Spread spectrum

In telecommunication and radio communication, spread-spectrum techniques are methods by which a signal (e.g., an electrical, electromagnetic, or acoustic signal) generated with a particular bandwidth is deliberately spread in the frequency domain, resulting in a signal with a wider bandwidth. These techniques are used for a variety of reasons, including the establishment of secure communications, increasing resistance to natural interference, noise and jamming, to prevent detection, and to limit power flux density (e.g., in satellite down links).

Spread-spectrum telecommunications

This is a technique in which a telecommunication signal is transmitted on a bandwidth considerably larger than the frequency content of the original information. Frequency hopping is a basic modulation technique used in spread spectrum signal transmission.

Spread-spectrum telecommunications is a signal structuring technique that employs direct sequence, frequency hopping, or a hybrid of these, which can be used for multiple access and/or multiple functions. This technique decreases the potential interference to other receivers while achieving privacy. Spread spectrum generally makes use of a sequential noise-like signal structure to spread the normally narrowband information signal over a relatively wideband (radio) band of frequencies. The receiver correlates the received signals to retrieve the original information signal. Originally there were two motivations: either to resist enemy efforts to jam the communications (anti-jam, or AJ), or to hide the fact that communication was even taking place, sometimes called low probability of intercept (LPI).

Frequency-hopping spread spectrum (FHSS), direct-sequence spread spectrum (DSSS), time-hopping spread spectrum (THSS), chirp spread spectrum (CSS), and combinations of these techniques are forms of spread spectrum. The first two of these techniques employ pseudorandom number sequences—created using pseudorandom number generators—to determine and control the spreading pattern of the signal across the allocated bandwidth. Wireless standard IEEE 802.11 uses either FHSS or DSSS in its radio interface.

  • Techniques known since the 1940s and used in military communication systems since the 1950s "spread" a radio signal over a wide frequency range several magnitudes higher than minimum requirement. The core principle of spread spectrum is the use of noise-like carrier waves, and, as the name implies, bandwidths much wider than that required for simple point-to-point communication at the same data rate.
  • Resistance to jamming (interference). DS (direct sequence) is good at resisting continuous-time narrowband jamming, while FH (frequency hopping) is better at resisting pulse jamming. In DS systems, narrowband jamming affects detection performance about as much as if the amount of jamming power is spread over the whole signal bandwidth, when it will often not be much stronger than background noise. By contrast, in narrowband systems where the signal bandwidth is low, the received signal quality will be severely lowered if the jamming power happens to be concentrated on the signal bandwidth.
  • Resistance to eavesdropping. The spreading code (in DS systems) or the frequency-hopping pattern (in FH systems) is often unknown by anyone for whom the signal is unintended, in which case it obscures the signal and reduces the chance of an adversary making sense of it. Moreover, for a given noise power spectral density (PSD), spread-spectrum systems require the same amount of energy per bit before spreading as narrowband systems and therefore the same amount of power if the bitrate before spreading is the same, but since the signal power is spread over a large bandwidth, the signal PSD is much lower — often significantly lower than the noise PSD — so that the adversary may be unable to determine whether the signal exists at all. However, for mission-critical applications, particularly those employing commercially available radios, spread-spectrum radios do not intrinsically provide adequate security; "...just using spread-spectrum radio itself is not sufficient for communications security".[1]
  • Resistance to fading. The high bandwidth occupied by spread-spectrum signals offer some frequency diversity, i.e. it is unlikely that the signal will encounter severe multipath fading over its whole bandwidth, and in other cases the signal can be detected using e.g. a rake receiver.
  • Multiple access capability, known as code-division multiple access (CDMA) or code-division multiplexing (CDM). Multiple users can transmit simultaneously in the same frequency band as long as they use different k codes.

