Lecture notes on Digital Communication Techniques

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Einstein College of Engineering Digital Communication (EC51) 1 www.annauniversityplus.com Einstein College of Engineering Chapter-1: Introduction The purpose of a Communication System is to transport an information bearing signal from a source to a user destination via a communication channel. MODEL OF A COMMUNICATION SYSTEM(ANALOG) I/P Signal Information TRANSMITTER Source and Input Transducer CHANNEL O/P Signal Destination RECEIVER and Output Transducer Fig. 1.1: Block diagram of Communication System. The three basic elements of every communication systems are Transmitter, Receiver and Channel. The Overall purpose of this system is to transfer information from one point (called Source) to another point, the user destination. The message produced by a source, normally, is not electrical. Hence an input transducer is used for converting the message to a time – varying electrical quantity called message signal. Similarly, at the destination point, another transducer converts the electrical waveform to the appropriate message. The transmitter is located at one point in space, the receiver is located at some other point separate from the transmitter, and the channel is the medium that provides the electrical connection between them. The purpose of the transmitter is to transform the message signal produced by the source of information into a form suitable for transmission over the channel. The received signal is normally corrupted version of the transmitted signal, which is due to channel imperfections, noise and interference from other sources.The receiver has the task of operating on the received signal so 2 www.annauniversityplus.com Einstein College of Engineering as to reconstruct a recognizable form of the original message signal and to deliver it to the user destination. Communication Systems are divided into 3 categories: 1. Analog Communication Systems are designed to transmit analog information using analog modulation methods. 2. Digital Communication Systems are designed for transmitting digital information using digital modulation schemes, and 3. Hybrid Systems that use digital modulation schemes for transmitting sampled and quantized values of an analog message signal. ELEMENTS OF DIGITAL COMMUNICATION SYSTEMS: The figure 1.2 shows the functional elements of a digital communication system. Source of Information: 1. Analog Information Sources. 2. Digital Information Sources. Analog Information Sources → Microphone actuated by a speech, TV Camera scanning a scene, continuous amplitude signals. Digital Information Sources → These are teletype or the numerical output of computer which consists of a sequence of discrete symbols or letters. An Analog information is transformed into a discrete information through the process of sampling and quantizing. Digital Communication System Source of Source Channel Information Encoder Encoder Modulator Channel Received Signal Source Channel User of Demodulator Decoder Information Decoder 3 www.annauniversityplus.com Einstein College of Engineering Fig 1.2: Block Diagram of a Digital Communication System SOURCE ENCODER / DECODER: The Source encoder ( or Source coder) converts the input i.e. symbol sequence into a binary sequence of 0‟s and 1‟s by assigning code words to the symbols in the input sequence. For eg. :-If a source set is having hundred symbols, then the number of bits used to represent each symbol will 7 be 7 because 2 =128 unique combinations are available. The important parameters of a source encoder are block size, code word lengths, average data rate and the efficiency of the coder (i.e. actual output data rate compared to the minimum achievable rate) At the receiver, the source decoder converts the binary output of the channel decoder into a symbol sequence. The decoder for a system using fixed – length code words is quite simple, but the decoder for a system using variable – length code words will be very complex. Aim of the source coding is to remove the redundancy in the transmitting information, so that bandwidth required for transmission is minimized. Based on the probability of the symbol code word is assigned. Higher the probability, shorter is the codeword. Ex: Huffman coding. CHANNEL ENCODER / DECODER: Error control is accomplished by the channel coding operation that consists of systematically adding extra bits to the output of the source coder. These extra bits do not convey any information but helps the receiver to detect and / or correct some of the errors in the information bearing bits. There are two methods of channel coding: 1. Block Coding: The encoder takes a block of „k‟ information bits from the source encoder and adds „r‟ error control bits, where „r‟ is dependent on „k‟ and error control capabilities desired. 