And, yes, that can actually be a good thing.

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 operators to mine the pre-distortion coefficients from the cable modem’s adaptive equalizer.

Multiple Recursion Echo

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 (or pre-equalization), 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 predistortion 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 they can reduce expensive truck rolls, either reactively or proactively.

As a result of data presented in the DOCSIS Proactive face-to-face meetings and from data gathered in experiments, it appears 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 Figure 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.

Wiring Diagrams - Echoes in a Lab

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.

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 at the bottom of Figure 3.

Single Recursion Echo

Creating a 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.

A single recursion echo can be canceled by an adaptive equalizer with enough taps to handle all of the significant recursions, and 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, and so forth, repeating endlessly.

It is suspected (and confirmed by preliminary field and lab data) that under the proper conditions, a multiple recursion echo can be canceled by a predistorted 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 already has propagated upstream past point A. A reflection created at reflection point A has propagated backwards 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 C 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. To be more precise: a = Aej2ðfT, where “A” is the amplitude of the echo, “f” is carrier frequency (MHz) and “T” is the delay of the echo. However, the equations are easier to present if we simply use “a.” 

The equalizer solution for a single recursion echo is single recursion echo So the result is what was expected: infinitely recursive. The first term “1” represents the main tap of the equalizer. The second term “-a” acts to cancel the echo by subtracting it. However, in doing so, it causes another, smaller echo in the response. This smaller echo requires the third term to cancel it. This produces another, yet smaller echo, which requires the fourth term to cancel it, and so on until we reach the end of the equalizer delay line. After that, any remaining echo energy (hopefully very small) is not canceled and shows up as reduced RxMER (received modulation error ratio), essentially a noise floor, in the receiver.

If “a” is a relatively big number, such as 0.707 (-3 dB), and the delay “T” of the echo is several symbol periods, we might run out of taps in the pre-equalizer before we get an accurate solution. DOCSIS 2.0 and later preequalizers have 24 taps, with seven taps normally assigned ahead of the main tap, leaving 16 taps to cancel the echo. For a small value of “a,” such as 0.1 (-20 dB), with a short echo delay, 16 taps is normally sufficient to cancel the echo with minimal residual energy.

Note that the recursions in the above equation have alternating signs. To check for this effect, we can examine the real and imaginary parts of the equalizer taps. If the response is alternating in sign, it is a hint that this type of solution may be present.

A multiple recursion echo may be modeled as: single recursion echo So its solution can be computed as: multiple ecursion solution which 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. To be precise, this example applies to an ideal case where the echo delay “T” equals a multiple of the symbol period, which for a 5.12 Mbps DOCSIS upstream symbol rate is Ts = 195 ns. So the pre-equalizer can exactly cancel the echo with a single tap if the single echo has delay T = 195 ns, 390 ns or 585 ns, etc. If the echo lies between these multiples, the equalizer will activate additional taps to provide interpolation. In that case, it will be more difficult to see the pattern of a single main recursion.

Comparison: Single Path Impulse Responses & Adaptive Equalizer 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.