Invention of frequency hopping

Frequency-hopping may date back to radio pioneer Jonathan Zenneck's 1908 German book Wireless Telegraphy although he states that Telefunken was using it previously. It saw limited use by the German military in World War I,[2] was put forward by Polish engineer Leonard Danilewicz in 1929,[3] showed up in a patent in the 1930s by Willem Broertjes (U.S. Patent 1,869,659, issued Aug. 2, 1932),[4] and in the top-secret US Army Signal Corps World War II communications system named SIGSALY.

During World War II, Golden Age of Hollywood actress Hedy Lamarr and avant-garde composer George Antheil developed an intended jamming-resistant radio guidance system for use in Allied torpedoes, patenting the device under US Patent 2,292,387 "Secret Communications System" on August 11, 1942. Their approach was unique in that frequency coordination was done with paper player piano rolls - a novel approach which was never put into practice.[5]

Spread-spectrum clock signal generation

Aaronia Spectrum Analyzer Software
Spread spectrum of a modern switching power supply (heating up period) incl. waterfall diagram over a few minutes. Recorded with a NF-5030 EMC-Analyzer

Spread-spectrum clock generation (SSCG) is used in some synchronous digital systems, especially those containing microprocessors, to reduce the spectral density of the electromagnetic interference (EMI) that these systems generate. A synchronous digital system is one that is driven by a clock signal and, because of its periodic nature, has an unavoidably narrow frequency spectrum. In fact, a perfect clock signal would have all its energy concentrated at a single frequency (the desired clock frequency) and its harmonics. Practical synchronous digital systems radiate electromagnetic energy on a number of narrow bands spread on the clock frequency and its harmonics, resulting in a frequency spectrum that, at certain frequencies, can exceed the regulatory limits for electromagnetic interference (e.g. those of the FCC in the United States, JEITA in Japan and the IEC in Europe).

Spread-spectrum clocking avoids this problem by using one of the methods previously described to reduce the peak radiated energy and, therefore, its electromagnetic emissions and so comply with electromagnetic compatibility (EMC) regulations.

It has become a popular technique to gain regulatory approval because it requires only simple equipment modification. It is even more popular in portable electronics devices because of faster clock speeds and increasing integration of high-resolution LCD displays into ever smaller devices. As these devices are designed to be lightweight and inexpensive, traditional passive, electronic measures to reduce EMI, such as capacitors or metal shielding, are not viable. Active EMI reduction techniques such as spread-spectrum clocking are needed in these cases.

However, spread-spectrum clocking, like other kinds of dynamic frequency change, can also create challenges for designers. Principal among these is clock/data misalignment, or clock skew.

Note that this method does not reduce total radiated energy, and therefore systems are not necessarily less likely to cause interference. Spreading energy over a larger bandwidth effectively reduces electrical and magnetic readings within narrow bandwidths. Typical measuring receivers used by EMC testing laboratories divide the electromagnetic spectrum into frequency bands approximately 120 kHz wide.[6] If the system under test were to radiate all its energy in a narrow bandwidth, it would register a large peak. Distributing this same energy into a larger bandwidth prevents systems from putting enough energy into any one narrowband to exceed the statutory limits. The usefulness of this method as a means to reduce real-life interference problems is often debated, as it is perceived that spread-spectrum clocking hides rather than resolves higher radiated energy issues by simple exploitation of loopholes in EMC legislation or certification procedures. This situation results in electronic equipment sensitive to narrow bandwidth(s) experiencing much less interference, while those with broadband sensitivity, or even operated at other higher frequencies (such as a radio receiver tuned to a different station), will experience more interference.

FCC certification testing is often completed with the spread-spectrum function enabled in order to reduce the measured emissions to within acceptable legal limits. However, the spread-spectrum functionality may be disabled by the user in some cases. As an example, in the area of personal computers, some BIOS writers include the ability to disable spread-spectrum clock generation as a user setting, thereby defeating the object of the EMI regulations. This might be considered a loophole, but is generally overlooked as long as spread-spectrum is enabled by default.

