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By Tom Williams, Holtzman Inc.
Damage to data bursts from linear distortion can be experienced, or it can be predicted from measurements. As cable operators switch their upstream modulation formats from QPSK (quadrature phase shift keying) to 16-QAM (quadrature amplitude modulation) it?s essential they learn methods for measuring linear distortions to prevent their harmful effects.
There are currently a number of methods for measuring linear distortion. One method is to use a link analysis system. This technology was designed to measure group delay and amplitude response over microwave links and also works over cable systems, although they must be taken out of service to make the measurements.
Using this method, you?ll need to frequency modulate a test carrier signal as it is swept. Agilent supplies this type of equipment. Another method is to send a burst reference test signal through the plant. Holtzman Inc. (the author?s company) supplies its test system Cable Scope to achieve this. It uses a single short-duration, high-power repeatable signal with good mathematical properties to characterize the 5-42 MHz return band. Because the burst test signal is very short, it minimizes interference with services, and FEC (forward error correction) circuits can correct any packet errors. An unimpaired burst test signal is launched into the network and received with linear distortion at the headend on a conventional digital oscilloscope. The distorted test signal is processed by a PC using a stored unimpaired test signal.
A plot of an unimpaired test signal is shown in Figure 1 in both the time domain (top) and frequency domains (bottom). A resulting analysis screen is shown in Figure 2. The second plot down in Figure 2 is the linear-scale magnitude component?what most in cable call upstream frequency response?of the complex frequency response from 5 to 42 MHz. The third plot down is a phase response over the same frequency range.
The phase plot loops from -180 degrees to +180 degrees. Group delay arises when the phase plot is not linear: that is, its slope changes. A group delay plot is derived from a slope of the phase plot, and is displayed as the bottom trace. The top plot is an impulse response of the entire return band. (An impulse response is how a network would react if a very narrow voltage spike excited it.) The impulse response is derived from the complex frequency response, and is useful for viewing long echoes. This test system tells the technician what the levels of linear distortion are, but it is still necessary to predict how much damage the measured linear distortion will do to unequalized data signals.
The frequency response that is illustrated in Figure 2 is from a typical short cascade with a few amplifiers and a fiber node. Micro-reflections can be observed as ripples in the magnitude plot. Note that ripples are larger at 15 MHz than they are at 35 MHz because of higher cable loss at 35 MHz.
As a side note, there is a theorem of network theory that states when the amplitude response of a minimum phase network is known, one should be able to calculate the phase response. Likewise, if the phase response is known, one can compute the amplitude response within a gain constant. Apparently, no one has translated this theorem into a solution yet, although most upstream networks are considered to have the minimum phase property.
Using MER to quantify linear distortion
When talking about the effects of uncorrected linear distortion, it is useful to express the impairment as a modulation error ratio (MER). MER is simply the power ratio of the unimpaired signal to the interference affecting it. The interference can be additive noise, or it can be created by linear distortion, and is probably some of both in real systems.
Figure 3 shows a set of plots that were created by a linear distortion simulation of a Data Over Cable Service Interface Specification (DOCSIS)-like signal with 16-QAM at 2.5 mega-symbols per second using frequency response data that was captured in the field and illustrated in Figure 2. The simulation was done with a program called ?eye.? The bottom two plots are in-phase voltage versus time and quadrature voltage versus time eye diagrams.
These plots are functionally the same as the plot in Figure 1 (in Part 1, December 2003, pg. 39), except they feature more symbols; the symbols are combined into a composite trace; and several traces have been distorted and overlaid. If there is an open space in the plot, the eye is said to be ?open.? The upper right plot is a plot of in-phase (I) voltage vs. quadrature (Q) voltage. If this plot is sampled at exactly the correct time for a maximum eye opening, the constellation in the upper left plot results. Ideally, each of the 16 quadrants should have all sampled points falling on one spot in each quadrant, but because of the linear distortion the points are spread out. The definition for MER is:
where I and Q are the real and imaginary parts of each sampled ideal signal vector. Similarly, delta I and delta Q are the real and imaginary parts of each error vector. The error vector is the distance that a received signal vector is from where it ideally is supposed to be.
Note in Figure 3 that there are two lines in the upper right quadrant representing vectors. The longer one is from the origin to an ideal point where samples would be landing without intersymbol interference (ISI). This vector is one of many contribution numerator terms in the equation. The shorter line is the distortion vector. It goes from the ideal point to an actual received point. This vector is a one of many contributing denominator terms in the equation.
For 16-QAM, a MER of 18 dB corresponds to the threshold of failure (excessively high error ratio). For QPSK, the failure point will be closer to 12 dB. These numbers are influenced somewhat by the level of FEC, packet size and nature of the MER.
