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67-439: 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

134-441: A constellation diagram , showing the amplitude of the I signal at the x-axis, and the amplitude of the Q signal at the y-axis, for each symbol. PSK and ASK, and sometimes also FSK, are often generated and detected using the principle of QAM. The I and Q signals can be combined into a complex-valued signal I + jQ (where j is the imaginary unit ). The resulting so called equivalent lowpass signal or equivalent baseband signal

201-418: A QPSK symbol can allow the phase of the signal to jump by as much as 180° at a time. 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

268-429: 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: A convenient method to represent 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

335-667: A certain protocol layer . Underlying protocol layers are replaced by a simplified model. The model may reflect channel performance measures such as bit rate , bit errors , delay , delay variation , etc. Examples of digital channel models include: In an analog channel model, the transmitted message is modeled as an analog signal . The model can be a linear or non-linear , time-continuous or time-discrete (sampled) , memoryless or dynamic (resulting in burst errors ), time-invariant or time-variant (also resulting in burst errors), baseband , passband (RF signal model), real-valued or complex-valued signal model. The model may reflect

402-513: A challenging topic in telecommunication systems and computer engineering. Such systems have many civil and military applications. Moreover, blind recognition of modulation type is an important problem in commercial systems, especially in software-defined radio . Usually in such systems, there are some extra information for system configuration, but considering blind approaches in intelligent receivers, we can reduce information overload and increase transmission performance. Obviously, with no knowledge of

469-438: A channel refers to a theoretical channel model with certain error characteristics. In this more general view, a storage device is also a communication channel, which can be sent to (written) and received from (reading) and allows communication of an information signal across time. Examples of communications channels include: All of these communication channels share the property that they transfer information. The information

536-534: A cosine waveform) and a quadrature phase signal (or Q, with an example being a sine wave) are amplitude modulated with a finite number of amplitudes and then summed. It can be seen as a two-channel system, each channel using ASK. The resulting signal is equivalent to a combination of PSK and ASK. In all of the above methods, each of these phases, frequencies or amplitudes are assigned a unique pattern of binary bits . Usually, each phase, frequency or amplitude encodes an equal number of bits. This number of bits comprises

603-508: A different frequency, the channels do not interfere with each other. At the destination end, the carrier signal is demodulated to extract the information bearing modulation signal. A modulator is a device or circuit that performs modulation. A demodulator (sometimes detector ) is a circuit that performs demodulation , the inverse of modulation. A modem (from mod ulator– dem odulator), used in bidirectional communication, can perform both operations. The lower frequency band occupied by

670-512: A discrete alphabet to be transmitted. This alphabet can consist of a set of real or complex numbers , or sequences, like oscillations of different frequencies, so-called frequency-shift keying (FSK) modulation. A more complicated digital modulation method that employs multiple carriers, orthogonal frequency-division multiplexing (OFDM), is used in WiFi networks, digital radio stations and digital cable television transmission. In analog modulation,

737-412: A finite number of M alternative symbols (the modulation alphabet ). A simple example: A telephone line is designed for transferring audible sounds, for example, tones, and not digital bits (zeros and ones). Computers may, however, communicate over a telephone line by means of modems, which are representing the digital bits by tones, called symbols. If there are four alternative symbols (corresponding to

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804-413: 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

871-416: A much higher frequency than the message signal does. This is because it is impractical to transmit signals with low frequencies. Generally, to receive a radio wave one needs a radio antenna with length that is one-fourth of wavelength. For low frequency radio waves, wavelength is on the scale of kilometers and building such a large antenna is not practical. In radio communication , the modulated carrier

938-412: A musical instrument that can generate four different tones, one at a time), the first symbol may represent the bit sequence 00, the second 01, the third 10 and the fourth 11. If the modem plays a melody consisting of 1000 tones per second, the symbol rate is 1000 symbols/second, or 1000 baud . Since each tone (i.e., symbol) represents a message consisting of two digital bits in this example, the bit rate

1005-429: A narrowband analog signal over an analog baseband channel as a two-level signal by modulating a pulse wave . Some pulse modulation schemes also allow the narrowband analog signal to be transferred as a digital signal (i.e., as a quantized discrete-time signal ) with a fixed bit rate, which can be transferred over an underlying digital transmission system, for example, some line code . These are not modulation schemes in

