16.4.1 Upstream Group Delay

Figure 16.2 illustrates the upstream group delay of an amplifier having a 42/52 split.¹ The left vertical scale shows the absolute group delay (defined in Equation (10.35)), and the right scale is the differential group delay in a 1-MHz frequency span. (If we were concerned about carrying NTSC video, we would measure the differential group delay over a frequency span of 3.58 MHz, and we would call it chroma/luma delay.) Notice that at the high end of the return path, the differential group delay increases significantly, as the frequency is approaching the low-pass cutoff of the diplexer. If the differential group delay is too great, then some spectrum at the high end of the band may not be usable. “Too much” group delay is a function of the modulation type and the particular system being used. Higher-density modulation systems (that is, those having a higher bandwidth efficiency) are more susceptible to group delay and other impairments than are lower-density modulation systems.

Figure 16.2 Upstream group delay due to diplex filter.

The group delay increase at the low end of the band is a result of a high-pass filter included in the amplifier measured. The high-pass filter is advantageous in that noise below the 5-MHz low cutoff is not as much of a factor in loading the return system.

Notice that the chart in Figure 16.2 reflects the group delay per amplifier. Multiply the group delay shown by the number of amplifiers in cascade. Optical nodes will exhibit somewhat less group delay because they have only one diplex filter (see Figure 16.1). Figures 10.15 through 10.17 show that two diplex filters are cascaded in an amplifier. Furthermore, amplifiers need more crossover attenuation than do nodes to avoid the stability issue described in Chapter 10.

16.6.1 Measurement of Return Signal Levels

In Chapter 4, the definition of “signal level” of a digital signal was presented as the level, expressed in dBmV, at which a sine wave would produce the same heating in a resistor as does the signal being measured. That is, the level of a digital signal is taken to be the average power. Most digital signals have the characteristic that the amplitude of the signal changes for different transmitted states, so the peak level is greater than this average. The peak-to-average ratio is small with QPSK, and indeed, would be zero were it not for transmitter filtering. Higher-order modulation exhibits a greater peak-to-average ratio, as shown in Chapter 4. Peak-to-average ratio is rather difficult to measure, so the NCTA Recommended Practices for Measurements on Cable Television Systems, “Upstream Transport Issues” section, recommends that each manufacturer state the peak-to-average ratio of his or her modulation.²

Many signals in the upstream direction employ time division multiple access (TDMA), a technique in which many transmitters transmit on the same frequency at different times. An explanation is presented in Chapter 4. Measurement of individual elements can be accomplished by triggering the measuring instrument (usually a spectrum analyzer) on some reference time, allowing one of the signals in the return “parade” to be identified. This triggering signal would normally be supplied by the system being analyzed. First-generation equipment does not necessarily have the capability to provide such a trigger, however.

If you set a spectrum analyzer to the zero span mode, it can be used to measure the signal level on only one frequency, with the bandwidth of the analyzer determining the bandwidth of the measurement. You may be restricted as to the measurement bandwidth due to adjacent carriers, and this will vastly complicate the measurement.

Figure 16.4 illustrates the measurement issues for a TDMA signal in the return path. Figure 16.4(a) shows the preferred test configuration: received signals are supplied to the using system and also to a spectrum analyzer used to measure signal level. Ideally, the using system would supply a triggering signal to the spectrum analyzer, which would allow identification of the return signal to be observed. Again ideally, the spectrum analyzer would have a trigger input and would have a time base setting that allows separation of the return signals into the individual elements. These ideal situations do not exist with all firstgeneration hardware, but it is hoped that future systems will allow for this type of observation.

Figure 16.4 Measurement of TDMA return signals. (a) Instrumentation to observe return levels. (b) Wideband measurement of amplitude. (c) Measurement with restricted bandwidth. (d) Measurement with severely restricted bandwidth.

The spectrum analyzer is set to the zero span mode, in which it operates as a fixed tuned receiver, plotting amplitude versus time of the signal, as shown in Figure 16.4(b), (c), and (d) for three different resolution bandwidths of the analyzer. If the resolution (IF) bandwidth of the analyzer is wider than the occupied bandwidth of the signal being measured, as shown at the left of Figure 16.4(b), the waveform might look as illustrated in (b). The TDMA parade consists of a number of responses from different transmitters, each being received at a slightly different level at the headend. Ideally, the long loop automatic level control (ALC) would bring all elements to the same level. However, there will be differences due to the limited resolution with which the transmitters can adjust level.

16.6.2 Long Loop Automatic Level Control

Figure 16.5 illustrates the critical points in the return signal level control issue. It is similar to Figure 9.8, which addresses the same issue from the headend. As described in Chapter 9, the return service includes a long loop automatic level control (ALC), wherein the signal level is measured in the headend (Lvl 1 in Figure 16.5), and a signal is sent to the home transmitter, TX4, to adjust its output such that the correct level is received at the headend. This corresponds to some level at the tap, Lvl 5, and to other levels at each RF amplifier (Lvl 4) and at the node, Lvl 3. The point is that, once the system controls the signal level at Lvl 1, all the other signal levels are set according to the design of the system.

Figure 16.5 Pertinent points in return signal level control.

An ALC loop is set up between the headend and each home system individually. The headend senses level of the return signal and adjusts the upstream transmitter such that the correct level is received at the headend receiver. The most critical level is that at the reverse optical transmitter, Lvl 3.

The most critical level is that at the return optical transmitter, Lvl 3. The dynamic range (from maximum signal level down to noise level) tends to be relatively low for return path optical transmitters, both due to technology and cost. Dynamic range is explored in more detail later. See Chapter 12 for a detailed discussion of optical technology.

The system must be set up to optimize the level at Lvl 3. However, Lvl 3 cannot be directly observed by the adjusting system. Instead, the gain between the point marked Lvl 3 and that marked Lvl 1, where the level observation is made, must be known and must be stable. The target value of Lvl 1, to which the system is adjusted, is set based on the desired value of Lvl 3. At the same time, it is necessary to set the gain in the system such that the input and output signal levels at all amplifiers, represented by Lvl 4, are correct. Attenuators and equalizers are often provided in the return amplifiers for this purpose and must be properly selected during system alignment. “Correct” is based on the manufacturer’s specified operating levels for the conditions under which the amplifier is being used. When these levels are set (by design and alignment of the system), then the level at the tap, Lvl 5, will be set by the tap value and the gain from there to the node.