An ability to disable spread-spectrum clocking in computer systems is considered useful for overclocking, as spread spectrum can lower maximum clock speed achievable due to clock skew.

See also


  1. ^ Shaw, William T. (2006). Cyber Security for SCADA Systems. PennWell Books. p. 76. ISBN 9781593700683.
  2. ^ Denis Winter, Haig's Command - A Reassessment
  3. ^ Danilewicz later recalled: "In 1929 we proposed to the General Staff a device of my design for secret radio telegraphy which fortunately did not win acceptance, as it was a truly barbaric idea consisting in constant changes of transmitter frequency. The commission did, however, see fit to grant me 5,000 złotych for executing a model and as encouragement to further work." Cited in Władysław Kozaczuk, Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War II, 1984, p. 27.
  4. ^ "Random Matrix Theory for Wireless Communications" (PDF).
  5. ^ Ari Ben-Menahem, Historical Encyclopedia of Natural and Mathematical Sciences, Volume 1, Springer Science & Business Media - 2009, pages 4527-4530
  6. ^ American National Standard for Electromagnetic Noise and Field Strength Instrumentation, 10 Hz to 40 GHz—Specifications, ANSI C63.2-1996, Section 8.2 Overall Bandwidth


External links

BPC (time signal)

BPC is the callsign of a time signal broadcasting from the BPC Shangqiu Low-Frequency Time-Code Radio Station, cooperatively constructed by the National Time Service Center of the Chinese Academy of Sciences and Xi’an Gaohua Technology Co., Ltd.[1], since April 25, 2002.

BPC transmits a time signal on 68.5 kHz, which can be used for synchronizing radio controlled clocks. As opposed to other time signal transmitters, the signal format is not published openly; a special license is required. The transmission site is situated near Shangqiu, Henan Province at 34.457°N 115.837°E / 34.457; 115.837.BPC broadcasts at 90 kW for 21 hours per day, with a 3-hour break from 05:00–08:00 (China Standard Time) daily (21:00–24:00 UTC). BPC includes both conventional amplitude modulated time code and additional spread-spectrum time code, about which little is known.

Channel access method

In telecommunications and computer networks, a channel access method or multiple access method allows more than two terminals connected to the same transmission medium to transmit over it and to share its capacity. Examples of shared physical media are wireless networks, bus networks, ring networks and point-to-point links operating in half-duplex mode.

A channel access method is based on multiplexing, that allows several data streams or signals to share the same communication channel or transmission medium. In this context, multiplexing is provided by the physical layer.

A channel access method is also based on a multiple access protocol and control mechanism, also known as medium access control (MAC). Medium access control deals with issues such as addressing, assigning multiplex channels to different users, and avoiding collisions. Media access control is a sub-layer in the data link layer of the OSI model and a component of the link layer of the TCP/IP model.

Channel allocation schemes

In radio resource management for wireless and cellular networks, channel allocation schemes allocate bandwidth and communication channels to base stations, access points and terminal equipment. The objective is to achieve maximum system spectral efficiency in bit/s/Hz/site by means of frequency reuse, but still assure a certain grade of service by avoiding co-channel interference and adjacent channel interference among nearby cells or networks that share the bandwidth.

Channel-allocation schemes follow one of two types of strategy:

Fixed: FCA, fixed channel allocation: manually assigned by the network operator


DCA, dynamic channel allocation

DFS, dynamic frequency selection

Spread spectrum


A chirp is a signal in which the frequency increases (up-chirp) or decreases (down-chirp) with time. In some sources, the term chirp is used interchangeably with sweep signal. It is commonly used in sonar, radar, and laser, but has other applications, such as in spread-spectrum communications.

In spread-spectrum usage, surface acoustic wave (SAW) devices such as reflective array compressors (RACs) are often used to generate and demodulate the chirped signals. In optics, ultrashort laser pulses also exhibit chirp, which, in optical transmission systems, interacts with the dispersion properties of the materials, increasing or decreasing total pulse dispersion as the signal propagates. The name is a reference to the chirping sound made by birds; see bird vocalization.

