Often, we want to use a range of frequencies that does not start at zero to send
information across a channel. For wireless channels, it is not practical to send
very low frequency signals because the size of the antenna needs to be a fraction
of the signal wavelength, which becomes large. In any case, regulatory constraints
and the need to avoid interference usually dictate the choice of frequencies.
Even for wires, placing a signal in a given frequency band is useful to let
different kinds of signals coexist on the channel. This kind of transmission is called
passband transmission because an arbitrary band of frequencies is used to pass
the signal.
Fortunately, our fundamental results from earlier in the chapter are all in terms of bandwidth, or the width of the frequency band. The absolute frequency values do not matter for capacity. This means that we can take a baseband signal that occupies 0 to B Hz and shift it up to occupy a passband of S to S +B Hz without changing the amount of information that it can carry, even though the signal will look different. To process a signal at the receiver, we can shift it back down to baseband, where it is more convenient to detect symbols.
Digital modulation is accomplished with passband transmission by regulating or modulating a carrier signal that sits in the passband. We can modulate the amplitude, frequency, or phase of the carrier signal. Each of these methods has a corresponding name. In ASK (Amplitude Shift Keying), two different amplitudes are used to represent 0 and 1.More than two levels can be used to represent more symbols. Similarly, with FSK (Frequency Shift Keying), two or more different tones are used. In the simplest form of PSK (Phase Shift Keying), the carrier wave is systematically shifted 0 or 180 degrees at each symbol period. Because there are two phases, it is called BPSK (Binary Phase Shift Keying). ‘‘Binary’’ here refers to the two symbols, not that the symbols represent 2 bits. A better scheme that uses the channel bandwidth more efficiently is to use four shifts, e.g., 45, 135, 225, or 315 degrees, to transmit 2 bits of information per symbol. This version is called QPSK (Quadrature Phase Shift Keying).
This kind of diagram is called a constellation diagram. Sixteen combinations of amplitudes and phase are used, so the modulation scheme can be used to transmit 4 bits per symbol. It is called QAM-16, where QAM stands for Quadrature Amplitude Modulation.It is called QAM-64. Even higher-order QAMs are used too. As you might suspect from these constellations, it is easier to build electronics to produce symbols as a combination of values on each axis than as a combination of amplitude and phase values. That is why the patterns look like squares rather than concentric circles.
The constellations we have seen so far do not show how bits are assigned to symbols. When making the assignment, an important consideration is that a small burst of noise at the receiver not lead to many bit errors. This might happen if we assigned consecutive bit values to adjacent symbols. With QAM-16, for example, if one symbol stood for 0111 and the neighboring symbol stood for 1000, if the receiver mistakenly picks the adjacent symbol it will cause all of the bits to be wrong. A better solution is to map bits to symbols so that adjacent symbols differ in only 1 bit position. This mapping is called a Gray code.
Now if the receiver decodes the symbol in error, it will make only a single bit error in the expected case that the decoded symbol is close to the transmitted symbol.
Fortunately, our fundamental results from earlier in the chapter are all in terms of bandwidth, or the width of the frequency band. The absolute frequency values do not matter for capacity. This means that we can take a baseband signal that occupies 0 to B Hz and shift it up to occupy a passband of S to S +B Hz without changing the amount of information that it can carry, even though the signal will look different. To process a signal at the receiver, we can shift it back down to baseband, where it is more convenient to detect symbols.
Digital modulation is accomplished with passband transmission by regulating or modulating a carrier signal that sits in the passband. We can modulate the amplitude, frequency, or phase of the carrier signal. Each of these methods has a corresponding name. In ASK (Amplitude Shift Keying), two different amplitudes are used to represent 0 and 1.More than two levels can be used to represent more symbols. Similarly, with FSK (Frequency Shift Keying), two or more different tones are used. In the simplest form of PSK (Phase Shift Keying), the carrier wave is systematically shifted 0 or 180 degrees at each symbol period. Because there are two phases, it is called BPSK (Binary Phase Shift Keying). ‘‘Binary’’ here refers to the two symbols, not that the symbols represent 2 bits. A better scheme that uses the channel bandwidth more efficiently is to use four shifts, e.g., 45, 135, 225, or 315 degrees, to transmit 2 bits of information per symbol. This version is called QPSK (Quadrature Phase Shift Keying).
. (a) A binary signal. (b) Amplitude shift keying. (c) Frequency
shift keying. (d) Phase shift keying.
We can combine these schemes and use more levels to transmit more bits per
symbol. Only one of frequency and phase can be modulated at a time because
they are related, with frequency being the rate of change of phase over time.
Usually, amplitude and phase are modulated in combination. The phase of a dot is indicated by the angle a line
from it to the origin makes with the positive x-axis. The amplitude of a dot is the
distance from the origin. This figure is a representation of QPSK.
This kind of diagram is called a constellation diagram. Sixteen combinations of amplitudes and phase are used, so the modulation scheme can be used to transmit 4 bits per symbol. It is called QAM-16, where QAM stands for Quadrature Amplitude Modulation.It is called QAM-64. Even higher-order QAMs are used too. As you might suspect from these constellations, it is easier to build electronics to produce symbols as a combination of values on each axis than as a combination of amplitude and phase values. That is why the patterns look like squares rather than concentric circles.
The constellations we have seen so far do not show how bits are assigned to symbols. When making the assignment, an important consideration is that a small burst of noise at the receiver not lead to many bit errors. This might happen if we assigned consecutive bit values to adjacent symbols. With QAM-16, for example, if one symbol stood for 0111 and the neighboring symbol stood for 1000, if the receiver mistakenly picks the adjacent symbol it will cause all of the bits to be wrong. A better solution is to map bits to symbols so that adjacent symbols differ in only 1 bit position. This mapping is called a Gray code.
Now if the receiver decodes the symbol in error, it will make only a single bit error in the expected case that the decoded symbol is close to the transmitted symbol.
(a) QPSK. (b) QAM-16. (c) QAM-64.
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