A few systems have attempted to use automatic gain control (AGC) in the return path. This is not recommended for a number of reasons. First, it fights the setting of levels as described earlier. Second, at times it may be normal for the number of carriers in the reverse direction to change. For example, some services employing time division multiple access (TDMA) may permit signal dropout as a normal condition at times. Further, as return services are added and deleted, it is not desirable that gain in the return path change. Next, real return paths often branch and have a different number of amplifiers in each branch. AGC can significantly complicate operation of such systems.

In some cases where reverse AGC has been employed, it has been done with a pilot tone generated somewhere near the end of the system and detected by all amplifiers and the node. This may work, but raises many questions when downstream signals branch after leaving the node. With branches having a different number of amplifiers in cascade, where do you put the pilot tone generator? You would logically place it at the end of one of the branches, but that leaves the other branches with no coverage.

16.6.3 Thermal Gain Control

It is often desirable to provide thermal control of return path equipment. Even at return frequencies, cable exhibits some variation in loss with temperature, and it may be desirable to also compensate for variations in the operating point of lasers. This is often done by using thermistors (temperature-sensitive resistors) to sense temperature level inside the return optical transmitter and adjust gain based on temperature variation. It is also practiced at times to cool the laser, as mentioned in Section 16.7.

16.6.4 Return Signal Levels at the Tap

Of interest to those designing or using systems needing the services of the return path is the issue of the signal level at the tap, Lvl 5, needed in order to produce the desired level at Lvl 3. Intuitively, we might assume that the difference between the lowest and highest levels would be about the same as the difference between the lowest and highest tap value in the system. Tap values are chosen such that the downstream level at the tap is more or less constant, fixed by system design. This calculation is done at the highest frequency of interest, where cable loss is maximum. At the return band, cable loss is much lower, so the level required at the tap, Lvl 5, would be lower at lower tap values. Generally, those lower value taps are located farther from an amplifier (in the downstream direction).

Analysis of the return gain characteristics of real nodes, however, shows that this line of reasoning is oversimplified. Sometimes low-value taps are located at the end of a long cable run, so there is little upstream loss at the low frequencies composing the return band. Other times, though, low-value taps are located after a directional coupler and near an amplifier. At those locations, the loss is primarily flat loss (not a function of frequency), and the required output at Lvl 5 will be higher.

Figure 16.6, from the analysis of one real node, shows the levels found to be required at the tap (Lvl 5 of Figure 16.5) in order to produce a level of 0 dBmV back at the node (Lvl 3). Each dot represents a tap of the value shown on the x axis, which requires the y-axis level at any tap port. Notice that low tap values exhibit a wide variation in level required, with the level range tending to compress slightly as you move to higher tap values. This slight compression is a result of having few places to use high-value taps, other than shortly after an amplifier. This data is from one node, but examination of other nodes owned by the same and other cable operators shows the same tendency.

Figure 16.6 Required signal level as a function of tap value.

It is not necessarily desirable to have a node that requires low signal levels at the return input. It is desirable to require the highest level that can be supported by the reverse amplifiers that supply signals to the node. This will help minimize the effect of noise entering the plant (primarily from homes). Of course, you must ensure that the requisite signal levels are available at the home transmitter. The use of 0 dBmV as the input to the node is not intended to be a real case but to provide a convenient normalized reference point.

Figure 16.7 illustrates the signal level issue another way. The population of taps having certain level requirements is plotted for the node of Figure 16.6. The distribution of levels appears to be a very crude approximation to a normal distribution. It illustrates that, though there is a clumping of levels, a significant number of taps will require a higher or lower level. The product designer must plan for the required level range, also allowing for variations from system to system, errors, and variations with temperature. Note that the level of the signals at the home will vary because of temperature-dependent changes in gain in the system.

Figure 16.7 Distribution of tap signal levels.

When the signal level received at the headend changes, this will cause the signal level commanded from the home to change, due to operation of the long loop ALC.

Reducing the required tap return level range would be desirable, in that a reduced level range specification would provide some reduction in cost and would enhance performance in at least some cases. Homes with the lowest signal level requirement are also the homes that have the greatest potential to introduce noise into the return path. A wide level range implies high output level capability from the device, which implies possible high noise emission when the level is set low. It also implies rather larger current drain since the output amplifier must have the capability to handle large signals with minimum distortion.

16.7.1 Data- or Video-Grade Classification

An early method of classifying return transmitters (and receivers) is to classify them as to data grade or video grade, with the implication that video-grade lasers are better. This method has proved unsatisfactory because it doesn’t take into account the real requirements placed on the system. A return path with many data signals requires at least as good a laser as does a return path with one analog video signal. Further, there is no standard criteria for classifying lasers: in at least one case, a manufacturer interpreted “data grade” to mean capable of handling one FSK return signal only. When it was used with multiple QPSK return signals, it was incapable of handling the job.

16.7.2 Discrete Carrier Testing and Classification

An older method of measuring the performance of return components is taken directly from downstream measuring practice. Either two or four CW carriers are used to excite the laser, and the results are measured on a spectrum analyzer. The second- and third-order beat products are recorded.

Figure 16.8 illustrates the method. Either two or four oscillators are combined, with identical output levels, to produce a spectrum, usually on the highest T-channel carrier frequencies used by the system. The performance of the system is reported as the composite second- (CSO) and third- (CTB) order beats and the cross modulation, as if this were a miniature downstream system. Typically, lasers tend to be more second-order than third-order limited, so CSO becomes the dominant specification.

Figure 16.8 Four-tone measurement of a return optical system.

The attenuators and bandpass filter are shown for practical reasons. The attenuators help isolate the signal sources so that you don’t suffer intermodulation distortion in the output circuits of the generators. The bandpass filter (BPF) tuned to the frequency of measurement prevents overload of the spectrum analyzer.

In evaluating the performance of the system for carrying a limited number of signals, some practitioners have tried to predict the frequencies at which the maximum distortion is present. These frequencies are then avoided in order to maximize the performance of the link. The cost of doing this is that many potentially useful frequencies are excluded. You are left with lower capacity and less ability to move carriers to avoid noise. Another problem with this approach is that, as we will show, when the laser goes into clipping, the normal model used for predicting the frequencies of distortion components is invalid. Also, this technique fails to stress the laser the same as it would be stressed with a number of real digital signals. Again, this is explained later.

