Constellation diagram
Fig. 4.3-11 4-PSK characteristics
We can extend this idea to 8-PSK. Instead of 90 degrees, we now vary the signal by shifts of 45 degrees. With 8 different phases, each shift can represent three bits (one tribit) at a time. (As you can see, the relationship of number of bits per shift to number of phases is a power of two. When we have four possible phases, we can send two bits at a time---22 equals 4. When we have eight possible phases, we can send three bits at a time—23 equals 8). Figure 4.3-12 shows the relationships between the phase shifts and the tribits each one represents. 8-PSK is three times faster than 2-PSK.
- Fig. 4.3-12 8-PSK characteristics
Bandwidth for PSK
The minimum bandwidth required for PSK transmission is the same as that required for ASK transmission---and for the same reasons. As we have seen, the maximum bit rate in PSK transmission, however, is potentially much greater than that of ASK. So while the maximum baud rates of ASK and PSK are the same for a given bandwidth, PSK bit rates using the same bandwidth can be two or more times greater (see Figure 4.3-13).
- Fig. 4.3-13 Bandwidth for PSK
Example 4.3-6
Find the bandwidth for a 4-PSK signal transmitting at 2000 bit/s. Transmission is in half-duplex mode.
Solution
For 4-PSK the baud rate is half of the bit rate. The baud rate is therefore l000. A PSK signal requires a bandwidth equal to its baud rate. Therefore, the bandwidth is l000 Hz.
Example 4.3-7
Given a bandwidth of 5000 Hz for an 8-PSK signal, what are the baud rate and bit rate? Solution
For PSK the baud rate is the same as the bandwidth, which means the baud rate is 5000. But in 8-PSK the bit rate is three times the baud rate. So the bit rate is 15,000 bit/s.
4.3.5 Quadrature Amplitude Modulation (QAM)
PSK is limited by the ability of the equipment to distinguish small differences in phase. This factor limits its potential bit rate.
So far, we have been altering only one of the three characteristics of a sine wave at a time to achieve our encoding, but what if we alter two? Bandwidth limitations make combinations of FSK with other changes practically useless. But why not combine ASK and PSK? Then we could have x variations in phase and y variations in amplitude, giving us x times y possible variations and the corresponding number of bits per variation. Quadrature amplitude modulation (QAM) does just that. The term quadrature is derived from the restrictions required for minimum performance and is related to trigonometry.
Quadrature amplitude modulation (QAM) means combining ASK and PSK in such a way that we have maximum contrast between each bit, dibit, tribit, quadbit, and so on.
Possible variations of QAM are numerous. Theoretically any measurable number of changes in amplitude can be combined with any measurable number of changes in phase. Figure 4.3-14 shows two possible configurations, 4-QAM and 8-QAM. In both cases, the number of amplitude shifts is fewer than the number of phase shifts. Because amplitude changes are susceptible to noise and require greater shift differences than do phase changes, the number of phase shifts used by a QAM system is always larger than the number of amplitude shifts. The time-domain plot corresponding to the 8-QAM signal in Figure 4.3-14 is shown in Figure 4.3-15.
4-QAM 8-QAM
1 amplitude, 4 phases 2 amplitudes, 4 phases
Figure 4.3-14 4-QAM and 8-QAM constellations
Other geometric relationships besides concentric circles are also possible. Three popular 16-QAM configurations are shown in Figure 4.3-16. The first example, three amplitudes and 12 phases, handles noise best because of a greater ratio of phase shift to amplitude. It is the ITU-T recommendation. The second example, four amplitudes and eight phases, is the OSI recommendation. If you examine the graph carefully, you will notice that although it is based on concentric circles, not every intersection of phase and amplitude is utilized. In fact, 4 times 8 should allow for 32 possible variations. But by using only half of those possibilities, the measurable differences between shifts are increased and greater signal readability is ensured. In addition, several QAM designs link specific amplitudes with specific phases. This means that even with the noise problem associated with amplitude shifting, the meaning of a shift can be recovered from phase information. In general, therefore, a second advantage of QAM encoding over ASK
encoding is its lower susceptibility to noise. Amplitude
- Fig. 4.3-15 Time domain for an 8-QAM signal
3 amplitudes, 12 phases
4 amplitudes, S phases
2 amplitudes,
8 phases
16-QAM 16-QAM 16-QAM
Fig. 4.3-16 16-QAM constellations
Bandwidth for QAM
The minimum bandwidth required for QAM transmission is the same as that required for ASK and PSK transmission. QAM has the same advantages as PSK over ASK.
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