Page 245 - From GMS to LTE

Long Term Evolution (LTE) and LTE-Advanced Pro 231

4.3.3 Quadrature Amplitude Modulation for Subchannels
As described above, the LTE air interface uses OFDM to transmit many slow data
streams (subcarriers) in parallel to achieve a very high overall speed. On each subcar-
rier, data is modulated using a number of different modulation schemes such as 16‐
QAM or 64‐QAM depending on the signal quality. QAM is the abbreviation for
Quadrature Amplitude Modulation and is a modulation technique that encodes several
bits per transmission step in the amplitude of a sine wave signal and, in addition, in a
phase shift compared to a reference signal. In other words, the bits are encoded in two
dimensions.
From a mathematical point of view the two dimensions can be expressed as a complex
number with an I‐component and a Q‐component. Figure 4.7 shows how bits are
encoded in two dimensions in a Cartesian coordinate system. Each point on this grid
represents four bits and has an I‐amplitude and a Q‐amplitude associated with it. In
total there are 16 combinations, hence this figure shows 16‐QAM modulation.
In a time‐based signal these amplitudes are represented as follows. The point repre-
senting the 4‐bit combination 1101 has an I‐amplitude of +1 and a Q‐amplitude of +1.
This means that this point is represented in a time signal by a sine wave with an ampli-
tude represented by the length of the arrow shown in the diagram and a phase shift of
45 degrees compared to an unaltered reference signal.
The point representing the 4‐bit combination 0000 has an I‐amplitude of −3 and a
Q‐amplitude of +3. In a time signal this is expressed as an amplitude represented by the
length of the arrow from the center of the grid to this point and a phase shift of 135
degrees compared to a reference signal.
From a mathematical point of view it can be shown that the amplitude and phase of a
sine wave can be changed by combining two sine waves that are oscillating at the same
frequency. The difference between the two signals is that one of the signals is phase
shifted by exactly 90 degrees compared to the other. This means that one of the sine
waves passes through 0 on the time axis one‐quarter of a full wave cycle earlier than the

Figure 4.7 16‐QAM modulation. Q

0000 0100 1100 1000

0001 1101 1001

I

0011 0111 1111 1011

0010 0110 1110 1010