Yet another problem encountered in comparing specifications between manufacturers by using discrete test tones is that some manufacturers, following downstream practice, quote specifications with equal level carriers. Others assume that some number of the carriers represent analog signals, and others represent digital signals that are carried at a lower level. They reduce the level of some of the signals when making measurements.

Still another problem in comparing specifications is that manufacturers may choose different channels on which to place the carriers. Depending on the placement, differing numbers of composite beat products will exist on the measurement frequencies. Only the most careful reading of the data sheet can reveal the exact conditions under which the measurements were made.

16.7.3 Noise Power Ratio Testing and Classification

A newer method of characterizing systems has become common practice. It comes much closer to testing the laser as it will be operated in service. The technique is not really new: it has been used in the telephone industry for years to characterize linear systems, such as FDM (frequency division multiplex) coax and radio systems. HFC systems are FDM systems because they employ multiple frequencies to carry different information.

Figure 16.9 illustrates the so-called noise power ratio (NPR) testing technique. A broadband white noise generator is used to simulate a spectrum filled with data signals. Data signals generally have a flat spectrum over the occupied bandwidth of the signal (see Chapter 4), so simulating them with a white noise signal is reasonable. (“White noise” simply means that the spectrum is flat over the frequency range of interest.) A bandpass filter limits the spectrum to that for which the system under test is rated.

Figure 16.9 Noise power ratio testing of a return path.

An attenuator is used to isolate the bandpass filter from a notch filter that follows. The notch filter removes the white noise in some measurement bandwidth. The total power in the signal is important, and would be measured using, ideally, a thermocouple type power meter. The variable attenuator is used to adjust the signal level supplied to the system under test.

A spectrum analyzer, protected if necessary by a bandpass filter tuned to the notch frequency, is used to observe the output. The notched frequency will be somewhat filled in by the system under test. At low signal levels, the filled in noise is due to noise introduced by the system under test. At higher signal levels, it is filled in by distortion introduced by the system under test. It is not possible to look at the filled in level and tell whether the fill is due to noise or distortion or both. The ratio of noise on the flat portion of the spectrum, and that in the notch, is called the noise power ratio (NPR). Some practitioners have called it carrier to noise plus intermodulation noise, or C/(N + IMD).

Use of NPR to Set Operating Level

If we were to plot the NPR against the power supplied to the laser, we would obtain a plot similar to that of Figure 16.10. The total power supplied to the laser is plotted on the x axis. Often the quantity plotted will be the power spectral density, which is the total power divided by the bandwidth over which the power exists.

Figure 16.10 NPR as a function of the total power into the laser.

At low signal levels, the NPR is noise limited. One would expect the NPR to increase 1 dB for every decibel increase in total power into the laser. In practice, there will often be a region on the left of the diagram in which the NPR increases faster than decibel for decibel.³ This is especially true for unisolated distributed feedback (DFB) lasers feeding long fiber-optic cables. The reason is that at low signal levels, lasers are susceptible to reflections from the optical cable, due to Rayleigh backscatter. The reflected light “pulls” the laser wavelength, creating noise. As the drive to the laser increases, the laser tends to “chirp” (change wavelength with instantaneous drive) more, reducing the pulling by reflected light. The reflected light is a function of the length of optical cable used: the longer the cable, the more reflection. DFB lasers tend to be more susceptible than are F-P lasers because their wavelength is chirped less by modulation, making them more susceptible to wavelength pulling by reflected light. Many modern lasers are isolated and tend to change NPR at about a 1:1 rate with signal level.

Wavelength pulling by reflected light is a phenomenon similar to the tendency of an oscillator to oscillate off of its normal frequency if a signal at a close frequency is supplied to the circuit. The more the separation between the two frequencies, the less the tendency to pull. Chirp refers to the changing of frequency (wavelength) of an oscillator (or light source) with applied modulation.

At some drive level, the NPR is maximized. Above this level, the NPR drops quickly. The initial drop may be due to distortion, primarily second order, but you quickly enter a region in which the primary effect is from laser clipping. Clipping noise tends to be the dominant mechanism by which the NPR is reduced on the right side of the graph, and is covered in greater detail later in this chapter.

NPR should not be confused with carrier-to-noise ratio, C/N. C/N represents the ratio of a signal to the noise lying under that signal. It is a function of signal level and the total noise provided from thermal sources plus the excess noise generated in real electronics. On the other hand, the noise in the notch of an NPR measurement either is a function of the thermal and excess noise or, at higher levels, is caused by distortion, which transfers noise from other frequencies into the notch. The mechanism may be the familiar second- and third-order distortion, or much of the noise filled in the notch may be clipping noise from the laser (or electronic amplifiers). Do not look for a simple and universal relationship between NPR and C/N. Later in this chapter, we show how to compute C/N from NPR.

One convenient way to establish the level at which to operate the laser is to determine the range of input signal levels across which some specified minimum NPR is obtained, as indicated in Figure 16.10. The laser should be operated with total power within this “dynamic range.” The engineer might be tempted to operate the laser at the total power that represents the highest NPR. This will work, but because the dropoff in performance is so steep on the right side, he or she may want to operate with slightly less power (to the left of the maximum NPR). (In some lasers, the slope on the right side has a region of gentler slope, where it is limited by second-order distortion. In other lasers, the slope tends to be quite steep just to the right of the peak. This indicates that the laser performance is limited more by clipping than by second-order distortion.)

A noise power ratio test has several advantages over a four-tone test. Noise has an amplitude probability distribution that is different from that of four carriers, but is similar to that of a number of digital carriers added together. The central limit theorem from statistics states that, when a number of independent variables having any arbitrary distribution are added together, the resultant distribution is normal. A normal distribution also describes the amplitude distribution of noise.

Further, the measurement is independent of the bandwidth of measurement, so long as the bandwidth is significantly less than the notch width. It is also independent of the characteristics of the spectrum analyzer detector, so repeatability is good. The only other instrument (besides a spectrum analyzer) needed is a thermocouple power meter, which is low in cost and very accurate.

Use of BER to Set Operating Level

An alternative way to look at the optimum laser operating point recognizes that the vast majority of signals likely to be carried in the reverse direction use low-density digital modulation. The return spectrum is loaded much as shown in Figure 16.9, except that a modulated (usually QPSK) signal is added into the notched frequency band. The bit error rate is plotted against the signal level.⁴

Figure 16.11 illustrates the principle. At low signal levels, the bit error rate (BER) is poor owing to noise corruption. As the signal level increases, the BER gets better (lower on the y axis is better BER). In the central part of the diagram, the BER is so good it is below the chart. Toward the right side of the graph, the BER again begins to deteriorate, due to clipping. The operating total signal level into the laser is set to be somewhere in the middle of the range where the BER is extremely good.

