Communications Technology PDF

TM355: COMMUNICATIONS TECHNOLOGY BLOCK 1 PART 1: CHANNELS FOR COMMUNICATIONS 1 Prepared by: Dr. Naser Zaeri Arab Open University  OUTLINE Introduction Analogue and digital signals Optical f...

TM355: COMMUNICATIONS TECHNOLOGY BLOCK 1 PART 1: CHANNELS FOR COMMUNICATIONS 1 Prepared by: Dr. Naser Zaeri Arab Open University  OUTLINE Introduction Analogue and digital signals Optical fibre Prepared by: Dr. Naser Zaeri 2  1. INTRODUCTION (1/6) The simplest type of communications system consists of a transmitter that sends a signal along a channel to a receiver. This first part of Block 1 is mainly concerned with the physical channel: the properties of optical fibre and copper cable, and the behaviour of radio waves. Each of these transmission media has its own merits and limitations, and this text discusses the suitability of the various types of media for different applications. There may be many transmitters and/or receivers, and it is necessary to ensure that the correct sender communicates with the correct recipient. Prepared by: Dr. Naser Zaeri 3  1. INTRODUCTION (2/6) One example is a local area network (LAN) – a computer network covering a relatively small area, such as a company site. Another example is the ordinary telephone system, referred to as the public switched telephone network (PSTN). Prepared by: Dr. Naser Zaeri 4  1. INTRODUCTION (3/6) Figure 1.1 distinguishes between the access network (the local exchange and its connections to the subscribers it serves) and the core network, which is everything beyond the local exchange. The technical demands of the access and core networks are rather different. The access network may serve millions of subscribers, each on a different site, but with only short distances involved. In contrast, trunk lines in the core network carry multiple calls between two places that may be hundreds of miles apart. Prepared by: Dr. Naser Zaeri 5  1. INTRODUCTION (4/6) Different techniques have evolved to meet these demands. At one time, the entire system was built with copper cables, which carry information as electrical signals. Later the technology of optical fibres was developed, in which messages are sent using light rays that are constrained to follow a path within the fibre. Optical fibre has a number of advantages over copper, particularly over long distances, so it now predominates in the core network, although copper still retains a key place in the access network. Between them, optical fibre and copper cable serve most of the needs of the PSTN and other fixed networks. Prepared by: Dr. Naser Zaeri 6  1. INTRODUCTION (5/6) Mobile communications systems require radio. This is a form of electromagnetic radiation like light, and can propagate through air or space in various ways. While the term ‘radio transmitter’ brings to mind the tall masts for radio and television broadcasting, smaller transmitters are everywhere: in mobile phones, computers (to provide a WiFi connection). Cables confine signals to a defined route, but radio waves spread out over a wide area. Prepared by: Dr. Naser Zaeri 7  1. INTRODUCTION (6/6) Radio is thus a shared medium, so many different transmissions are competing for attention everywhere, and a receiver has to be able to select the right one. The shared nature of radio leads to problems of resource allocation. Radio also has security implications, as signals can easily be intercepted. Prepared by: Dr. Naser Zaeri 8  2. ANALOGUE AND DIGITAL SIGNALS (1/2) The term ‘signal’ describes the form in which a message is sent along a communications channel. In the case of copper cable, the signal is a varying electrical voltage. For both optical fibre and radio, the signal is a varying electromagnetic wave. Prepared by: Dr. Naser Zaeri 9  2. ANALOGUE AND DIGITAL SIGNALS (2/2) Figure 1.2(a) illustrates part of a speech signal as produced by the microphone in a telephone. The voltage signal follows the air vibrations and is called an analogue signal because the voltage is analogous to the fluctuating air pressure. Figure 1.2(b) represents a data signal as might be seen on a cable to a computer on a LAN (such a connection between a home PC and a router.) Prepared by: Dr. Naser Zaeri 10  2.1 BENEFITS OF TRANSMITTING DIGITAL SIGNALS (1/2) Whenever a signal is sent along a communications channel, two things happen to it: it gets smaller (it attenuates) and it gets distorted (the shape changes). This is illustrated in Figure 1.3 for both an analogue signal and a digital signal. It is possible to compensate for attenuation by amplifying the received signal. With digital signals, on the other hand, we can in principle get rid of the distortion entirely by the process of regeneration, provided the distortion is not too great (threshold detection). Another reason for using digital technologies in communications is that voice, music and video can all be handled by the same techniques as computer data if they are first converted to a digital form. Prepared by: Dr. Naser Zaeri 11 2.1 BENEFITS OF TRANSMITTING DIGITAL SIGNALS (2/2) Prepared by: Dr. Naser Zaeri 12  2.2 CONVERTING ANALOGUE TO DIGITAL (1/3) Analogue-to-digital converters (ADCs) and digital- to-analogue converters (DACs) are electronic devices that convert between analogue and digital in each direction. To convert an analogue signal to digital form, it is first sampled by measuring its value at regular intervals in time. Prepared by: Dr. Naser Zaeri 13  2.2 CONVERTING ANALOGUE TO DIGITAL (2/3) The next step is to encode each of the possible quantisation levels with a binary number. To restrict the measured values to a discrete set, the values are quantised. Since a binary number n bits long can take any of 2𝑛 different values, the number of quantisation levels allowed is normally a power of two. Thus a 4-bit number can represent 24 = 16 different levels, and an 8-bit number can represent 28 = 256 different levels. Prepared by: Dr. Naser Zaeri 14  2.2 CONVERTING ANALOGUE TO DIGITAL (3/3) For a given range of variation, a large value of n improves the accuracy of the conversion because the quantisation levels are closer together; conversely, a small n results in a smaller amount of binary data at the expense of conversion accuracy. In converting an analogue signal to digital, it appears that information has been lost in two different ways: a) The signal is not measured at every instant of time but only at the sampling points. b) An approximation has been made by rounding the samples to the nearest quantisation level. Prepared by: Dr. Naser Zaeri 15  2.3 ANALYSING SIGNALS 2.3.1 SINUSOIDS (1/2) Sinusoids are important not only because they turn up naturally in a wide variety of situations, but also for their mathematical simplicity. A sinusoid is a periodic signal  repeats at regular time intervals. A section of a periodic signal between two consecutive corresponding points, such as the maxima, is called a cycle, and the duration of a cycle is the period. The number of cycles in one second is the frequency. The unit of frequency is the hertz (Hz), where 1 Hz = 1 cycle per second. f=1/T Amplitude is the maximum value of the sinusoid. Prepared by: Dr. Naser Zaeri 16  2.3.1 SINUSOIDS (2/2) Another characteristic of a sinusoidal signal is its phase. This relates to the point that the sinusoid has reached at a particular time. For example, at zero time the signal is zero and rising. Shifting the signal to the right or left changes its phase. One of the reasons that sinusoids are so significant in communications is that they form the components of other periodic signals. Prepared by: Dr. Naser Zaeri 17 2.3.2 OTHER PERIODIC SIGNALS (1/4) An important result in communications theory, due to Joseph Fourier (1768–1830), shows that any periodic signal may be expressed as a sum of multiple sinusoids. The graph on the left of Figure 1.7(a) shows a sinusoid as it progresses in time, while the graph on the right shows another representation of the signal: a function of frequency.  These are known respectively as time-domain and frequency-domain representations. The frequency domain is also known as the spectrum. Prepared by: Dr. Naser Zaeri 18 2.3.2 OTHER PERIODIC SIGNALS (2/4) Prepared by: Dr. Naser Zaeri 19 2.3.2 OTHER PERIODIC SIGNALS (3/4) Any signal can be represented in either the time or the frequency domain. A sinusoid, is shown as a single line in the frequency domain because it represents a single frequency of a particular strength. Figure 1.7(b) shows a periodic signal with a different shape (or waveform as it is sometimes called), known as a saw-tooth wave from its appearance. The corresponding frequency-domain representation reveals that it is made up of the sum of sinusoids of decreasing amplitude.  Notice that the frequencies of these sinusoids are exact whole-number multiples of the lowest frequency. These higher-frequency sinusoids are called harmonics. Prepared by: Dr. Naser Zaeri 20 2.3.2 OTHER PERIODIC SIGNALS (4/4) The waveform in Figure 1.7(c), known as a square wave, may be regarded as a binary signal with alternate 1s and 0s. In the frequency domain there are again sinusoids at multiples of the lowest frequency, though in this case the even multiples (or harmonics) are missing. A consequence of this theory is that a communications channel that can transmit, say, a 1 MHz sine wave correctly may not be able to transmit a 1 MHz periodic signal with a different waveform, unless it can also transmit sinusoids at 2 MHz, 3 MHz and so on. A complete frequency-domain representation would also include phase. For many purposes, though, phase is less important than frequency; it is not a consideration in allocating radio spectrum, for example. Prepared by: Dr. Naser Zaeri 21 2.3.3 NON-PERIODIC SIGNALS (1/2) Non-periodic signals (also known as aperiodic signals) also have both a time-domain and a frequency-domain representation, but the details are different.  