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38-397: The CIR resembles the carrier-to-noise ratio (CNR or C/N ), which is the signal-to-noise ratio (SNR or S/N ) of a modulated signal before demodulation. A distinction is that interfering radio transmitters contributing to I may be controlled by radio resource management , while N involves noise power from other sources, typically additive white Gaussian noise (AWGN). The CIR ratio

76-531: A capacity. But such an errorless channel is an idealization, and if M is chosen small enough to make the noisy channel nearly errorless, the result is necessarily less than the Shannon capacity of the noisy channel of bandwidth B {\displaystyle B} , which is the Hartley–Shannon result that followed later. Claude Shannon 's development of information theory during World War II provided

114-540: A channel of bandwidth B {\displaystyle B} hertz was 2 B {\displaystyle 2B} pulses per second, to arrive at his quantitative measure for achievable line rate. Hartley's law is sometimes quoted as just a proportionality between the analog bandwidth , B {\displaystyle B} , in Hertz and what today is called the digital bandwidth , R {\displaystyle R} , in bit/s. Other times it

152-461: A coding technique which allows the probability of error at the receiver to be made arbitrarily small. This means that theoretically, it is possible to transmit information nearly without error up to nearly a limit of C {\displaystyle C} bits per second. The converse is also important. If the probability of error at the receiver increases without bound as the rate is increased, so no useful information can be transmitted beyond

190-483: A communication link, a bound on the maximum amount of error-free information per time unit that can be transmitted with a specified bandwidth in the presence of the noise interference, assuming that the signal power is bounded, and that the Gaussian noise process is characterized by a known power or power spectral density. The law is named after Claude Shannon and Ralph Hartley . The Shannon–Hartley theorem states

228-487: A digital message signal, or high SNR of an analog message signal. The carrier-to-noise ratio is defined as the ratio of the received modulated carrier signal power C to the received noise power N after the receiver filters: When both carrier and noise are measured across the same impedance , this ratio can equivalently be given as: where V C {\displaystyle V_{C}} and V N {\displaystyle V_{N}} are

266-533: A known variance. Since the variance of a Gaussian process is equivalent to its power, it is conventional to call this variance the noise power. Such a channel is called the Additive White Gaussian Noise channel, because Gaussian noise is added to the signal; "white" means equal amounts of noise at all frequencies within the channel bandwidth. Such noise can arise both from random sources of energy and also from coding and measurement error at

304-492: A noise process consisting of adding a random wave whose amplitude is 1 or −1 at any point in time, and a channel that adds such a wave to the source signal. Such a wave's frequency components are highly dependent. Though such a noise may have a high power, it is fairly easy to transmit a continuous signal with much less power than one would need if the underlying noise was a sum of independent noises in each frequency band. For large or small and constant signal-to-noise ratios,

342-550: A signal-to-noise ratio, but achieving reliability through error-correction coding rather than through reliably distinguishable pulse levels. If there were such a thing as a noise-free analog channel, one could transmit unlimited amounts of error-free data over it per unit of time (Note that an infinite-bandwidth analog channel could not transmit unlimited amounts of error-free data absent infinite signal power). Real channels, however, are subject to limitations imposed by both finite bandwidth and nonzero noise. Bandwidth and noise affect

380-505: A very conservative value of M {\displaystyle M} to achieve a low error rate. The concept of an error-free capacity awaited Claude Shannon, who built on Hartley's observations about a logarithmic measure of information and Nyquist's observations about the effect of bandwidth limitations. Hartley's rate result can be viewed as the capacity of an errorless M -ary channel of 2 B {\displaystyle 2B} symbols per second. Some authors refer to it as

418-407: A way to quantify information and its line rate (also known as data signalling rate R bits per second). This method, later known as Hartley's law, became an important precursor for Shannon's more sophisticated notion of channel capacity. Hartley argued that the maximum number of distinguishable pulse levels that can be transmitted and received reliably over a communications channel is limited by

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456-519: Is a stub . You can help Misplaced Pages by expanding it . Carrier-to-noise ratio In telecommunications , the carrier-to-noise ratio , often written CNR or C/N , is the signal-to-noise ratio (SNR) of a modulated signal. The term is used to distinguish the CNR of the radio frequency passband signal from the SNR of an analog base band message signal after demodulation . For example, with FM radio,

494-483: Is a limit to the amount of information that can be transferred by a signal of a bounded power, even when sophisticated multi-level encoding techniques are used. In the channel considered by the Shannon–Hartley theorem, noise and signal are combined by addition. That is, the receiver measures a signal that is equal to the sum of the signal encoding the desired information and a continuous random variable that represents