2. Convolution Coding: The information bearing message stream is encoded in a continuous fashion by continuously interleaving information bits and error control bits. 4 www.annauniversityplus.com Einstein College of Engineering The Channel decoder recovers the information bearing bits from the coded binary stream. Error detection and possible correction is also performed by the channel decoder. The important parameters of coder / decoder are: Method of coding, efficiency, error control capabilities and complexity of the circuit. MODULATOR: The Modulator converts the input bit stream into an electrical waveform suitable for transmission over the communication channel. Modulator can be effectively used to minimize the effects of channel noise, to match the frequency spectrum of transmitted signal with channel characteristics, to provide the capability to multiplex many signals. DEMODULATOR: The extraction of the message from the information bearing waveform produced by the modulation is accomplished by the demodulator. The output of the demodulator is bit stream. The important parameter is the method of demodulation. CHANNEL: The Channel provides the electrical connection between the source and destination. The different channels are: Pair of wires, Coaxial cable, Optical fibre, Radio channel, Satellite channel or combination of any of these. The communication channels have only finite Bandwidth, non-ideal frequency response, the signal often suffers amplitude and phase distortion as it travels over the channel. Also, the signal power decreases due to the attenuation of the channel. The signal is corrupted by unwanted, unpredictable electrical signals referred to as noise. The important parameters of the channel are Signal to Noise power Ratio (SNR), usable bandwidth, amplitude and phase response and the statistical properties of noise. Advantages of Digital Communication 1. The effect of distortion, noise and interference is less in a digital communication system. This is because the disturbance must be large enough to change the pulse from one state to the other. 5 www.annauniversityplus.com Einstein College of Engineering 2. Regenerative repeaters can be used at fixed distance along the link, to identify and regenerate a pulse before it is degraded to an ambiguous state. 3. Digital circuits are more reliable and cheaper compared to analog circuits. 4. The Hardware implementation is more flexible than analog hardware because of the use of microprocessors, VLSI chips etc. 5. Signal processing functions like encryption, compression can be employed to maintain the secrecy of the information. 6. Error detecting and Error correcting codes improve the system performance by reducing the probability of error. 7. Combining digital signals using TDM is simpler than combining analog signals using FDM. The different types of signals such as data, telephone, TV can be treated as identical signals in transmission and switching in a digital communication system. 8. We can avoid signal jamming using spread spectrum technique. Disadvantages of Digital Communication: 1. Large System Bandwidth:- Digital transmission requires a large system bandwidth to communicate the same information in a digital format as compared to analog format. 2. System Synchronization:- Digital detection requires system synchronization whereas the analog signals generally have no such requirement. Channels for Digital Communications The modulation and coding used in a digital communication system depend on the characteristics of the channel. The two main characteristics of the channel are BANDWIDTH and POWER. In addition the other characteristics are whether the channel is linear or nonlinear, and how free the channel is free from the external interference. 6 www.annauniversityplus.com Einstein College of Engineering Five channels are considered in the digital communication, namely: telephone channels, coaxial cables, optical fibers, microwave radio, and satellite channels. Telephone channel: It is designed to provide voice grade communication. Also good for data communication over long distances. The channel has a band-pass characteristic occupying the frequency range 300Hz to 3400hz, a high SNR of about 30db, and approximately linear response. For the transmission of voice signals the channel provides flat amplitude response. But for the transmission of data and image transmissions, since the phase delay variations are important an equalizer is used to maintain the flat amplitude response and a linear phase response over the required frequency band. Transmission rates upto16.8 kilobits per second have been achieved over the telephone lines. Coaxial Cable: The coaxial cable consists of a single wire conductor centered inside an outer conductor, which is insulated from each other by a dielectric. The main advantages of the coaxial cable are wide bandwidth and low external interference. But closely spaced repeaters are required. With repeaters spaced at 1km intervals the data rates of 274 megabits per second have been achieved. Optical Fibers: An optical fiber consists of a very fine inner core made of silica glass, surrounded by a concentric layer called cladding that is also made of glass. The refractive index of the glass in the core is slightly higher than refractive index of the glass in the cladding. Hence if a ray of light is launched into an optical fiber at the right oblique acceptance angle, it is continually refracted into the core by the cladding. That means the difference between the refractive indices of the core and cladding helps guide the propagation of the ray of light inside the core of the fiber from one end to the other. Compared to coaxial cables, optical fibers are smaller in size and they offer higher transmission bandwidths and longer repeater separations. Microwave radio: A microwave radio, operating on the line-of-sight link, consists basically of a transmitter and a receiver that are equipped with antennas. The antennas are placed on towers at sufficient height to have the transmitter and receiver in line-of-sight of each other. The operating frequencies range from 1 to 30 GHz. 7 www.annauniversityplus.com Einstein College of Engineering Under normal atmospheric conditions, a microwave radio channel is very reliable and provides path for high-speed digital transmission. But during meteorological variations, a severe degradation occurs in the system performance. Satellite Channel: A Satellite channel