Introduction to Naval Weapons Engineering

Digital Communication Methods
Figure 1

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:

1. Analog data, analog signal;
2. Digital data, analog signal;
3. Analog data, digital signal;
4. Digital data, digital signal.
The first case was discussed in the chapter on analog modulation. In this chapter, we discuss the remaining three combinations.

# 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:
2. Frequency Shift Keying (FSK), and
3. 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:

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.

## FSK

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, 1011.

Figure 3. BFSK signal.

## PSK

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.

## Amplitude-Phase Keying

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.

## Capacity

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
W 1/(2td)

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 capacity:

C = R Log (1 + S/N)

where:
C = capacity in bits per second (bps)
S/N = signal-to-noise ratio (depends of modulation type and noise).

Example:

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:
1. Take measurements at regular sampling intervals , and
2. Convert the value of the measurement into binary code.

### Sampling

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 aliasing.
Figure 5. Digital sampling.

### Encoding

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:

• NRZ-M ( non return to zero mark). 1: no change in level from last pulse. 0: level changes from last pulse.
• NRZ-S (non return to zero space). This is the same as NRZ-M but with the logic levels reversed. 1: level changes from last pulse. 0: no change in level from last pulse.
• Bi-Phase-L (bi-phase level). The level always changes in the middle of the pulse. 1: level changes from high to low. 0: level changes from low to high.
• Bi-Phase-M. (bi-phase mark). The level always changes at the beginning of each pulse. 1: level changes in the middle of the pulse. 0: no level change in the middle of the pulse.
• Bi-Phase-S (bi-phase space). This is the same as Bi-Phase-L but with the logic levels reversed. 1: no level change in middle of pulse. 0: level changes in the middle of the pulse.
• DBi-Phase-M (differential bi-phase mark). The level always changes in the middle of the pulse. 1: no level change at beginning of the pulse. 0: level change at beginning of the pulse.
• DBi-Phase-S (differential bi-phase space). This is the same as DBi-phase-M but with the logic levels reversed. 1: level change at beginning of the pulse. 0: no level change at the beginning of the pulse.
• Figure 7. PCM formats.

### Parity Checksum

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 01001110.