Figure 16.11 BER versus signal level.

16.8.1 Fabry-Perot Lasers

Fabry-Perot lasers have their frequency controlled by the spacing of mirrors at each end of the laser. The frequency control mechanism is such that the laser can oscillate simultaneously, or jump in rapid succession, to several wavelengths that are close to each other. Each wavelength propagates through the fiber at slightly different velocity due to chromatic dispersion in the fiber.⁵ As shown in Chapter 12, this results in restricted performance in terms of carrier-to-noise ratio or NPR on the low side.

Figure 16.12 illustrates the NPR performance of a real F-P laser diode using the NPR test described earlier. On the left side of the graph, the performance is limited by inherent noise in the device. It increases almost precisely 1 dB for every decibel increase in signal level. Above the level of peak NPR performance, the drop in performance is precipitous as the laser rapidly enters the region in which the signal is clipped.

Figure 16.12 NPR performance of an F-P return laser diode.

Note that Figure 16.12 is the same plot as Figure 16.10, except that Figure 16.12 is for a real laser. A strategy for setting the level into the laser is to operate near or just to the left of the point of greatest NPR. You would apportion the total power desired, perhaps +15 dBmV for the transmitter shown, over the actual occupied bandwidth of all signals. This subject is covered more fully later in the chapter.

16.8.2 Distributed Feedback Lasers

DFB lasers operate in a similar manner to F-P lasers, except that a diffraction grating restricts the operating wavelength of the laser primarily to a single mode (wavelength) of oscillation. This means that, relative to an F-P laser, the DFB laser exhibits a lot less noise and distortion as a result of multiple propagation speeds in the fiber.

Figure 16.13 illustrates the NPR of an uncooled DFB return laser diode on the same NPR scale as the F-P laser of Figure 16.12. (The absolute values on the x axis are irrelevant and may vary from one transmitter to another.) Both diodes (Figures 16.12 and 16.13) were measured using the same 9-dB path loss. The increase in NPR with increasing signal level on the left side is only slightly greater than decibel for decibel, because the laser is isolated. That is, optical power reflected to the optical transmitter due to Rayleigh backscatter is diverted in an isolator and not allowed to enter the laser. Chapter 12 explains Rayleigh backscatter and the deleterious effect it can have on transmitter operation.

Figure 16.13 NPR performance of a DFB return laser diode.

As shown in Figure 16.13, the NPR performance of the laser is somewhat better in terms of carrier-to-noise ratio and dynamic range at room temperature and below than it is at high temperature. For this reason, cooled DFB lasers are sometimes used in return path operation, and they may be necessary where high power levels are required. However, the added cost and power drain (which adds heat to the node) often argue against adding a cooler. The performance of uncooled DFB lasers is considered adequate for many purposes, though long, heavily loaded paths may benefit from a cooled laser. The laser of Figure 16.13 was embedded in a temperature-compensated transmitter module. Had it not been, the performance range with temperature would have been worse.

Effect of Distance on DFB Link Performance

Figure 16.14 compares the NPR curves for one isolated DFB transmitter with different lengths of fiber, expressed as the loss of the fiber and connectors. Shown are 3-dB through 15-dB links. As expected, with longer fiber lengths the peak NPR curve drops, as a result of lower received signal level. Had the test been done with nonisolated lasers, the performance on the left would have dropped off much faster, as a result of Rayleigh backscatter noise reflecting into the laser.⁶

Figure 16.14 NPR Performance of a DFB laser for different return path lengths.

Digital Return

Yet a third technology for returning signals is available. This is to digitize the return band at the node and to transport the digitized signals to the headend. At the headend, the digitized signals are converted again to RF in order to allow interface with legacy headend systems.

Figure 16.15 illustrates a digital return system. Compare it with Figure 16.1, which shows the same node with RF return. In the digital return system, the outputs of the two-diplexer low-pass sections are individually digitized in the two analog-to-digital (A/D) converters, and then applied to a multiplexer (mux), which alternately passes data from one A/D converter and then from the other. The data is serialized and supplied to a digital transmitter for transport to the headend. At the headend, the data is demultiplexed into two signal streams, which are converted to RF in digital-to-analog (D/A) converters. The RF signals can then be supplied to the normal headend upstream receiving equipment, such as DOCSIS CMTSs for data.

Figure 16.15 Digital return system.

As explained in Chapter 6, in order to avoid sampling artifacts, it is necessary to sample data at more than twice the highest frequency to be sampled. If the high end of the return band is 42 MHz, then the sampling rate must be above 84 MHz. A convenient sampling frequency is 100 megasamples per second (Ms/s). Commonly, a 10-bit digital system is used. This means that the data rate from each of the two A/D converters is 1 Gb/s (100 million samples each second, times 10 bits per sample) before any control overhead is added. Two A/D converters multiplexed together yield a need for a data rate of 2 Gb/s before adding overhead. This fits nicely into an OC-48 transmitter, which runs at a wire rate (the actual data rate) of 2.488 Gb/s. Transmitters and receivers for this data rate are commonly available.

There are several advantages to using digital return transmission. The first is cost. A digital transmitter is lower in cost than is an analog transmitter, because power levels can generally be somewhat lower and because the specifications on a digital transmitter are much looser. Furthermore, by comparing Figures 16.1 and 16.15, you see that only one return transmitter is required, rather than two. Of course, somewhat offsetting the cost reductions is the need for two high-speed A/D converters and the other digital processing circuitry. But you do realize net savings in many cases, at least where you need more than one return path.

Digital returns can be particularly advantageous in longer-distance paths, because the NPR curve does not degrade with distance, at least not until you hit the well-known wall, beyond which digital signals just don’t work at all. Yet another advantage is gain stability, since the signal received at the headend is not dependent on the optical signal level received. However, there is inevitable delay in the process of packetizing the signal for transmission, and this delay must be controlled to prevent trouble with some return systems, such as that used in DOCSIS.

Figure 16.16 shows the NPR curve for a 10-bit digital return system on the same scale as is used for the analog return systems shown earlier. The temperature variation is a reflection of the inevitable shift in operating point of the A/D converter and perhaps a function of RF components preceding the A/D converter. It is not a function of shifts in the laser operating point, as is the case in analog transmission. The familiar precipitous drop on the right side is due to saturation of the A/D converter rather than to clipping in the laser.