Chirp spread spectrum

In digital communications, chirp spread spectrum (CSS) is a spread spectrum technique that uses wideband linear frequency modulated chirp pulses to encode information. A chirp is a sinusoidal signal of frequency increase or decrease over time (often with a polynomial expression for the relationship between time and frequency). In the picture is an example of an upchirp in which the frequency increases linearly over time. Sometimes the frequency of upchirps increase exponentially over time.

Code-division multiple access

Code-division multiple access (CDMA) is a channel access method used by various radio communication technologies.CDMA is an example of multiple access, where several transmitters can send information simultaneously over a single communication channel. This allows several users to share a band of frequencies (see bandwidth). To permit this without undue interference between the users, CDMA employs spread spectrum technology and a special coding scheme (where each transmitter is assigned a code).CDMA is used as the access method in many mobile phone standards. IS-95, also called "cdmaOne", and its 3G evolution CDMA2000, are often simply referred to as "CDMA", but UMTS, the 3G standard used by GSM carriers, also uses "wideband CDMA", or W-CDMA, as well as TD-CDMA and TD-SCDMA, as its radio technologies.

Direct-sequence spread spectrum

In telecommunications, direct-sequence spread spectrum (DSSS) is a spread spectrum modulation technique used to reduce overall signal interference. The spreading of this signal makes the resulting wideband channel more noisy, allowing for greater resistance to unintentional and intentional interference.A method of achieving the spreading of a given signal is provided by the modulation scheme. With DSSS, the message signal is used to modulate a bit sequence known as a Pseudo Noise (PN) code; this PN code consists of a radio pulse that is much shorter in duration (larger bandwidth) than the original message signal. This modulation of the message signal scrambles and spreads the pieces of data, and thereby resulting in a bandwidth size nearly identical to that of the PN sequence. In this context, the duration of the radio pulse for the PN code is referred to as the chip duration. The smaller this duration, the larger the bandwidth of the resulting DSSS signal; more bandwidth multiplexed to the message signal results in better resistance against interference.Some practical and effective uses of DSSS include the Code Division Multiple Access (CDMA) channel access method and the IEEE 802.11b specification used in Wi-Fi networks.

Frequency-hopping spread spectrum

Frequency-hopping spread spectrum (FHSS) is a method of transmitting radio signals by rapidly switching a carrier among many frequency channels, using a pseudorandom sequence known to both transmitter and receiver. It is used as a multiple access method in the code division multiple access (CDMA) scheme frequency-hopping code division multiple access (FH-CDMA).

Each available frequency band is divided into sub-frequencies. Signals rapidly change ("hop") among these in a predetermined order. Interference at a specific frequency will only affect the signal during that short interval. FHSS can, however, cause interference with adjacent direct-sequence spread spectrum (DSSS) systems.

Adaptive frequency-hopping spread spectrum (AFH), a specific type of FHSS, is used in Bluetooth wireless data transfer.

Hedy Lamarr

Hedy Lamarr (), born Hedwig Eva Maria Kiesler; November 9, 1914 – January 19, 2000) was an Austrian-born American film actress and inventor.After a brief early film career in Czechoslovakia, including the controversial Ecstasy (1933), she fled from her husband, a wealthy Austrian ammunition manufacturer, and secretly moved to Paris. Traveling to London, she met Metro-Goldwyn-Mayer studio head Louis B. Mayer, who offered her a movie contract in Hollywood. She became a film star with her performance in Algiers (1938). Her MGM films include Lady of the Tropics (1939), Boom Town (1940), H.M. Pulham, Esq. (1941), and White Cargo (1942). Her greatest success was as Delilah in Cecil B. DeMille's Samson and Delilah (1949). She also acted on television before the release of her final film, The Female Animal (1958). She was honored with a star on the Hollywood Walk of Fame in 1960.At the beginning of World War II, she and composer George Antheil developed a radio guidance system for Allied torpedoes that used spread spectrum and frequency hopping technology to defeat the threat of jamming by the Axis powers. Although the US Navy did not adopt the technology until the 1960s, the principles of their work are incorporated into Bluetooth technology and are similar to methods used in legacy versions Wi-Fi. This work led to their induction into the National Inventors Hall of Fame in 2014.

