Modulation error ratio
Encyclopedia
The modulation error ratio or MER is a measure used to quantify the performance of a digital radio 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.
Transmitter MER can be measured by specialised 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.
The modulation error ratio is equal to the ratio of the root mean square
(RMS) power of the error vector to the power of the reference. It is defined in dB
as:
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:
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.
Quadrature amplitude modulation
Quadrature amplitude modulation is both an analog and a digital modulation scheme. It conveys two analog message signals, or two digital bit streams, by changing the amplitudes of two carrier waves, using the amplitude-shift keying digital modulation scheme or amplitude modulation analog...
). A signal sent by an ideal transmitter or received by a receiver would have all constellation points
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 scatter diagram in the complex plane at symbol sampling instants...
precisely at the ideal locations, however various imperfections in the implementation (such as noise, low image rejection ratio
Image rejection ratio
In radio, the image rejection ratio, or image frequency rejection ratio, is the ratio of the intermediate-frequency signal level produced by the desired input frequency to that produced by the image frequency. The image rejection ratio is usually expressed in dB...
, phase noise
Phase noise
Phase noise is the frequency domain representation of rapid, short-term, random fluctuations in the phase of a waveform, caused by time domain instabilities...
, carrier suppression, distortion
Distortion
A distortion is the alteration of the original shape of an object, image, sound, waveform or other form of information or representation. Distortion is usually unwanted, and often many methods are employed to minimize it in practice...
, etc.) or signal path cause the actual constellation points to deviate from the ideal locations.
Transmitter MER can be measured by specialised equipment, which demodulates
Demodulation
Demodulation is the act of extracting the original information-bearing signal from a modulated carrier wave.A demodulator is an electronic circuit that is used to recover the information content from the modulated carrier wave.These terms are traditionally used in connection with radio receivers,...
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.
Definition
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
Root mean square
In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids...
(RMS) power of the error vector to the power of the reference. It is defined in dB
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
as:
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
Percentage
In mathematics, a percentage is a way of expressing a number as a fraction of 100 . It is often denoted using the percent sign, “%”, or the abbreviation “pct”. For example, 45% is equal to 45/100, or 0.45.Percentages are used to express how large/small one quantity is, relative to another quantity...
in a compatible (but reciprocal) way:
with the same definitions.
MER is closely related to error vector magnitude
Error vector magnitude
The error vector magnitude or EVM is a measure used to quantify the performance of a digital radio transmitter or receiver...
(EVM), but MER is calculated from the average power of the signal. MER is also closely related to signal-to-noise ratio
Signal-to-noise ratio
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. It is defined as the ratio of signal power to the noise power. A ratio higher than 1:1 indicates more signal than noise...
. MER includes all imperfections including deterministic amplitude imbalance, quadrature error and distortion
Distortion
A distortion is the alteration of the original shape of an object, image, sound, waveform or other form of information or representation. Distortion is usually unwanted, and often many methods are employed to minimize it in practice...
, while noise is random by nature.