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By Tom Williams, Holtzman Inc.
Many cable operators are switching their upstream modulation formats from QPSK (quadrature phase shift keying) to 16-QAM (quadrature amplitude modulation) to increase throughput. Unfortunately, this switch increases their network?s vulnerability to linear distortions, which can impair upstream cable modem transmissions.
Linear distortions are problems that are created by a signal being subjected to a channel with either non-flat amplitude response, or bent-line phase response, or both. Linear distortions include impairments such as group delay, discrete echoes (e.g. reflections, ghosts or multipath distortion), micro-reflections and amplitude tilt. Two linear impairments?group delay and micro-reflections?can cause serious damage to upstream data, and most commonly used sweep test equipment does not measure these impairments. Understanding frequency response can help you conquer linear distortions.
Frequency response is a complex entity. Complex means that a frequency response includes both magnitude and phase components, or, if one prefers, real and imaginary parts. Upstream frequency response traditionally is measured with a conventional sweep system, which gives the magnitude portion, but not the phase response. If there is a problem with the amplitude response steadily changing with frequency, the signal path has amplitude ?tilt.? Likewise, if the phase response is not a straight line, you have ?group delay.?
It is easy to determine if an impairment is a linear or a nonlinear one. If the carrier level is increased or decreased in the channel and the level of the impairment remains the same relative to the carrier, it is a linear impairment. For example, if you increase a digital carrier by 10 dB, an echo created by the carrier also will increase by 10 dB, so echoes are linear impairments.
Group delay simply means that signals at different frequencies propagate through a network with different time delays. For example, with group delay, a 30-MHz sine wave burst can get through the network faster than a 40-MHz sine wave burst.
If a channel 2 downstream NTSC transmission had a group delay problem, the color information would be miss-registered on the screen. This is because the luminance information is at 55.25 MHz, while the color information is 3.58 MHz higher at 58.83 MHz. Filters in two-way amplifiers create group delay. Typically, upstream group delay has a bathtub shaped response. Group delay in the 5-10 MHz band is caused by AC power blocking filters, and group delay in the 35-42 MHz band is caused by diplex filters. As a point of interest, group delay also occurs in fiber optic cables but is called ?chromatic dispersion,? which is a material property of the glass fiber.
Group delay is the rate of change of phase with respect to frequency and is given by:
where phi is the phase, typically expressed in radians, and omega is the frequency, typically expressed in radians per second.1
A single echo shows up as a periodic ripple in both the magnitude and the group delay plots. Figure 1 can explain this. The large stationary vector on the horizontal axis is a main carrier, and the smaller vector represents a 20 percent echo. The magnitude is a length of a vector sum of main carrier plus the echo. As the frequency changes, the small echo vector rotates counter-clockwise.
Observe that both the magnitude and the phase angle will change as the echo vector rotates. When a delay time associated with the echo is longer, a rate of rotation versus frequency change increases. Because group delay is the rate of change of phase versus frequency, the faster the rate of change of phase with frequency, the larger the peak-to-peak group delay ripple. This means that for a given amplitude echo with a longer delay, the group delay ripple on a spectral plot will have larger amplitude and smaller period.
A phenomenon that has been observed on many upstream links is micro-reflections. Micro-reflections are caused by impedance mismatches at both the source and load in a transmission line, and they create many small reflections between devices in the coaxial plant, such as between amplifiers and taps, or between power inserters and splitters, or between taps etc.
Micro-reflections were predicted on the downstream path, but were relatively benign because the high attenuation of the downstream cable damps out the reflections between devices. In the upstream however, the cable loss is so low that the micro-reflections have become an observable phenomena as well as a problem. If the vector diagram of Figure 1 were showing micro-reflections, the vector sum would comprise several smaller echoes, each with a different magnitude and rate of rotation with frequency.
Linear distortion is a problem for digital transmissions because it creates a problem called inter-symbol interference (or ISI). Figure 2 is a plot of two symbols that were transmitted one symbol period apart. The first symbol goes positive, and the second goes negative. The plot axes are voltage versus time.
Normally, on an oscilloscope you would see only one trace, but the single trace has been decomposed to show the two individual symbols. The symbols are sin(x)/(x) waveforms (impulse response of a ?brick wall? filter), and the timing ticks at the top of the plot show the correct sampling times. Small circles on the plot also note correct sampling time.
Note that the first symbol component hits a positive peak just to the left of center, and the second symbol peak hits a negative peak just to the right of center, as noted by ?x.? Observe that while any symbol is going through a peak, the other symbol is going through zero. If the channel has linear distortion, the waveforms will be ?smeared? and no longer cross through zero at the sampling instant. A composite plot of many symbols that have been laid one atop the other is called an ?eye? diagram, and will be described in detail later. A measure of inter-symbol interference is modulation error ratio (MER), which is a combination of linear distortions plus any additive interference, such as random noise or ingress, in the channel. MER also will be described in detail later.
A good place to observe echoes is on a magnitude plot. An echo?s amplitude can be calculated from the peak-to-peak excursions in the magnitude response that are caused by the echo. As an example, if the amplitude varies by plus and minus 7 percent, the peak-to-valley ripple will be 20*log(1.07/0.93)= 1.22 dB. The echo is down 20*log(.07)=23.09 dB relative to a carrier. One problem with observing echoes is that many conventional sweep systems have a frequency resolution that is much too coarse to display ripple.
