At first it may seem strange to prefer this more complicated method of modulation. Simple on/off modulation can easily be demodulated by a cheap circuit like an Envelope Detector, but to demodulate BPSK we require the receiver to detect changes in the phase of the signal, not its amplitude. The reasons for the preference can be understood by considering how much power we have to transmit to communicate the information patterns.
When the signal is received and presented to a demodulator, the desired signal will always be accompanied by some random noise. Hence we need the difference between the signal for a ‘0’ and that for a ‘1’ to be large enough to be recognisable above this noise. To consider this we can use a plot of the kind shown in Figure 19.4.
The plot on the left of Figure 19.4 shows how we can represent the amplitude and phase of the symbol used to represent a given chunk of information. We can plot the carrier amplitude, 
, and phase, 
, to represent a symbol as a dot on the graph. The plot on the right of Fig 19.4 then represents the effect of noise upon reception. If the typical level of noise is represented by 
then we can draw a circle of radius 
around the intended/transmitted position. This represents the area on the plot where a received symbol is likely to appear as a result of being ‘moved’ by the noise. (Note that the effects of real random noise are more complex than described here.)
We can now use this approach to draw the examples shown in Figure 19.5. The left-hand plot of 19.5 shows the on/off modulation example. We can see that we have to ensure that 
to keep the two ‘noise circles’ from overlapping and avoid a symbol being interpreted incorrectly upon reception. For the on/off modulation this means that one type of symbol has an amplitude of zero, and the other has an amplitude of 
However for the biphase modulation we can use the same magnitude of symbol amplitude for the ‘0’ as for the ‘1’. This is illustrated in the right-hand plot of Figure 19.5. Here we can see that we can maintain the same distance between the symbols with symbol amplitudes of 
and 
. i.e. BPSK only requires half the symbol (signal) amplitude required by OOK to avoid the results being upset by noise.
Now for a sequence of bits which has roughly equal numbers of ‘0’s and ‘1’s, the on/off modulation will have an amplitude of 
, and hence a power proportional to 
half the time, and an amplitude and power of zero half the time. Hence the time-averaged power of the on/off modulation will be proportional to 
. Whereas with the biphase modulation the power of every symbol is proportional to 
. i.e. it requires a mean power of 
. This means that the two systems can convey signals with the same level of reliability, but the biphase system only requires half the power, on average. It also means we don’t have to ensure the transmitter and circuitry can handle peak powers as high as the on/off system requires to transmit a ‘1’.
For the above reasons, the biphase modulation is more power efficient than on/off modulation. (It also means that if we’d used the same power as for on-off modulation, BPSK would have provided a higher level of protection from noise.) The drawback is that we require more complicated receivers that can recognise the phases of the received signals.
More than one at a time
Given that we can modulate the carrier phase we can now consider using even more complicated forms of modulation by allowing the system to use more than two possible carrier phases for distinct symbols – and also more than one choice of carrier amplitude.
Figure 19.6 shows the use of Quadrature Phase Shift Keying (QPSK) modulation. This is similar to BPSK in that all the symbols have the same amplitude, but in this case we have four carrier phases to choose between. Since we now have four possible symbols we can use them to represent more than one bit per symbol. In effect, we can now communicate more than one bit at a time. Each possible QPSK symbol can be ‘labelled’ and used to represent two bits.
Looking at the example of QPSK illustrated in Figure 19.6 we can see that the four distinct symbol patterns can be spaced an amplitude, 
, apart, but since we are now doing this in two dimensions the actual amplitude of the carrier will be 
in each case. The carrier phase can be any one of the four values, 
.
An alternative way to describe this is to define the signal in the form
and say that we can represent pairs of bits for each symbol according to a table like the one below.
Note that QPSK provides twice the information per symbol that BPSK provides, but that it requires the signal amplitude, 
, to increase from 
to 
. This means that the signal carrier power for QPSK must be twice that of BPSK for the same Symbol Rate. Thus we pay for the doubling in information capacity by having to provide double the power.
Having discovered that we can use a symbol to convey more than one bit at a time, we can extend this by allowing a choice of amplitudes as well of phases. A common example of this is Quadrature Amplitude Modulation (QAM). This comes in various forms, and a typical example would be called something like ‘16QAM’ or ‘64QAM’ where the number indicates how many distinct symbols are available. Figure 19.7 shows an example. Note that it is common to describe the array of symbols displayed in this way as a Constellation of symbol values.
For simplicity we can consider ‘square’ arrays of symbol locations, so we can expect these to have a number of symbols which is is the square of an integer – i.e. have a number of symbols, 
1, 2, 4, 9, or 16, etc, in the constellation.
The example in Figure 19.7 is 16QAM and hence has 
4 
4 = 16 symbols. For such an array the amplitude of the locations which are furthest from the center (i.e. the symbols which require the maximum symbol amplitude) will be 
. The carrier power required to transmit these highest-amplitude symbols will be
which, when 
is reasonably large will approximate to
However the number of bits per symbol, 
, varies with the number of symbols, 
according to
Hence we can expect that the peak required carrier power will (approximately) tend to vary with the number of bits per symbol as
For this reason the peak powers required for QAM tends to rise steeply as we wish to convey more bits per symbol. Hence in practice we may will to avoid choosing too high a value for 
, and hence for 
.
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University of St. Andrews, St Andrews, Fife KY16 9SS, Scotland.
