Time Division Multiplexing TDM Data Streams Computer Science Essay

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The circuit that combines signals at the source (transmitting) end of a communications link is known as a multiplexer. It accepts the input from each individual end user, breaks each signal into segments, and assigns the segments to the composite signal in a rotating, repeating sequence. The composite signal thus contains data from multiple senders. At the other end of the long-distance cable, the individual signals are separated out by means of a circuit called a demultiplexer, and routed to the proper end users. A two-way communications circuit requires a multiplexer/demultiplexer at each end of the long-distance, high-bandwidth cable.

If many signals must be sent along a single long-distance line, careful engineering is required to ensure that the system will perform properly. An asset of TDM is its flexibility. The scheme allows for variation in the number of signals being sent along the line, and constantly adjusts the time intervals to make optimum use of the available bandwidth. The Internet is a classic example of a communications network in which the volume of traffic can change drastically from hour to hour.

History

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Time-division multiplexing was first developed in telegraphy; see multiplexing in telegraphy: Émile Baudot developed a time-multiplexing system of multiple Hughes machines in the 1870s.

In 1962, engineers from Bell Labs developed the first D1 Channel Banks, which combined 24 digitised voice calls over a 4-wire copper trunk between Bell central office analogue switches. A channel bank sliced a 1.544 Mbit/s digital signal into 8,000 separate frames, each composed of 24 contiguous bytes. Each byte represented a single telephone call encoded into a constant bit rate signal of 64 Kbit/s. Channel banks used a byte's fixed position (temporal alignment) in the frame to determine which call it belonged to.

Transmission using Time Division Multiplexing

In circuit switched networks such as the public switched telephone network (PSTN) there exists the need to transmit multiple subscribers' calls along the same transmission medium.To accomplish this, network designers make use of TDM. TDM allows switches to create channels, also known as tributaries, within a transmission stream. A standard DS0 voice signal has a data bit rate of 64 kbit/s, determined using Nyquist's sampling criterion. TDM takes frames of the voice signals and multiplexes them into a TDM frame which runs at a higher bandwidth. So if the TDM frame consists of n voice frames, the bandwidth will be n*64 kbit/s.

Each voice sample timeslot in the TDM frame is called a channel. In European systems, TDM frames contain 30 digital voice channels, and in American systems, they contain 24 channels. Both standards also contain extra bits (or bit timeslots) for signaling and synchronization bits.

Multiplexing more than 24 or 30 digital voice channels is called higher order multiplexing. Higher order multiplexing is accomplished by multiplexing the standard TDM frames. For example, a European 120 channel TDM frame is formed by multiplexing four standard 30 channel TDM frames. At each higher order multiplex, four TDM frames from the immediate lower order are combined, creating multiplexes with a bandwidth of n x 64 kbit/s, where n = 120, 480, 1920, etc.

When the transmitter and receiver switches are synchronized, the signals will be fed in the proper sequence to the receiver channels. The samples from transmitter channel one will be fed to receiver channel one. In this way, many channels of audio are combined to form a single output (multiplexed) chain. Time spacing occurs between the components of the separate channels. The chain is transmitted (via wire or radio path) to distant demultiplexing receivers.

Each receiving channel functions to select and reconstruct only the information included in the originally transmitted channel. In most present day applications, electronic switching is used as the sampling component.

The main advantage to electronic sampling is the longer life of an electronic switch when compared to an electromechanical switch. We use a mechanical system in our example to make this concept easier for you to see. Now in the figure B, where channel one is sampled four times. (This is the output of channel one in our transmitter.). Figure C, shows all six channels being sampled four times during each cycle. (This is the output of the rotating switch in our transmitter.)

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Here we see a continuous, time-sharing waveform. More than six channels (perhaps 24+) may be used. As we increase the number of channels, the width of each sample segment must be reduced. The problem with reducing the width of the pulse is that the bandwidth necessary for transmission is greatly increased. Decreasing the pulse width decreases the minimum required rise time of the sampling pulse and increases the required bandwidth. When you increase the number of channels, you increase the bandwidth. The bandwidth is also affected by the shape of the sampling pulse and the method used to vary the pulse.

