Naval Weapons Engineering
A communications system may be digital either by the nature of the information
(also known as data) which is passed or in the nature of the signals which
are transmitted. If either of these is digital then for our purposes it
is considered to be a digital communications system. There are four possible
combinations of data and signal types:
The first case was discussed in the chapter on analog modulation. In this
chapter, we discuss the remaining three combinations.
Analog data, analog signal;
Digital data, analog signal;
Analog data, digital signal;
Digital data, digital signal.
Digital Data with Analog Signals
This method is used to send computer information over transmission channels
that require analog signals, like a fiber optic networks, computer modems,
cellular phone networks, and satellite systems. In each of this systems,
an electromagnetic carrier wave is used to carry the information over great
distances and connect digital information users at remote locations. The
digital data is used to modulate one or more of the parameters of the carrier
wave, This basic process is given the name "shift-keying" to differentiate
it from the purely analog systems like AM and FM. As with analog modulation,
there are three parameters of the carrier wave to vary and therefore three
basic types of shift keying:
Amplitude Shift Keying (ASK)
Frequency Shift Keying (FSK), and
Phase Shift Keying (PSK).
In amplitude shift keying, the carrier wave amplitude is changed between
discrete levels (usually two) in accordance with the digital data. A typical
ASK signal might look like this:
Figure 2. BASK signal.
The digital data to be transmitted is the binary number 1011. Two amplitudes
are used to directly represent the data, either 0 or 1. In this case, the
modulation is called binary amplitude shift keying or BASK. The signal
is divided into four pulses of equal duration which represent the bits
in the digital data. The number of bits used for each character is a function
of the system, but is typically eight, seven of which represent the 128
possible characters, the last bit is used to check for errors, and is explained
at the end of this chapter.
In frequency shift keying, the carrier frequency is changed between discrete
values. If only two frequencies are used then this will be called BFSK,
for binary frequency shift keying. In this figure, the same data is represented,
Figure 3. BFSK signal.
The phase of the carrier wave at the beginning of the pulse is changed
between discrete values. This particular case is the same code shown above
but in BPSK.
Figure 4. BPSK signal.
M-ary Frequency/Phase Keying
In binary shift keying, there were only two choices for the parameter of
the carrier wave which was varied in accordance with the digital data.
In BASK, there are two possibilities for amplitude, which corresponded
to zero and one. Likewise for BFSK and BPSK. This matches nicely with the
binary number system, which also uses two possibilities for each bit, 0
and 1. It is possible to increase the data transfer rate by putting more
choices into each bit. As and example, 4-ary (or Quaternary PSK) uses four
different phases: 0, 90, 180, and 270 degrees. This gives four
possible values at each pulse, corresponding to two independent streams
(channels) of data. Likewise, 16-ary FSK can send four channels of data
at the same time.
This process uses combinations of amplitude and phase keying. For example,
if we use two levels of amplitude and two levels of phase together, there
will be a total of four possibilities. This is used to transmit two independent
channels of digital data simultaneously. This particular case is called
Quadrature AM or Quaternary PSK. They are identical, although
it may not be obvious at this level. Because of the equivalence, the basic
process is called amplitude-phase keying. This process may be extended
to higher numbers of possibilities. The completely general term is M-ary
APK, which is not specific about which parameter has which number of
possibilities. 16-APK may have 2 amplitudes and 8 phases or 4 each, it
matters little. The upshot is that the number of separate channels that
can be sent simultaneously is increased. If M designates the number of
possible combinations, from the M-ary APK system, then the number of channels
of digital data that may be transmitted simultaneously is given by
N = Log2M.
All of these methods which utilize a sequence of equally spaced pulses
to modulate a carrier wave have similar bandwidths. The bandwidth determined
by the duration of each pulse, designated as td.
It is a general result, that the minimum bandwidth required to create this
pulse , W, is given by
Given a specific bandwidth limitation, the rate at which data can be
transferred can be determined. If the bandwidth is W (in Hz), and the modulation
type is M-ary, the rate at which data can be transferred, given in bits
per second (also known as the baud rate), R, is given by:
R = W Log2 M
It would now appear that the free lunch principle (i.e. there is none)
has been violated. Given the same bandwidth, which is determined by the
pulse duration, the data rate may be extended by using a higher M-ary modulation
type. As you may suspect, this will not succeed indefinitely. Ultimately,
increasing the bit content of each pulse has the effect of lowering the
signal-to-noise ratio. A way to illustrate this is to consider M-ary FSK.
