Constellation shaping

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Constellation shaping is an energy efficiency enhancement method for digital signal modulation that improves upon amplitude and phase-shift keying (APSK) and conventional quadrature amplitude modulation (QAM) by modifying the uniform distribution [ disambiguation needed ] of the data symbols to match the channel. In a channel corrupted by an additive white Gaussian noise (AWGN), this implies transmitting low-energy signals more frequently than high-energy signals with the target to approach a Gaussian distribution of the transmission power.

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In digital signal modulation, information bits modulate the carrier electromagnetic wave signal to a set of desired phase, frequency and amplitude states. This set of allowed states is called a constellation. Typically, the probability of an information bit to be a 0 is the same as that of a 1, leading to all states from the constellation to appear with an equal probability. However, optimal transmission through most practical channels, like the AWGN, require a non-equal probability of the transmission symbols. [1]

A shaped constellation transmission sends some signal combinations more often and others less frequently to optimize the signal quality at the destination, or to maintain the same quality using less transmission energy.

Probabilistic constellation shaping

Probabilistic constellation shaping attempts to directly modify the Probability mass function by applying a distribution matcher between the user data and the mapper to constellation symbols. A practical transmitter and receiver architecture which achieves that was proposed in. [2] This technique gathered more interest in September 2016 when Nokia Bell Labs demonstrated working 1  Tbit/s data transmission channels between German cities. [3] In October 2016, Alcatel-Lucent and Bell Labs claimed to have achieved 65 Tbit/s transmission over a 6,600 km (4,100 mile) single mode fiber in laboratory trials. [4] The industry's first commercial field trial was completed in 2018 by China Telecom and Huawei Technologies. [5]

Geometric constellation shaping

Geometric constellation shaping attempts to modify the distribution of transmission power by optimizing the constellation states themselves. In an AWGN channel, this typically implies gathering more constellation points around the area where the amplitude is small, and fewer points in the areas of high amplitude. Other types of channels require that high-amplitude points are clipped altogether, due to e.g. problems with amplifier efficiency. A notable examples are satellite links, where an APSK constellation is preferred to QAM.

The benefits of geometric constellation shaping is that no distribution matcher is required, which simplifies the digital signal processing at the transmitter and receiver. However, geometric constellation shaping does not typically allow Gray code labeling of the constellation points, leading to a performance degradation. Probabilistic shaping is thus slightly more effective than geometric shaping.

Related Research Articles

In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a separate signal called the modulation signal that typically contains information to be transmitted. For example, the modulation signal might be an audio signal representing sound from a microphone, a video signal representing moving images from a video camera, or a digital signal representing a sequence of binary digits, a bitstream from a computer.

Quadrature amplitude modulation (QAM) is the name of a family of digital modulation methods and a related family of analog modulation methods widely used in modern telecommunications to transmit information. It conveys two analog message signals, or two digital bit streams, by changing (modulating) the amplitudes of two carrier waves, using the amplitude-shift keying (ASK) digital modulation scheme or amplitude modulation (AM) analog modulation scheme. The two carrier waves are of the same frequency and are out of phase with each other by 90°, a condition known as orthogonality or quadrature. The transmitted signal is created by adding the two carrier waves together. At the receiver, the two waves can be coherently separated (demodulated) because of their orthogonality. Another key property is that the modulations are low-frequency/low-bandwidth waveforms compared to the carrier frequency, which is known as the narrowband assumption.

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.

Quadrature may refer to:

Hybrid fiber-coaxial (HFC) is a broadband telecommunications network that combines optical fiber and coaxial cable. It has been commonly employed globally by cable television operators since the early 1990s.

Amplitude-shift keying (ASK) is a form of amplitude modulation that represents digital data as variations in the amplitude of a carrier wave. In an ASK system, a symbol, representing one or more bits, is sent by transmitting a fixed-amplitude carrier wave at a fixed frequency for a specific time duration. For example, if each symbol represents a single bit, then the carrier signal could be transmitted at nominal amplitude when the input value is 1, but transmitted at reduced amplitude or not at all when the input value is 0.

<span class="mw-page-title-main">Cable modem termination system</span> Equipment used to provide high speed data services

A cable modem termination system is a piece of equipment, typically located in a cable company's headend or hubsite, which is used to provide high speed data services, such as cable Internet or Voice over Internet Protocol, to cable subscribers. A CMTS provides many of the same functions provided by the DSLAM in a DSL system.

Carrierless amplitude phase modulation (CAP) is a variant of quadrature amplitude modulation (QAM). Instead of modulating the amplitude of two carrier waves, CAP generates a QAM signal by combining two PAM signals filtered through two filters designed so that their impulse responses form a Hilbert pair. If the impulse responses of the two filters are chosen as sine and a cosine, the only mathematical difference between QAM and CAP waveforms is that the phase of the carrier is reset at the beginning of each symbol. If the carrier frequency and symbol rates are similar, the main advantage of CAP over QAM is simpler implementation. The modulation of the baseband signal with the quadrature carriers is not necessary with CAP, because it is part of the transmit pulse.

<span class="mw-page-title-main">Constellation diagram</span> Signal representation

A constellation diagram is a representation of a signal modulated by a digital modulation scheme such as quadrature amplitude modulation or phase-shift keying. It displays the signal as a two-dimensional xy-plane scatter diagram in the complex plane at symbol sampling instants. In a manner similar to that of a phasor diagram, the angle of a point, measured counterclockwise from the horizontal axis, represents the phase shift of the carrier wave from a reference phase; the distance of a point from the origin represents a measure of the amplitude or power of the signal.

