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Baseband Pulse and Digital Signaling Chap. 3
In summary, multilevel signaling, where L > 2, is used to reduce the bandwidth of a
digital signal compared with the bandwidth required for binary signaling. In practice,
filtered multilevel signals are often used to modulate a carrier for the transmission of digital
information over a communication channel. This provides a relatively narrowband digital
signal.
Spectral Efficiency
DEFINITION. The spectral efficiency of a digital signal is given by the number of bits
per second of data that can be supported by each hertz of bandwidth. That is,
h = R B (bits/s)/Hz
(3–55)
where R is the data rate and B is the bandwidth.
In applications in which the bandwidth is limited by physical and regulatory
constraints, the job of the communication engineer is to choose a signaling technique that
gives the highest spectral efficiency while achieving given cost constraints and meeting
specifications for a low probability of bit error at the system output. Moreover, the
maximum possible spectral efficiency is limited by the channel noise if the error is to be
small. This maximum spectral efficiency is given by Shannon’s channel capacity formula,
Eq. (1–10),
h max = C B = log 2a1 + S N b
(3–56)
Shannon’s theory does not tell us how to achieve a system with the maximum theoretical
spectral efficiency; however, practical systems that approach this spectral efficiency usually
incorporate error correction coding and multilevel signaling.
Example 3–12 MAXIMUM SPECTRAL EFFICIENCY
Plot h max as a function of the SN dB , that is, where the SN is expressed in dB units. See
Example3_12.m for the solution.
The spectral efficiency for multilevel polar NRZ signaling is obtained by substituting
Eq. (3–54) into Eq. (3–55). We obtain
h =/(bit/s) Hz (multilevel polar NRZ signaling)
(3–57)
where is the number of bits used in the DAC. Of course, cannot be increased without
limit to an infinite efficiency, because it is limited by the signal-to-noise ratio as given in
Eq. (3–56).
The spectral efficiencies for all the line codes studied in the previous sections can be
easily evaluated from their PSDs. The results are shown in Table 3–6. Unipolar NRZ, polar
NRZ, and bipolar RZ are twice as efficient as unipolar RZ or Manchester NRZ.