1072-594: A proper class. Another recent approach is based on feature extraction. Digital baseband modulation changes the characteristics of a baseband signal, i.e., one without a carrier at a higher frequency. This can be used as equivalent signal to be later frequency-converted to a carrier frequency, or for direct communication in baseband. The latter methods both involve relatively simple line codes , as often used in local buses, and complicated baseband signalling schemes such as used in DSL . Pulse modulation schemes aim at transferring

1139-420: A transition probability p(i, o) . Semantically, the transition probability is the probability that the symbol o is received given that i was transmitted over the channel. Statistical and physical modeling can be combined. For example, in wireless communications the channel is often modeled by a random attenuation (known as fading ) of the transmitted signal, followed by additive noise. The attenuation term

1206-409: A transition probability that specifies an output distribution for each possible sequence of channel inputs. In information theory , it is common to start with memoryless channels in which the output probability distribution only depends on the current channel input. A channel model may either be digital or analog. In a digital channel model, the transmitted message is modeled as a digital signal at

1273-425: Is synchronous modulation . The most common digital modulation techniques are: MSK and GMSK are particular cases of continuous phase modulation. Indeed, MSK is a particular case of the sub-family of CPM known as continuous-phase frequency-shift keying (CPFSK) which is defined by a rectangular frequency pulse (i.e. a linearly increasing phase pulse) of one-symbol-time duration (total response signaling). OFDM

1340-444: Is a complex-valued representation of the real-valued modulated physical signal (the so-called passband signal or RF signal ). These are the general steps used by the modulator to transmit data: At the receiver side, the demodulator typically performs: As is common to all digital communication systems, the design of both the modulator and demodulator must be done simultaneously. Digital modulation schemes are possible because

1407-584: Is a simplification of the underlying physical processes and captures the change in signal power over the course of the transmission. The noise in the model captures external interference or electronic noise in the receiver. If the attenuation term is complex it also describes the relative time a signal takes to get through the channel. The statistical properties of the attenuation in the model are determined by previous measurements or physical simulations. Communication channels are also studied in discrete-alphabet modulation schemes. The mathematical model consists of

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1474-425: Is based on the idea of frequency-division multiplexing (FDM), but the multiplexed streams are all parts of a single original stream. The bit stream is split into several parallel data streams, each transferred over its own sub-carrier using some conventional digital modulation scheme. The modulated sub-carriers are summed to form an OFDM signal. This dividing and recombining help with handling channel impairments. OFDM

1541-439: Is carried through the channel by a signal . Mathematical models of the channel can be made to describe how the input (the transmitted signal) is mapped to the output (the received signal). There exist many types and uses of channel models specific to the field of communication. In particular, separate models are formulated to describe each layer of a communication system. A channel can be modeled physically by trying to calculate

1608-407: Is considered as a modulation technique rather than a multiplex technique since it transfers one bit stream over one communication channel using one sequence of so-called OFDM symbols. OFDM can be extended to multi-user channel access method in the orthogonal frequency-division multiple access (OFDMA) and multi-carrier code-division multiple access (MC-CDMA) schemes, allowing several users to share

1675-490: Is functionally equivalent to 2-QAM modulation. The general form for BPSK follows the equation: This yields two phases, 0 and π. In the specific form, binary data is often conveyed with the following signals: where f is the frequency of the base band. Hence, the signal space can be represented by the single basis function where 1 is represented by E b ϕ ( t ) {\displaystyle {\sqrt {E_{b}}}\phi (t)} and 0

1742-409: 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

1809-405: Is one of the most spread modulation schemes in application to LEO satellite communications. This variant of QPSK uses two identical constellations which are rotated by 45° ( π / 4 {\displaystyle \pi /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

1876-437: Is only one bit per symbol, this is also the symbol error rate. Sometimes this is known as quadriphase PSK , 4-PSK, or 4- QAM . (Although the root concepts of QPSK and 4-QAM are different, the resulting modulated radio waves are exactly the same.) 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

1943-459: Is represented by − E b ϕ ( t ) {\displaystyle -{\sqrt {E_{b}}}\phi (t)} . This assignment is arbitrary. This use of this basis function is shown at the end of the next section in a signal timing diagram. The topmost signal is a BPSK-modulated cosine wave that the BPSK modulator would produce. The bit-stream that causes this output