Estimating MER with plots
There are a couple of different methods for determining MER from amplitude tilt and group delay numbers. One method is to use the curves of Figures 4 and 5 (see pages 26 and 27, respectively) to look up the MER from the anticipated or measured group delay and magnitude tilt numbers. Note that the curves were generated using dB of tilt and group delay over 2.5 MHz. For reference, note that the assumed characteristics in the DOCSIS 1.0 specification would produce 500 ns of group delay over 2.5 MHz and 2.5 dB of amplitude ripple over 2.5 MHz. This level of group delay is too much for QPSK transmissions at the highest symbol rate. However, the assumed amplitude tilt numbers are relatively benign. Using 16-QAM will result in a set of slightly different plots.
Using measured data to estimate MER
A second method that is used by ?eye? is to import real frequency response data from software and run the simulation with measured data. This method was used to generate the eye diagrams of Figure 3 from the plot of Figure 2. Figure 2 was created in a cable plant with four-cascaded upstream amplifiers plus a node. The simulation was done with a carrier center frequency of 39.6 MHz where group delay distortion is severe. Note that the MER values show only a 2 dB of margin from failure at 18 dB, and no additive noise was used in the simulation. An operator was having problems keeping 16-QAM modems on line in this node. If the simulation is repeated with a center frequency of 26.6 MHz where group delay is relatively benign, the much improved eye diagrams of Figure 6 result. The advantage of using measured field data in a simulation is that all linear impairments are accounted for simultaneously, including amplitude tilt, group delay and echoes.
Assuming a prudent operator would want uncorrected linear distortion no closer than 6 dB from the failure point. 16-QAM should be operated with a linear distortion MER of 24 dB or higher. Similarly QPSK should have an MER from linear distortion of 18 dB or more. From Figure 5, at 2.56 Msymbols/sec the highest group delay that should be tolerated is 100 ns for 16-QAM and 200 ns for QPSK over 2.5 MHz. This works out to 40 ns per MHz for 16-QAM, and 80 ns per MHz for QPSK. This is far more stringent than the assumed upstream RF channel transmission characteristics in the DOCSIS specifications. Figure 4 shows that amplitude tilt can be as bad as 2.3 dB for 16-QAM and 4.2 dB for QPSK.
If a channel is experiencing an echo, and the echo?s delay is longer than a symbol period, the MER is going to be approximately equal to the echo?s magnitude. Therefore, for 16-QAM the largest long-delay single echo should be less than 24 dB, and for QPSK the largest long-delay echo should be less than 18 dB. This is also a more severe requirement than the DOCSIS-assumed characteristics.
Conclusions
Linear distortions are important impairments to measure because some upstream data receivers as in DOCSIS 1.0 do not have adaptive equalizers. In particular, group delay and micro-reflections have a potential to impair reception of data bursts, especially 16-QAM at higher symbol rates. Unfortunately, most conventional sweep equipment can?t measure complex frequency response or show micro-reflections. After the complex frequency response is determined, estimates of MER can be determined from the MER vs. group delay and MER vs. amplitude tilt plots in Figures 4 and 5. DOCSIS assumed upstream characteristics for group delay and echoes are insufficient for successful operation, especially for highest symbol rate 16-QAM.
Tom Williams is president of Holtzman Inc. Email him at .
Did this article help you? Email comments to .
The author would like to thank the people who contributed to this article.
References
"Return Path Linear Distortion and Its Effect on Data Transmissions" by Tom Williams, pp. 54-71, 2000 NCTA Technical Papers.
?Managing DOCSIS? Transitions? pp. 461-478 by Roberts, Rude, and Sowinski, 2003 Cable-Tec Expo Proceedings Manual.
Bottom Line
Measuring Linear Distortions
Linear distortions are important impairments to measure because some upstream data receivers as in DOCSIS 1.0 do not have adaptive equalizers. In particular, group delay and micro-reflections have a potential to impair reception of data bursts, especially 16-QAM at higher symbol rates. Unfortunately, most conventional sweep equipment can?t measure complex frequency response or show micro-reflections. After the complex frequency response is determined, estimates of MER can be determined from the MER vs. group delay and MER vs. amplitude tilt plots. DOCSIS assumed upstream characteristics for group delay and echoes are insufficient for successful operation, especially for highest symbol rate 16-QAM.
Figure 1: Unimpaired Burst Reference Signal*
Figure 2: Impulse Response and Complex Frequency Response*
Figure 3: Simulations Results, 39.6 MHz Center Frequency*
Figure 4: MER vs. Channel Amplitude Tilt*
Figure 5: MER vs. Group Delay Variation*
Figure 6: Simulation Results, 26.6 MHz Center Frequency*
 Back to December 2003 Issue
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