There are no longer lines at particular frequencies; instead, the spectrum is spread out over a continuous range of frequencies. Prepared by: Dr. Naser Zaeri 22 2.3.3 NON-PERIODIC SIGNALS (2/2) For example, a speech signal ranges from around 100 Hz to a few thousand Hz (for telephone-quality speech, a range of 300 Hz to 3400 Hz is often assumed). In practical communications, exactly periodic signals are the exception. Signals that carry real information, such as speech, music or video, do not repeat endlessly. Prepared by: Dr. Naser Zaeri 23  3. OPTICAL FIBRE (1/2) Optical fibre can transmit large amounts of information rapidly over long distances using light signals, and so has become the preferred technology for trunk cable communications and increasingly for LANs. A basic optical-fibre link has three main components (Figure 1.10): a suitable source of light (not necessarily within the visible range), controlled by input data in the form of an electrical signal the optical fibre itself, which carries the resulting pulses of light to … a detector, which converts the pattern of light and dark back to an electrical signal. Prepared by: Dr. Naser Zaeri 24 3. OPTICAL FIBRE (2/2) Prepared by: Dr. Naser Zaeri 25  3.1 ELECTROMAGNETIC RADIATION (1/6) Electromagnetic radiation includes radio waves, light, the radiation felt as heat, and ultraviolet radiation from the Sun. Light, as an electromagnetic wave, is a wave pattern carried by interdependent electric and magnetic fields. In electromagnetic wave, electricity and magnetism are in fact intimately related. Electric fields, like magnetic fields, are invisible but can exert forces on objects. Strong electric fields form in thunderclouds and break down when lightning strikes. Prepared by: Dr. Naser Zaeri 26  3.1 ELECTROMAGNETIC RADIATION (2/6) Electric fields and magnetic fields can both store and release energy. They are also linked together by a set of relationships known as Maxwell’s equations. Changing electric fields generate changing magnetic fields, and vice versa. The effect of all of this is that disturbances in the fields can be self-sustaining, and spread outwards like waves in a pond. Prepared by: Dr. Naser Zaeri 27  3.1 ELECTROMAGNETIC RADIATION (3/6) Figure 1.13 represents a an electromagnetic wave in terms of its electric and magnetic components. The axis along the direction of travel measures distance along the wave. The other axes represent the strength of the electric and magnetic fields at any point along the wave. Prepared by: Dr. Naser Zaeri 28  3.1 ELECTROMAGNETIC RADIATION (4/6) The electric field and magnetic field are both sinusoidal and are at right angles to each other. This is just a snapshot of the wave at one particular instant in time. The whole wave pattern moves forward at the speed of light, which in free space (a vacuum) is about 300 000 000 m/s = 3×108 m/s and is conventionally denoted c. All electromagnetic waves travel at this same speed in free space. Prepared by: Dr. Naser Zaeri 29  3.1 ELECTROMAGNETIC RADIATION (5/6) In free space, the electric field contains half the power in an electromagnetic wave and the magnetic field contains the other half. As the wave moves forward, it conveys energy. So, for example, light from the Sun can be converted to electrical energy by solar panels. The power generated by such a panel is simply the energy it produces per unit time. Prepared by: Dr. Naser Zaeri 30  3.1 ELECTROMAGNETIC RADIATION (6/6) Note on Energy and Power: Power is the rate of flow of energy, and is measured in watts (W). Energy and power are related as follows: energy = power × time. Example: Suppose a 2 kW kettle takes three minutes to boil. Three minutes is 0.05 hours, so the energy used is: 2000 W × 0.05 h = 100 Wh or 0.1 kWh (kilowatt-hours). However, although energy is quoted as kWh on electricity bills, the SI unit of energy is the joule (J), where energy in joules is the power in watts multiplied by the time in seconds. Repeating the kettle example using SI units gives: 2000 W × 180 s = 360 000 J or 360 kJ. Prepared by: Dr. Naser Zaeri 31 3.1.1 WAVELENGTH AND FREQUENCY Electromagnetic waves are characterised by their wavelength, the distance between two consecutive peaks (or other corresponding points.) Light waves have short wavelengths, measured in nanometres (nm, 10−9 m). Light of different wavelengths is perceived as different colours, for example 650 nm is red and 520 nm is green. A wave can also be described by its frequency, where: 𝒄=𝝀×𝒇 Prepared by: Dr. Naser Zaeri 32  3.1.2 THE ELECTROMAGNETIC SPECTRUM Figure 1.14 shows the complete electromagnetic spectrum. Prepared by: Dr. Naser Zaeri 33  3.2 LIGHT WAVES IN OPTICAL FIBRE (1/3) In optical fibres, light travels through highly transparent glass along guided paths, so there are some differences from propagation in free space. For one thing, light travels significantly more slowly in glass than in a vacuum (or in air). The speed of light, 𝒗, in a medium such as glass is found by: 𝒗 = 𝒄/𝒏 where “𝒏” is the refractive index and depends on the material. It is around 1.5 for most optical glasses. Prepared by: Dr. Naser Zaeri 34  3.2 LIGHT WAVES IN OPTICAL FIBRE (2/3) So what keeps light guided along its path in an optical fibre? Why does the light not just stop when it comes to the first bend? Optical fibres work because the refractive index is not the same all the way across the fibre, but is higher in the central core than it is in the cladding around the core. Light can change direction by two processes, refraction and reflection, which take place in lenses and mirrors respectively. Refraction can occur when a ray of light travels from one medium to another medium with a different refractive index. The light continues within the second medium, but on a diverted path (Figure 1.15a). Prepared by: Dr. Naser Zaeri 35  3.2 LIGHT WAVES IN OPTICAL FIBRE (3/3) However, if light is directed from one medium towards another with a lower refractive index, and it hits the boundary at a sufficiently small angle, it is not refracted but reflected back into the first medium. This process is known as total internal reflection (Figure 1.15b). Thus in an optical fibre, provided the light enters the fibre from the right direction (not too large an angle from the axis of the fibre), it will continue all the way along the fibre, relying on total internal reflection to keep it on course. Prepared by: Dr. Naser Zaeri 36  3.3 TYPES OF FIBRE (1/4) The diameter of the core is a key feature of an optical fibre. the larger the diameter of the fibre, the more light it will let through. A large-diameter fibre also has some practical advantages: aligning fibres to join them together becomes easier. However, when it comes to transmitting data over distances at high data rates, it turns out that a large diameter is not necessarily the best. A fibre with a core diameter that is large in comparison with the wavelength is known as a multimode fibre because light can travel along it in a variety of ways. Prepared by: Dr. Naser Zaeri 37  3.3 TYPES OF FIBRE (2/4) Commonly, the diameter of the core for a multimode fibre is 50 μm, much larger than the wavelengths typically used (which are in the order of 1.5 μm). The cladding diameter is 125 μm. From Fig. 1.16, some paths that the light can take are more direct than others, meaning two rays of light that set off at the same time may not reach the other end of the fibre exactly simultaneously. A fibre (as the one shown in Fig. 1.16) where the refractive index changes abruptly between core and cladding is called a step-index fibre. Prepared by: Dr. Naser Zaeri 38  3.3 TYPES OF FIBRE (3/4) Another variant of the multimode fibre is called a graded-index fibre (Fig. 1.17)  the refractive index varies smoothly from a maximum in the centre of the core to a minimum within the cladding. This means waves that take slightly longer paths travel slightly faster, and so different waves setting off at the same time arrive nearly simultaneously at the other end of the fibre. Prepared by: Dr. Naser Zaeri 39  3.3 TYPES OF FIBRE (4/4) If the core diameter of a step-index fibre is reduced, there are fewer ways or modes in which the wave can propagate. There comes a point where only one mode can propagate, and signals all travel along the same path. This happens when the core is a few wavelengths in diameter – typically 10 μm. This type of fibre is called a single-mode fibre, and it provides the best performance over long distances in a number of respects. For this reason, single-mode fibre is preferred over multimode types for long-haul communications. The cladding diameter is typically 125 μm, the same as for multimode fibre. Prepared by: Dr. Naser Zaeri 40  TM355: COMMUNICATIONS TECHNOLOGY BLOCK 1 PART 1 (CONT.): CHANNELS FOR COMMUNICATIONS 1 Prepared By: Dr. Naser Zaeri Arab Open University  OUTLINE 3.4: limitations of optical fibre 3.5: Components of an optical-fibre link 4. Copper cable 5. radio 6. Analogue modulation Prepared By: Dr. Naser Zaeri 2  3.4 LIMITATIONS OF OPTICAL FIBRE 3.4.1 ATTENUATION AND DECIBELS (1/4) Modern optical fibres are extremely transparent and so can carry optical signals long distances. However, some of the energy supplied by the source is eventually absorbed by the fibre as the signal passes along it. The process by which the signal gradually loses power as it travels along a transmission medium is called attenuation. Manufacturers of optical fibres specify how much a fibre attenuates in terms of so much attenuation in decibels (dB) per kilometre length. The decibel is a logarithmic measure of the ratio between two powers. Prepared By: Dr. Naser Zaeri 3  3.4.1 ATTENUATION AND DECIBELS (2/4) More specifically, Power loss (or gain) in decibels (dB) is given by: 𝑃2 𝑃 = 10𝑙𝑜𝑔10 𝑃1 Where 𝑃1 is the transmitted power and 𝑃2 is the received power. Note: The two powers to be compared may represent a loss, as in fibre attenuation, or a gain, as when a signal is amplified. 0 dB, meaning ‘no loss’. increasing a power by 3 dB doubles the power attenuating a power by 3 dB halves the power. Prepared By: Dr. Naser Zaeri 4  3.4.1 ATTENUATION AND DECIBELS (3/4) Example: Suppose a fibre-optic link consists of three sections. Half the power is lost in the first section, another half of the remaining power is lost in the second section, and 95% of the remaining power is lost in the third section. Find the total power loss in dB at the end of the third section. Sol.: The total fraction remaining is: 0.5 × 0.5 × 0.05 = 0.0125 𝑃2 0.0125𝑃1  In dB: 𝑃 = 10𝑙𝑜𝑔10 = 10𝑙𝑜𝑔10 = -19 dB. 𝑃1 𝑃1 Prepared By: Dr. Naser Zaeri 5  3.4.1 ATTENUATION AND DECIBELS (4/4) Although multimode fibre has a higher figure for attenuation, it is generally preferred for short-distance applications because of lower component costs and greater ease of use than single- mode fibre. 