IEC 61334

IEC 61334, known as Distribution automation using distribution line carrier systems, is a standard for low-speed reliable power line communications by electricity meters, water meters and SCADA.

It is also known as spread frequency-shift keying (S-FSK) and was formerly known as IEC 1334 before IEC's most recent renumbering. It is actually a series of standards describing the researched physical environment of power lines, a well-adapted physical layer, a workable low-power media access layer, and a management interface. Related standards use the physical layer (e.g. Internet Protocol over S-FSK), but not the higher layers.The physical layer synchronizes a small packet of tones to the zero-crossing of the power line's voltage. The tones are chosen by utilities, not specified in the standard. Tones are usually between 20 kHz and 100 kHz, and should be separated by at least 10 kHz to prevent cross talk. One tone is chosen for mark (i.e. a binary 1), and the other for space (i.e. 0). The standard permits each zero-crossing to convey 1, 2, 4 or 8 bits, with increased sensitivity to timing as the number of bits increases. In multiphase power lines, a separate signal might be sent on each phase to speed up the transmission.

The standard's low speed is caused by the limited number of bits per power line cycle. The high reliability comes from its reliable timing system (i.e. zero crossing), high signal to noise ratio (frequencies are chosen to avoid common power line noise), lack of intermodulation distortion, and adaptive signal detection.

The most significant bits are sent first, unlike a conventional serial port. The data from zero crossings should be collected into 8-bit bytes. Each byte is collected into 42-byte packets. The first four bytes of each packet are a preamble to measure the channel's current condition. This is followed by 38 bytes of data, and 3 byte-times of silence.

The physical layer is adaptive. The silence and the preamble allow the receiver's signal processing to measure the channel's noise ratios. Depending on the signal to noise ratios, the bits can be recovered from the difference between the power of the mark and space tones, the power of the mark tones only, or the space tones only. The system should be able to adjust the receiving method on each 42-byte packet.

The bytes from the low-layer packets are reformed into bytes for the higher layers. The higher link-layer strongly resembles HDLC, except with a novel feature that allows selected stations to retransmit messages. The management interface layer provides remote control of a station's protocol layers, including diagnostics and configuration. For example, it lets a central controller read a unit's signal to noise ratios, and set the bit that enables a station to retransmit weak stations.The protocol layers are designed to integrate with any application layer, but the presence of a management interface suggests a design targeted to DLMS/COSEM, a widely used EU standard for the application layer of meters and SCADA. DLMS/COSEM requires a management interface.

IEEE 802.15.4a

IEEE 802.15.4a (formally called IEEE 802.15.4a-2007) was an amendment to IEEE 802.15.4-2006 specifying that additional physical layers (PHYs) be added to the original standard.

It has been merged into and is superseded by IEEE 802.15.4-2011.

Jim K. Omura

Jimmy K. Omura (born September 8, 1940 in San Jose, California) is an electrical engineer and information theorist.

Omura received his B.S. and M.S. from MIT, and his Ph.D. from Stanford University. He was a professor of electrical engineering at UCLA for 15 years. His notable work includes the design of a number of spread spectrum communications systems, and the Massey-Omura cryptosystem (with James Massey). With Andrew Viterbi he co-authored Principles of Digital Communication and Coding (ISBN 0070675163), a standard textbook in digital communications. He also co-authored the Spread Spectrum Communications Handbook (ISBN 0071382151).

