More About Modulation Error Ratio

Modulation error ratio is digital complex baseband SNR - in fact, in the data world, the terms "SNR" and "MER" are often used interchangeably, adding to the confusion about SNR, especially considering that, as mentioned previously, in the telecommunications world, the terms "CNR" and "SNR" are often used interchangeably.

Why use MER to characterize a data signal? It is a direct measure of modulation quality and has linkage to bit error rate. Modulation error ratio is normally expressed in decibels, so it is a measurement that is familiar to cable engineers and technicians. It is a useful metric with which to gauge the end-to-end health of a network, although by itself, MER provides little insight about the type of impairments that exist.⁹

Figure 13 illustrates a 16-QAM constellation. A perfect, unimpaired 16-QAM digitally modulated signal would have all of its symbols land at exactly the same 16 points on the constellation over time. Real-world impairments cause most of the symbol landing points to be spread out somewhat from the ideal symbol landing points. Figure 13 shows the vector for a target symbol - the ideal symbol we want to transmit. Because of one or more impairments, the transmitted symbol vector (or received symbol vector) is a little different than ideal. Modulation error is the vector difference between the ideal target symbol vector and the transmitted symbol vector. That is,

[Eq. 19]

Figure 13. Modulation Error Is a Measure of Modulation Quality. (Source: Hewlett-Packard)

If a constellation diagram is used to plot the landing points of a given symbol over time, the resulting display forms a small "cloud" of symbol landing points rather than a single point. Modulation error ratio is the ratio of average symbol power to average error power (refer to Figure 14):

MER(dB) = 10log(Average symbol power ÷ Average error power) [Eq. 20]

In the case of MER, the higher the number, the better.

Figure 14. Modulation Error Ratio Is the Ratio of Average Symbol Power to Average Error Power. (Source: Hewlett-Packard)

Mathematically, a more precise definition of MER (in decibels) follows:

[Eq. 21]

where I and Q are the real (in-phase) and imaginary (quadrature) parts of each sampled ideal target symbol vector, and are the real (in-phase) and imaginary (quadrature) parts of each modulation error vector. This definition assumes that a long enough sample is taken so that all the constellation symbols are equally likely to occur.

In effect, MER is a measure of how "fuzzy" the symbol points of a constellation are. Table 4 summarizes the approximate ES/N0 range that will support valid MER measurements for various DOCSIS modulation constellations. The two values in the table for the lower threshold correspond to ideal uncoded symbol error rate (SER) = 10-2 and 10-3, respectively. The upper threshold is a practical limit based on receiver implementation loss. Outside the range between the lower and upper thresholds, the MER measurement is likely to be unreliable. The threshold values depend on receiver implementation. Some commercial QAM analyzers may have values of the lower ES/N0 threshold 2 to 3 dB higher than those shown in the table.

Table 4. Valid MER Measurement Range

Modulation Format	Lower ES/N0 Threshold	Upper ES/N0 Threshold
QPSK	7-10 dB	40-45 dB
16 QAM	15-18 dB	40-45 dB
64 QAM	22-24 dB	40-45 dB
256 QAM	28-30 dB	40-45 dB

Good engineering practice suggests keeping RxMER in an operational system at least 3 to 6 dB or more above the lower ES/N0 threshold.¹⁰ This guideline will accommodate temperature-related signal-level variations in the coaxial plant, amplifier, and optoelectronics misalignment; test equipment calibration and absolute amplitude accuracy; and similar factors that can affect operating headroom. The lower ES/N0 threshold can be thought of as an "MER failure threshold" of sorts. That is, when unequalized RxMER approaches the lower ES/N0 threshold, the channel may become unusable with the current modulation. Possible workarounds include switching to a lower order of modulation, using adaptive equalization, or identifying and repairing what is causing the low RxMER in the first place.