Applications

The plesiochronous digital hierarchy (PDH) system, also known as the PCM system, for digital transmission of several telephone calls over the same four-wire copper cable (T-carrier or E-carrier) or fiber cable in the circuit switched digital telephone network

The SDH and synchronous optical networking (SONET) network transmission standards, that have surpassed PDH.

The RIFF (WAV) audio standard interleaves left and right stereo signals on a per-sample basis

The left-right channel splitting in use for stereoscopic liquid crystal shutter glasses

TDM can be further extended into the time division multiple access (TDMA) scheme, where several stations connected to the same physical medium, for example sharing the same frequency channel, can communicate. Application examples include:

The GSM telephone system

The Tactical Data Links Link 16 and Link 22

Advantages of TDM

High reliability and efficient operation as the circuitry required is digital.

Relatively small interchannel cross-talk arising from nonlinearities in the amplifiers that handle the signals in the transmitter and receiver.

Disadvantages of TDM

Timing jitter

Pulse Amplitude Modulation (PAM)

Pulse Amplitude Modulation (PAM) is the simplest form of pulse modulation. This technique transmits data by varying the voltage or power amplitudes of individual pulses in a timed sequence of electromagnetic pulses. In other words, the data to be transmitted is encoded in the amplitude of a series of signal pulses. PAM can also be used for generating additional pulse modulations.

In this from, the possible pulse amplitudes in pulse amplitude modulation can be infinite. This is the case with analog pulse amplitude modulation. A 2-level pulse amplitude modulation causes the resulting signal to be digitized while a 4-level pulse amplitude modulation has 22 possible discrete pulse amplitudes. An 8-level pulse amplitude modulation has 23, and 16-level pulse amplitude modulation has 24 discrete pulse amplitudes.

Regarding various pulse amplitude modulation, some systems maintain the amplitude of each pulse directly proportional to the instantaneous modulating-signal amplitude at the time of pulse occurrence. In other pulse amplitude modulation systems, the reverse is true, that is, inversely proportional to the instantaneous modulating-signal amplitude at the time of pulse occurrence. In other pulse amplitude modulation systems, the amplitude is dependent on additional factors related to the modulating signal such as the instantaneous frequency and phase, which may be different than its strength.

However, in practical telecommunication applications, pulse amplitude modulation is a rare use technology, having been superceded by other techniques such as pulse position modulation and pulse code modulation. Additionally, a technology called quadrature amplitude modulation is widely used in telephone modems with a data transfer rate of more than 300 Kbps.

While newer technologies are fast making their presence known, it should be noted that pulse amplitude modulation is still useful in the popular Ethernet communication standard. For example, 100BASE-T2 operating at 100Mb/s, Ethernet medium is using 5 level PAM modulations running at 25 mega pulses/sec over four wires. Later developments include the 100BASE-T medium which raised the bar to 4 wire pairs, running each at 125 mega pulses/sec in order to achieve 1000 Mbps data transfer rates, but still with the same PAM5 for each pair.

More recently, PAM12 and PAM8 have gained consideration in the newly proposed IEEE 802.3an standard for 10GBase-T - ten gigabyte Ethernet over copper wire.

Applications

In Ethernet

Some versions of the Ethernet communication standard are an example of PAM usage. In particular, the Fast Ethernet 100BASE-T2 medium (now defunct), running at 100 Mbit/s, uses five-level PAM modulation (PAM-5) running at 25 megapulses/sec over two wire pairs. A special technique is used to reduce inter-symbol interference between the unshielded pairs. Current common 100 Mbit networking technology is 100BASE-TX which delivers 100 Mbit in each direction over a single twisted pair - one for each direction. Later, the gigabit Ethernet 1000BASE-T medium raised the bar to use four pairs of wire running each at 125 megapulses/sec to achieve 1000 Mbit/s data rates, still utilizing PAM-5 for each pair.

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The concept is also used for the study of photosynthesis using a PAM fluorometer. This specialized instrument involves a spectrofluorometric measurement of the kinetics of fluorescence rise and decay in the light-harvesting antenna of thylakoid membranes, thus querying various aspects of the state of the photosystems under different environmental conditions.

In electronic drivers for LED lighting

Pulse-amplitude modulation has also been developed for the control of light-emitting diodes (LEDs), especially for lighting applications. LED drivers based on the PAM technique offer improved energy efficiency over systems based upon other common driver modulation techniques such as Pulse Width Modulation as the forward current passing through an LED is relative to the intensity of the light output and the LED efficiency increases as the forward current is reduced.