6  3.4.2 PULSE SPREADING (1/3) As well as attenuation, various effects distort signals in optical fibres by smearing out sharp transitions between light and dark sections of the signal. This limits the data rate that can be obtained over a length of fibre, because parts of the signal start to merge into each other. As with attenuation, the effects are cumulative  the longer the fibre, the worse it gets. Figure 1.21 illustrates the problem: The signal transmitted is called a pulse, so the effect is known as pulse spreading. Prepared By: Dr. Naser Zaeri 7  3.4.2 PULSE SPREADING (2/3) One reason for pulse spreading in multimode fibres: different path lengths result in different timings for the trip through the fibre  This is called multimode distortion (Fig. 1.22) and is the main cause of pulse spreading in multimode fibres. Prepared By: Dr. Naser Zaeri 8  3.4.2 PULSE SPREADING (3/3) Although this effect is eliminated in single-mode fibres, other mechanisms can still cause pulse spreading: Dispersion, or ‘chromatic dispersion’, is caused by light of different wavelengths travelling at different speeds. Polarisation mode distortion affects single-mode fibres and is caused by another variation in the speed of light: the speed varies with the orientation of the light wave in the fibre. Prepared By: Dr. Naser Zaeri 9  3.5 COMPONENTS OF AN OPTICAL-FIBRE LINK 3.5.1 OPTICAL TRANSMITTERS AND DETECTORS (1/3) Optical transmitter: converts input data in the form of an electrical signal into a light signal that is sent along the fibre. There are two main types, both semiconductor devices: the light-emitting diode (LED) and the laser diode LEDs for optical transmitters are similar in principle to the LEDs seen in displays and as indication lights in consumer goods. However, rather than emitting visible light, they emit in the infrared region of the spectrum, where optical fibres are most transparent. Laser diodes are also found in CD, DVD and Blu-ray drives, where they read and write data from the disc. Prepared By: Dr. Naser Zaeri 10  3.5.1 OPTICAL TRANSMITTERS AND DETECTORS (2/3) LEDs are inexpensive compared to laser diodes and so are used in some multimode fibre systems. However, they have a number of disadvantages: they are lower in power and emit over a range of wavelengths, leading to dispersion. LEDs emit a relatively broad cone of radiation, whereas a laser diode emits a strongly aligned beam. Laser diode is much more efficient at transferring its energy to the fibre. The data rate that can be obtained from the transmitter depends on how fast the beam can be modulated. Again, the laser diode has an advantage over the LED in the speed at which it can switch. Prepared By: Dr. Naser Zaeri 11  3.5.1 OPTICAL TRANSMITTERS AND DETECTORS (3/3) At the other end of the fibre, a detector converts the light signal back into an electrical signal. The type of detector commonly used is called a photodiode. It provides a current output that varies with the intensity of the light it receives. Prepared By: Dr. Naser Zaeri 12  3.5.2 OPTICAL AMPLIFIERS (1/3) Optical fibres attenuate markedly over long distances. For example, the best-case attenuation in Table 1.1 is 0.35 dB km−1, which over a 300 km link would amount to 105 dB, a huge drop in power. One way of increasing the range of an optical-fibre link is to use a repeater or regenerator. These are devices that counteract the effects of attenuation by restoring an optical signal to its original form. The optical signal is converted back to an electrical signal, which is then processed electronically and retransmitted optically. Prepared By: Dr. Naser Zaeri 13  3.5.2 OPTICAL AMPLIFIERS (2/3) Repeaters and regenerators are distinguished by the extent of the processing that is carried out, the term ‘repeater’ tending to include simpler devices than ‘regenerator’. A repeater amplifies the signal to bring it back to its original amplitude, but at the same time it may also amplify any noise that is mixed with the signal. A regenerator does further processing, so that the degraded received pulse would be reshaped and retimed as well as being restored to its original amplitude. Thus the regenerated pulse is a copy of the original transmitted pulse with any noise removed, provided the signal has not deteriorated too far. 14  3.5.2 OPTICAL AMPLIFIERS (3/3) In principle, any distance can be covered using a chain of regenerators, but there are some practical disadvantages: these devices have to be powered and maintained, and many of them may be needed to cover long distances. This is a particular problem for international cables, which often run under the ocean, making power provision and maintenance very difficult. Optical amplifiers have been developed as a better solution for long-haul links. They amplify the optical signal directly, without converting it back to an electrical signal. The idea: allows energy to be ‘pumped’ into the atoms of a material and then released later when ‘stimulated’ by radiation, thus creating more radiation of the same wavelength. Prepared By: Dr. Naser Zaeri 15  4. COPPER CABLE The sender and receiver in most communications systems operate with electrical signals Copper cable is a simple solution because it does not involve any conversions to other types of energy (light or radio waves). Prepared By: Dr. Naser Zaeri 16  4.1 TRANSMISSION IN CABLES (1/2) Figure 1.26 shows a general type of circuit in which a power source sends power to a load. The source and load might be a battery and bulb in a torch, or the house mains supply and a toaster, or (in the case of communications) a transmitter and receiver. Voltage is the force that sends the current around the circuit. It is measured in volts (V). Batteries may be 1.5 V, 9 V and so on, and in the UK electricity is supplied to houses at a nominal 230 V. Current represents the movement of electrons and is measured in amperes or amps (A). 17 4.1 TRANSMISSION IN CABLES (2/2) Communications signals with high frequencies or data rates involve effects in cables that are not apparent in other circuits, such as house wiring. At the high frequencies and data rates used in communications, the speed of a signal in a copper cable depends on the construction of the cable. A typical figure is 2 ×108 m/s, which is comparable to the speed of signals in optical fibres. Prepared By: Dr. Naser Zaeri 18 4.1.1 MAGNETIC AND ELECTRIC FIELDS (1/2) A conductor carrying current has both magnetic and electric fields associated with it. A magnetic field encircles a conductor carrying an electric current. The field may be strong enough to exert appreciable forces on ferrous objects, particularly when the field is concentrated as it is in an electric motor. Conductors also have associated electric fields. In high-voltage lines, the electric field ionises the intervening atmosphere and creates a spark. Prepared By: Dr. Naser Zaeri 19 4.1.1 MAGNETIC AND ELECTRIC FIELDS (2/2) The low voltages and currents used in computer networks and phones generate tiny fields in comparison to these examples. Signal propagation in cables can in fact be regarded as another type of electromagnetic wave. Because of the wave nature of signals in cables, effects such as reflection are possible, whereby some of the signal moves back along the cable. Prepared By: Dr. Naser Zaeri 20 4.1.2 CROSSTALK AND RADIATION Commonly, copper cables carrying different signals run alongside each other for convenience – they may, for example, share a conduit along a street. Many cables have multiple pairs of conductors rather than just one, so that several independent signals can be carried. There is a potential problem, though, in that the electric and/or magnetic fields associated with one pair of conductors may couple with the conductors next to them to some extent, so that a weak version of the signal is transferred to the other conductor pair. This is called crosstalk and can be minimised by appropriate design of the cable. Prepared By: Dr. Naser Zaeri 21 4.2 ATTENUATION AND DISTORTION IN CABLES (1/2) All ordinary conductors have a property called resistance: electrons do not flow along conductors entirely freely, but are subject to frequent collisions. This results in loss of electrical energy, which is converted to heat. Resistance is particularly important in power distribution, where it must be kept as low as possible to avoid wasting energy, but it also affects communications systems that use copper cables. The two conductors in a pair are kept apart by a non-conducting material, usually plastic, known as an insulator or dielectric. Prepared By: Dr. Naser Zaeri 22 4.2 ATTENUATION AND DISTORTION IN CABLES (2/2) Resistance and leakage both increase in proportion to the length of the cable, so they need to be taken into account particularly over long-distance links. At high frequencies or high data rates, the material separating the conductors can have an effect in increasing the attenuation over and above that observed at low frequencies. This is because a small part of the energy in the electromagnetic fields is wasted as heat in a process known as dielectric loss. Distortion can also occur in cables when signals of different frequencies travel at different speeds (just as in optical fibre.) Prepared By: Dr. Naser Zaeri 23  4.3 TYPES OF CABLE (1/2) Figure 1.28 illustrates two of the many types of cable that are used for transmitting digital data and other high-frequency signals: unshielded twisted pair (UTP) and coaxial cable. In a UTP cable, a pair of conductors is twisted together along its length. The effect of the twisting is that any interference entering the cable will affect both conductors equally, and can be cancelled out by using a receiver that is sensitive only to the difference in voltage between the two conductors. Prepared By: Dr. Naser Zaeri 24  4.3 TYPES OF CABLE (2/2) So the twisting gives some protection against crosstalk. In coaxial cable, the two conductors take the form of a centre conductor with a conducting shield around it. An advantage of this construction is that the electric and magnetic fields are confined within the shield. This gives the cable good immunity to interference and minimises losses due to radiation. A common use of coaxial cable is for connection to TV antennas. Prepared By: Dr. Naser Zaeri 25  5. RADIO Radio waves are another form of electromagnetic radiation but at a much lower frequency than light or infrared, 300 GHz often being regarded as the upper limit. Their electric and magnetic fields are generated directly from electrical signals in structures known as antennas, or sometimes aerials. A receiving antenna converts a radio signal back to an electrical signal. An antenna simply consists of one or more conductors, and is effective at launching (or receiving) a radio wave at a particular frequency or band of frequencies by virtue of its physical shape and dimensions. An antenna that is effective at transmitting at a given frequency is also effective at receiving at the same frequency. Prepared By: Dr. Naser Zaeri 26 5.1 BANDWIDTH AND RECEPTION (1/3) The amount of spectrum occupied by a signal is called the bandwidth. The bandwidth is equal to the difference between the highest and lowest frequencies, 𝒇𝟐 − 𝒇𝟏. The larger the bandwidth, the more information the signal can convey. The centre frequency of this transmission, halfway between 𝒇𝟏 and 𝒇𝟐. In many modulation schemes, the centre frequency is the same as the frequency of the unmodulated signal. Prepared By: Dr. Naser Zaeri 27 5.1 BANDWIDTH AND RECEPTION (2/3) Prepared By: Dr. Naser Zaeri 28 5.1 BANDWIDTH AND RECEPTION (3/3) Figure 1.30 shows what the response of an ideal receiver would look like, with the response of a typical practical receiver by way of comparison. The range of frequencies that the receiver responds best to is called the passband: Extends from a lower cut-off frequency to a higher cut-off frequency. The cut-off frequencies are the points where the signal strength in volts has fallen to 0.707 of the maximum (a voltage drop of this magnitude corresponds to a drop in power of 3 dB). Prepared By: Dr. Naser Zaeri 29 5.2 SOME PROPERTIES OF RADIO WAVES 5.2.1 THE INVERSE SQUARE LAW The inverse square law describes the reduction in power with distance from the transmitter, due to spreading. Figure 1.31 represents a wave moving outwards from a transmitter, which is assumed here to radiate equally well in all directions – isotropically. A receiver that is n times as far from the transmitter will receive 𝟏 of the power. 