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40-519: They are named after Solomon A. Zadoff, David C. Chu and Robert L. Frank. Zadoff–Chu sequences exhibit the useful property that cyclically shifted versions of themselves are orthogonal to one another. A generated Zadoff–Chu sequence that has not been shifted is known as a root sequence . The complex value at each position n of each root Zadoff–Chu sequence parametrised by u is given by where Zadoff–Chu sequences are CAZAC sequences ( constant amplitude zero autocorrelation waveform ). Note that

80-451: A variety of other organizations as associate members ("market representation partners"). The 3GPP organizes its work into three different streams: Radio Access Networks , Services and Systems Aspects, and Core Network and Terminals. The project was established in December 1998 with the goal of developing a specification for a 3G mobile phone system based on the 2G GSM system, within

120-472: A , g , and n ) versions of 802.11 Wi-Fi ; WiMAX ; ITU-T G.hn , DVB-T , the terrestrial digital TV broadcast system used in most of the world outside North America; and DMT (Discrete Multi Tone), the standard form of ADSL . In OFDM, the subcarrier frequencies are chosen so that the subcarriers are orthogonal to each other, meaning that crosstalk between the subchannels is eliminated and intercarrier guard bands are not required. This greatly simplifies

160-1092: A Market Representation Partner to take part in 3GPP, which: As of June 2021 , the Market Representation Partners are: 3GPP standards are structured as Releases . Discussion of 3GPP thus frequently refers to the functionality in one release or another. TSG SA groups focused on further enhancements to the 5G system and enablers for new features and services: Enhanced support of: non-public networks, industrial Internet of Things , low complexity NR devices, edge computing in 5GC, access traffic steering, switch and splitting support, network automation for 5G, network slicing , advanced V2X service, multiple USIM support, proximity-based services in 5GS, 5G multicast broadcast services, Unmanned Aerial Systems (UAS), satellite access in 5G, 5GC location services, Multimedia Priority Service... Each release incorporates hundreds of individual Technical Specification and Technical Report documents, each of which may have been through many revisions. Current 3GPP standards incorporate

200-439: A Project Coordination Group, which is the highest decision-making body. Its missions include the management of overall timeframe and work progress. 3GPP standardization work is contribution-driven. Companies ("individual members") participate through their membership to a 3GPP Organizational Partner. As of December 2020, 3GPP is composed of 719 individual members. Specification work is done at WG and at TSG level: 3GPP follows

240-582: A cyclically shifted version of itself is zero, i.e., it is non-zero only at one instant which corresponds to the cyclic shift. 4. The cross-correlation between two prime length Zadoff–Chu sequences, i.e. different values of u , u = u 1 , u = u 2 {\displaystyle u,u=u_{1},u=u_{2}} , is constant 1 / N ZC {\displaystyle 1/{\sqrt {N_{\text{ZC}}}}} , provided that u 1 − u 2 {\displaystyle u_{1}-u_{2}}

280-501: A mono signal, equivalent to a stereo signal in which both channels carry identical (in-phase) signals. 3GPP The 3rd Generation Partnership Project ( 3GPP ) is an umbrella term for a number of standards organizations which develop protocols for mobile telecommunications . Its best known work is the development and maintenance of: 3GPP is a consortium with seven national or regional telecommunication standards organizations as primary members ("organizational partners") and

320-469: A right angle or something related to a right angle. In mathematics , orthogonality is the generalization of the geometric notion of perpendicularity to the linear algebra of bilinear forms . Two elements u and v of a vector space with bilinear form B {\displaystyle B} are orthogonal when B ( u , v ) = 0 {\displaystyle B(\mathbf {u} ,\mathbf {v} )=0} . Depending on