Pulse-amplitude modulation LED drivers are able to synchronize pulses across multiple LED channels to enable perfect colour matching. Due to the inherent nature of PAM in conjunction with the rapid switching speed of LEDs it is possible to use LED lighting as a means of wireless data transmission at high speed.

TDM for PAM signals

Suppose we wish to time-multiplex two signals using PAM. Digital logic circuitry is usually employed to implement the timing operations.

The time-multiplexed PAM output is

Sampling rate

The sampling rate depends on the bandwidth of the signals. For example, if the signals are low-pass and band-limited to 3kHz. The sampling theorem states that each must be sampled at a rate no less than 6kHz. This requires a 12kHz minimum clock rate for the two-channel system.

Transmission bandwidth

The time-multiplexed PAM signal can be sent out on a line (baseband communications) or used to modulate a transmitter (passband communications).

Theoretically, the bandwidth occupied by a pulse is infinite. However, we are transmitting the information of the signals (f1(t), f2(t)), not the information of the pulses. If the time spacing between adjacent samples is Tx (In this example, Tx =t/2 ), the minimum bandwidth is Bx = 1/(2Tx)

For example, if the time-multiplexed PAM signal is filtered with a low-pass filter with bandwidth Tx=1/(2Bx), the impulses become sinx/x terms.

Because we have chosen the spacing between successive samples to be 1/(2Bx), contributions from all adjacent channels are exactly zero at the correct sampling instant. Therefore, by sampling the output at the correct instant, one can exactly reconstruct the original sampled values.

The results refer to the case in which impulse sampling and ideal filtering. In practice, neither of these conditions can be achieved and wider bandwidth is required.

The required bandwidth depends on the allowable cross-talk (interference) between channels.

Synchronization of the clock and the commutator in the time-multiplex receiver can be achieved by sending some pre-assigned code which, when identified at the receiver, serves to synchronize the timing.

After time multiplexing and filtering, the pulse-modulated waveform may be transmitted directly on a pair of wire lines. For long distance transmission, the multiplexed signal is used as the modulating signal to modulate a carrier. For example, PAM/AM

OUR IMPLEMENTATION OF TDM USING TWO PAM SIGNALS

Consider a signal, m1, a sinusoid having frequency 'wc1' on the time axis base of 0 to 0.4 divided into 40001 distinct points. The MATLAB commands for generating such a signal would be:

t= 0:1/(1e5):0.4;

wc1=2*pi*5;

m1=sin(wc1*t);

And the results would be:

C:\Users\Khurram M. Waziri\Desktop\us\s1.jpg

We then take another signal, m2, identical to m1 but having slightly less amplitude (just for visual difference) and frequency 'wc2':

wc2=2*pi*6;

m2=0.75*sin(w2*t);

The signal formed is:

C:\Users\Khurram M. Waziri\Desktop\us\s2.jpg

The next step is to create two PAM signals corresponding to the signals m1 and m2 above. For that we generate two pulse-trains, both having frequency 'ws' and slight difference in time-periods but equal duty-cycle. Multiplying the two pulse trains with the two signals will give us our two PAM signals. The MATLAB routine for generating pulse trains would be:

ws = 2.2*wc; % The sampling frequency

u = 1/ws; % Time-period interval length

d1 = 0:u:0.4; % Time-period of pulse train 1

w = u/3; % Duty Cycle for both the pulse trains

p1 = pulstran(t,d1,@rectpuls,w); % Using a rectangular pulse and built-in MATLAB function 'pulstran'

plot(t,p1,'r');

axis([0 0.4 -0.1 1.1]);grid;

title('Pulse Train1');xlabel('T(sec)');ylabel('Amplitude')

And we get pulse-train 1 as:

C:\Users\Khurram M. Waziri\Desktop\us\p1.jpg

Next we select the time-period of pulse-train 2 such that when we multiplex the two PAMs they 'fit' into each other perfectly. PAM1 will have values where PAM2=0 and PAM2 will have values where PAM1=0.

d2= d1+(u/2); % A marginal increase in time-period

p2=pulstran(t,d2,@rectpuls,w); %Generating pulse-train from rectangular pulse

plot(t,p2,'k');

axis([0 0.4 -0.1 1.1]);grid;

title('Pulse Train2');xlabel('T(sec)');ylabel('Amplitude')