𝒏𝟐 30  5.2.2 REFLECTION (1/2) Radio waves can be both reflected by specular reflection (from smooth, flat surfaces) and scattered. Radio waves are reflected by many surfaces, including the ground, buildings and vehicles. They are particularly well reflected by metal surfaces, for example in satellite dishes. Prepared By: Dr. Naser Zaeri 31  5.2.2 REFLECTION (2/2) Scattering occurs when reflecting objects or features are small compared to the wavelength. Radio waves can be scattered by a variety of objects, ranging from small dust particles to meteors high in the atmosphere. Scattering by intervening objects or particles can result in a loss of useful energy between the transmitter and receiver, reducing the received signal. Prepared By: Dr. Naser Zaeri 32  5.2.4 ABSORPTION Radio waves can be absorbed by the medium they travel through. The attenuation due to absorption is measured in decibels per metre or kilometre. The loss due to absorption is separate from, and additional to, any power loss due to spreading as accounted for by the inverse square law. Absorption is dependent on frequency, and this is one of the reasons why certain frequency bands are preferred for different radio applications. Prepared By: Dr. Naser Zaeri 33  5.2.5 DIFFRACTION Diffraction: is the spreading or bending of an electromagnetic wave when it passes through a gap or encounters a sharp corner. Diffraction is very dependent on the dimensions of a gap or the sharpness of an edge. Prepared By: Dr. Naser Zaeri 34  5.4 PROPAGATION 5.4.4 PROPAGATION MODELS Propagation: at low frequencies, long-distance transmission depends on the state of the ionosphere, while multipath propagation causes fading at high frequencies. Propagation in terrestrial environments is complex, and so computer models have been developed to help with prediction. The inverse fourth-power law is often invoked as a first approximation for propagation at VHF and above in typical terrestrial environments. With the inverse fourth-power law the received power decreases in proportion to 1 𝑑4. Prepared By: Dr. Naser Zaeri 35  6. ANALOGUE MODULATION In communications, the types of signal that can be transmitted over a channel are often very different from the original message signal. Radio waves at the frequencies found in sound are not easy to transmit and receive, and do not propagate well. A transmitter that converts a sound signal directly to a radio wave, while possible, is of limited use anyway; if there was more than one of them, they would effectively talk over each other. The idea of using different frequencies from the original message is not confined to radio, but also applies to other media such as cable, in the process known as modulation, the message signal is converted to a suitable form for transmission Modulation is usually a matter of varying one or more properties of the sine wave in a way that represents the information to be conveyed. Prepared By: Dr. Naser Zaeri 36 6.1 AMPLITUDE MODULATION (1/4) In amplitude modulation (AM) the amplitude of the carrier waveform is altered in proportion to the information signal, referred to as the modulating signal. The term envelope is used to describe the varying strength, or shape, of the modulating signal After modulation, the carrier’s amplitude takes on the envelope of the modulating signal. The modulated signal is created by multiplying the modulating signal and the carrier signal together. Done using a device known as a mixer. A mixer is used to shift power at one frequency to power at another frequency. Prepared By: Dr. Naser Zaeri 37 6.1 AMPLITUDE MODULATION (2/4) The carrier waveform is usually generated using a local oscillator, which is an electronic circuit that produces a periodic electronic signal – in this case a sine wave with frequency 𝑓𝑐. Advantage of AM is its simplicity. Disadvantage of AM signal is highly susceptible to noise. 38 6.1 AMPLITUDE MODULATION (3/4) Mathematically: if the carrier waveform is represented by 𝑣𝑐 𝑡 = 𝑣𝑐 cos(𝜔𝑐 𝑡), and the information or modulating signal is also represented by a sinusoid, 𝑣𝑚 𝑡 = 𝑣𝑚 cos(𝜔𝑚 𝑡), then 𝑣𝐴𝑀 𝑡 = 𝑣𝑚 cos(𝜔𝑚 𝑡) x 𝑣𝑐 cos(𝜔𝑐 𝑡) 𝑣𝑚 𝑣𝑐 = cos 𝜔𝑐 + 𝜔𝑚 𝑡 + cos 𝜔𝑐 − 𝜔𝑚 𝑡 2  The modulated signal comprises two components, known as the upper sideband, at (𝜔𝑐 + 𝜔𝑚 ), and the lower sideband, at (𝜔𝑐 - 𝜔𝑚 ). Prepared By: Dr. Naser Zaeri 39 6.1 AMPLITUDE MODULATION (4/4) Bandwidth of the modulated signal, 𝐵𝐴𝑀 , is twice that of the original information signal, 𝐵𝑚  𝐵𝐴𝑀 = 2𝐵𝑚. Prepared By: Dr. Naser Zaeri 40 6.2 FREQUENCY MODULATION (1/3) In frequency modulation (FM) the frequency of the carrier waveform is altered in proportion to the envelope of the modulating signal, so the amplitude and the phase remain the same. The modulated signal is usually created using a voltage-controlled oscillator (VCO). This is an electronic circuit that takes a voltage signal as an input and produces a periodic electronic signal – in this case a sine wave – as an output. Prepared By: Dr. Naser Zaeri 41 6.2 FREQUENCY MODULATION (2/3) Prepared By: Dr. Naser Zaeri 42 6.2 FREQUENCY MODULATION (3/3) The frequency deviation, Δf: defined as the maximum deviation of the FM-modulated frequency from the carrier frequency. The modulation index, β: ratio of the frequency deviation to the highest frequency component in the modulating signal (modulating frequency), 𝑓𝑚 : ∆𝑓 𝛽= 𝑓𝑚 Bandwidth of frequency modulated signal is: 𝐵𝐹𝑀 = 2 ∆𝑓 + 𝑓𝑚 = 2(1 + 𝛽)𝑓𝑚 Prepared By: Dr. Naser Zaeri 43  6.3 PHASE MODULATION In the third analogue modulation technique, phase modulation (PM), the phase of the carrier waveform is altered in proportion to the amplitude of the modulating signal. Prepared By: Dr. Naser Zaeri 44  TM355: COMMUNICATIONS TECHNOLOGY BLOCK 1 PART 2: AN INTRODUCTION TO THE THEORY OF SIGNALS 1 Prepared By: Dr. Naser Zaeri Arab Open University  OUTLINE Introduction Time and frequency domains Digital modulation Quadrature modulation schemes Prepared By: Dr. Naser Zaeri 2  1. INTRODUCTION In this part of Block 1: We focus is on the underlying theory behind signals and modulation. We understand the time and frequency domains and why these are important. Prepared By: Dr. Naser Zaeri 3 2. TIME AND FREQUENCY DOMAINS 2.1 TIME-DOMAIN REPRESENTATION OF SINE WAVES [1/3] Basic radio waves, called carrier waves, are sinusoidal. Time-domain representation of a signal: how the strength of the signal varies over time. Mathematically represented by: 𝑣 𝑡 = 𝐴 sin 2𝜋𝑓𝑡 + 𝜑 = 𝐴 sin(𝜔𝑡 + 𝜑) A is the amplitude (or maximum value) measured in volts (V) f is frequency measured in hertz (Hz). T is time period (measures in second), where f=1/T. ω is the angular frequency = 2𝜋f, measured in radians per second (rad/s). 𝝋 is the relative phase, measured in radians or degrees. Prepared By: Dr. Naser Zaeri 4 2.1 TIME-DOMAIN REPRESENTATION OF SINE WAVES [2/3] Note: the relative phase 𝝋, is the phase of the signal where it: describes the position of the waveform relative to time at 0 seconds. describes where in the cycle of the waveform it begins its first cycle. It can be negative or positive in value, with a negative value representing a delay and a positive value an advance in time. Measured in either degrees (°) or radians (rad), and 360° or 2𝜋 rad is equivalent to a shift in a sinusoidal waveform through a complete period. If 𝜑 = +𝜋/2, this would result in a shift of the waveform to the left by a quarter of a cycle  cosine wave: 𝑣 𝑡 = 𝐴 co𝑠(𝜔𝑡) Prepared By: Dr. Naser Zaeri 5 2.1 TIME-DOMAIN REPRESENTATION OF SINE WAVES [3/3] Sine waves and cosine waves are the same shape but, they start at different points in the cycle  phase shift between them. Both are referred to as sinusoids and both are used to represent electromagnetic waveforms. Prepared By: Dr. Naser Zaeri 6 2.2 FREQUENCY-DOMAIN REPRESENTATION OF SINE WAVES [1/2] A sinusoid waveform can be plotted in terms of its frequency. The frequency-domain representation is often much more useful than the time-domain representation when it comes to designing communications systems and understanding how they work. Prepared By: Dr. Naser Zaeri 7 2.2 FREQUENCY-DOMAIN REPRESENTATION OF SINE WAVES [2/2] The phase component of the waveform can be illustrated similarly, in a separate diagram with frequency as the x-axis. These two diagrams together give the sinusoid’s complete frequency-domain representation – also called the spectrum. Often the plot of amplitude against frequency that provides the interesting information phase diagram is frequently omitted. Prepared By: Dr. Naser Zaeri 8  2.3 PERIODIC SIGNALS AND THE FOURIER SERIES [1/6] The spectrum, with a distinct frequency component represented by a single line or spike at frequency 𝒇, is the simplest example of a discrete spectrum. All periodic signals have a discrete spectrum  spectrum can be represented by a line or series of lines (or spikes) at specific frequencies. Periodic signals that are not simple sinusoids have spectra that contain multiple spikes. This is because, all periodic signals can be represented as a sum of sinusoidal components – that is, a series of different sine or cosine waves – and each spike represents one of these components. Each frequency component of a periodic signal is a multiple, known as a harmonic, of the fundamental frequency 𝒇. This series of components is the Fourier series of a signal. 