2010-427: Is shown above the signal (the other parts of this figure are relevant only to QPSK). After modulation, the base band signal will be moved to the high frequency band by multiplying cos ⁡ ( 2 π f c t ) {\displaystyle \cos(2\pi f_{c}t)} . The bit error rate (BER) of BPSK under additive white Gaussian noise (AWGN) can be calculated as: Since there

2077-414: Is the simplest form of phase shift keying (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°. Therefore, it handles the highest noise level or distortion before the demodulator reaches an incorrect decision. That makes it

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2144-451: Is transmitted through space as a radio wave to a radio receiver . Another purpose of modulation is to transmit multiple channels of information through a single communication medium , using frequency-division multiplexing (FDM). For example, in cable television (which uses FDM), many carrier signals, each modulated with a different television channel , are transported through a single cable to customers. Since each carrier occupies

2211-554: Is twice the symbol rate, i.e. 2000 bits per second. According to one definition of digital signal , the modulated signal is a digital signal. According to another definition, the modulation is a form of digital-to-analog conversion . Most textbooks would consider digital modulation schemes as a form of digital transmission , synonymous to data transmission; very few would consider it as analog transmission . The most fundamental digital modulation techniques are based on keying : In QAM, an in-phase signal (or I, with one example being

2278-712: Is used for information transfer of, for example, a digital bit stream , from one or several senders to one or several receivers . A channel has a certain capacity for transmitting information, often measured by its bandwidth in Hz or its data rate in bits per second . Communicating an information signal across distance requires some form of pathway or medium. These pathways, called communication channels, use two types of media: Transmission line -based telecommunications cable (e.g. twisted-pair , coaxial , and fiber-optic cable ) and broadcast (e.g. microwave , satellite , radio , and infrared ). In information theory ,

2345-445: The bit error rate (BER) – sometimes misperceived as twice the BER of BPSK. The mathematical analysis shows that QPSK can be used either to double the data rate compared with a BPSK system while maintaining the same bandwidth of the signal, or to maintain the data-rate of BPSK but halving the bandwidth needed. In this latter case, the BER of QPSK is exactly the same as

2412-422: 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

2479-465: The frequency of the carrier wave is varied by the modulation signal. These were the earliest types of modulation , and are used to transmit an audio signal representing sound in AM and FM radio broadcasting . More recent systems use digital modulation , which impresses a digital signal consisting of a sequence of binary digits (bits), a bitstream , on the carrier, by means of mapping bits to elements from

2546-411: The symbol that is represented by the particular phase, frequency or amplitude. If the alphabet consists of M = 2 N {\displaystyle M=2^{N}} alternative symbols, each symbol represents a message consisting of N bits. If the symbol rate (also known as the baud rate ) is f S {\displaystyle f_{S}} symbols/second (or baud ),

2613-482: The BER of BPSK – and believing differently is a common confusion when considering or describing QPSK. The transmitted carrier can undergo numbers of phase changes. Given that radio communication channels are allocated by agencies such as the Federal Communications Commission giving a prescribed (maximum) bandwidth, the advantage of QPSK over BPSK becomes evident: QPSK transmits twice

2680-517: The QAM modulation principle are used to drive switching amplifiers with these FM and other waveforms, and sometimes QAM demodulators are used to receive the signals put out by these switching amplifiers. Automatic digital modulation recognition in intelligent communication systems is one of the most important issues in software-defined radio and cognitive radio . According to incremental expanse of intelligent receivers, automatic modulation recognition becomes

2747-529: The complex domain, transitions between symbols never pass through 0. 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 {\displaystyle \pi /4} -QPSK lends itself to easy demodulation and has been adopted for use in, for example, TDMA cellular telephone systems. Digital modulation This carrier wave usually has

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2814-450: The conventional sense since they are not channel coding schemes, but should be considered as source coding schemes, and in some cases analog-to-digital conversion techniques. Communications channel A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking . A channel

2881-487: 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. BPSK (also sometimes called PRK, phase reversal keying, or 2PSK)

2948-440: The data rate in a given bandwidth compared to BPSK - at the same BER. The engineering penalty that is paid is that QPSK transmitters and receivers are more complicated than the ones for BPSK. However, with modern electronics technology, the penalty in cost is very moderate. As with BPSK, there are phase ambiguity problems at the receiving end, and differentially encoded QPSK is often used in practice. The implementation of QPSK