Figure 16.16 NPR curve for a 10-bit digital return path.

16.8.3 Return Path Combining at the Headend

In order to save the cost of multiple RF receivers in the headend, it is a frequent practice to combine several reverse path signals into one. This can work if adequate total data capacity (called “bandwidth” by data communications engineers) is available to service multiple nodes as one. This combining is usually done electrically so that there is one optical receiver for each node. RF combining (in the headend, after the optical receiver) can be done satisfactorily as long as adequate carrier-to-noise ratio is maintained, considering both thermal noise and ingress. The transfer gain from the electrical reverse input to the node, to the point of combining in the headend, must be the same for all return paths that are combined. Otherwise, the return operating level of at least one of the nodes will be incorrect.

However, some operators like to do optical combining to further save the cost of optical receivers. Optical combining must be done carefully, if at all, because if the lasers operate at close to the same wavelength then interference (beats) between the lasers will develop in the receiver. These can increase the noise level much more than would be expected from the addition of incoming noise from each transmitter. Also, the received power from each return laser must be the same. Optical combining is not a recommended practice.

Since DFB lasers have relatively narrow ranges of operational wavelengths, it may be possible to combine them. You must ensure that the wavelengths will stay sufficiently separate over life, temperature, and modulation. Because F-P lasers have a less well-defined wavelength operating range, optical combining when F-P lasers are being used is particularly dangerous. Optical combining may work when it is first implemented, but if at a later date the two lasers drift to the same wavelength, the link could fail.

16.9.1 Plant Unavailability Analysis Based on Undesired Signals

Measurement of the quality of the upstream signal path is complicated by the absence of a spectrum of steady-state known signals and by the varying nature and presence of the undesired signals.

Generally, the dominant interfering signals are common path distortion (CPD), discrete ingress signals, and electrical transients. The first two result in signals that may be present for relatively long periods, but occupy narrow frequency bands, whereas transients are present for a very short duty cycle, but may have broad spectral content.

It is important to be able to measure these two classes of signals separately since their effects and the required countermeasures are different:

The following two measurement techniques are offered as examples of emerging industry practice in this area. The first measures the entire spectrum and range of possible operating levels, but includes only discrete signals, whereas the second measures multiple types of interference, but on only a single channel at a single defined operating level.

16.9.2 Discrete Interfering Signal Probability (DISP)

An NCTA recommended practice for quantification of discrete interfering signals is discrete interfering signal probability (DISP).⁸ This procedure was developed by Large and Bullinger as a result of extensive field testing.⁹

Continuous spectrum analyzer measurements are taken over the entire upstream spectrum. The operating parameters are set up to reject transients so that the measurements reflect only discrete signals. The level reading at each frequency on each sweep is downloaded to an attached computer for analysis. Each reading is compared with several predefined thresholds to create a three-dimensional matrix whose axes are frequency, time, and level, and whose values are the probability that a signal is present at a given frequency and time whose amplitude exceeds a given threshold.

From this matrix, postprocessing is used to derive overall discrete signal/CPD performance of the system as a function of threshold, system availability as a function of frequency and operating level, channel availability as a function of time and operating level, and other data as required.

16.9.3 Plant Unavailability Analysis Based on Threshold Boundaries

Studies have been made of the availability of return plant using a CW tester developed at Cable Television Laboratories (CableLabs).¹⁰ The technique uses a CW carrier in the return band and analyzes the characteristics of the signal received at the headend to predict the error rate of a signal at that frequency and with that bandwidth. From that data, we can predict the percent availability of a channel. Whereas the DISP measurement was based on interference amplitude measurement, the CableLabs technique analyzes the errors in location of a point in the data constellation (see Chapter 4 for an explanation of the data constellation).

Figure 16.18 illustrates the CW tester block diagram and the resulting con-stellation. A CW carrier is added somewhere in the node to be studied. At the headend, the carrier is up-converted to the normal TV IF of 44 MHz and passed through a SAW filter. After AGC (not shown), the signal is supplied to a phase locked loop, which generates quadrature demodulating carriers (see Chapter 4).

Figure 16.18 CW tester block diagram and constellation.

The outputs of the demodulator are supplied to a digital-sampling oscilloscope and to a window comparator that determines when the signal is outside the accurate decoding window. The accurate decoding window is shown in the figure; as shown, it is the decoding window for 16-QAM. While the constellation point is in the window, the correct state is decoded. While it is outside the window, a totalizing counter counts pulses from an 11-MHz clock. The output of the totalizing counter is accumulated by a computer, along with output data from the oscilloscope.

The constellation diagram at the bottom of the figure illustrates the data point crossing the threshold to the region occupied by another state. Assume for a moment that the study concerns use of 16-QAM modulation on the return carrier. The box defining the threshold region, in which the signal will be correctly demodulated, is shown. If a disturbance of any kind causes the carrier to go outside the box, then the totalizing counter is started, and it measures the total time the signal is out of the box. From this information, we obtain the symbol error rate (SER) equal to the proportion of time out of the accurate decoding region. If we assume that the channel is available when the SER is below some level (10⁻⁵ in the example shown), then we can chart the percent of unavailability of the channel.

Notice that the parameter measured is called the symbol error rate rather than the bit error rate. This is because it is the symbol that is subject to error, and typically each symbol comprises two or more bits. Chapter 4 explains the differences between bits and symbols in the context of data transmission.

Figure 16.19 illustrates the symbol error rate and consequent percentage of unavailability of nodes in several cable systems based on one set of tests. Each was observed for about one week. To the left is a logarithmic scale showing the symbol error rate, and to the right is a scale showing the percent of unavailability. Note node A2, which was a new node with no subscribers. Its good performance is evidence of the observation made by others — that drops and house wiring tend to be responsible for many return path problems.

Figure 16.19 SER and percent unavailability of selected nodes.

Nodes C1 and C2 were studied with and without noise-blocking filters. Noise-blocking filters are high-pass filters placed on taps to preclude in-home-generated noise from reaching the return path. In node C2, interference developed from an amateur radio operator during the testing; nonetheless, the percent of unavailability dropped significantly when the filters were added. The symbol error rate and unavailability improved dramatically in node C1 when the filters were added. This observation again lends credence to the hypothesis that the home is responsible for most of the problems in return path operation. It also attests to the efficacy of noise-blocking filters (covered in more detail later in the chapter).

