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Digital Signal Analysis
Digital signals such as QPSK & QAM use many different factors to determine the quality and performance of the signal. This page will describe some of the most common factors used in digital signal analysis.
QAM Signal to Noise Ratio (SNR) vs. BER
The theoretical bit-error rate of the QAM signal as a function of the SNR is provided for reference.
To obtain an estimated BER of the QAM signal, one can use the following diagram to get theoretical values for BER. In the case that the QAM 64 mode SNR is >32, it indicates 10-12 BER. It should be noted that changing the S/N value by as little as 1 dB alters approximately one decade. The diagram below depicts the theoretical BER vs. SNR:
QAM Signal to Noise Ratio
The following table depicts the theoretical maximum values for various orders of QAM:
Order of QAM |
SNR max |
|---|---|
4 |
46.0 dB |
16 |
46.0 dB |
32 |
43.0 dB |
64 |
46.0 dB |
128 |
43.0 dB |
256 |
46.0 dB |
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:
| Order of QAM | MERRMS |
MERPK |
MERPK |
MERdB |
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 |
The term “Modulation Error Ratio” and the prescribed method of calculation were declared an international standard by the DVB Measurement Group.