QAM MER — Modulation Error Ratio
The modulation error is a calculated quantity indicating the mean or the maximum deviation of the I/Q values from ideal signal states and thus provides a measure of signal quality.
The following diagram shows the vectors used for calculating the modulation error:
The modulation error is specified as rms and as peak value. To calculate the modulation error, all decisions fields are investigated on after the other.
To obtain peak modulation error, the maximum magnitude of the difference vector (error vector) formed by the vector of the ideal and the actual signal status is determined for each decision field. From the maximum value of these results, the peak MER (modulation error ratio) is calculated using the following formula:
To obtain the rms modulation error, the squares of the magnitude of all differential vectors formed by the ideal-status and actual-status vectors are added up, and the number of symbols is counted. Then the rms modulation error is calculated as follows:
The peak and rms modulation error can also be specified on a logarithmic scale. Conversion is done using the following formula:
For quantized I/Q values, the peak value is output in discrete form only since no averaging is performed in the calculation. The rms modulation error can be calculated within the limit values specified in the following table. The limit values are obtained for quantized I/Q values:
Orderof QAM , MERRMS min, MERPK min, MERPK min , MERdB min
4 , 0.5 % 1.563 % 98.44 % 46 dB
16 , 0.5 % 1.398 % 43.32 % 46 dB
32 , 0.7 % 1.976 % 29.33 % 43 dB
64 , 0.5 % 1.364 % 20.46 % 46 dB
128 , 0.7 % 1.952 % 13.66 % 43 dB
256 , 0.5 % 1.356 % 9.471 % 46 dB
Attached herewith the Vector diagram and Formulas to calculate the MER.