veex_veex 23/05/2013 17:41 Page 1
Understanding Equalizer Measurements
est instruments are designed to make measurements in the network, note its good health or discover problems. The instrument’s set of measurements and the interpretation of these results g ives insight into the source of the problem. Correcting the problem is much easier when each measurement is understood. With QAM analysis measurements, the Equalizer plays a key role.
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Impairments of the QAM Signal
The QAM (Quadrature Amplitude Modulation) signal travels from the QAM modulator in the headend to the demodulator in the CPE equipment. In between are many elements, including combiners, optical modulators, fibre link, fibre node, coaxial cable, amplifiers, multi-taps, drop cable, and splitters. It is no surprise that the signal at the far end is not as clean as it is at the modulator. One inherent impairment source is thermal noise, which is a random voltage variation proportional to temperature, bandwidth and resistance. At room temperature, in 6 MHz bandwidth and 75 ohms circuit, the thermal noise is approximately -60 dBmV. Through amplification, the noise level can get much higher. All other impairments are 'manmade' and depend on the design, implementation and operation of all the elements in the signal chain. Impairments can be classified as Linear and Non-linear distortions. The Linear distortion’s characteristic is that it applies equally to all signal components. For instance, the filter response is independent of the signal amplitude. Another example is an echo or micro-reflection, with the delay and attenuation of the echo also being independent of the signal amplitude. Theoretically, all the network components can be characterized and a perfect network response model can be defined, predicting its effect on the signal, symbol by symbol. The Non-Linear distortion is variable, either in time or amplitude, and is practically
Rob Richards, vice president, CATV R&D, VeEX Inc shares his thoughts on the pivotal role the Equalizer plays in QAM analysis measurements.
unpredictable. One example is thermal noise, with its instantaneous amplitude being unpredictable. We measure only its average amplitude and mathematically we can derive its statistical distribution over a period of time. Other types of Non-Linear distortions are CTB and CSO, which are very dependent on signal amplitudes, the desired signal and other network signals. The QAM demodulator has to contend with Non-Linear distortions, but it can counteract
Samples are taken close enough in time, not losing the details. They are queued, adding new ones and removing older ones in the registers of the buffer. If a reference position in the queue is selected, the samples received earlier represent the past, and those received later represent the future relative to this reference point. The digital filter operates by taking a given portion of the past and future samples and adding them to the reference sample. The ratio of sampled signal to the desired portion is defined by the Coefficient, with one coefficient per sample or register. These Coefficients are complex—in other words they have inphase and quadrature components (or amplitude and phase). Figure 2a shows a graph of a continuous signal over a given time period. It has fast variations superimposed on a low frequency wave. Let’s take a 5 sample long sliding window (also known as a 5 tap). If we take 1/8, then 1/4, 1/4, 1/4 and 1/8 of 5 adjacent sam-
Linear distortions; here the Equalizer comes into play.
The Equalizer
The Equalizer is a filter that compensates for Linear distortions. This filter has an amplitude and phase response that is the inverse of the QAM modulator, plus the network, plus the QAM demodulator. To compensate at any location, for any QAM signal, at any time, the filter must track Linear distortions. The filter is adaptive and determines the proper responses via a trial and error process, slightly changing the parameters. If the QAM signal is improved, it retains this change; if it is degraded it cancels it. The constant cycle of trial and error converges after a period of time. Linear distortions are removed and only NonLinear distortions remain. Consequently, the Equalizer has improved MER (Modulation Error Ration) as much as possible.
ples and sum them, as in Figure 1, we have smoothed out the signal (Figure 2b, in blue) and have created a Low-pass filter. On the other hand, if we take the difference between 2 adjacent taps, and make the sum of 4 of these differences, we have enhanced the fast variations and removed the low frequency wave (Figure 2b, in red), creating a High-pass filter. By controlling the Coefficients of a filter, all desired responses can be achieved. The more elaborate the response, the larger the number of taps required.
Equalizer Implementation
The Equalizer uses two digital filters in cascade, the FFE (Feed Forward Equalizer) and DFE (Decision Feedback Equalizer). In FFE, the reference tap is the last one (of 16 taps), so it processes the future (relative to the reference tap). With DFE, the output is fed back to its input. Its length is 108 taps long, processing the past.
Digital Filter
The first step is digitizing the signal.
Equalizer Coefficients
Once the Equalizer has converged, the
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