Omura founded the data security company Cylink, which had an IPO in 1996 and was acquired by SafeNet in 2003. He was the Technology Strategist for the Gordon and Betty Moore Foundation during 2002 - 2011.

In 2005 Jim Omura received the IEEE Alexander Graham Bell Medal. He was elected to the National Academy of Engineering in 1997 and was inducted into the Silicon Valley Engineering Hall of Fame in 2009.

Multi-carrier code-division multiple access

Multi-carrier code-division multiple access (MC-CDMA) is a multiple access scheme used in OFDM-based telecommunication systems, allowing the system to support multiple users at the same time over same frequency band.

MC-CDMA spreads each user symbol in the frequency domain. That is, each user symbol is carried over multiple parallel subcarriers, but it is phase-shifted (typically 0 or 180 degrees) according to a code value. The code values differ per subcarrier and per user. The receiver combines all subcarrier signals, by weighing these to compensate varying signal strengths and undo the code shift. The receiver can separate signals of different users, because these have different (e.g. orthogonal) code values.

Since each data symbol occupies a much wider bandwidth (in hertz) than the data rate (in bit/s), a ratio of signal to noise-plus-interference (if defined as signal power divided by total noise plus interference power in the entire transmission band) of less than 0 dB is feasible.

One way of interpreting MC-CDMA is to regard it as a direct-sequence CDMA signal (DS-CDMA), which is transmitted after it has been fed through an inverse FFT (fast Fourier transform).

Pseudorandom noise

In cryptography, pseudorandom noise (PRN ) is a signal similar to noise which satisfies one or more of the standard tests for statistical randomness. Although it seems to lack any definite pattern, pseudorandom noise consists of a deterministic sequence of pulses that will repeat itself after its period.In cryptographic devices, the pseudorandom noise pattern is determined by a key and the repetition period can be very long, even millions of digits.

Pseudorandom noise is used in some electronic musical instruments, either by itself or as an input to subtractive synthesis, and in many white noise machines.

In spread-spectrum systems, the receiver correlates a locally generated signal with the received signal. Such spread-spectrum systems require a set of one or more "codes" or "sequences" such that

Like random noise, the local sequence has a very low correlation with any other sequence in the set, or with the same sequence at a significantly different time offset, or with narrow band interference, or with thermal noise.

Unlike random noise, it must be easy to generate exactly the same sequence at both the transmitter and the receiver, so the receiver's locally generated sequence has a very high correlation with the transmitted sequence.In a direct-sequence spread spectrum system, each bit in the pseudorandom binary sequence is known as a chip and the inverse of its period as chip rate; compare bit rate and symbol rate.

In a frequency-hopping spread spectrum sequence, each value in the pseudorandom sequence is known as a channel number and the inverse of its period as the hop rate. FCC Part 15 mandates at least 50 different channels and at least a 2.5 Hz hop rate for narrow band frequency-hopping systems.

GPS satellites broadcast data at a rate of 50 data bits per second – each satellite modulates its data with one PN bit stream at 1.023 million chips per second and the same data with another PN bit stream at 10.23 million chips per second.

GPS receivers correlate the received PN bit stream with a local reference to measure distance. GPS is a receive-only system that uses relative timing measurements from several satellites (and the known positions of the satellites) to determine receiver position.

Other range-finding applications involve two-way transmissions. A local station generates a pseudorandom bit sequence and transmits it to the remote location (using any modulation technique). Some object at the remote location echoes this PN signal back to the location station – either passively, as in some kinds of radar and sonar systems, or using an active transponder at the remote location, as in the Apollo Unified S-band system. By correlating a (delayed version of) the transmitted signal with the received signal, a precise round trip time to the remote location can be determined and thus the distance.

Quantum network

Quantum networks form an important element of quantum computing and quantum communication systems. Quantum networks facilitate the transmission of information in the form of quantum bits, also called qubits, between physically separated quantum processors. A quantum processor is a small quantum computer being able to perform quantum logic gates on a certain number of qubits. Quantum networks work in a similar way to classical networks. The main difference, as will be detailed more in later paragraphs, is that quantum networking like quantum computing is better at solving certain problems, such as modeling quantum systems.