Starting with BFSK, the bandwidth limits the difference between the two
frequencies. If the same interval is further subdivided to make 16-ary
FSK, the difference between any two adjacent frequencies has been reduced
by 1/16 making it more difficult to tell them apart (especially in the
presence of noise). This is quantified as a reduction in the signal-to-noise
ratio. This is also true for all other M-ary systems. Continued operation
of a system will low SNR will lead to an increase in the error rate
Probability of Error as SNR
Clearly, the data rate cannot be increased indefinitely without affecting
performance. This result is expressed in the Hartley-Shannon law for the
C = R Log (1 + S/N)
C = capacity in bits per second (bps)
S/N = signal-to-noise ratio (depends of modulation type and noise).
High definition television (HDTV) will still use the 6 MHz channel used
for broadcast TV. Using 16-QAM and S/N of 6.0 , they can send 6 x 4 x Log
(7) = 20.3 Mbps of digital data into the same 6 MHz band.
Minimum Shift Keying (MSK)
This is a technique used to find the minimum signal bandwidth for a particular
method (usually FSK). In BFSK, is the two frequencies are not chosen to
be far enough apart, then it will become impossible to discriminate the
two levels. The condition for the difference in frequencies, DfMSK,
such that the two levels can be determined accurately is
DfMSK = 1/(4td)
where td is the pulse duration
as previously discussed. MSK is considered to be the most efficient way
to use a given bandwidth. It maximizes the reliability (which is related
to S/N) within a given bandwidth.
Analog Data with Digital Signals
A digital signal can be transmitted over a dedicated connection between
two or more users. In order to transmit analog data, it must first be converted
into a digital form. This process is called sampling, or encoding. Sampling
involves two steps:
Take measurements at regular sampling intervals , and
Convert the value of the measurement into binary code.
The amplitude of a signal is measured at regular intervals. The interval
is designated as ts, and is called
the sample interval. The sample interval must be chosen to be short enough
that the signal does not change greatly between measurements. The sampling
rate, which is the inverse of the sample interval should be greater than
twice the highest frequency component of the signal which is being sampled.
This sample rate is known as the Nyquist frequency. If you sample
at a lower rate, you run the risk of missing some information, known as
Figure 5. Digital sampling.
Once the samples are obtained, the must be encoded into binary. For a given
number of bits, each sample may take on only a finite number of values.
This limits the resolution of the sample. If more bits are used for each
sample, then a higher degree of resolution is obtained. For example, if
the sampling is 8-bit, each sample may only take on 256 different values.
16-bit sampling would give 65,536 unique values for the signal in each
sample interval. Higher bit sampling requires more storage for data and
requires more bandwidth to transmit.
Example: Compact disk.
Audio compact disk stores analog information (music) as a digital signal.
The amplitude of the music is sampled at a high rate, about 41,000 samples/sec.
The highest frequency component in any audio signal is 20 kHz. Therefore
the Nyquist rate is 40 kHz, which explains the reason for a sampling rate
of 41,000 samples/sec. Each sample is given a binary representation using
16 -bits, which gives over 65,000 possible values for the sample amplitude
at any one time. The signal can take on value from 1 to 65,000 in arbitrary
units (usually voltage). Power, which goes like voltage squared can range
from 1 to 4.3 x 109 units. This variation in power is called
the dynamic range and is expressed in decibels. If we convert 4.3 x 109
into decibels, the dynamic range is 96 dB.
Digital - Digital
We have already discussed how computers use a binary number system to perform
operations. In its simplest form, digital data is a collection of zeroes
and ones, where the value at any one time is called a bit. In order for
two digital users (like computers) to communicate there must be an agreement
on the format used. There are several different ways in which a binary
number by be formatted. This is called pulse code modulation or PCM. The
most straightforward PCM format is designated as NRZ-L, for non return
to zero level. In this format, the level directly represents the binary
value: low level = 0, high level = 1.
Figure 6. NRZ-L format of PCM.
There are many other varieties, which are explained below:
Figure 7. PCM formats.
It is possible for an error to occur somewhere in the transmission process.
One way to increase the reliability of transmitted PCM signals is to add
a checksum bit to each piece of data. For example, in an eight-bit byte,
seven of the bits can be used for data and the last reserved for a checksum
bit. In one method, the checksum bit is determined by parity (meaning an
even or odd number). In even parity checksums, a 0 or 1 is added to make
the overall number of ones (including the checksum) even. In odd parity,
a 0 or 1 is added to make the overall number of ones odd.
Example: the seven-bit data field is 0100111, which already has an even
number of ones. In even parity, a 0 would be added as the checksum to make