9  2.3 PERIODIC SIGNALS AND THE FOURIER SERIES [2/6] In general terms, a Fourier series looks like the following equation: 𝒗(𝒕) = 𝑨𝟎 + 𝑨𝟏 cos(𝝎𝒕 + 𝝋𝟏 ) + 𝑨𝟐 cos(𝟐𝝎𝒕 + 𝝋𝟐 ) + 𝑨𝟑 cos(𝟑𝝎𝒕 + 𝝋𝟑 ) + … + 𝑨𝒏 cos(𝒏𝝎𝒕 + 𝝋𝒏 ) The frequency of each component is a multiple of the fundamental frequency: 𝜔, 2𝜔, 3𝜔…. The first term, 𝑨𝟎 , represents a component at zero frequency. Prepared By: Dr. Naser Zaeri 10  2.3 PERIODIC SIGNALS AND THE FOURIER SERIES [3/6] For example, a periodic square waveform can be represented by the following Fourier series: Prepared By: Dr. Naser Zaeri 11  2.3 PERIODIC SIGNALS AND THE FOURIER SERIES [4/6] Figure 2.9(a) shows the original square waveform (with V=1), Figures 2.9(b) to (e) show the four sinusoidal components that were represented as spikes in Figure 2.8. 12  2.3 PERIODIC SIGNALS AND THE FOURIER SERIES [5/6] Figure 2.10(a) shows the result of adding the first two sinusoidal components (Figures 2.9b + c). This is a much closer approximation to the original square wave than part (b) on its own. Adding the third and fourth sinusoids brings the result closer still to the original, as seen in Figure 2.10(b) and (c) respectively. An infinite number of components is needed to reconstruct the square wave exactly. 13  2.3 PERIODIC SIGNALS AND THE FOURIER SERIES [6/6] Although a square wave theoretically has an infinite bandwidth (because in theory the series of high-frequency components continues indefinitely), the energy in the components decreases with increasing frequency. This means that if only the first few components are used, not much information in the reconstruction of the original signal is lost. Prepared By: Dr. Naser Zaeri 14  3. DIGITAL MODULATION [1/4] Digital modulation has many advantages over analogue modulation: Has a greater immunity to noise and other types of interference. Enables techniques to be used such as error control coding, which enables the performance to be improved, Encryption for securing transmissions. Prepared By: Dr. Naser Zaeri 15  3. DIGITAL MODULATION [2/4] The three basic digital modulation schemes are: amplitude-shift keying (ASK) frequency-shift keying (FSK) phase-shift keying (PSK). The term ‘keying’ originates from the keys used to generate early telegraphy messages. 16  3. DIGITAL MODULATION [3/4] There are a number of variants of each of these schemes that have been developed to overcome the challenges each one faces and in response to the need for higher data rates. One that is of particular interest, and is widely used in today’s systems, combines elements of PSK and ASK and is called quadrature amplitude modulation (QAM). Popular because they are more spectrally efficient than other schemes. Can achieve higher data rates without requiring more spectrum. Prepared By: Dr. Naser Zaeri 17  3. DIGITAL MODULATION [4/4] There are many factors to take into account when comparing digital modulation schemes and deciding which one is most suitable for a specific application: bandwidth efficient power efficient performs well in multipath fading channels cost effective and simple to implement. Unfortunately there isn’t one scheme that satisfies them all. There are trade-offs to be made: Before a modulation scheme is chosen for a particular application, it is important to consider the most important requirement. Prepared By: Dr. Naser Zaeri 18 3.1 THE FREQUENCY DOMAIN AND NON-PERIODIC SIGNALS [1/4] We saw how the Fourier series can be used to represent a periodic signal and consequently illustrate the spectra of such signals. The Fourier transform is used to give the frequency- domain representation of non-periodic signals. Whereas periodic signals have spectra comprising discrete frequency components, non-periodic signals have spectra comprising a continuous spectrum, which means a continuous distribution of frequency components. Prepared By: Dr. Naser Zaeri 19 3.1 THE FREQUENCY DOMAIN AND NON-PERIODIC SIGNALS [2/4] Continuous spectra are often described using the terms spectral nulls, main lobe and side lobes.  The spectral nulls are where the spectral curve crosses the x-axis – that is, where the spectral energy is zero. The first pair of spectral nulls in this example occur at -1/𝜏 and 1/ 𝜏. Prepared By: Dr. Naser Zaeri 20 3.1 THE FREQUENCY DOMAIN AND NON-PERIODIC SIGNALS [3/4] The main lobe is the large area in the middle, bounded by the first pair of spectral nulls, and is the range of frequencies that contain most of the signal’s energy. The side lobes are what look like ripples that occur on either side of the main lobe with much smaller amplitudes. As the pulse waveforms get narrower, the spacing between the first pair of spectral nulls gets larger. That is, the narrower a pulse, the broader its spectrum. For example, if a pulse has duration 10 ms, most of the spectral energy lies within a 200 Hz range. If a pulse has a much shorter duration, say 10 ns, most of the spectral energy lies within a 200 MHz range. Prepared By: Dr. Naser Zaeri 21  3.1 THE FREQUENCY DOMAIN AND NON-PERIODIC SIGNALS [4/4] This relationship shows why, if everything else remains the same, as data rates increase (i.e. more data is transmitted per second, which means a shorter pulse duration) a larger bandwidth is needed. 22  3.2 AMPLITUDE-SHIFT KEYING (ASK) [1/4] ASK is a special case of AM, so it is the amplitude of the carrier signal that is modified. The simplest version of this is also called on–off keying (OOK). Suffers from problems: synchronisation the receiver have difficulty establishing exactly how many bits have been received might potentially think that the transmission has ended (while it is not!). Prepared By: Dr. Naser Zaeri 23  3.2 AMPLITUDE-SHIFT KEYING (ASK) [2/4] Other versions of ASK use different (non- zero) amplitudes to represent 1 and 0 also exist. Bandwidth of an ASK signal is generally approximated by BASK = 2B, where B is the bandwidth of the modulating signal. 24  3.2 AMPLITUDE-SHIFT KEYING (ASK) [3/4] Representation in time domain: the modulated signal would look like a segment of a sinusoid – that is, a short burst of a sinusoid. Prepared By: Dr. Naser Zaeri 25  3.2 AMPLITUDE-SHIFT KEYING (ASK) [4/4] In frequency domain, the resulting spectrum is a function of the spectra of the original two signals. In this case, it is the original spectrum of the pulse but shifted to a centre frequency, 𝑓𝑐. Prepared By: Dr. Naser Zaeri 26 3.3 FREQUENCY-SHIFT KEYING (FSK) FSK is a type of frequency modulation, so it is the frequency of the carrier signal that is modified. The bandwidth of an FSK-modulated signal: BFSK = 2(Δf + B), where Δf is the separation of the two frequencies used: Prepared By: Dr. Naser Zaeri 27  3.4 PHASE-SHIFT KEYING (PSK) PSK is the most widely used in one form or another. There are many variations of PSK. In BPSK (Binary Phase-Shift Keying), 0 and 1 are represented by segments of sinusoids that differ in their phase. At the demodulator, distinguishing between the two segments is easier if their phases differ by as much as possible, so they are invariably separated by half a cycle (equivalent to 𝜋 radians or 180°). A BPSK-modulated signal is almost as simple to produce as an ASK signal, but with the added advantage that it is less susceptible to additive noise. Bandwidth: BPSK = 2B. 28 3.5 POWER EFFICIENCY AND BIT ERROR RATES [1/2] With respect to noise and interference, power efficiency is concerned with what signal power levels a transmitter needs to operate at in order to ensure that the number of bits received in error is at an acceptable level. Bit error rate (BER) is defined as the number of bits received in error divided by the number of bits transmitted; therefore a low BER is desirable. Different schemes result in different BERs, and plotting these against the ratio of signal power to noise power is a useful indicator of their power efficiency. Prepared By: Dr. Naser Zaeri 29  3.5 POWER EFFICIENCY AND BIT ERROR RATES [2/2] For example, take a bit error rate of 1 error in 10,000,000 bits transmitted –which is equivalent to a BER of 10−7. If this can be achieved at a lower transmitting power by one scheme than a second, then the first would be deemed to be more power efficient. PSK requires less signal power to achieve the same BER performance as FSK and ASK, meaning that PSK is the most power efficient. Prepared By: Dr. Naser Zaeri 30  4. QUADRATURE MODULATION SCHEMES Driven by the need for higher data rates, multiple variations of the three basic digital modulation schemes have been developed. Here, we are concerned with higher-order modulation methods that use an increased number of carrier states to achieve higher data rates. We look at how elements of PSK and ASK can be combined to enable non-binary schemes to be used, which can achieve higher data rates without requiring more spectrum. Prepared By: Dr. Naser Zaeri 31  4.1 SYMBOLS AND BAUD [1/3] The different carrier states are what are known as symbols. If there are more than two possible carrier states – that is, more than two symbols available – then it is possible for each symbol to represent more than one bit. In Figure 2.23 there are four possible amplitude levels.  it is possible to associate each symbol uniquely with a 2-bit binary number  four possible 2-bit binary numbers: 11, 10, 01 and 00. Prepared By: Dr. Naser Zaeri 32  4.1 SYMBOLS AND BAUD [2/3] If the number of bits that can be represented by a symbol, n, and the number of available symbols, M, then: 𝑀 = 2𝑛. Data rates: the number of bits transmitted per second. Sometimes the symbol rate is also used in communication systems The term baud refers to the number of symbols per second, where one baud is one symbol per second. Prepared By: Dr. Naser Zaeri 33  4.1 SYMBOLS AND BAUD [3/3] Increasing the number of bits a symbol can represent means that higher data rates can be achieved. The two most widely used digital modulation schemes in wireless communications systems are: Quadrature Phase-Shift Keying (QPSK) Quadrature Amplitude Modulation (QAM). Higher-order PSK and ASK are used in quadrature modulation methods. Quadrature techniques are used in WiFi, digital television, 3G and 4G mobile telecommunications. Prepared By: Dr. Naser Zaeri 34 4.2 QUADRATURE PHASE-SHIFT KEYING (QPSK) [1/8] BPSK uses segments of two sinusoidal waves that differ in phase by a half-cycle (𝜋 radians or 180°) to represent its two symbols. Instead of thinking of Figure 2.24(b) as a phase-shifted version of Figure 2.24(a), we can think of it now as having an amplitude of −1 relative to Figure 2.24(a). Prepared By: Dr. Naser Zaeri 35 4.2 QUADRATURE PHASE-SHIFT KEYING (QPSK) [2/8] The essence of quadrature modulation methods is the application of complementary pairs of amplitudes to two simultaneous sinusoidal waves differing in phase by one-quarter of a cycle. It is customary to refer to one of these waves as the I wave, or in-phase wave or component, and the other as the Q wave, or quadrature wave or component. Remember: a sine wave and a cosine wave happen to be a quarter of a cycle apart  I wave can also be thought of as a sine wave and the Q wave as a cosine wave. Prepared By: Dr. Naser Zaeri 36 4.2 QUADRATURE PHASE-SHIFT KEYING (QPSK) [3/8] The preservation of the quadrature relationship between the I and Q waves, despite the inversion of either or both of the waves, means that both waves can be modulated using BPSK and the quadrature relationship between them is preserved.  