DOCSIS cable modems are currently generating data that cable operators are not making full use of. Some of the data can be used to improve overall plant performance.

CableLabs has established a “DOCSIS Proactive” working group with the goal of utilizing the data in DOCSIS-based communications systems to improve plant operations. The group’s first task is to produce a recommended practices document that enables cable operators to mine the pre-distortion coefficients from the cable modem’s adaptive equalizer.

Cable lines typically have many small echoes, so-called micro-reflections, that will disrupt digital transmissions if not canceled. This is particularly true for high-speed upstream signals having a higher order modulation, such as 64 QAM, or having wider bandwidth, such as 6.4 MHz. The system chosen by DOCSIS uses pre-distortion, where a burst transmission is distorted prior to transmission and arrives at a CMTS receiver with the plant’s distortion canceled.

The idea is that by reading the CM’s pre-distortion coefficients using a network management system, technicians can tell what plant impairments a CM is compensating for and then compute what may be wrong with the cable plant. By reading the data from many CMs, you can localize the problems using maps or connectivity data.

The process of programming the pre-distortion coefficients in the cable modem is handled during a periodic ranging process, which is controlled by the CMTS.

The group’s name, DOCSIS Proactive, is somewhat limiting, as the techniques being developed show a reactive ability to speed time-to repair. The utility of the techniques is that it can reduce expensive truck rolls, either reactively or proactively.

As a result of data presented in the DOCSIS Proactive face-to-face meetings and my own experiments, I now believe that upstream cable plant has two distinctly different types of echoes, with different mathematical properties.

The first type is echoes – call them “multiple recursion” – that are created by two or more impedance discontinuities inside the cable. This type of echo has a characteristic impulse response of a main signal followed by several echoes, with each succeeding echo having smaller amplitude. (An impulse response is nothing more than a time plot of how the signal path would respond to a narrow voltage spike.)

The second type – call it “single recursion” – are echoes that are created by signals that find two different routes upstream. This type of echo has a characteristic impulse response of a main signal followed by a single echo. The good news is that the existing upstream adaptive equalizer corrects both automatically.

Also, if the echoes are not strong, only the first recursion is significant in both cases. That is, the second recursion of a -20 dB echo is -40 dB, which is generally below the noise threshold.

In this echo situation, an upstream transmission gets bounced back and forth between two impedance discontinuities. The multiple recursion echo may be created in a situation like is shown in the top of Figure 1. An upstream signal travels from right to left through an amplifier, a span of cable with taps and another amplifier.

There are two labeled impedance mismatches, labeled “reflection points,” which cause a portion of the upstream signal to reflect back and forth until the reflections eventually die out. The bottom of Fig. 1 shows the impulse response of the upstream channel. Note that there is a main signal followed by multiple recursions, each caused by a re-reflection. In this example, the echo is very strong, so there are many significant recursions.

The multiple recursion scenario has also been observed in a drop cable, where a filter on one end has bad upstream return loss, and a house on the other end also has bad return loss due to un-terminated splitters. A CM’s transmission from the house picks up multiple recursions.

multiple recursion echo

This multiple recursion echo situation can be created in a lab environment with the diagram shown in the top of Figure 2. A pair of directional couplers is chosen, with tap values selected to adjust the strength of the echo. A cable length is chosen to give the desired echo delay. The tap leg of each directional coupler is left open to create a reflection. Assuming two-way splitters are used with 3.5 dB of insertion loss on each leg, and cable loss is 2 dB, first recursion echo strength is computed as:

Main path dB - echo path dB = (3.5 + 2.0 + 3.5) – (3.5 + 2.0 + 3.5 + 3.5 + 2.0 + 3.5 + 3.5 + 2.0 + 3.5) = 9.0 - 25.0 = 16 dB.

wring diagrams

In this echo situation, the transmission finds two different paths upstream.  One scenario for this echo situation is illustrated in the top of Figure 3. A signal is being transmitted from a house into a 28 dB tap. Unfortunately, this tap has a port to output isolation of only 35 dB.

The CM’s signal travels upstream attenuated by the tap’s value (28 dB), but the signal also travels downstream attenuated by only 35 dB. When the signal reaches the end of the line, it encounters a two-way splitter that is not terminated. The lack of a termination causes the signal to reflect back upstream, where it rejoins, after some time delay, the main signal. Because the input return loss of the amplifier and 28 db tap is excellent, there is no further recursion of the echo. The resulting impulse response is shown the bottom of Figure 3.

single recursion echo

A single recursion echo can be created by the wiring diagram in the bottom of Figure 2. A signal is split by a first splitter on the left. One leg of the left splitter connects to a short piece of cable, and the other connects to a long piece of cable. The ends of the two cables are combined to make an output signal in the right combiner. An attenuator (not shown) may be put in line with the long piece of cable to attenuate the echo to a desired strength.

It is well known by digital signal processing engineers that a single recursion echo can be canceled by an adaptive equalizer with enough taps to handle all of the significant recursions, and that several recursions may be needed to cancel a strong echo. Multiple recursions are necessary to cancel a single echo because the adaptive equalizer sums an echo-corrupted received signal with a delayed echo-corrupted copy. You cancel the first recursion of the echo, but echo in the delayed signal is not canceled. So yet another recursion is needed to take out the echo in the signal you used for cancellation.

I hypothesize that a multiple recursion echo can be canceled by a pre-distorted signal with only one recursion. How this works is explained in Figure 4. This diagram is a snapshot in time. At the illustrated point in time, a main signal’s impulse has already propagated upstream past Point A. A reflection created at Reflection Point A has propagated backward and is now at Point C. The CM has already transmitted an inverse first recursion, shown at Point D. When the signals propagating from Point B and Point D meet at Reflection Point B, they sum together and cancel. End of echo – period. No more recursions.

multiple recursion echo canceled w/ pre-distortion

A single recursion echo can be modeled by: 1 + a, where 1.0 is the main signal amplitude and ‘a’ is the echo’s amplitude in linear terms. That is, for a -3 dB echo, a = 0.707. In a baseband channel, ‘a’ is real, but in an RF channel, ‘a’ may be complex.

The equalizer solution for a single recursion echo is:
equalizer solution for single recursion 

So the result is what was expected – infinitely recursive. If ‘a’ is a big number, you might run out of taps before you get an accurate solution.

A multiple recursion echo may be is modeled as:
multiple recursion echo modeled 

So its solution can be computed as:
solution computed 

This shows that an infinitely recursive echo can be canceled by a single recursion. So you should be able to cancel a multiple recursion echo with an adaptive equalizer, with only two taps: one for the main signal and one for the echo.

signal path impulse responses and programming...

Figure 5 summarizes both types of echoes and the resulting programming that could be found in the adaptive equalizer to cancel the echoes.

Upstream cable plant can have two distinctly different types of echoes, but if the echoes are relatively weak, the differences may not be significant. If the echoes are strong, the differences can be exploited to help a cable technician diagnose and fix the cause of the strong echo.