As stated previously, QAM involves sending digital information by periodically adjusting the phase and amplitude of a sinusoidal electromagnetic wave. Four-QAM uses four combinations of phase and amplitude. Moreover, each combination is assigned a 2-bit digital pattern. For example, suppose you want to generate the bitstream (1,0,0,1,1,1). Because each symbol has a unique 2-bit digital pattern, these bits are grouped in two’s so that they can be mapped to the corresponding symbols. In our example, the original bitstream (1,0,0,1,1,1) is grouped into the three symbols (10,01,11).
In the following figure, 4-QAM consists of four unique combinations of phase and amplitude. These combinations—called symbols—are shown as the white dots on the constellation plot in Figure 2. The red lines represent the phase and amplitude transitions from one symbol to another. Labeled on the constellation plot is the digital bit pattern that each symbol represents. Thus, a digital bit pattern can be sent over a carrier signal by generating unique combinations of phase and amplitude.
Figure 2. 4-QAM Symbol Map
How do these digital bit patterns correspond to I/Q data? Figure 3 shows both the I/Q data (top) and the 2-bit digital pattern (in a constellation plot, bottom) relating to 4-QAM. The black dashed line in the top graphic corresponds to the black square marker in the bottom graphic, so you can follow the phase and amplitude changes as the I/Q parameters also change.
Figure 3. (top) 4-QAM Baseband I/Q Data (bottom) 4-QAM Constellation Plot
The constellation plot in Figure 2 shows the symbol map of 4-QAM with each possible phase (Θ) and amplitude (A) of a carrier signal in polar coordinate form. Notice how in the bottom graphic of Figure 3 the square marker passes over each symbol at least once.
While it is possible to send up to two bits per symbol when using 4-QAM modulation, it is also possible to send data at even higher rates by increasing the number of symbols in our symbol map. By convention, the number of symbols in a symbol map is called the symbol map “M” and is considered the “M-ary” of the modulation scheme. In other words, 4-QAM has an M-ary of four and 256-QAM has an M-ary of 256. Moreover, the number of bits that can be represented by a symbol has a logarithmic relationship to the M-ary. For example, we know that two bits can be represented by each symbol in 4-QAM. While this makes sense intuitively, it is defined by the equation bits per symbol = log2 (M).
Using this equation, each symbol in 256-QAM can be used to represent an 8-bit digital pattern (log2 (256) = 8). Because the M-ary of a QAM modulation scheme affects the number of bits per symbol, the M-ary has a significant affect on the actual data transmission rate.