This is the basis of QPSK. 37 4.2 QUADRATURE PHASE-SHIFT KEYING (QPSK) [4/8] Another way of describing the I and Q waves is that they are orthogonal to each other. Orthogonality is an important concept in communications systems. ‘Orthogonal’ in the context of two orthogonal lines, in which it means they are ‘at right angles’ or perpendicular to each other. It can also mean ‘statistically independent’ or uncorrelated’. If two signals are orthogonal: when they are transmitted simultaneously, one can be completely recovered at the receiver without any interference from the second, and vice versa. Prepared By: Dr. Naser Zaeri 38 4.2 QUADRATURE PHASE-SHIFT KEYING (QPSK) [5/8] Signal constellation diagram: the points on the diagram represent the different symbols that the carrier can assume. For BPSK: there is no quadrature wave and the two symbols are simply represented as two points on the I-axis (x-axis) at +1 and −1. 39 4.2 QUADRATURE PHASE-SHIFT KEYING (QPSK) [6/8] Signal constellation diagram for QPSK: can be thought of as two BPSK waveforms in quadrature.  two symbols on the I-axis and two on the Q-axis. QPSK can achieve twice the data rate of a comparable BPSK scheme for a given bandwidth  Makes QPSK such an attractive option. Prepared By: Dr. Naser Zaeri 40 4.2 QUADRATURE PHASE-SHIFT KEYING (QPSK) [7/8] Figure 2.30 shows a different, but equally valid, representation. This constellation diagram looks like the original one in Figure 2.29, but rotated through 𝜋/4 radians or 45°. Prepared By: Dr. Naser Zaeri 41 4.2 QUADRATURE PHASE-SHIFT KEYING (QPSK) [8/8] Constellation diagrams are useful for representing the symbols of a modulation scheme. As the number of symbols increases, the scheme becomes more bandwidth efficient  the more symbols there are on the constellation diagram, the more data bits are transmitted per symbol  higher data rates for a given bandwidth. However, as the constellation becomes more densely packed with symbols, the distance separating the points becomes smaller.  can have negative effects on performance. Prepared By: Dr. Naser Zaeri 42  4.3 QUADRATURE AMPLITUDE MODULATION (QAM) [1/2] In considering how to increase the number of available symbols further than QPSK can provide, there are two options: The first possibility: the amplitude of the modulated signal remains fixed but the number of different phases the carrier wave can take continues to increase. This is the principle applied in M-PSK schemes or PSK of the order M, where M is the number of possible symbols. Prepared By: Dr. Naser Zaeri 43  4.3 QUADRATURE AMPLITUDE MODULATION (QAM) [2/2] The second possibility: is to combine QPSK with ASK techniques and introduce more amplitude levels as well as phases. This is the principle of quadrature amplitude modulation (QAM). Schemes of this kind are referred to as M-QAM or QAM of the order M. 16-QAM is much more widely used in practice than 16-PSK, along with higher-order schemes such as 64- QAM, 128-QAM and 256-QAM. This is because it performs better in noisy channels. Prepared By: Dr. Naser Zaeri 44  TM355: COMMUNICATIONS TECHNOLOGY BLOCK 1 PART 3: NOISE, INTERFERENCE AND COEXISTENCE 1 Prepared By: Dr. Naser Zaeri Arab Open University  OUTLINE Introduction Noise and interference Mobility and urban environments Noise and signal power Noise and data rate Noise and bit error rate Spectrum management Prepared By: Dr. Naser Zaeri 2  1. INTRODUCTION So far, this block has mostly considered communications links as isolated systems. However, this is an idealisation; the reality in practical communications systems is that noise and interference are always present and can adversely affect performance. This final part of Block 1 focuses on the effects of noise and interference in real- world communications. Prepared By: Dr. Naser Zaeri 3 2. NOISE AND INTERFERENCE [1/4] Examples of interference: Interference from unwanted stations on AM or FM radio. Mobile phones interference with unrelated equipment radio transmitter. Domestic appliances or power tools. Natural sources of noise including electrical storms and the effects of the sun. Noise generated within the receiver. Prepared By: Dr. Naser Zaeri 4 2. NOISE AND INTERFERENCE [2/4] The terms ‘noise’ and ‘interference’ are sometimes used interchangeably or lumped together However, a distinction can be made: Noise: from natural sources, which tends to be unavoidable. Interference: from unwanted transmissions. Prepared By: Dr. Naser Zaeri 5 2. NOISE AND INTERFERENCE [3/4] How might mutual interference be avoided? Use two different frequencies However, the amount of spectrum available is finite, so there is a practical limit to the number of transmitters that can transmit at the same time. If the two transmitters are in separate places, then we may use the same frequency Transmit at different times Design of antennas Different polarisations (horizontal and vertical). Directional antennas could be used to beam the transmissions in different directions. Prepared By: Dr. Naser Zaeri 6 2. NOISE AND INTERFERENCE [4/4] To mitigate the causes and effects of interference, electromagnetic compatibility (EMC) is a major factor in the design of electrical goods. Standards must be complied with concerning two key areas: emissions – the amount of power a device is allowed to radiate at different frequencies is limited. immunity – the device must function normally in the presence of radio waves up to a certain power at different frequencies. Prepared By: Dr. Naser Zaeri 7  3. MOBILITY AND URBAN ENVIRONMENTS Noise and interference from sources outside the communications link are not the only factors that affect communications in the real world. Urban environments present particular difficulties in radio propagation at VHF and above, due to the large number of obstructions and reflecting surfaces. Two types of fading are commonly distinguished: slow fading and fast fading. Prepared By: Dr. Naser Zaeri 8  3.1 FADING [1/3] The terms ‘slow’ and ‘fast’ here relate to how quickly the signal changes as the receiver or transmitter moves around. Fast fading: the changes happen with only a small change in position. Slow fading: a larger movement is needed to have an effect. Both slow and fast fading are due to obstacles and reflections. Prepared By: Dr. Naser Zaeri 9  3.1 FADING [2/3] The variation in power in slow fading can be modelled by a log-normal distribution. Note: the variation due to slow fading is additional to any power variation due to the inverse fourth-power law. Prepared By: Dr. Naser Zaeri 10  3.1 FADING [3/3] Fast fading: the mobile phone receives reflections from two different buildings. When two waves come together having travelled along paths of different lengths, they may reinforce each other, or cancel out, or the effect could be somewhere in between. When there is no line of sight, as with Figure 3.3, the Rayleigh distribution is a good approximation. When there is a predominant line-of- sight signal, the Rician distribution is used. Prepared By: Dr. Naser Zaeri 11  3.2 DOPPLER SHIFT Doppler shift: occurs when radio receivers in vehicles suffer from a problem due to their speed causing a shifting of frequency when a transmitter and receiver are moving relative to each other. When they are moving towards each other, the received signal is higher in frequency than the signal transmitted, and when they are moving apart, it is lower. 𝑣  𝑓𝑟 = 𝑓𝑡 (1 + ) 𝑐 Orthogonal frequency-division multiplexing (discussed in Block 3) uses a large number of narrow-band subcarriers, and Doppler shift places a practical limit on how closely they can be spaced. Prepared By: Dr. Naser Zaeri 12  3.3 FREQUENCY REUSE [1/2] Mobile communications networks illustrate how sometimes a restricted range of propagation – as characterised by the inverse fourth-power law – can actually be a benefit, because frequencies can be reused. Suppose the transmitting power of a base station is sufficient to serve mobile devices up to 1 km away with an adequate signal. If an inverse square law applied (as in free-space propagation) then at 5 km from the base station, the received power would be 1/25 as much as it was at 1 km. But with an inverse fourth-power law, the received power at 5 km would be only 1/625 of the power at 1 km. Prepared By: Dr. Naser Zaeri 13  3.3 FREQUENCY REUSE [2/2] Another aspect of propagation that is exploited in mobile communications is the use of directional antennas. The area covered by a base station may be divided into sectors, with a directional antenna covering each sector. A mast can be placed at a point where three cells join up, with each antenna serving a different cell. Prepared By: Dr. Naser Zaeri 14  3.4 MULTIPLE ANTENNAS AND MIMO [1/4] Question: Can performance be improved by using more than one antenna? Answer: there are a number of benefits that can be obtained by using multiple antennas at the transmitter, at the receiver or at both, though at the cost of increased complexity. Arrays of antennas have long been used at the transmitter or receiver to increase gain and/or to achieve desired directional properties. Prepared By: Dr. Naser Zaeri 15  3.4 MULTIPLE ANTENNAS AND MIMO [2/4] Because the signals received at multiple antennas are likely to differ in quality, it would make sense to select the best one, so that if one signal suffers from fading then a better one is chosen to take over. Another approach is to combine all the received signals in some way, so that no contribution goes to waste. Unfortunately, it is not enough simply to add the signals together, as the amplitudes and phases would differ and so the signals could destructively interfere with each other. However, the signals can be combined effectively by more sophisticated digital signal-processing techniques. Prepared By: Dr. Naser Zaeri 16  3.4 MULTIPLE ANTENNAS AND MIMO [3/4] Beam steering: also called beamforming, is a technique that uses multiple transmitter antennas. It is used when communicating with