In telecommunications, the carrier-to-noise ratio, often written CNR or C/N, is the signal-to-noise ratio of a modulatedsignal. The term is used to distinguish the CNR of the radio frequencypassband 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. Digitally modulated signals are basically made of two CW carriers. In fact, the information 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, instead of signal-to-noise-ratio, 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 of a digital message signal, or high SNR of an analog message signal.
Definition
The carrier-to-noise ratio is defined as the ratio of the received modulated carrier signalpowerC to the received noise powerN 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 voltagelevels of the carrier signal and noise respectively. C/N ratios are often specified in decibels : or in term of voltage:
The C/N ratio is measured in a manner similar to the way the signal-to-noise ratio 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, and the carrier-to-noise-and-interference ratio, C/ 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, and that is why CNR estimation techniques are timely and important.
In satellite communications, carrier-to-noise-density ratio is the ratio of the carrier power C to the noise power densityN0, 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 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, N0=kT, is the receiver noise power per hertz, which can be written in terms of the Boltzmann constantk and the noise temperatureT .
