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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 an audio frequency analog message signal. If this distinction is not necessary, the term SNR is often used instead of CNR, with the same definition.

- Definition
- Measurements and estimation
- Carrier-to-noise density ratio
- See also
- References
- Further reading

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, 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 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 and are 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, 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.^{ [1] } 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 is why CNR estimation techniques are timely and important.

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In satellite communications, **carrier-to-noise-density ratio** (* C/N_{0}*) is the ratio of the carrier power

It determines whether a receiver can lock on to 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 dBHz.

The noise power density, *N _{0}*=

- C/I: carrier-to-interference ratio
- E
_{b}/N_{0}(energy per bit relative to noise power spectral density) - E
_{s}/N_{0}(energy per symbol relative to noise power spectral density) - Signal-to-interference ratio (SIR or
*S*/*I*) - Signal-to-noise ratio (SNR or
*S*/*N*) - SINAD (ratio of signal-plus-noise-plus-distortion to noise-plus-distortion)

**Frequency modulation** (**FM**) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The term and technology are used in computing, signal processing and telecommunications.

In telecommunications, **orthogonal frequency-division multiplexing** (**OFDM**) is a type of digital transmission and a method of encoding digital data on multiple carrier frequencies. OFDM has developed into a popular scheme for wideband digital communication, used in applications such as digital television and audio broadcasting, DSL internet access, wireless networks, power line networks, and 4G/5G mobile communications.

In digital transmission, the number of **bit errors** is the number of received bits of a data stream over a communication channel that have been altered due to noise, interference, distortion or bit synchronization errors.

**Noise figure** (NF) and **noise factor** (*F*) are measures of degradation of the signal-to-noise ratio (SNR), caused by components in a signal chain. It is a number by which the performance of an amplifier or a radio receiver can be specified, with lower values indicating better performance.

In electronics, **noise temperature** is one way of expressing the level of available noise power introduced by a component or source. The power spectral density of the noise is expressed in terms of the temperature that would produce that level of Johnson–Nyquist noise, thus:

**Phase-shift keying** (**PSK**) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal. 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.

**Signal-to-noise ratio** is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in decibels. A ratio higher than 1:1 indicates more signal than noise.

**Signal-to-noise and distortion ratio** (**SINAD**) is a measure of the quality of a signal from a communications device, often defined as

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 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.

**Additive white Gaussian noise** (**AWGN**) is a basic noise model used in information theory to mimic the effect of many random processes that occur in nature. The modifiers denote specific characteristics:

In signal processing, a **matched filter** is obtained by correlating a known delayed signal, or *template*, with an unknown signal to detect the presence of the template in the unknown signal. This is equivalent to convolving the unknown signal with a conjugated time-reversed version of the template. The matched filter is the optimal linear filter for maximizing the signal-to-noise ratio (SNR) in the presence of additive stochastic noise.

In digital communication or data transmission, ** E_{b}/N_{0}** is a normalized signal-to-noise ratio (SNR) measure, also known as the "SNR per bit". It is especially useful when comparing the bit error rate (BER) performance of different digital modulation schemes without taking bandwidth into account.

**Friis formula** or **Friis's formula**, named after Danish-American electrical engineer Harald T. Friis, is either of two formulas used in telecommunications engineering to calculate the signal-to-noise ratio of a multistage amplifier. One relates to noise factor while the other relates to noise temperature.

**dBc** is the power ratio of a signal to a carrier signal, expressed in decibels. For example, phase noise is expressed in dBc/Hz at a given frequency offset from the carrier. dBc can also be used as a measurement of Spurious-Free Dynamic Range (SFDR) between the desired signal and unwanted spurious outputs resulting from the use of signal converters such as a digital-to-analog converter or a frequency mixer.

**Signal-to-Quantization-Noise Ratio** is widely used quality measure in analysing digitizing schemes such as PCM and multimedia codecs. The SQNR reflects the relationship between the maximum nominal signal strength and the quantization error introduced in the analog-to-digital conversion.

In electronics, **noise** is an unwanted disturbance in an electrical signal. Noise generated by electronic devices varies greatly as it is produced by several different effects.

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

**Effective number of bits** (**ENOB**) is a measure of the dynamic range of an analog-to-digital converter (ADC), digital-to-analog converter, or their associated circuitry. The resolution of an ADC is specified by the number of bits used to represent the analog value. Ideally, a 12-bit ADC will have an effective number of bits of almost 12. However, real signals have noise, and real circuits are imperfect and introduce additional noise and distortion. Those imperfections reduce the number of bits of accuracy in the ADC. The ENOB describes the effective resolution of the system in bits. An ADC may have 12-bit resolution, but the effective number of bits when used in a system may be 9.5.

The **signal-to-interference ratio**, also known as the **carrier-to-interference ratio**, is the quotient between the average received modulated carrier power *S* or *C* and the average received co-channel interference power *I*, i.e. cross-talk, from other transmitters than the useful signal.

In information theory and telecommunication engineering, the **signal-to-interference-plus-noise ratio** (**SINR**) is a quantity used to give theoretical upper bounds on channel capacity in wireless communication systems such as networks. Analogous to the signal-to-noise ratio (SNR) used often in wired communications systems, the SINR is defined as the power of a certain signal of interest divided by the sum of the interference power and the power of some background noise. If the power of noise term is zero, then the SINR reduces to the signal-to-interference ratio (SIR). Conversely, zero interference reduces the SINR to the SNR, which is used less often when developing mathematical models of wireless networks such as cellular networks.

- ↑ Islam, A. K. M. Najmul; Lohan, E. S.; Renfors, M. (Mar 2008). "Moment based CNR estimators for BOC/BPSK modulated signal for Galileo/GPS".
*2008 5th Workshop on Positioning, Navigation and Communication*. pp. 129–136. doi:10.1109/WPNC.2008.4510366. ISBN 978-1-4244-1798-8.

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