So what are the symptoms of linear distortion on the upstream plant? One symptom is that Data Over Cable Service Interface Specification (DOCSIS) 1.0 cable modems have trouble ranging and registering, but the 1.1 and 2.0 modems (which have adaptive equalizers) work fine. Unfortunately, as of this writing, there are not a lot of DOCSIS 1.1 and 2.0 deployments that take advantage of adaptive equalization.
Another clue is modems dropping off-line but without any apparent background noise problem. However, there are plenty of other reasons why modems may fail to range and register, or drop off-line. Another symptom is that distant modems have more problems registering and staying registered, because distant modems have to traverse more cascaded upstream amplifiers, and each amplifier adds more group delay and micro-reflections.
A cable system also might experience that the modems have more problems ranging and staying connected as the upstream operating frequency is increased closer to the diplexer cutoff frequency. Group delay distortion is worst near the diplexer cutoff, which is typically 42 MHz in North America.
Yet another indication of a linear distortion problem is that QPSK works, but 16-QAM doesn?t, and there is no background noise problem that would explain the difference. Because linear distortions will be worse when the occupied bandwidth is wider, increasing the symbol rate (occupied bandwidth) will aggravate problems if a channel has linear distortion.
Because the relative level of linear distortion remains the same as the signal level is raised, be suspicious if elevating the signal level in the channel does not help much. Regrettably, as the level of uncorrected linear distortions increase, the tolerable level of background additive noise drops.
The traditional remedy for linear impairments is to use an adaptive equalizer. For cable upstream plant, adaptive equalizers are implemented using digital filter technology to create a filter response that approximates the frequency domain inverse of the channel?s frequency response. When the linearly distorted channel is cascaded with the digital filter, the linear distortion is greatly reduced.
As a standard supporting data services, DOCSIS is an unqualified success. However, the requirements for adaptive equalization have been evolving.
DOCSIS 1.0 provides for two upstream modulation formats: 16-QAM and QPSK. The allowable symbol rates are 160k, 320k, 640k, 1280k and 2560k symbols per second, which results in occupied bandwidths of 200 kHz to 3.2 MHz. Adaptive equalization was made optional.
As a practical matter, adaptive equalization generally is not available for DOCSIS 1.0 equipment. As a net result, many systems are operating their plant with QPSK and at less than the maximum symbol rates to avoid linear distortion problems. Increasingly operators are switching over to 16-QAM to increase upstream capacity.
DOCSIS 1.1 provides for the same 16-QAM and QPSK upstream modulation formats and the same symbol rates. However, adaptive equalization is a requirement, not an option, and is specified in detail. An 8-tap equalizer is required. (In this context, ?tap? refers to a register or memory element in a digital filter.)
DOCSIS 2.0 provides for a number of additional modulation formats with one higher symbol rate at 5120k symbols per second, which doubles the occupied bandwidth to 6.4 MHz. DOCSIS 2.0 also allows for both synchronous code division multiple access (S-CDMA) and advanced time division multiple access (A-TDMA). DOCSIS 2.0 requires a mandatory 24-tap adaptive equalizer.
The DOCSIS 1.1 and 2.0 specifications call for a pre-distortion adaptive equalizer. When a cable modem goes through its ranging process, the linear distortion is measured in the cable modem termination system?s (CMTS?s) upstream receiver, and the coefficients to eliminate the distortion are sent over the downstream link to program the pre-distortion filter in the cable modem?s transmitter. Periodically the ranging process readjusts the pre-distortion filter to adapt for changes in the plant. If there is any additional equalization occurring in the CMTS receiver, it will be as a vendor-specific feature added as an option to the DOCSIS specification.
If rapid changes to the channel?s frequency response occur because of mechanically intermittent connections, and a channel is using 64-QAM or 128-TCM, the time to re-range may be too long to wait for services such as telephony. Therefore, it may be important to assess CMTS performance in this situation.
The current issue for cable operators is a large population of DOCSIS 1.0 cable modems that don?t support adaptive equalizers. These modems will be in service for a long time to come. A common solution for error-free transmissions is to use the more-robust QPSK modulation at a lower symbol rate. Unfortunately, QPSK has only half of the spectral efficiency of 16-QAM, and many operators are facing a shortage of upstream bandwidth. Some operators are successfully using 16-QAM, but are finding that some links perform better than others. Thus, there is a need to find out why there is a difference.
1?Return Path Linear Distortion and Its Effect on Data Transmissions,? by Tom Williams, pp. 54-71, 2000 NCTA Technical Papers.
In Part 2, Tom Williams will detail methods for measuring linear distortions.
Tom Williams is president of Holtzman Inc. Email him at .
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Many cable operators are switching their upstream modulation formats from QPSK (quadrature phase shift keying) to 16-QAM (quadrature amplitude modulation) to increase throughput. Unfortunately, this switch increases their networks? vulnerability to linear distortions, which can impair upstream cable modem transmissions.
Group delay and micro-reflections are two common forms of linear distortions. Symptoms of linear distortions on the upstream plant include:
- DOCSIS 1.0 cable modems fail to range and register, while DOCSIS 1.1 and 2.0 modems work fine.
- Cable modems drop off-line but without any apparent background noise problem.
- Distant modems have difficulty registering and staying registered.
- QPSK works but 16-QAM doesn?t.
Figure 1: A Vector Diagram Showing Magnitude and Phase Ripples on a Spectral Plot
Figure 2: Two Symbols Without Inter-Symbol Interference
 Back to November 2003 Issue
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