532-439: Is essentially as good as the best possible code; the theorem is proved through the statistics of such random codes. Shannon's theorem shows how to compute a channel capacity from a statistical description of a channel, and establishes that given a noisy channel with capacity C {\displaystyle C} and information transmitted at a line rate R {\displaystyle R} , then if there exists

570-440: Is quoted in this more quantitative form, as an achievable line rate of R {\displaystyle R} bits per second: Hartley did not work out exactly how the number M should depend on the noise statistics of the channel, or how the communication could be made reliable even when individual symbol pulses could not be reliably distinguished to M levels; with Gaussian noise statistics, system designers had to choose

608-434: Is studied in interference limited systems, i.e. where I dominates over N , typically in cellular radio systems and broadcasting systems where frequency channels are reused in view to achieve high level of area coverage. The C/N is studied in noise limited systems. If both situations can occur, the carrier-to-noise-and-interference ratio (CNIR or C/(N+I) ) may be studied. This article related to telecommunications

646-630: Is the bandwidth (in hertz). The quantity 2 B {\displaystyle 2B} later came to be called the Nyquist rate , and transmitting at the limiting pulse rate of 2 B {\displaystyle 2B} pulses per second as signalling at the Nyquist rate . Nyquist published his results in 1928 as part of his paper "Certain topics in Telegraph Transmission Theory". During 1928, Hartley formulated

684-411: Is why CNR estimation techniques are timely and important. In satellite communications , carrier-to-noise-density ratio ( C/N 0 ) is the ratio of the carrier power C to the noise power density N 0 , expressed in dB-Hz . When considering only the receiver as a source of noise, it is called carrier-to-receiver-noise-density ratio . It determines whether a receiver can lock on to

722-506: The C/N ratio is equivalent to the S/N ratio. The C/N ratio resembles the carrier-to-interference ratio ( C/I , CIR ), and the carrier-to-noise-and-interference ratio , C/(N+I) or CNIR . C/N estimators are needed to optimize the receiver performance. Typically, it is easier to measure the total power than the ratio of signal power to noise power (or noise power spectral density), and that

760-459: The channel capacity C {\displaystyle C} , meaning the theoretical tightest upper bound on the information rate of data that can be communicated at an arbitrarily low error rate using an average received signal power S {\displaystyle S} through an analog communication channel subject to additive white Gaussian noise (AWGN) of power N {\displaystyle N} : where During

798-411: The root mean square (RMS) voltage levels of the carrier signal and noise respectively. C / N ratios are often specified in decibels (dB): or in term of voltage: The C/N ratio is measured in a manner similar to the way the signal-to-noise ratio ( S/N ) is measured, and both specifications give an indication of the quality of a communications channel. In the famous Shannon–Hartley theorem ,

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836-484: The additive noise is not white (or that the ⁠ S / N {\displaystyle S/N} ⁠ is not constant with frequency over the bandwidth) is obtained by treating the channel as many narrow, independent Gaussian channels in parallel: where Note: the theorem only applies to Gaussian stationary process noise. This formula's way of introducing frequency-dependent noise cannot describe all continuous-time noise processes. For example, consider

874-500: The capacity formula can be approximated: When the SNR is large ( S / N ≫ 1 ), the logarithm is approximated by in which case the capacity is logarithmic in power and approximately linear in bandwidth (not quite linear, since N increases with bandwidth, imparting a logarithmic effect). This is called the bandwidth-limited regime . where Similarly, when the SNR is small (if ⁠ S / N ≪ 1 {\displaystyle S/N\ll 1} ⁠ ), applying

912-649: The carrier and if the information encoded in the signal can be retrieved, given the amount of noise present in the received signal. The carrier-to-receiver noise density ratio is usually expressed in dB-Hz . The noise power density, N 0 = kT , is the receiver noise power per hertz , which can be written in terms of the Boltzmann constant k (in joules per kelvin ) and the noise temperature T (in kelvins). [REDACTED]  This article incorporates public domain material from Federal Standard 1037C . General Services Administration . Archived from

950-473: The channel capacity. The theorem does not address the rare situation in which rate and capacity are equal. The Shannon–Hartley theorem establishes what that channel capacity is for a finite-bandwidth continuous-time channel subject to Gaussian noise. It connects Hartley's result with Shannon's channel capacity theorem in a form that is equivalent to specifying the M in Hartley's line rate formula in terms of