16.11.1 Effect of Laser Clipping – Frequency Domain View

One can analyze the effect of laser clipping in the frequency domain, as done by West.¹⁴ Figure 16.21(a) illustrates no laser clipping. The laser transfer characteristic curve shows that, with laser bias current (the x axis), there is no light output until a threshold current is reached, above which the light output power is proportional to the current through the laser. The input signal is shown below the transfer curve, and the output is shown to the right. So long as the input signal remains such that the light output never drops to zero, changes in the output light are proportional to changes in the input current.

Figure 16.21 Laser in linear region and in mild clipping. (a) No clipping. (b) Clipping. (c) Quasi impulse of clipping signal.

As shown in Figure 16.21(b), if the input signal current is such that the light output ceases for a portion of the input signal, then the light output “clips” the signal. The portion of the signal represented by the dotted line is not really transmitted, so the signal is distorted. One way to model this is to assume that the signal was converted to light with no clipping, but then a signal was added, exactly equal in amplitude and opposite in phase, to the portion of the signal clipped. This added signal is shown in Figure 16.21(c). It represents a series of near impulses, which have a frequency spectrum that extends from some very low frequency equal to the lowest beat note between any elements of the input signal to very high frequencies. Thus, the spectrum of the clipping energy extends from very low frequencies to frequencies generally exceeding the bandwidth of the return path. The result is noise degradation, as represented by the degradation in NPR on the right side of Figure 16.16 and earlier figures.

16.11.2 Effect of Laser Clipping-Time Domain View

Kenny¹⁵ has demonstrated the effect of clipping on a single data signal being carried in the reverse path. The effect is extended to more than one carrier by the central limit theorem. He found that, with a variety of lasers, the effect of clipping is to compress the signals, which compromises bit error rate, as shown by West.

As shown in Figure 16.22, the test setup is similar to that for the NPR test of Figure 16.9. A signal from CW generator G2 is placed in the noise notch, and in one test the noise source, G1, is replaced by a second signal generator. The observation of test results follows a technique developed by Cable Television Laboratories, which is described in Section 16.9.3. A CW carrier may be thought of as “1-QAM” modulation: a single state in a constellation diagram. This is not useful for communicating information, but much can be learned about the communications channel with this test. (For a discussion of levels of QAM modulation, see Chapter 4.)

Figure 16.22 Time domain analysis technique. (a) Test configuration. (b) Constellation with noise causing clipping. (c) Constellation with CW signal causing clipping.

Generator G1 is adjusted to sufficient amplitude to cause the laser to clip. The “signal” is demodulated by quadrature detectors, which produce in-phase (I) and quadrature (Q) components. (Chapter 4 describes the resultant constellation display in detail.) The phase of the two channels is adjusted to place the recovered “information” in the first quadrant, as shown on the oscilloscope screen. As expected, the spot that should represent the state of the modulation is smeared owing to the noise that fills in the notch, as shown in the description of NPR testing. The smear is circular, indicating phase effects as well as amplitude effects, due to clipping noise falling on the frequency of the test carrier. The location of the smear is toward the origin, indicating a reduction of signal level as expected.

In a second test, the noise source was replaced with a CW generator, whose frequency was chosen such that distortion products did not fall within the passband of the receive filter (the frequency of the test carrier). The laser was forced into clipping by increasing the amplitude of the CW generator that replaced the noise generator, and the resultant constellation spread is as illustrated in Figure 16.22(c). The spot turned into a line along the radial from the origin, again indicating that the laser was clipping the desired signal, but showing the lack of intermodulation products at the test frequency.

When a laser is in clipping, its light is cut off for some short time. During this time, all signals being transmitted by the laser are cut off, not just that largest signal. Since the signal is cut off for some time, typically for a fraction of a cycle, the amplitude of that signal will be reduced. In the display of Figure 14.22, reduction in amplitude results in the spot on the oscilloscope moving toward the center of the screen, as shown in (c).

16.11.3 Amplifier Characteristics

RF amplifiers tend to react similarly to the peaky nature of the return signals. Typically, the dynamic range in which satisfactory performance is achieved is somewhat better than with return lasers, but many of the same concerns apply. Currently, there is considerable investigation into the ideal characteristics of return amplifiers.

16.13.1 Option 1: Drop Filters

Drop filters can be used to remove return band energy that might be coming out of the house. Two alternatives, la and lb, are shown in Figure 16.23. Option la is a high-pass filter that cuts off below about 54 MHz, the low end of the forward band. It is intended for use at homes not taking any services requiring two-way facilities. With typically 25 to 40 dB of attenuation in the return band, it does not allow return band signal power in the home to reach the hard-line plant.

Filter option lb is similar to la except that a bypass is added to allow signals in a narrow band, often between 10 and 15 MHz, to pass. These are used when the home has an RF-IPPV converter, which must communicate back to the headend on these frequencies. Interference from the home that occurs in the passband obviously appears in the hard-line plant, but interference coming out of the house at other frequencies is blocked.

Filters are usually placed at the tap though they may be placed at the side of the home in some cases. They are sometimes seen as a stopgap measure because they don’t remove the root cause of the problem, and they interfere with provision of modern two-way services in the home. When it becomes the practice to allow the customer to purchase two-way hardware at retail and install it himself or herself (a desirable way to sell data services), the filter can cause particular difficulties. Also, the filter is seen by some as an undesirable expenditure at homes not paying for enhanced two-way services. Countering this last argument is the thought that use of the filters postpones the day that homes not taking two-way services will have to have their internal distribution wiring improved.

Even when two-way services are added to the home, it may be possible to split signals at some point, with a new cable supplying only the device requiring return facilities. The filter can then be placed in the path to all services not requiring two-way facilities.

16.13.2 Option 2: Return Attenuation

A second interference mitigation option is to provide, in the tap or externally, two diplex filters, which separate the upstream frequency band (5–40 MHz) from the downstream band (54 + MHz). An attenuator is inserted into the low side of the diplex filter chain so that the loss is increased in the return direction while not changing the loss in the forward direction. The rationale is that tap values are selected to yield the correct signal level at the highest downstream frequency. Since cable loss is roughly proportional to the square root of the frequency, the loss in the upstream direction is considerably lower than in the downstream direction. Thus, whereas the downstream received level is the same at all houses (within a certain range), the upstream transmit level is significantly different between homes.