<span class="mw-page-title-main">Fiber-optic communication</span> Method of transmitting information

Fiber-optic communication is a method of transmitting information from one place to another by sending pulses of infrared or visible light through an optical fiber. The light is a form of carrier wave that is modulated to carry information. Fiber is preferred over electrical cabling when high bandwidth, long distance, or immunity to electromagnetic interference is required. This type of communication can transmit voice, video, and telemetry through local area networks or across long distances.

In digital communications shaping codes are a method of encoding that changes the distribution of signals to improve efficiency.

The following outline is provided as an overview of and topical guide to telecommunication:

<span class="mw-page-title-main">Amplitude and phase-shift keying</span>

Amplitude and phase-shift keying (APSK) is a digital modulation scheme that conveys data by modulating both the amplitude and the phase of a carrier wave. In other words, it combines both amplitude-shift keying (ASK) and phase-shift keying (PSK). This allows for a lower bit error rate for a given modulation order and signal-to-noise ratio, at the cost of increased complexity, compared to ASK or PSK alone.

<span class="mw-page-title-main">Polarization-division multiplexing</span> Method for multiplexing signals

Polarization-division multiplexing (PDM) is a physical layer method for multiplexing signals carried on electromagnetic waves, allowing two channels of information to be transmitted on the same carrier frequency by using waves of two orthogonal polarization states. It is used in microwave links such as satellite television downlinks to double the bandwidth by using two orthogonally polarized feed antennas in satellite dishes. It is also used in fiber optic communication by transmitting separate left and right circularly polarized light beams through the same optical fiber.

Multiple-input, multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) is the dominant air interface for 4G and 5G broadband wireless communications. It combines multiple-input, multiple-output (MIMO) technology, which multiplies capacity by transmitting different signals over multiple antennas, and orthogonal frequency-division multiplexing (OFDM), which divides a radio channel into a large number of closely spaced subchannels to provide more reliable communications at high speeds. Research conducted during the mid-1990s showed that while MIMO can be used with other popular air interfaces such as time-division multiple access (TDMA) and code-division multiple access (CDMA), the combination of MIMO and OFDM is most practical at higher data rates.

Coherent optical module refers to a typically hot-pluggable coherent optical transceiver that uses coherent modulation (BPSK/QPSK/QAM) rather than amplitude modulation (RZ/NRZ/PAM4) and is typically used in high-bandwidth data communications applications. Optical modules typically have an electrical interface on the side that connects to the inside of the system and an optical interface on the side that connects to the outside world through a fiber optic cable. The technical details of coherent optical modules were proprietary for many years, but have recently attracted efforts by multi-source agreement (MSA) groups and a standards development organizations such as the Optical Internetworking Forum. Coherent optical modules can either plug into a front panel socket or an on-board socket. Coherent optical modules form a smaller piece of a much larger optical module industry.

In quantum physics, light is in a squeezed state if its electric field strength Ԑ for some phases has a quantum uncertainty smaller than that of a coherent state. The term squeezing thus refers to a reduced quantum uncertainty. To obey Heisenberg's uncertainty relation, a squeezed state must also have phases at which the electric field uncertainty is anti-squeezed, i.e. larger than that of a coherent state. Since 2019, the gravitational-wave observatories LIGO and Virgo employ squeezed laser light, which has significantly increased the rate of observed gravitational-wave events.

Non-orthogonal frequency-division multiplexing (N-OFDM) is a method of encoding digital data on multiple carrier frequencies with non-orthogonal intervals between frequency of sub-carriers. N-OFDM signals can be used in communication and radar systems.

Spatial modulation is a technique that enables modulation over space, across different antennas (radio) at a transmitter. Unlike multiple-input and multiple-output (MIMO) wireless, in spatial modulation, only a single antenna among all transmitting antennas is active and transmitting, while all other remaining transmitting antennas sit idle. The duty of the receiver is: to estimate the active antenna index at the transmitter and to decode the symbol sent by the transmitting antenna.

Probabilistic numerics is an active field of study at the intersection of applied mathematics, statistics, and machine learning centering on the concept of uncertainty in computation. In probabilistic numerics, tasks in numerical analysis such as finding numerical solutions for integration, linear algebra, optimization and simulation and differential equations are seen as problems of statistical, probabilistic, or Bayesian inference.

References

  1. ↑ Thomas M. Cover, Joy A. Thomas, Elements of Information Theory, 2nd Edition ISBN   978-0-471-24195-9 July 2006
  2. ↑ G. Böcherer, F. Steiner and P. Schulte, "Bandwidth Efficient and Rate-Matched Low-Density Parity-Check Coded Modulation," in IEEE Transactions on Communications, vol. 63, no. 12, pp. 4651-4665, Dec. 2015, doi: 10.1109/TCOMM.2015.2494016.
  3. ↑ "Optical fiber transmits one terabit per second". Technical University of Munich. 2016-09-16. Archived from the original on 2016-09-23. Retrieved 2016-09-23.
  4. ↑ Jeffrey, Colin (October 13, 2016). "Nokia's super-fast subsea data cable torpedos [sic] the competition". newatlas.com. Retrieved 2016-10-14.
  5. ↑ Huawei 11/21/2018, Partner Perspectives. "China Telecom & Huawei Jointly Completed the Industry's First PCS-based 200G/400G Ultra-Long-Haul Field Trial in a Commercial WDM Network". Light Reading. Retrieved 2020-10-28.{{cite web}}: CS1 maint: numeric names: authors list (link)
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