360-649: A three-stage methodology as defined in ITU-T Recommendation I.130: Test specifications are sometimes defined as stage 4, as they follow stage 3. Specifications are grouped into releases. A release consists of a set of internally consistent set of features and specifications. Timeframes are defined for each release by specifying freezing dates. Once a release is frozen, only essential corrections are allowed (i.e. addition and modifications of functions are forbidden). Freezing dates are defined for each stage. The 3GPP specifications are transposed into deliverables by

400-487: A time axis determined by a rapidity of motion is hyperbolic-orthogonal to a space axis of simultaneous events, also determined by the rapidity. The theory features relativity of simultaneity . In quantum mechanics , a sufficient (but not necessary) condition that two eigenstates of a Hermitian operator , ψ m {\displaystyle \psi _{m}} and ψ n {\displaystyle \psi _{n}} , are orthogonal

440-448: Is time-division multiple access (TDMA), where the orthogonal basis functions are nonoverlapping rectangular pulses ("time slots"). Another scheme is orthogonal frequency-division multiplexing (OFDM), which refers to the use, by a single transmitter, of a set of frequency multiplexed signals with the exact minimum frequency spacing needed to make them orthogonal so that they do not interfere with each other. Well known examples include (

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480-464: Is a strategy allowing the deprotection of functional groups independently of each other. In supramolecular chemistry the notion of orthogonality refers to the possibility of two or more supramolecular, often non-covalent , interactions being compatible; reversibly forming without interference from the other. In analytical chemistry , analyses are "orthogonal" if they make a measurement or identification in completely different ways, thus increasing

520-417: Is called an orthogonal map. In philosophy , two topics, authors, or pieces of writing are said to be "orthogonal" to each other when they do not substantively cover what could be considered potentially overlapping or competing claims. Thus, texts in philosophy can either support and complement one another, they can offer competing explanations or systems, or they can be orthogonal to each other in cases where

560-589: Is done in Technical Specification Groups (TSGs) and Working Groups (WGs). There are three Technical Specifications Groups, each of which consists of multiple WGs: The closure of GERAN was announced in January 2016. The specification work on legacy GSM/EDGE system was transferred to RAN WG, RAN6. RAN6 was closed in July 2020 ( https://www.3gpp.org/news-events/2128-r6_geran ). The 3GPP structure also includes

600-416: Is easier to verify designs that neither cause side effects nor depend on them. An instruction set is said to be orthogonal if it lacks redundancy (i.e., there is only a single instruction that can be used to accomplish a given task) and is designed such that instructions can use any register in any addressing mode . This terminology results from considering an instruction as a vector whose components are

640-484: Is multiplied by the same number. 1. They are periodic with period N ZC {\displaystyle N_{\text{ZC}}} . 2. If N ZC {\displaystyle N_{\text{ZC}}} is prime, the Discrete Fourier Transform of a Zadoff–Chu sequence is another Zadoff–Chu sequence conjugated, scaled and time scaled. 3. The auto correlation of a Zadoff–Chu sequence with

680-569: Is relatively prime to N ZC {\displaystyle N_{\text{ZC}}} . Zadoff–Chu sequences are used in the 3GPP Long Term Evolution (LTE) air interface in the Primary Synchronization Signal (PSS), random access preamble (PRACH), uplink control channel (PUCCH), uplink traffic channel (PUSCH) and sounding reference signals (SRS). By assigning orthogonal Zadoff–Chu sequences to each LTE eNodeB and multiplying their transmissions by their respective codes,

720-520: Is that they correspond to different eigenvalues. This means, in Dirac notation , that ⟨ ψ m | ψ n ⟩ = 0 {\displaystyle \langle \psi _{m}|\psi _{n}\rangle =0} if ψ m {\displaystyle \psi _{m}} and ψ n {\displaystyle \psi _{n}} correspond to different eigenvalues. This follows from

760-400: Is the generalization of the geometric notion of perpendicularity . Whereas perpendicular is typically followed by to when relating two lines to one another (e.g., "line A is perpendicular to line B"), orthogonal is commonly used without to (e.g., "orthogonal lines A and B"). Orthogonality is also used with various meanings that are often weakly related or not related at all with