Figures 16.6 and 16.7 illustrate the range of levels that could be expected in a particular node that was analyzed for return level. Generally, as you move downstream from an amplifier, the tap value is reduced to compensate for signal loss at the high end of the downstream band. Since return signals suffer much less loss, the required upstream transmit level is reduced as you move downstream from an amplifier. Since the taps farther from an amplifier require lower transmit level, they also admit more potential interference from the house.

The thought behind adding the attenuator in the return direction is that this will bring taps requiring a low signal level up to requiring a higher signal level. In the process, it will attenuate interference coming out of those homes. It would not deter return services from being installed, as might filters. However, the diplexers will add some group delay.

Option 2a: Factory Selection of Attenuation Based on Tap Value

Within the spectrum of options for the return band attenuators is the possibility that the value of return attenuation is selected at the factory, based on the tap value. This would not place additional burden on field installation personnel, who treat the tap as they would any other tap. The problem with this approach, however, is that the range of transmit levels required at any particular value tap (Figure 16.6) is so great that factory selection of an attenuator value would be very difficult.

Figure 16.24 illustrates an attempt in one real node to add reverse attenuation. In this example, all tap values 23 dB and below had reverse attenuation added such that the total attenuation in the reverse spectrum equaled 23 dB. Dots show the required levels before addition of the reverse attenuation, and + marks show the required levels after. Notice that after adding attenuation, some of the low-value taps now require the highest return levels. The reason is that some low-value taps are placed after a lot of cable attenuation, so they benefit from a lot of added attenuation. Other low-value taps follow a directional coupler so that the loss is primarily flat (frequency insensitive) loss, and the return signal level required after addition of the attenuation is high. This is not a good condition since it could require excessive output level from a transmitter.

Figure 16.24 Required tap level with and without reverse attenuation.

Preliminary analysis has raised questions about the efficacy of factory selection of attenuator values. If the amount of attenuation added is low enough to prevent possible excessive level requirement, the benefit derived is minimal.

16.13.3 Option 3: Move Diplexers and Attenuator to Midspan

Others have suggested that the diplexer be moved from the tap to approximately midspan between amplifiers, and the attenuation used be selected to make the transmit levels required downstream of the diplexer to be roughly equal to those before the diplexer. This would reduce the number of diplexers required by somewhere around a factor of three or four, compared with putting them in taps. It does necessitate inserting another device into the hard-line cable. Co-locating the diplexers with an equalizer has been suggested, but this does not seem to be optimum.

Preliminary analysis indicates that such placement, combined with optimum attenuation selection in the field, would significantly reduce the signal level range required of transmitters. However, the estimated improvement in ingress is not particularly good, raising questions about the efficacy of the technique.

Notice that the industry has not firmed up its philosophy for applying these ingress countermeasures. Future work may reveal advantages that are not obvious at this time and may result in newer techniques that yield more benefit. Also, it is possible that the industry will learn how to improve performance of problem homes without having to use any of the techniques shown in this section.

16.13.4 Option 4: Frequency Hopping

Many services that use return plant service have provisions for frequency hopping. They can move from one frequency to another if their original frequency develops interference problems that make communications unreliable. This subject is covered in some detail in Chapter 6.

16.13.5 Option 5: Error Correction

Error correction is often added to digital datastreams to allow correction of any bits that are corrupted in transmission. The effect is to sharpen the curve of error rate versus carrier-to-noise (or interference) ratio. As noise increases, the recovered signal retains its quality longer, but at some point, the quality will collapse rapidly with worsening carrier-to-noise ratio. Chapter 3 describes error correction as it is being applied in the cable industry.

16.14.1 Few Return Services, F-P Laser

The first example illustrates the apportionment of signal power for a fairly simple node having only a few return path services and using a Fabry-Perot (F-P) laser. The laser is the one illustrated in figure 16.12. The chosen operating point is a total signal power into the transmitter of +15 dBmV, where the laser exhibits about a 42-dB NPR at room temperature. In practice, you may want to operate slightly lower on the curve to allow more room for error, but we take this point for illustration.

The services assumed include the following:

A significant omission from this list, done to keep the example simple, is an allocation for future expansion. It is essential that all future services be allocated the amount of power they will need when added. Failure to do so can result in extreme laser clipping later, and possibly a situation where a node that previously worked no longer does. Also, we have not allowed for ingress. It is advisable to allow some power for ingress.

One technique used to allocate signal level is the so-called constant power density method. In this method, each signal is set at the same amplitude per unit of occupied bandwidth. That is, if one signal is twice as wide as another, it will be set at twice the amplitude of the narrower signal.

The signal levels are set such that the total signal power is equal to the total at the operating point of the NPR curve, for example, +15 dBmV in Figure 16.12. The signals must be added on a power basis. If the levels of the three signals are L1, L2, and L3, in dBmV, then the power must add to the target power, in this case +15 dBmV:

Note that, though signal level is expressed in dBmV, as is customary in the cable television industry, we are actually manipulating signal power, expressed in dBmV in a 75-ohm system. For computation, we must express this level in terms of power, because it is necessary to add the drive power contributed by several signals. One cannot add power when that power is expressed in decibels. In the inner expressions — taking the power level, dividing by 10, and raising 10 to the power of the result — we are taking the antilog of the level expressed in dBmV. Thus, we have legitimate power units, though they are not commonly used units such as milliwatts.

In the apportionment philosophy shown here, the constant power density method is modified to give more power to services requiring a higher carrier-to-noise ratio. See Chapter 4 for a discussion of the carrier-to-noise ratio (C/N) required to meet a certain bit error rate (BER). The power ratios for different modulation formats are based on the distances between state boundaries in the constellation diagrams, with the average level of the signals held constant. In order to exhibit the same BER, a QPSK signal must have a 3-dB-higher C/N than that needed by a BPSK signal. Thus, in the example, the QPSK signal is allowed 3-dB (times 2) more level per hertz than is the BPSK signal. Similarly, the 16-QAM signal needs approximately 7.1-dB (times 5.13) better C/N than does a BPSK signal to yield the same BER. (10 log (5.13) = 7.1 dB.) Thus, we shall allocate twice the power density to a QPSK signal than we allocate to a BPSK (or FM, since we are treating the two the same, for better or for worse). We shall allocate 5.13 times the power density to a 16-QAM signal as to a BPSK signal.

