Data (bit-) rate and signalling rate:

The 'data-rate' or 'bit-rate' is the number of bits (binary digits) per second.The 'signalling-rate' is the number of 'symbols' per second. Units for the signalling rate are 'bauds'. A

symbol is a voltage pulse whose shape and amplitude is chosen from a set of two or more possibilities. With binary signalling, there are two possible symbols, say a rectangular pulse ofamplitude +V and a rectangular pulse of amplitude −V. In this case the signalling rate can be equal tothe data rate if no redundancy is included for error checking.

Often 'ternary' signalling is used with pulses of amplitude +V, 0, and −V. Now the signalling rate can

 be less than the bit-rate. We could send three-bits using two ternary (+V, 0, -V) symbols becausethere are 8 possible 3-bit binary numbers and nine different ways of combining two ternary pulses.Hence the bit-rate could be 1.5 times the signalling (baud) rate.

With 'quaternary' signalling, there are four possible symbols and therefore the bit-rate can be twicethe symbol rate.

The symbol period will always be T seconds, therefore the signalling-rate will be 1/T baud.Asynchronous transmission (low data rates):A digital transmitter must apply suitably shaped symbols to the channel at times specified by a

timing reference or 'clock'. The clock is a circuit which generates a 'timing waveform' which is

usually a regular sequence of rectangular timing pulses. The timing waveform is normally not

transmitted. A timing waveform must also be available at the receiver to indicate the time-points at

which the channel may be examined to extract a symbol. The receiver's timing waveform must have

the same frequency as that used at the transmitter. Also, it must be synchronised with the symbols

 being received, even though delay will have been introduced by the channel. It is usual for the

receiver to extract the exact symbol frequency and symbol synchronisation from the signal received

from the channel, even though in many cases this signal will be distorted in various ways. If lengthy

transmissions are intended, the receiver clock must be very accurately matched to the clock

frequency of the transmitter since any small discrepancy will accumulate over time to produce large

timing errors. However for short block-length transmissions as used for transmitting 8-bit binary

numbers between computers and peripherals over short distances, for example, the transmitter and

receiver clocks need only be approximately matched and they may resynchronise at the beginning of

each short block. This is often referred to as 'asynchronous' transmission and is the basis of the well

known RS232 standard.. Data is sent in short words, say 8 bits long, with synchronising start and

stop bits. The receiver clock resynchronises itself at each start-bit. Consider the transmission of 8-bit

ASCII characters according to the RS232 protocol. When idle, the line remains high at voltage V1.

Asynchronous operation usually has a “start-bit” to signify the start of a transmission. This bit is

always “0”. The eight bits of data are then transmitted using “non-return to zero” (NRZ) pulses and

finally a number of “1” stop-bits (in this case two) are transmitted to ensure that the next character is

not sent immediately.

Synchronous transmission:Synchronous techniques are used for the efficient transmission of continuous data for long periods of

time, often at data rates close to the maximum possible over a channel of specified bandwidth. A

synchronising code (say 10101010) is sent at start of transmission, and thereafter, the receiver clock

 

must be kept synchronised in frequency and symbol-timing from the transmission itself. To achieve

the required bandwidth efficiency, pulses must be appropriately shaped, usually by a filter whose

impulse response is the required shape. More about this later. To detect the presence or absence of a

 pulse, the receiver samples the received waveform at the correct symbol timing point.

Estimation of 'bit-error probability' using the 'complementary error function Q(z)':

The channel and the receiver may be assumed to add white Gaussian noise of zero mean and fixed

variance σ2

to the transmitted signal. The receiver of a binary coded signal, receiving +V volt

rectangular pulses for '1' and zero volts for '0' may set a threshold at +V/2 and decide whether this is

exceeded at sampling points taken in the centre of each rectangular pulse. If the amplitude of the

noise exceeds +V/2 at a sampling point, an error may occur.