800-507: The Sophia Antipolis technology park in France. The seven 3GPP Organizational Partners are from Asia, Europe and North America. Their aim is to determine the general policy and strategy of 3GPP and perform the following tasks: Together with the Market Representation Partners (MRPs) perform the following tasks: The Organizational Partners are: The 3GPP Organizational Partners can invite

840-534: The cross-correlation of simultaneous eNodeB transmissions is reduced, thus reducing inter-cell interference and uniquely identifying eNodeB transmissions. Zadoff–Chu sequences are an improvement over the Walsh–Hadamard codes used in UMTS because they result in a constant-amplitude output signal, reducing the cost and complexity of the radio's power amplifier . Orthogonality In mathematics , orthogonality

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880-568: The web site of the Thyssen-Bornemisza Museum states that "Mondrian ... dedicated his entire oeuvre to the investigation of the balance between orthogonal lines and primary colours." Archived 2009-01-31 at the Wayback Machine Orthogonality in programming language design is the ability to use various language features in arbitrary combinations with consistent results. This usage was introduced by Van Wijngaarden in

920-612: The bilinear form, the vector space may contain null vectors , non-zero self-orthogonal vectors, in which case perpendicularity is replaced with hyperbolic orthogonality . In the case of function spaces , families of functions are used to form an orthogonal basis , such as in the contexts of orthogonal polynomials , orthogonal functions , and combinatorics . In optics , polarization states are said to be orthogonal when they propagate independently of each other, as in vertical and horizontal linear polarization or right- and left-handed circular polarization . In special relativity ,

960-418: The design of Algol 68 : The number of independent primitive concepts has been minimized in order that the language be easy to describe, to learn, and to implement. On the other hand, these concepts have been applied “orthogonally” in order to maximize the expressive power of the language while trying to avoid deleterious superfluities. Orthogonality is a system design property which guarantees that modifying

1000-400: The design of both the transmitter and the receiver. In conventional FDM, a separate filter for each subchannel is required. When performing statistical analysis, independent variables that affect a particular dependent variable are said to be orthogonal if they are uncorrelated, since the covariance forms an inner product. In this case the same results are obtained for the effect of any of

1040-420: The explanatory variables and model residuals. In taxonomy , an orthogonal classification is one in which no item is a member of more than one group, that is, the classifications are mutually exclusive. In chemistry and biochemistry, an orthogonal interaction occurs when there are two pairs of substances and each substance can interact with their respective partner, but does not interact with either substance of

1080-846: The fact that Schrödinger's equation is a Sturm–Liouville equation (in Schrödinger's formulation) or that observables are given by Hermitian operators (in Heisenberg's formulation). In art, the perspective (imaginary) lines pointing to the vanishing point are referred to as "orthogonal lines". The term "orthogonal line" often has a quite different meaning in the literature of modern art criticism. Many works by painters such as Piet Mondrian and Burgoyne Diller are noted for their exclusive use of "orthogonal lines" — not, however, with reference to perspective, but rather referring to lines that are straight and exclusively horizontal or vertical, forming right angles where they intersect. For example, an essay at

1120-525: The geometric sense discussed above, both as observed data (i.e., vectors) and as random variables (i.e., density functions). One econometric formalism that is alternative to the maximum likelihood framework, the Generalized Method of Moments , relies on orthogonality conditions. In particular, the Ordinary Least Squares estimator may be easily derived from an orthogonality condition between

1160-454: The independent variables upon the dependent variable, regardless of whether one models the effects of the variables individually with simple regression or simultaneously with multiple regression . If correlation is present, the factors are not orthogonal and different results are obtained by the two methods. This usage arises from the fact that if centered by subtracting the expected value (the mean), uncorrelated variables are orthogonal in