It is possible to construct a table that will allow assignment of levels to each of the signals. We can express the power of each signal as follows. Let p represent the power per hertz in the BPSK signal. Table 16.1 illustrates how power is added. We multiply the power per hertz, p, by the occupied bandwidth of the service. The QPSK STT return is assigned twice the power because it is twice (10 log 2 = 3 dB) as sensitive to noise as are the signals of the BPSK services, and so on. With this weighting factor, the total power, shown at the bottom of the chart, is 4,788p. Equating this to the total power to be distributed among the services, +15 dBmV, we obtain

Table 16.1 Power Assigned to Each Service, Node with F–P Laser

(16.1)

We are working legitimately in power, but the units are not common units, so we just call them power units. Since we will convert back to dBmV consistently, we can get away with any arbitrary power units. We simply convert to power in order to add several signals. This may be converted back to dBmV:

(16.2)

We can then determine the total power of each BPSK signal by adding 10 log(bandwidth) to the signal level in dBmV. For the status-monitoring signal (300 kHz wide), this gives a total power of

(Note that we took bandwidth in kilohertz, to be consistent.)

We can estimate C/N as follows. From Figure 16.12, the NPR at the selected operating point is 42 dB. This means that the noise per hertz is 42 dB below the signal level per hertz (this is the definition of NPR). The total signal power at the selected operating point is +15 dBmV, and this signal was assumed to be spread over 35 MHz (5–40 MHz). Thus, the signal power per hertz is

Since the noise level is 42 dB lower yet, it is −102.44 dBmV/Hz.

The status-monitoring signal is assumed to be 300 kHz wide, so the noise level is 10 log (300,000) = 54.77 dB higher than −102.44 dBmV/Hz; that is, the noise level in the passband of the status-monitoring signal is −102.44 + 54.77 =-47.67 dBmV. This compares with the previously computed signal level of 2.97 dBmV, so

(16.3)

This is a bit optimistic, because we assumed that the receive filter for the statusmonitoring system has zero excess bandwidth. This is not realistic, so we will lose some C/N because the filter is wide enough to admit somewhat more noise than we assumed. In this case, the C/N is so far above what we need that we have nothing to worry about. A more precise computation would have to take this excess bandwidth into account, though.

Thus, we have so far established that the total amplitude (when the entire signal is measured) of the status-monitoring signal is +2.97 dBmV at the input to the return transmitter and that the carrier-to-noise ratio is 50.6 dB. It remains to determine what we would see on a spectrum analyzer if we looked at this signal. In order to determine this, we must make some assumptions concerning the way the analyzer works and how it is set. For the purpose of illustration, we assume that the analyzer is set to a resolution bandwidth of 100 kHz, narrower than any of the real signals being observed. We further assume that the noise bandwidth of the analyzer is 1.2 times the resolution bandwidth, or 120 kHz. The ratio of resolution bandwidth to noise bandwidth depends on the types of filters used in the spectrum analyzer. We will not use a detector correction factor, though the analyzer manufacturer may have one that should be taken into account; each analyzer model can be different in this respect. From the foregoing, we have the level of the status-monitoring signals as 2.97 dBmV measured in a bandwidth of 300 kHz, so if it is observed in a bandwidth of 120 kHz, the level we should see is given by

(16.4)

In a similar manner, we can determine the operating point of the STT return QPSK and the DOCSIS 16-QAM signals. When we compute the amplitude of the STT return signal, we must recall that it is twice what we compute for the BPSK signals, as a result of adding 3 dB (that is, multiplying by 2) to the level of the BPSK signals. The amplitude of the 16-QAM signal is multiplied by 5.13 to account for its greater susceptibility to noise. The results are shown in Figure 16.25. For each of the three signals, the higher, thicker line indicates the true amplitude of the signal when measured over at least its occupied bandwidth. The width of the line indicates the occupied bandwidth. Beneath each signal is a thinner line that represents what a spectrum analyzer with the specified characteristics would read. In order to correct the analyzer reading for the actual signal level, we would have to add to the reading 10 log (ratio of occupied bandwidth to measuring bandwidth).

Figure 16.25 Signal level apportionment, F-P laser, limited services.

Further, note that the analyzer reading for the 16-QAM signal is substantially below the actual signal level, because the 16-QAM signal is so much wider than the analyzer’s measurement bandwidth. The difference is less dramatic for the QPSK signal, because it is not as wide as is the 16-QAM signal. Also, note that the difference between the analyzer readings for the QPSK and BPSK signals is 3 dB, the level by which they differ on a per-hertz basis.

Figure 16.25 is not to be taken as a spectrum analyzer display: The lines with the labels next to them show the frequency and total amplitude of the signal. The lines below show what a spectrum analyzer would display under one set of conditions. Under other conditions, the spectrum analyzer will display a different level.

Also note that the example did not include an allowance for ingress, nor did it include an allowance for errors in level of the various return signals. As shown in Section 16.6.2, the signal levels at the return laser transmitter are controlled from the headend. Inevitably there will be some error in the control of the levels. Finally, allowance was not made for future services; you would be wise to allow for such future expansion of offerings.

16.14.2 Many Return Services, DFB Laser

The next example involves a DFB return laser carrying a greater number of signals. Power is apportioned first to the analog signal, giving it the level required to allow it to operate at the desired C/N. Next, the remaining signal capability of the laser is apportioned to the digital signals using a philosophy of constant power per hertz within a type of modulation. As in the first example, the power per hertz allocated to a signal is offset based on the modulation type, with denser modulation formats receiving a proportionately larger share of the power per hertz, to allow for their greater sensitivity to noise.

For the DFB transmitter, we’ll select an input level of 18 dBmV and a corresponding NPR of 47 dB as our operating point.

The following signals were included in this example:

The digital signals “get” their allocation of power from the power left after the analog signal receives enough power allocation to yield the desired carrier-to-noise ratio.

Figure 16.26 summarizes the level of all signals, using the procedure already outlined. The telephony QPSK signal is the widest of the digital signals, so the difference between its actual level and the level indicated on the spectrum analyzer is the largest difference. The two QPSK signals have the same power density, which is proportional to what is read on the spectrum analyzer as long as its noise bandwidth is less than the occupied bandwidth of the signal.

Figure 16.26 Signal apportionment, DFB Laser, many services.

In this case, the actual level of some of the digital signals is higher than the level of the analog signal. This is simply a result of the way we allocated power for the analog signal. We set its level to yield a C/N of 50 dB and then subtracted that level from the total +18-dBmV signal level. The remaining signal level happened to be enough that we could allocate more to the digital signals needing the most. Of course, you could say that this link is overdesigned, since the C/N provided is much higher than needed.