3015-407: The data rate is N f S {\displaystyle Nf_{S}} bit/second. For example, with an alphabet consisting of 16 alternative symbols, each symbol represents 4 bits. Thus, the data rate is four times the baud rate. In the case of PSK, ASK or QAM, where the carrier frequency of the modulated signal is constant, the modulation alphabet is often conveniently represented on

3082-408: The description given for BPSK above. The binary data that is conveyed by this waveform is: 11000110 . Offset quadrature phase-shift keying ( OQPSK ) is a variant of phase-shift keying modulation using four 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

3149-417: 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

3216-442: The following channel impairments: These are examples of commonly used channel capacity and performance measures: In networks, as opposed to point-to-point communication, the communication media can be shared between multiple communication endpoints (terminals). Depending on the type of communication, different terminals can cooperate or interfere with each other. In general, any complex multi-terminal network can be considered as

3283-426: 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,

3350-447: The magnitude of jumps is smaller in OQPSK when compared to QPSK. 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

3417-426: The modulation is applied continuously in response to the analog information signal. Common analog modulation techniques include: In digital modulation, an analog carrier signal is modulated by a discrete signal. Digital modulation methods can be considered as digital-to-analog conversion and the corresponding demodulation or detection as analog-to-digital conversion. The changes in the carrier signal are chosen from

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3484-405: The modulation signal is called the baseband , while the higher frequency band occupied by the modulated carrier is called the passband . In analog modulation , an analog modulation signal is "impressed" on the carrier. Examples are amplitude modulation (AM) in which the amplitude (strength) of the carrier wave is varied by the modulation signal, and frequency modulation (FM) in which

3551-489: The most robust of all the PSKs. 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. In the presence of an arbitrary phase-shift introduced by the communications channel , the demodulator (see, e.g. Costas loop ) is unable to tell which constellation point is which. As a result, the data is often differentially encoded prior to modulation. BPSK

3618-406: The odd-numbered bits have been assigned to the in-phase component and the even-numbered 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

3685-444: 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

3752-402: 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 π / 4 {\displaystyle \pi /4} -QPSK are between OQPSK and non-offset QPSK. One property this modulation scheme possesses is that if the modulated signal is represented in

3819-403: 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 OQPSK (since the signals no longer change together), but they are less severe. In other words,

3886-583: 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. There are three major classes of digital modulation techniques used for transmission of digitally represented data: All convey data by changing some aspect of

3953-498: The physical processes which modify the transmitted signal. For example, in wireless communications, the channel can be modeled by calculating the reflection from every object in the environment. A sequence of random numbers might also be added to simulate external interference or electronic noise in the receiver. Statistically, a communication channel is usually modeled as a tuple consisting of an input alphabet, an output alphabet, and for each pair (i, o) of input and output elements,

4020-436: 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: 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 signal-space analysis above. Here,

4087-541: The same physical medium by giving different sub-carriers or spreading codes to different users. Of the two kinds of RF power amplifier , switching amplifiers ( Class D amplifiers ) cost less and use less battery power than linear amplifiers of the same output power. However, they only work with relatively constant-amplitude-modulation signals such as angle modulation (FSK or PSK) and CDMA , but not with QAM and OFDM. Nevertheless, even though switching amplifiers are completely unsuitable for normal QAM constellations, often

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4154-401: 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

4221-421: 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

4288-478: 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.) SOQPSK modulation can be represented as the hybrid of QPSK and MSK : SOQPSK has the same signal constellation as QPSK, however the phase of SOQPSK is always stationary. The standard description of SOQPSK-TG involves ternary symbols . SOQPSK

4355-413: 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. Although QPSK can be viewed as a quaternary modulation, it is easier to see it as two independently modulated quadrature carriers. With this interpretation,

4422-496: The transmitted data and many unknown parameters at the receiver, such as the signal power, carrier frequency and phase offsets, timing information, etc., blind identification of the modulation is made fairly difficult. This becomes even more challenging in real-world scenarios with multipath fading, frequency-selective and time-varying channels. There are two main approaches to automatic modulation recognition. The first approach uses likelihood-based methods to assign an input signal to

4489-549: The transmitter-receiver pair has prior knowledge of how data is encoded and represented in the communications system. In all digital communication systems, both the modulator at the transmitter and the demodulator at the receiver are structured so that they perform inverse operations. Asynchronous methods do not require a receiver reference clock signal that is phase synchronized with the sender carrier signal . In this case, modulation symbols (rather than bits, characters, or data packets) are asynchronously transferred. The opposite

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