And it looks like:

C:\Users\Khurram M. Waziri\Desktop\us\p2.jpg

Now to create PAM1 and PAM2 we simply multiply the signals m1 and m2 with pulse-train1 and pulse-train2 respectively, pretty easy, yeah?

pam1=m1.*p1; % Creating PAM1

plot(t,pam1,'r');

axis([0 0.4 -1.1 1.1]);grid;

title('Sampled Signal1');xlabel('T(sec)');ylabel('Amplitude')

pam2=m2.*p2; % Creating PAM2

plot(t,pam2,'k');

axis([0 0.4 -1.1 1.1]);grid;

title('Sampled Signal2');xlabel('T(sec)');ylabel('Amplitude')

PAM1 looks like:

C:\Users\Khurram M. Waziri\Desktop\us\pam1.jpg

And PAM2 as:

C:\Users\Khurram M. Waziri\Desktop\us\pam2.jpg

Notice how PAM1 and PAM2 take values where the other takes a NULL.

To demonstrate TIME-DIVISION MULTIPLEXING (TDM), we add the two PAMs together, on a single time-axis base, to create a multiplexed signal with alternating values of PAM1 and PAM2.

Multi = pam1 + pam2;

plot(t,Multi);

axis([0 0.4 -1.1 1.1]);grid;

title('TDM of Signal 1&2'); xlabel('T(sec)'); ylabel('Amplitude')

Here is the result:

C:\Users\Khurram M. Waziri\Desktop\us\multiplex.jpg

We can also demultiplex above signal by multiplying it with a pulse-train again. But which pulse-train is to be used now? The answer lies in the fact that signal PAM1 will be recovered if we multiply the above signal with pulse-train1 and signal PAM2 will be recovered on multiplying with pulse-train2! This is how it is done in MATLAB:

s1=multi.*p1; %S1 is the 'recovered' PAM1 signal

plot(t,s1,'r');

axis([0 0.4 -1.1 1.1]);grid;

title('Signal1 After demultiplexing');xlabel('T(sec)');ylabel('Amplitude')

C:\Users\Khurram M. Waziri\Desktop\us\rpam1.jpg

Notice how the recovered signal looks exactly the same as original PAM1.

To recover PAM2, we follow similar steps again, but this time multiplying the multiplexed signal with pulse-train2:

s2=multi.*p2;

plot(t,s2,'k');

axis([0 0.4 -1.1 1.1]);grid;

title('Signal2 After demultiplexing');xlabel('T(sec)');ylabel('Amplitude')

And it looks as:

C:\Users\Khurram M. Waziri\Desktop\us\rpam2.jpg

Now that the PAMs are recovered we can further recover our original signals m1 and m2 by passing these recovered PAMs through a filter. We will use a Butterworth Filter design to achieve this; here is how it is done:

[p,z] = butter(5,0.0005,'low');

F=filter(p,z,s1);

plot(t,F,'m');

axis([0 0.4 -0.5 0.5]);grid;

title('Signal1 after filtering');xlabel('T(sec)');ylabel('Amplitude')

F2=filter(p,z,s2);

plot(t,F2,'g');

axis([0 0.4 -0.5 0.5]);grid;

title('Signal2 after filtering');xlabel('T(sec)');ylabel('Amplitude')

Recovered signal m1 looks like:

C:\Users\Khurram M. Waziri\Desktop\us\rs1.jpg

And recovered m2 looks like:

C:\Users\Khurram M. Waziri\Desktop\us\rs2.jpg

Notice how the shapes of the recovered signals differ very slightly as compared to the original signals m1 and m2. This is because of the non-ideal filter design and verifies the fact that an analog waveform can be recovered 100% identical only in ideal conditions. There is an amplitude drop here in the recovered signals which may be corrected using an amplifier device.

SIMULINK MODEL OF TDM MULTIPLEXED SIGNALS:

We can also copy the exact same procedure in Simulink using desired blocks. Below is the Simulink model for achieving a TDM signal and then demultiplexing it back to the original signals. The results are shown in 'SCOPE' block.

C:\Users\Khurram M. Waziri\Desktop\us\simulink.jpg