a single receiver, and its purpose is to improve reception at this target device. In this technique, the relative amplitudes and phases of the signals from each antenna are adjusted so that when they arrive at the target receiver, they add together constructively. This increases the strength of the received signal and provides some resistance to fading. Prepared By: Dr. Naser Zaeri 17  3.4 MULTIPLE ANTENNAS AND MIMO [4/4] Multiple Input Multiple Output (MIMO): uses multiple antennas at both the transmitter and the receiver, with a consequent increase in the number of paths available. Applications: LTE (4G) for mobile telephony and IEEE 802.11ac and 802.11n (WiFi) for wireless networking. Prepared By: Dr. Naser Zaeri 18  4. NOISE AND SIGNAL POWER 4.1 POWER CALCULATION [1/2] Most sources of noise and interference also have continuous spectra, though some have well-defined frequencies. The total amount of power in a signal can be measured in watts. Figure 3.6 shows an example in which a total transmitted power of 100 mW is spread evenly over a portion of spectrum. Prepared By: Dr. Naser Zaeri 19  4.1 POWER CALCULATION [2/2] In Figure 3.6 the vertical or y-axis is not power, but power density: Power density=Power/Bandwidth The total power of 100 mW is represented by the area under the graph. Since the power is spread over a bandwidth of: 2422 MHz − 2402 MHz = 20 MHz the power density = 5 mW/MHz. Prepared By: Dr. Naser Zaeri 20  4.2 SIGNAL-TO-NOISE RATIO [1/2] The signal-to-noise ratio (or S/N ratio, also abbreviated to SNR) is the signal power divided by the noise power. The higher the signal-to-noise ratio, the less the signal is affected by noise – and furthermore, as it turns out, the higher the data rate that can be obtained. Because it is a ratio of two powers, signal-to-noise ratio can be expressed either as a simple ratio or in decibels. Prepared By: Dr. Naser Zaeri 21  4.2 SIGNAL-TO-NOISE RATIO [2/2] Figure 3.8 shows a signal spectrum and a noise spectrum. Of the three receivers, receiver B would be the best one to use. Receiver A could lose data because it would not receive all the frequency components in the signal, and receiver C would allow through more noise than necessary. Prepared By: Dr. Naser Zaeri 22  4.3 THE EFFECT OF NOISE ON DATA AND ERROR RATES Increased noise power would make errors more likely. If the set of symbols is large, then the chance of misinterpreting a symbol is also increased. By, increasing the signal power the chance of errors is reduced, as the symbols will be more different from each other and less likely to be misinterpreted. Prepared By: Dr. Naser Zaeri 23  5. NOISE AND DATA RATE 5.1 THE SAMPLING THEOREM [1/2] The sampling theorem is a fundamental result in communications theory. Assume that the spectrum of the signal to be sampled has frequency components ranging from zero to 𝒇 Hz. The sampling theorem states that the signal can be exactly reconstructed from its samples (at least in principle) if the samples are taken at a rate exceeding 𝟐𝒇 samples per second. Prepared By: Dr. Naser Zaeri 24  5.1 THE SAMPLING THEOREM [2/2] Figure 3.9(a) shows a sine wave sampled at a rate less than 𝟐𝒇. Figure 3.9(b) shows the samples on their own. Figure 3.9(c) shows what could happen if an attempt at reconstruction was made using Figure 3.9(b). It is clear that Figure 3.9(c) is entirely different from Figure 3.9(a).  This effect is called aliasing. 25  5.2 DATA RATE IN A NOISE-FREE CHANNEL [1/3] The sampling theorem, or variants of it, was formulated independently by a number of people, notably Kotelnikov and Shannon. The figure of twice the bandwidth is often referred to as the ‘Nyquist rate’. After Harry Nyquist (1889–1976), an electronics engineer who made significant contributions to early communications problems and information theory. Prepared By: Dr. Naser Zaeri 26  5.2 DATA RATE IN A NOISE-FREE CHANNEL [2/3] Nyquist’s key result can be stated as follows: “The maximum rate at which symbols can be sent through a noise-free channel is 𝟐𝑩 symbols per second (where 𝑩 is the bandwidth of the channel in Hz).” The maximum data rate, 𝑫, in bits per second in a noise-free channel with bandwidth 𝑩 and a set of 𝑴 symbols is given by: 𝑫 = 𝟐𝑩 𝒍𝒐𝒈𝟐 𝑴  To find the data rate in bits per second, the symbol rate is multiplied by the number of bits that can be represented by a single symbol. Prepared By: Dr. Naser Zaeri 27  5.2 DATA RATE IN A NOISE-FREE CHANNEL [3/3] Remember: if number of bits per symbol, n, given by a set of M different symbols then: 𝑛 = 𝑙𝑜𝑔2 𝑀 16-QAM, which has 24 = 16 different symbols, can send four bits as one symbol. 64-QAM, with 26 = 64 symbols, can send six bits. Example: if the bandwidth is 10 kHz then, 64-QAM can support a maximum data rate of: 2 × 10 000 Hz × 6 = 120 000 bits per second= 120 kbit/s (Note: 𝑙𝑜𝑔2 (64) = 6 (or 26 = 64)). Prepared By: Dr. Naser Zaeri 28 5.3 DATA RATE IN A NOISY CHANNEL It may appear from Nyquist’s formula that the data rate could be increased indefinitely just by increasing the number of different symbols in the set. Remember, though, that this is for a noise-free channel. As the number of symbols increases, the more difficult they are to distinguish, and the more susceptible they become to corruption by noise. Prepared By: Dr. Naser Zaeri 29  5.3.1 SHANNON’S EQUATION [1/3] The incidence of errors can be reduced in various ways: by using error-correcting coding, or reducing the data rate, or increasing the signal power. How low the data rate needs to be is given by a result discovered by Claude Shannon (1916 – 2001) A cryptographer and electronics engineer who made important contributions to the field of information theory. He showed that there is a theoretical maximum rate at which data can be transmitted in a noisy communications channel at an arbitrarily low error rate. Prepared By: Dr. Naser Zaeri 30  5.3.1 SHANNON’S EQUATION [2/3] This is expressed mathematically as: 𝑪 = 𝑾 𝒍𝒐𝒈𝟐 (𝟏 + 𝑺 𝑵) 𝑪 is the theoretical maximum channel capacity, measured in bits per second. 𝑾 is the bandwidth of the channel, in hertz. 𝑺 is the signal power and 𝑵 is the noise power, so that 𝑺/𝑵 is the signal-to-noise ratio. 𝑙𝑜𝑔10 (𝑥) Note: 𝑙𝑜𝑔2 𝑥 =. 0.301 Note also that while bandwidth is often denoted as 𝐵, 𝑊 is the notation used by Shannon. Prepared By: Dr. Naser Zaeri 31  5.3.1 SHANNON’S EQUATION [3/3] An example of Shannon’s equation in action is provided by space probes, which send data from millions or even billions of kilometres away from Earth. The transmitters are modest in power, typically around 20W. As energy supplies are limited, several techniques are used to get the best possible S/N ratio: The antenna at the probe is designed to have a very high gain and is pointed at the Earth. Even so, the amount of power reaching any particular location on Earth is tiny. The receiving antenna is a dish antenna with a large collecting area. Even so, the signal power collected may be only femtowatts (10−15 W) or less. The noise generated at the receiver is kept to a minimum. Prepared By: Dr. Naser Zaeri 32 6. NOISE AND BIT ERROR RATE (BER) A noisy channel, perfectly error-free communication is not attainable in practice. At the most basic level, this means that noise and interference can cause a demodulated received bit to differ from the original transmitted bit. The BER is the number of bits received in error divided by the number of bits transmitted in total. Prepared By: Dr. Naser Zaeri 33  7. SPECTRUM MANAGEMENT [1/2] Because there are so many competing uses of the radio spectrum, there is a need for some planning. Users of the spectrum include not only broadcasters, and mobile phone networks, but also: Radar and radio-navigation Meteorological Earth-exploration satellites Radio astronomy As radio waves cross borders, the effect on neighbours must be taken into account. A radio broadcaster may wish to operate a high-power transmitter to obtain good coverage all over the country, but it could interfere with services in neighbouring countries. Prepared By: Dr. Naser Zaeri 34  7. SPECTRUM MANAGEMENT [2/2] When allocating services to different parts of the spectrum, a number of technical issues should be considered: Line-of-sight. Long-distance terrestrial communication, using the surface wave or the sky wave, is limited to the lower frequency bands. It is not possible to accommodate wide bandwidths in low- frequency bands. Communication between a satellite and the ground requires a window through the atmosphere where absorption is low and the ionosphere is transparent. Transmitters and receivers for the highest frequencies present significant engineering challenges. Prepared By: Dr. Naser Zaeri 35  TM355: COMMUNICATIONS TECHNOLOGY BLOCK 2 PART 1: CHANNEL CODING 1 Prepared By: Dr. Naser Zaeri Arab Open University  OUTLINE Introduction Error detection Error-correction coding basics Techniques of error correction Advanced block codes Convolutional coding and trellis-coded modulation Hybrid automatic repeat request (HARQ) Comparing and choosing codes Prepared By: Dr. Naser Zaeri 2  1. INTRODUCTION [1/3] The best performance of the channel cannot be achieved by modulation alone. A combination of channel coding and modulation is needed. Prepared By: Dr. Naser Zaeri 3  1. INTRODUCTION [2/3] Figure 1.2 shows the main function of the channel coding layer: reducing the error rate. Channel coding and decoding can correct most of the errors that occur in the channel. Controlling errors is the main function of channel coding. Prepared By: Dr. Naser Zaeri 4  1. INTRODUCTION [3/3] There are two different types of error-control coding: error- detection and error-correction coding. Error-detection coding only allows to know when received data contains errors, whereas error-correction coding also allows to correct those errors. With error detection, if there is a return channel so that the destination can send a signal back to the source, it is possible to request the retransmission of data that is found to contain errors. Some systems require the error-free receipt of data to be acknowledged, and the retransmission is triggered automatically if no receipt is forthcoming within a predetermined time interval.  