988-415: The dynamic range of the signal amplitude and the precision with which the receiver can distinguish amplitude levels. Specifically, if the amplitude of the transmitted signal is restricted to the range of [− A ... + A ] volts, and the precision of the receiver is ±Δ V volts, then the maximum number of distinct pulses M is given by By taking information per pulse in bit/pulse to be the base-2- logarithm of

1026-469: The ideas of Nyquist and Hartley, and then formulated a complete theory of information and its transmission. In 1927, Nyquist determined that the number of independent pulses that could be put through a telegraph channel per unit time is limited to twice the bandwidth of the channel. In symbolic notation, where f p {\displaystyle f_{p}} is the pulse frequency (in pulses per second) and B {\displaystyle B}

1064-527: The information (bits or symbols) is carried by given combinations of phase and/or amplitude of the I and Q components. It is for this reason that, in the context of digital modulations, digitally modulated signals are usually referred to as carriers. Therefore, the term carrier-to-noise-ratio (CNR), instead of signal-to-noise-ratio (SNR), is preferred to express the signal quality when the signal has been digitally modulated. High C/N ratios provide good quality of reception, for example low bit error rate (BER) of

1102-422: The late 1920s, Harry Nyquist and Ralph Hartley developed a handful of fundamental ideas related to the transmission of information, particularly in the context of the telegraph as a communications system. At the time, these concepts were powerful breakthroughs individually, but they were not part of a comprehensive theory. In the 1940s, Claude Shannon developed the concept of channel capacity, based in part on

1140-412: The net data rate that can be approached with coding is equivalent to using that M {\displaystyle M} in Hartley's law. In the simple version above, the signal and noise are fully uncorrelated, in which case S + N {\displaystyle S+N} is the total power of the received signal and noise together. A generalization of the above equation for the case where

1178-404: The next big step in understanding how much information could be reliably communicated through noisy channels. Building on Hartley's foundation, Shannon's noisy channel coding theorem (1948) describes the maximum possible efficiency of error-correcting methods versus levels of noise interference and data corruption. The proof of the theorem shows that a randomly constructed error-correcting code

Signal-to-interference ratio - Misplaced Pages Continue

1216-400: The noise. This addition creates uncertainty as to the original signal's value. If the receiver has some information about the random process that generates the noise, one can in principle recover the information in the original signal by considering all possible states of the noise process. In the case of the Shannon–Hartley theorem, the noise is assumed to be generated by a Gaussian process with

1254-401: The number of distinct messages M that could be sent, Hartley constructed a measure of the line rate R as: where f p {\displaystyle f_{p}} is the pulse rate, also known as the symbol rate, in symbols/second or baud . Hartley then combined the above quantification with Nyquist's observation that the number of independent pulses that could be put through

1292-600: The original on 2022-01-22.  (in support of MIL-STD-188 ). Shannon%E2%80%93Hartley theorem In information theory , the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise . It is an application of the noisy-channel coding theorem to the archetypal case of a continuous-time analog communications channel subject to Gaussian noise . The theorem establishes Shannon's channel capacity for such

1330-455: The power ratio back to a voltage ratio, so the number of levels is approximately proportional to the ratio of signal RMS amplitude to noise standard deviation. This similarity in form between Shannon's capacity and Hartley's law should not be interpreted to mean that M {\displaystyle M} pulse levels can be literally sent without any confusion. More levels are needed to allow for redundant coding and error correction, but

1368-446: The rate at which information can be transmitted over an analog channel. Bandwidth limitations alone do not impose a cap on the maximum information rate because it is still possible for the signal to take on an indefinitely large number of different voltage levels on each symbol pulse, with each slightly different level being assigned a different meaning or bit sequence. Taking into account both noise and bandwidth limitations, however, there

1406-425: The sender and receiver respectively. Since sums of independent Gaussian random variables are themselves Gaussian random variables, this conveniently simplifies analysis, if one assumes that such error sources are also Gaussian and independent. Comparing the channel capacity to the information rate from Hartley's law, we can find the effective number of distinguishable levels M : The square root effectively converts

1444-466: The strength of the 100 MHz carrier with modulations would be considered for CNR, whereas the audio frequency analogue message signal would be for SNR; in each case, compared to the apparent noise. If this distinction is not necessary, the term SNR is often used instead of CNR, with the same definition. Digitally modulated signals (e.g. QAM or PSK ) are basically made of two CW carriers (the I and Q components, which are out-of-phase carriers). In fact,

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