1200-448: The instruction fields. One field identifies the registers to be operated upon and another specifies the addressing mode. An orthogonal instruction set uniquely encodes all combinations of registers and addressing modes. In telecommunications , multiple access schemes are orthogonal when an ideal receiver can completely reject arbitrarily strong unwanted signals from the desired signal using different basis functions . One such scheme

1240-449: The latest revision of the GSM standards. The documents are made available without charge on 3GPP's web site. The Technical Specifications cover not only the radio part (" Air Interface ") and Core Network, but also billing information and speech coding down to source code level. Cryptographic aspects (such as authentication , confidentiality ) are also specified. The 3GPP specification work

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1280-428: The left and right stereo channels in a single groove. The V-shaped groove in the vinyl has walls that are 90 degrees to each other, with variations in each wall separately encoding one of the two analogue channels that make up the stereo signal. The cartridge senses the motion of the stylus following the groove in two orthogonal directions: 45 degrees from vertical to either side. A pure horizontal motion corresponds to

1320-472: The mathematical meanings. The word comes from the Ancient Greek ὀρθός ( orthós ), meaning "upright", and γωνία ( gōnía ), meaning "angle". The Ancient Greek ὀρθογώνιον ( orthogṓnion ) and Classical Latin orthogonium originally denoted a rectangle . Later, they came to mean a right triangle . In the 12th century, the post-classical Latin word orthogonalis came to mean

1360-481: The other pair. For example, DNA has two orthogonal pairs: cytosine and guanine form a base-pair, and adenine and thymine form another base-pair, but other base-pair combinations are strongly disfavored. As a chemical example, tetrazine reacts with transcyclooctene and azide reacts with cyclooctyne without any cross-reaction, so these are mutually orthogonal reactions, and so, can be performed simultaneously and selectively. In organic synthesis , orthogonal protection

1400-401: The prone to error device or method. The failure mode of an orthogonally redundant back-up device or method does not intersect with and is completely different from the failure mode of the device or method in need of redundancy to safeguard the total system against catastrophic failure. In neuroscience , a sensory map in the brain which has overlapping stimulus coding (e.g. location and quality)

1440-420: The reliability of the measurement. Orthogonal testing thus can be viewed as "cross-checking" of results, and the "cross" notion corresponds to the etymologic origin of orthogonality . Orthogonal testing is often required as a part of a new drug application . In the field of system reliability orthogonal redundancy is that form of redundancy where the form of backup device or method is completely different from

1480-592: The scope of the International Telecommunication Union's International Mobile Telecommunications-2000 , hence the name 3GPP. It should not be confused with 3rd Generation Partnership Project 2 (3GPP2), which developed a competing 3G system, CDMA2000 . The 3GPP administrative support team (known as the "Mobile Competence Centre") is located at the European Telecommunications Standards Institute headquarters in

1520-456: The scope, content, and purpose of the pieces of writing are entirely unrelated. In board games such as chess which feature a grid of squares, 'orthogonal' is used to mean "in the same row/'rank' or column/'file'". This is the counterpart to squares which are "diagonally adjacent". In the ancient Chinese board game Go a player can capture the stones of an opponent by occupying all orthogonally adjacent points. Stereo vinyl records encode both

1560-464: The special case q = 0 {\displaystyle q=0} results in a Chu sequence,. Setting q ≠ 0 {\displaystyle q\neq 0} produces a sequence that is equal to the cyclically shifted version of the Chu sequence by q {\displaystyle q} , and multiplied by a complex, modulus 1 number, where by multiplied we mean that each element

1600-591: The technical effect produced by a component of a system neither creates nor propagates side effects to other components of the system. Typically this is achieved through the separation of concerns and encapsulation , and it is essential for feasible and compact designs of complex systems. The emergent behavior of a system consisting of components should be controlled strictly by formal definitions of its logic and not by side effects resulting from poor integration, i.e., non-orthogonal design of modules and interfaces. Orthogonality reduces testing and development time because it

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