In high-speed data communications, the industry has evolved and implemented complex modulation schemes which vary a signal's voltage (amplitude), phase, and frequency in order to transmit more data, faster. The following will cover these methods in order to describe how Quadrature Amplitude Modulation (QAM) works in DOCSIS communications.

We live in an analog world. Sure, today we are surrounded by “digital” technology and advertisements of “all digital communications”, but the basis of all digital communications is analog as I will explain. Okay, there is the exception in the virtual world of computer software where pure Boolean logic can exist without analog, but when software meets hardware, it becomes analog – a disclaimer for the purists.

TTL (transistor-to-transistor logic) logic circuits have been a fundamental building block of digital circuits since 1961[1]. Digital technology and communications at its primal level is made up of 0’s and 1’s. All data is communicated using these two values. For hardware to transmit a “zero” or a “one”, the hardware “transmitter” must use some means of stimulus such that the hardware “receiver” can differentiate a one from a zero. An example is TTL logic, in which case a zero is represented by any voltage level from 0 to +0.8 Vdc and a one is represented by any voltage level from +2.2 to +5.0 Vdc[2]. Anything greater than +0.8 Vdc and less than +2.2 Vdc is ignored by the receiver. So in this example, a transmitter uses analog voltage to transmit digital data to the receiver.

Fundamentally, every complex signal can be represented by the following equation:

where s(t) is the signal as a function of time (t),

A is the amplitude or voltage of the signal

is, well that’s “pi” and is approximated by 3.14

is the frequency of the signal, in my blog on RF Fundamentals I discussed that the DOCSIS downstream would be between 54 – 1000 MHz, so could be 500 MHz as an example

is the phase in degrees of the signal

Just like in the TTL example above, if amplitude, frequency or phase is varied in the signal above, data can be transmitted as will be illustrated below.

Amplitude Modulation (AM) is a method of communicating data when a carrier wave is varied in direct proportion to that of a modulating signal (i.e. baseband digital data).

**What is Amplitude? It is the peak to peak voltage of a signal, “A” in the signal equation.****In Amplitude Modulation the Amplitude of the signal varies peak to peak****What is Frequency? The rate of change per second given in Hz. i.e. A radio station always remains at the same frequency. It is constant.**

An AM receiver consists primarily of a tunable filter and an envelope detector, which in simpler sets is a single diode. Its output is a signal at the carrier frequency, with peaks that trace the amplitude of the un-modulated signal. Amazingly, this is all that is needed to recover the original audio! In practice, a capacitor is used to undo the DC shift introduced by the transmitter and to eliminate the carrier frequency by connecting the signal peaks. The output is then fed to an audio amplifier.

The figure below shows data (the red line) being “modulated” onto the carrier frequency (green line and f_{0}) from our equation above.The net result is the blue modulated sine wave, which is transmitting the desired data.A device on the receiving end will be able to demodulate the signal and interpret the transmitted data.

Like amplitude modulation, Frequency Modulation (FM) also has a carrier wave (f_{0}), but the amplitude is kept constant.In order to transmit data in a FM modulation scheme, it is actually f_{0} that is modulated by the data to be transmitted.The carrier wave frequency is varied in direct proportion to changes in the amplitude of an input signal.

**Frequency of signal varies. In the figure below,****the signal peaks are no longer evenly spaced. They are now separated mimicking the signal being imposed on the carrier****Amplitude of signal is constant. The peak to peak voltage does not change as seen in the graph below**

The figure below shows the data (red line) modulating the carrier signal (green line) for a resulting modulated signal (blue line). Notice that the blue signal is a sine wave that has non-constant variations between periods of the sine waves. This is what the signal looks like in the time domain. This indicates that the sine wave is getting faster and slower as the data is “modulating” the sine wave, or as f_{0} is being modulated.

Phase modulation (PM) is a form of modulation which represents information as variations in the instantaneous phase of a carrier wave.

Note:Variation of frequency implies a variation of phase; mathematically these two types of Modulation are complementary through derivatives and integrals.

The figure below shows the data (red) modulating the carrier signal (green).The resulting signal in blue appears similar to frequency modulation as indicated in the “note” above due to the relationship between FM and PM. However, the actual modulation is a change in phase rather than in frequency. Therefore, the receiver is a bit more complex to make than a standard FM receiver.

Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). Any digital modulation scheme uses a finite number of distinct states to represent digital data. In the case of PSK, a finite number of phases are used. Each of these phases is assigned a unique pattern of binary bits. Usually, each phase encodes an equal number of bits. Each pattern of bits forms the symbol that is represented by the particular phase. The demodulator, which is designed specifically for the symbol-set used by the modulator, determines the phase of the received signal and maps it back to the symbol it represents, thus recovering the original data. This requires the receiver to be able to compare the phase of the received signal to a reference signal — such a system is termed coherent.

The figure below shows an example of a PSK system with binary data mapped to the phase shifts of the relevant signal.

So far, all of the modulation schemes discussed are capable of transmitting data, some at high speeds, but for DOCSIS very high speeds are needed. In order to achieve this, complex modulations are needed which use a combination of he modulations described so far. The modulation used in the DOCSIS downstream is called Quadrature Amplitude Modulation (QAM), pronounced “kwam”. QAM transmits data by changing the amplitude of two carriers simultaneously. Since the two carriers are 90? out of phase, the sum of resulting signals have both level and phase variations. This provides for a large variation of data transition points, adding to the data throughput of a QAM signal. The mathematical formula for a QAM signal is as follows:

A representation of an 8-QAM signal is shown in the following figure.

So finally we arrive at the conclusion of this blog, which is QAM modulation, specifically 64-QAM and 256-QAM under the J.83 Annex B (Annex A for Europe) standard. These are the two modulations identified in the DOCSIS specification for downstream data transmission. 64-QAM has six (6) bits per symbol, contrasted to the three bits per symbol in the Complex Modulation diagram above shown in the "Complex Modulation" section. 256-QAM has eight bits per symbol. 64-QAM is able to transmit about 30 mega-bits-per second (Mbps) while 256-QAM can transmit about 40 Mbps. Looking at the analog signals in the time domain can be quite messy, so it is common to use a technique called constellation analysis to view these modulations. See the following figures:

Constellation analysis is valuable for viewing high order, complex modulations because it allows one to see how many symbols are present in the modulation, 64 or 256 in the above case, in addition, one can see if impairments are present in the signal, which will be covered later in my posts on DOCSIS Troubleshooting.

Tune in next time when I will cover DOCSIS upstream modulation types, which builds upon this blog.

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[1] Buie, J. Coupling Transistor Logic and Other Circuits. (U.S. Patent 3,283,170). 1 November 1966. United States Patent and Trademark Office. 1 November 1966.

[2] Transistor-Transistor Logic (TTL). siliconfareast.com. 2005. Retrieved 17 September 2008