by adding 0° to the current phase. In differentially-encoded QPSK, the phase-shifts are 0°, 90°, 180°, -90° corresponding to data '00', '01', '11', '10'. This kind of encoding may be demodulated in the same way as for non-differential PSK but the phase ambiguities can be ignored. Thus, each received symbol is demodulated to one of the M points in the constellation and a comparator then computes the difference in phase between this received signal and the preceding one. In Electronics, a comparator is a device which compares two Voltages or currents and switches its output to indicate which is larger The difference encodes the data as described above.
The modulated signal is shown below for both DBPSK and DQPSK as described above. It is assumed that the signal starts with zero phase, and so there is a phase shift in both signals at t = 0.
Analysis shows that differential encoding approximately doubles the error rate compared to ordinary M-PSK but this may be overcome by only a small increase in Eb / N0. Furthermore, this analysis (and the graphical results below) are based on a system in which the only corruption is additive white Gaussian noise. However, there will also be a physical channel between the transmitter and receiver in the communication system. This channel will, in general, introduce an unknown phase-shift to the PSK signal; in these cases the differential schemes can yield a better error-rate than the ordinary schemes which rely on precise phase information.
At the kth time-slot call the bit to be modulated bk, the differentially-encoded bit ek and the resulting modulated signal mk(t). Assume that the constellation diagram positions the symbols at ±1 (which is BPSK). The differential encoder produces:
where indicates binary or modulo-2 addition. The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 0 and 1. In Mathematics, modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic) is a system of Arithmetic for Integers
So ek only changes state (from binary '0' to binary '1' or from binary '1' to binary '0') if bk is a binary '1'. Otherwise it remains in its previous state. This is the description of differentially-encoded BPSK given above.
The received signal is demodulated to yield ek = ±1 and then the differential decoder reverses the encoding procedure and produces:
Therefore, bk = 1 if ek and ek − 1 differ and bk = 0 if they are the same. Hence, if both ek and ek − 1 are inverted, bk will still be decoded correctly. Thus, the 180° phase ambiguity does not matter.
Differential schemes for other PSK modulations may be devised along similar lines. The waveforms for DPSK are the same as for differentially-encoded PSK given above since the only change between the two schemes is at the receiver.
The BER curve for this example is compared to ordinary BPSK on the right. As mentioned above, whilst the error-rate is approximately doubled, the increase needed in Eb / N0 to overcome this is small. The performance degradation is a result of noncoherent transmission - in this case it refers to the fact that tracking of the phase is completely ignored.
For a signal that has been differentially encoded, there is an obvious alternative method of demodulation. Instead of demodulating as usual and ignoring carrier-phase ambiguity, the phase between two successive received symbols is compared and used to determine what the data must have been. When differential encoding is used in this manner, the scheme is known as differential phase-shift keying (DPSK). Note that this is subtly different to just differentially-encoded PSK since, upon reception, the received symbols are not decoded one-by-one to constellation points but are instead compared directly to one another.
Call the received symbol in the kth timeslot rk and let it have phase φk. Assume without loss of generality that the phase of the carrier wave is zero. Denote the AWGN term as nk. Then
The decision variable for the k − 1th symbol and the kth symbol is the phase difference between rk and rk − 1. That is, if rk is projected onto rk − 1, the decision is taken on the phase of the resultant complex number:
where superscript * denotes complex conjugation. In Mathematics, the complex conjugate of a Complex number is given by changing the sign of the Imaginary part. In the absence of noise, the phase of this is θk − θk − 1, the phase-shift between the two received signals which can be used to determine the data transmitted.
The probability of error for DPSK is difficult to calculate in general, but, in the case of DBPSK it is:
which, when numerically evaluated, is only slightly worse than ordinary BPSK, particularly at higher Eb / N0 values.
Using DPSK avoids the need for possibly complex carrier-recovery schemes to provide an accurate phase estimate and can be an attractive alternative to ordinary PSK.
In optical communications, the data can be modulated onto the phase of a laser in a differential way. Optical communication is any form of Telecommunication that uses Light as the transmission medium A laser is a device that emits Light ( Electromagnetic radiation) through a process called Stimulated emission. The modulation is a laser which emits a continuous wave, and a Mach-Zehnder modulator which receives electrical binary data. A continuous wave or continuous waveform ( CW) is an Electromagnetic wave of constant Amplitude and Frequency; and in Mathematical For the case of BPSK for example, the laser transmits the field unchanged for binary '1', and with reverse polarity for '0'. The demodulator consists of a delay line interferometer which delays one bit, so two bits can be compared at one time. A delay line interferometer ( DLI) can be a Mach-Zehnder interferometer or Michelson interferometer based on two-beam Interference, in which one In further processing, a photo diode is used to transform the optical field into an electric current, so the information is changed back into its original state. A photodiode is a type of Photodetector capable of converting Light into either current or Voltage, depending upon the mode of operation The optical field is a term used in physics and vector calculus to designate the electric field shown as E in the Electromagnetic wave equation which can be derived
The bit-error rates of DBPSK and DQPSK are compared to their non-differential counterparts in the graph to the right. The loss for using DBPSK is small enough compared to the complexity reduction that it is often used in communications systems that would otherwise use BPSK. For DQPSK though, the loss in performance compared to ordinary QPSK is larger and the system designer must balance this against the reduction in complexity.
Like all M-ary modulation schemes with M = 2^b symbols, when given exclusive access to a fixed bandwidth, the channel capacity of any phase shift keying modulation scheme rises to a maximum of b bits/s as the SNR increases.
The notation and theoretical results in this article are based on material presented in the following sources: