Modulation error ratio

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The modulation error ratio or MER is a measure used to quantify the performance of a digital radio (or digital TV) transmitter or receiver in a communications system using digital modulation (such as QAM). A signal sent by an ideal transmitter or received by a receiver would have all constellation points precisely at the ideal locations, however various imperfections in the implementation (such as noise, low image rejection ratio, phase noise, carrier suppression, distortion, etc.) or signal path cause the actual constellation points to deviate from the ideal locations.

Digital radio is the use of digital technology to transmit or receive across the radio spectrum. Digital transmission by radio waves includes digital broadcasting, and especially digital audio radio services.

Quadrature amplitude modulation (QAM) is the name of a family of digital modulation methods and a related family of analog modulation methods widely used in modern telecommunications to transmit information. It conveys two analog message signals, or two digital bit streams, by changing (modulating) the amplitudes of two carrier waves, using the amplitude-shift keying (ASK) digital modulation scheme or amplitude modulation (AM) analog modulation scheme. The two carrier waves of the same frequency are out of phase with each other by 90°, a condition known as orthogonality or quadrature. The transmitted signal is created by adding the two carrier waves together. At the receiver, the two waves can be coherently separated (demodulated) because of their orthogonality property. Another key property is that the modulations are low-frequency/low-bandwidth waveforms compared to the carrier frequency, which is known as the narrowband assumption.

Constellation diagram

A constellation diagram is a representation of a signal modulated by a digital modulation scheme such as quadrature amplitude modulation or phase-shift keying. It displays the signal as a two-dimensional xy-plane scatter diagram in the complex plane at symbol sampling instants. The angle of a point, measured counterclockwise from the horizontal axis, represents the phase shift of the carrier wave from a reference phase. The distance of a point from the origin represents a measure of the amplitude or power of the signal.


Transmitter MER can be measured by specialized equipment, which demodulates the received signal in a similar way to how a real radio demodulator does it. Demodulated and detected signal can be used as a reasonably reliable estimate for the ideal transmitted signal in MER calculation.

Demodulation is extracting the original information-bearing signal from a carrier wave. A demodulator is an electronic circuit that is used to recover the information content from the modulated carrier wave. There are many types of modulation so there are many types of demodulators. The signal output from a demodulator may represent sound, images or binary data.


An error vector is a vector in the I-Q plane between the ideal constellation point and the point received by the receiver. The Euclidean distance between the two points is its magnitude.

The modulation error ratio is equal to the ratio of the root mean square (RMS) power (in Watts) of the reference vector to the power (in Watts) of the error. It is defined in dB as:

In mathematics and its applications, the root mean square is defined as the square root of the mean square . The RMS is also known as the quadratic mean and is a particular case of the generalized mean with exponent 2. RMS can also be defined for a continuously varying function in terms of an integral of the squares of the instantaneous values during a cycle.

The decibel is a unit of measurement used to express the ratio of one value of a power or field quantity to another, on a logarithmic scale, the logarithmic quantity being called the power level or field level, respectively. It can be used to express a change in value or an absolute value. In the latter case, it expresses the ratio of a value to a fixed reference value; when used in this way, a suffix that indicates the reference value is often appended to the decibel symbol. For example, if the reference value is 1 volt, then the suffix is "V", and if the reference value is one milliwatt, then the suffix is "m".

where Perror is the RMS power of the error vector, and Psignal is the RMS power of ideal transmitted signal.

MER is defined as a percentage in a compatible (but reciprocal) way:

Percentage Number or ratio as a fraction of 100

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", or the abbreviations "pct.", "pct"; sometimes the abbreviation "pc" is also used. A percentage is a dimensionless number.

with the same definitions.

MER is closely related to error vector magnitude (EVM), but MER is calculated from the average power of the signal. MER is also closely related to signal-to-noise ratio. MER includes all imperfections including deterministic amplitude imbalance, quadrature error and distortion, while noise is random by nature.

The error vector magnitude or EVM is a measure used to quantify the performance of a digital radio transmitter or receiver. A signal sent by an ideal transmitter or received by a receiver would have all constellation points precisely at the ideal locations, however various imperfections in the implementation cause the actual constellation points to deviate from the ideal locations. Informally, EVM is a measure of how far the points are from the ideal locations.

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.

Distortion is the alteration of the original shape of something. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signal representing sound or a video signal representing images, in an electronic device or communication channel.

See also

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Carrier recovery

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