Modulation Techniques (line codes)

QAM and CAP modulation

QAM ( Quadrature Amplitude M odulation) also known as I&Q modulation, is a combination of amplitude modulation (data is represented by differing amplitudes) and phase shift keying (data is represented by shifting each wave relative to the wave that came before it).
In a QAM signal, there are two carriers, each having the same frequency but differing in phase by 90 degrees (one quarter of a cycle, from which the term quadrature arises). One signal is called the I signal, and the other is called the Q signal . Mathematically, one of the signals can be represented by a sine wave, and the other by a cosine wave. Each of the two carriers are modulated via two separate balanced modulators (BM), and then combined (algebraically summed) at the source for transmission. At the destination, the carriers are separated; the data is extracted from each, and then combined into the original modulating information. 

CAP (Carrierless amplitude/phase) modulation, which was the original approach for DSL (and the choice of many modems manufacturers in the past), produce the same form of signal as QAM, without requiring in-phase and quadrature components of the carrier to first be generated.

 
Figure 1 . Conceptual CAP transmitter
The Constellation Encoder maps the incoming data into two stream a₁..a_n and b₁..b_n.
Those streams are then passed to the two filters which are designed so that their impulse response
form a hilbert pair( i.e. one signal is phase-shifted by 90 degree regarding the other).

CAP splits the data into two bit streams and alters both symbol rate and modulation levels to change the bit rate,
causing modems to be symbol rate adaptive to varying line condition.   The carrier itself is suppressed before transmission (it contains no information, and can be reconstructed at the receiver), hence the adjective carrierless.
CAP also uses frequency division multiplexing to eliminate the need for echo cancellation techniques.
Another advantage is the cost element implementing the technology, which is relatively low.  

DMT modulation

DMT ( Discrete MultiTone ) is a version of multicarrier modulation in which the data is distributed over a large number of subcarriers, or channels, each of which uses a form of QAM modulation.
DMT modems divide the downstream bandwidth into 256 channels of 4 kHz each, and can transmit up to 15 bits/Hz in each channel.  The modems can adapt to different impairments in different lines by evaluating the signal-to-noise ratio (SNR) in each subchannel and sending more data in those with higher quality.

Figure 2 . Conceptual DMT transmitter
The input data is buffered, and each bit is assigned or mapped into one of
N complex (QAM) multi-level sub-channel symbols by the DMT symbol encoder. 
Since these are complex numbers, they can be treated as discrete frequency-domain
representation of the signal.  using IFFT we can convert it to its time-domain representation
(the receiver will use FFT to convert it back).  The resulting time domain function
is then sent serially through the D/A converter and line filter.

 DMT upstream and downstream channels overlap; therefore, echo cancellation techniques are needed.  Discrete Wavelet Multitone (DWMT), a developmental variant of DMT, will provide better subchannel isolation by using a digital wavelet transform instead of the Fourier transform used in standard DMT.

DMT xDSL transceivers based on the Standard have been proven to provide high-grade performance in the field, are more reliable, and considered the preferred Modulation Technique for DSL.

FMT modulation

FMT ( Filtered MultiTone) is a multicarrier modulation scheme which can be viewed as a combination of the other two methods. The modulation is achieved by splitting the data into several streams, each of them applied to one of the inputs of a filter-bank. Because of implementation complexity, the number of channels is considerably less than in DMT.

Figure 3 . Conceptual FMT transmitter
The input goes through an IFFT module, and then filtered by an FIR filter. 
At the end it goes serial using P/S converter.

one of its main advantages is that the frequency band provided is better utilized in the border parts of the spectrum designed for individual transmission direction, where in the case of DMT losses in the transmission rate occur. The out of band emission is eliminated almost completely.
FMT plays the rule of a strong candidate for the VDSL modulation method.

Next: Factors effecting line conditions