automatic repeat request (ARQ). Therefore to distinguish between error detection combined with ARQ on the one hand, and error-correction coding on the other, the latter is often called forward error correction (FEC). Prepared By: Dr. Naser Zaeri 5  2. ERROR DETECTION 2.1 PARITY CHECKS [1/3] The simplest idea in error-control coding is the parity check. The principle: for a given block of bits, you add one further bit – the parity bit – which is chosen to be a 1 or a 0 so as to ensure that the total number of 1s in the block of bits, including the parity bit, is an even number. All the discussions assume the use of ‘even parity’, which is the most common. However, parity checking can be done just as well for odd parity, in which case the parity bit is chosen to ensure that the total number of 1s in the block is odd. Prepared By: Dr. Naser Zaeri 6  2.1 PARITY CHECKS [2/3] Any single error in the block will now make the parity of the block of bits odd, because an error changes either a 1 to a 0 or a 0 to a 1 – and in either case the number of 1s in the block changes from even to odd. The receiver can therefore just count the number of 1s in the received block of bits; if the number is odd, it knows there has been at least one error. Generally, systems operate with low error rates, meaning that the probability of there being more than one error in a block of bits is small, so a parity check is a good way of being reasonably confident that there are no errors. Prepared By: Dr. Naser Zaeri 7  2.1 PARITY CHECKS [3/3] Question: Which of the following might be valid code words using even parity? a) 01101010 b) 01001100 c) 11110010 d) 11110110 From the list given, (a) and (d) contain an even number of 1s so may be valid. The other two contain an odd number of 1s so must be invalid. Prepared By: Dr. Naser Zaeri 8  2.2 CYCLIC REDUNDANCY CHECKS (CRCS) [1/5] Although cyclic redundancy check coding is done on binary data, it is convenient to explain the principles using ‘ordinary’ (denary or base 10) numbers. Assume that a denary message, M, consists of a collection of denary digits, say 7654321. We divide this message number by a shorter number: G. Assume G = 99. The idea is to write 7654321 in terms of the largest number less than 7654321 that is divisible exactly by 99, plus a remainder:  7654321 = 77316 × 99 + 37. We say that the result of division leaves a remainder, R, which in this case is 37. Prepared By: Dr. Naser Zaeri 9  2.2 CYCLIC REDUNDANCY CHECKS (CRCS) [2/5] The idea behind CRCs is that the remainder (the digits of which are the check digits) is sent to the decoder together with the message. The decoder then calculates the remainder for itself and compares its own locally calculated value with the value it received from the encoder: if they are the same, it is assumed that all is well and there have been no errors. Prepared By: Dr. Naser Zaeri 10  2.2 CYCLIC REDUNDANCY CHECKS (CRCS) [3/5] Question: Suppose, with G = 99, that a decoder receives the following messages and check digits: a) message 234567, check digits 36 b) message 345678, check digits 22. In which case must there have been errors? Solution: a) The remainder on dividing 234567 by 99 is 36, which is the same as the received check, so there is no reason to suspect that there have been any errors. b) The remainder on dividing 345678 by 99 is 69, which is not the same as the received check, so there must have been some errors. Prepared By: Dr. Naser Zaeri 11  2.2 CYCLIC REDUNDANCY CHECKS (CRCS) [4/5] Question: Suppose that we use a denary cyclic redundancy check, with G = 999. a) What is the code word if the message is 45454545? b) The following code words are received at a decoder. What are the message digits in each case, and do they appear to contain errors? i. 32132132296 ii. 52310642002 Prepared By: Dr. Naser Zaeri 12  2.2 CYCLIC REDUNDANCY CHECKS (CRCS) [5/5] Solution: a) The check digits is calculated as follows:  45454545/ 999 = 45500.045, meaning the remainder is 45 454 545 – 45 500 × 999 = 45.  So the transmitted sequence is 45454545045. b) i. For 32132132296, the data is 32132132 and the received check digits are 296. Calculating the check digits (from 32132132 divided by 999) gives 296. This is the same as the received check digits, so does not indicate any errors. ii. For 52310642002, the data is 52310642 and the received check digits are 002. Calculating the check digits (from 52310642 divided by 999) gives 005. This is different from the received check digits, so there must have been errors. Prepared By: Dr. Naser Zaeri 13  2.3 GENERATOR POLYNOMIALS FOR BINARY CRCS [1/3] In practice, CRCs work directly on binary sequences. It uses a special sort of arithmetic known as modulo-2 arithmetic. Modulo-2 arithmetic can be performed on binary sequences very easily and rapidly in either hardware or software. Also, employing modulo-2 arithmetic leads to a simplification in the method used to check for errors at a decoder  just have to divide the received sequence by G and see if there is any remainder: If there is no remainder (that is, if the remainder is 0) then there is no evidence of errors. If it is anything other than zero, there must have been at least one error. Prepared By: Dr. Naser Zaeri 14  2.3 GENERATOR POLYNOMIALS FOR BINARY CRCS [2/3] CRCs are specified by the value of G, which is a binary number G is usually described by a polynomial, the ‘generator polynomial’. Example: the polynomial 𝑥 4 + 𝑥 3 + 1 represents the binary number 11001. Prepared By: Dr. Naser Zaeri 15  2.3 GENERATOR POLYNOMIALS FOR BINARY CRCS [3/3] CRC error-detecting capabilities: A CRC with a suitably chosen generator in which the highest power is n has the following features: It is capable of detecting all odd numbers of errors. It is capable of detecting all bursts of length n or shorter. The probability of any burst longer than n + 1 escaping detection, assuming that all error patterns within the burst 𝟏 are equally probable, is 𝒏. 𝟐 The probability of a burst of length exactly equal to n + 1 escaping detection, again assuming that all error patterns 𝟏 within the burst are equally probable, is 𝒏−𝟏. 𝟐 Prepared By: Dr. Naser Zaeri 16 3. ERROR-CORRECTION CODING BASICS Two types of error-correcting code: Rectangular coding: rarely used in practice, but is an easy way to show how forward error correction becomes possible by using multiple parity checks on a block of data. Hamming coding: very efficient method of error correction which, as well as having practical applications. Prepared By: Dr. Naser Zaeri 17  3.1 RECTANGULAR CODES [1/5] Rectangular code (also known as a product code) can detect the presence of a single error, and also identify which bit is in error and therefore correct it. A rectangular code is an example of a block code. The general concept of a (binary) block code in the context of error-control coding is that the encoder takes the input data in successive blocks of k bits and encodes them as n bits, where n > k so that the encoded data has some redundancy. The code is described as an (n, k) block code. Block coding is one of the two broad categories of error- correcting code. The other category is convolutional Coding. One feature that distinguishes a block code from a convolutional code is that a block code is memoryless. The encoding of the k bits does not depend upon what went before. Prepared By: Dr. Naser Zaeri 18  3.1 RECTANGULAR CODES [2/5] If no more than one error occurs per block, a rectangular code can locate and hence correct it. Any one error will cause the parity check to fail in one row and one column. Knowing which row and which column have failed provides the coordinates that identify the bit that is in error – and once the location of this bit is known, it can be corrected. If two errors (or any even number of errors) occur in the same row, the parity check for that row will still pass – so although there will be failed parity checks in the affected columns, it will not be possible to tell which row is the one that contains the errors. The same is true for an even number of errors in the same column. Rectangular codes are therefore not very good at correcting error bursts. Prepared By: Dr. Naser Zaeri 19  3.1 RECTANGULAR CODES [3/5] Although rectangular codes are very simple, they are not very efficient because they use a relatively large number of parity digits per data digit. One measure of the efficiency of an (n, k) block code is the ratio k/n, which is called the code rate. Another related measure is the code 𝑛−𝑘 redundancy, given by:𝑅 = 𝑛 Prepared By: Dr. Naser Zaeri 20  3.1 RECTANGULAR CODES [4/5] Question: The figure represents a code word from a rectangular code. a) How many parity digits are used per code word to check for errors? b) Describe this code using the (n, k) notation. c) Calculate the code rate and the redundancy of this code. d) Assuming that no more than one digit is in error, how many different errors can be corrected using this code? Prepared By: Dr. Naser Zaeri 21  3.1 RECTANGULAR CODES [5/5] Solution: a) The diagram shows that eight parity digits are used to check for errors, out of 20 digits in total. b) n is the total number of bits in the code, 20, and k is the number of bits in the message, which is 12. The code is therefore a (20, 12) code. c) The code rate = k/n = 12/20 = 60%. 𝑛−𝑘 20−12 The redundancy = 𝑅 = = = 40%. 𝑛 20 a) The rectangular code can correct a single error at any digit position, including the parity digits. Prepared By: Dr. Naser Zaeri 22  3.2 HAMMING CODES [1/8] For any integer m, it is possible to construct a Hamming code that uses m parity digits to correct any single error in a code word of size n digits, where: 𝑛 = 2𝑚 − 1 The n digits of the code word are made up of the k message digits and the m parity digits, so n = k + m. Prepared By: Dr. Naser Zaeri 23  3.2 HAMMING CODES [2/8] Activity: a) What would be the total number of digits per Hamming code word if four of the digits were used for parity checks? b) Describe this code using the (n, k) notation and calculate its code rate. Solution: a) four corresponds to m, the number of parity digits. Substituting m = 4 the total number of digits:  𝑛 = 24 − 1 = 15. b) Of the 15 digits, four are parity digits and 11 are the digits of the original message, so n is 15 and k is 11  It is a (15, 11) code and the code rate is 11/15 = 0.73. Prepared By: Dr. Naser Zaeri 24  3.2 HAMMING CODES [3/8] The parity-check digits in a Hamming code are applied to groups of message digits in such a way that a single error can be located, and then corrected. The parity digits can be positioned in the coded word so that a binary number representing the result of the checks, the syndrome, points directly to the error, if there is one. Prepared By: Dr. Naser Zaeri 25  3.2 HAMMING CODES [4/8] Figure 1.6 represents a seven-digit Hamming code for a four-digit message. Prepared By: Dr. Naser Zaeri 26 3.2 HAMMING CODES [5/8] Prepared By: Dr. Naser Zaeri 27  3.2 HAMMING CODES [6/8] Activity: If the following codes are received, state whether there have been any errors, and give the decoded output. (Assume that the probability of there being more th