SATA Express

SATA Express (abbreviated from Serial ATA Express and sometimes unofficially shortened to SATAe) is a computer bus interface that supports both Serial ATA (SATA) and PCI Express (PCIe) storage devices, initially standardized in the SATA 3.2 specification. The SATA Express connector used on the host side is backward compatible with the standard SATA data connector, while it also provides two PCI Express lanes as a pure PCI Express connection to the storage device.Instead of continuing with the SATA interface's usual approach of doubling its native speed with each major version, SATA 3.2 specification included the PCI Express bus for achieving data transfer speeds greater than the SATA 3.0 speed limit of 6 Gbit/s. Designers of the SATA interface concluded that doubling the native SATA speed would take too much time to catch up with the advancements in solid-state drive (SSD) technology, would require too many changes to the SATA standard, and would result in a much greater power consumption compared with the existing PCI Express bus. As a widely adopted computer bus, PCI Express provides sufficient bandwidth while allowing easy scaling up by using faster or additional lanes.In addition to supporting legacy Advanced Host Controller Interface (AHCI) at the logical interface level, SATA Express also supports NVM Express (NVMe) as the logical device interface for attached PCI Express storage devices. While the support for AHCI ensures software-level backward compatibility with legacy SATA devices and legacy operating systems, NVM Express is designed to fully utilize high-speed PCI Express storage devices by leveraging their capability of executing many I/O operations in parallel.

Spread-spectrum time-domain reflectometry

Spread-spectrum time-domain reflectometry (SSTDR) is a measurement technique to identify faults, usually in electrical wires, by observing reflected spread spectrum signals. This type of time-domain reflectometry can be used in various high-noise and live environments. Additionally, SSTDR systems have the additional benefit of being able to precisely locate the position of the fault. Specifically, SSTDR is accurate to within a few centimeters for wires carrying 400 Hz aircraft signals as well as MIL-STD-1553 data bus signals. AN SSTDR system can be run on a live wire because the spread spectrum signals can be isolated from the system noise and activity.

At the most basic level, the system works by sending spread spectrum signals down a wireline and waiting for those signals to be reflected back to the SSTDR system. The reflected signal is then correlated with a copy of the sent signal. Mathematical algorithms are applied to both the shape and timing of the signals to locate either the short or the end of an open circuit.


Time-hopping (TH) is a communications signal technique which can be used to achieve anti-jamming (AJ) or low probability of intercept (LPI). It can also refer to pulse-position modulation, which in its simplest form employs 2k discrete pulses (referring to the unique positions of the pulse within the transmission window) to transmit k bit(s) per pulse.


A watermark is an identifying image or pattern in paper that appears as various shades of lightness/darkness when viewed by transmitted light (or when viewed by reflected light, atop a dark background), caused by thickness or density variations in the paper.

Watermarks have been used on postage stamps, currency, and other government documents to discourage counterfeiting. There are two main ways of producing watermarks in paper; the dandy roll process, and the more complex cylinder mould process.

Watermarks vary greatly in their visibility; while some are obvious on casual inspection, others require some study to pick out. Various aids have been developed, such as watermark fluid that wets the paper without damaging it. A watermark is very useful in the examination of paper because it can be used for dating, identifying sizes, mill trademarks and locations, and determining the quality of a sheet of paper.

The word is also used for digital practices that share similarities with physical watermarks. In one case, overprint on computer-printed output may be used to identify output from an unlicensed trial version of a program. In another instance, identifying codes can be encoded as a digital watermark for a music, video, picture, or other file.

Spread spectrum in digital communications
Main articles
Spread spectrum methods
CDMA schemes
Major implementations
Major concepts
Network topology
and switching

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