Digital Communication Methods

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:

- Analog data, analog signal;
- Digital data, analog signal;
- Analog data, digital signal;
- Digital data, digital signal.

- Amplitude Shift Keying (ASK)
- Frequency Shift Keying (FSK), and
- Phase Shift Keying (PSK).

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.

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:

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

Clearly, the data rate cannot be increased indefinitely without affecting performance. This result is expressed in the Hartley-Shannon law for the capacity:

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.

where t_{d} 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.

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

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 10^{9} units. This variation in power is called
the dynamic range and is expressed in decibels. If we convert 4.3 x 10^{9}
into decibels, the dynamic range is 96 dB.

There are many other varieties, which are explained below:

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.