consists of a satellite in geostationary orbit, an uplink from ground station, and a down link to another ground station. Both link operate at microwave frequencies, with uplink the uplink frequency higher than the down link frequency. In general, Satellite can be viewed as repeater in the sky. It permits communication over long distances at higher bandwidths and relatively low cost. Bandwidth: Bandwidth is simply a measure of frequency range. The range of frequencies contained in a composite signal is its bandwidth. The bandwidth is normally a difference between two numbers. For example, if a composite signal contains frequencies between 1000 and 5000, its bandwidth is 5000 - 1000, or 4000. If a range of 2.40 GHz to 2.48 GHz is used by a device, then the bandwidth would be 0.08 GHz (or more commonly stated as 80MHz).It is easy to see that the bandwidth we define here is closely related to the amount of data you can transmit within it - the more room in frequency space, the more data you can fit in at a given moment. The term bandwidth is often used for something we should rather call a data rate, as in “my Internet connection has 1 Mbps of bandwidth”, meaning it can transmit data at 1 megabit per second. Geometric representation of Signals: Analog signal: If the magnitudes of a real signal s(t) over its range of definition, T1≤ t ≤ T2, are real numbers (there are infinite such values) within a finite range, say, Smin ≤ S(t) ≤ Smax, the signal is analog. A digital signal s(t), on the contrary, can assume only any of a finite number of values. Usually, a digital signal implies a discrete-time, discrete-amplitude signal. Energy signal: If, for a signal s(t), i.e. the energy of the signal is finite,the signal is called an energy signal. However, the same signal may have large power.The voltage generated by 8 www.annauniversityplus.com Einstein College of Engineering lightning (which is of short duration) is a close example of physical equivalent of a signal with finite energy but very large power. Power signal: A power signal, on the contrary, will have a finite power but may have finite or infinite energy. Mathematically, While electrical signals, derived from physical processes are mostly energy signals,several mathematical functions, usually deterministic, represent power signals. Deterministic and random signals: If a signal s(t), described at t = t1 is sufficient for determining the signal at t = t2 at which the signal also exists, then s(t) represents a deterministic signal. Continuous time signal: Assuming the independent variable „t‟ to represent time, if s(t) is defined for all possible values of t between its interval of definition (or existence), T1≤ t ≤ T2. Then the signal s(t) is a continuous time signal.If a signal s(t) is defined only for certain values of t over an interval T1≤ t ≤ T2, it is a discrete-time signal. A set of sample values represent a discrete time signal. Periodic signal: If s(t) = s(t + T), for entire range of t over which the signal s(t) is defined and T is a constant, s(t) is said to be periodic or repetitive. „T‟ indicates the period of the signal and 1/T is its frequency of repetition. 9 www.annauniversityplus.com Einstein College of Engineering Chapter-2 SAMPLING: A message signal may originate from a digital or analog source. If the message signal is analog in nature, then it has to be converted into digital form before it can transmitted by digital means. The process by which the continuous-time signal is converted into a discrete–time signal is called Sampling. Sampling operation is performed in accordance with the sampling theorem. SAMPLING THEOREM FOR LOW-PASS SIGNALS:- Statement:- “If a band –limited signal g(t) contains no frequency components for ׀f׀ W, then it is completely described by instantaneous values g(kT ) uniformly spaced in time s with period T ≤ 1/2W. If the sampling rate, fs is equal to the Nyquist rate or greater (fs ≥ s 2W), the signal g(t) can be exactly reconstructed. g(t) s (t) δ -2Ts -Ts 0 1Ts 2Ts 3Ts 4Ts g (t) δ -2Ts -Ts 0 Ts 2Ts 3Ts 4Ts Fig : Sampling process 10 www.annauniversityplus.com Einstein College of Engineering Proof:- Part - I If a signal x(t) does not contain any frequency component beyond W Hz, then the signal is completely described by its instantaneous uniform samples with sampling interval (or period ) of Ts 1/(2W) sec. Part – II The signal x(t) can be accurately reconstructed (recovered) from the set of uniform instantaneous samples by passing the samples sequentially through an ideal (brick-wall) lowpass filter with bandwidth B, where W ≤ B fs – W and fs = 1/(Ts). If x(t) represents a continuous-time signal, the equivalent set of instantaneous uniform samples x(nTs) may be represented as, x(nTs)≡ xs(t) = Σ x(t).δ(t- nTs) 1.1 where x(nTs) = x(t)⎢t =nTs , δ(t) is a unit pulse singularity function and „n‟ is an integer.The continuous-time signal x(t) is multiplied by an (ideal) impulse train to obtain x(nTs) and can be rewritten as, xs(t) = x(t).Σ δ(t- nTs) -1.2 Now, let X(f) denote the Fourier Transform F(T) of x(t), i.e. -1.3 Now, from the theory of Fourier Transform, we know that the F.T of Σ δ(t- nTs), the impulse train in time domain, is an impulse train in frequency domain: FΣ δ(t- nTs) = (1/Ts).Σ δ(f- n/Ts) = fs.Σ δ(f- nfs) -1.4 If Xs(f) denotes the Fourier transform of the energy signal xs(t), we can write using Eq. (1.2.4) and the convolution property: Xs(f) = X(f) FΣ δ(t- nTs) = X(f)fs.Σ δ(f- nfs) = fs.X(f)Σ δ(f- nfs) 1.5 This equation, when interpreted appropriately, gives an intuitive proof to 11 www.annauniversityplus.com Einstein College of Engineering Nyquist‟s theorems as stated above and also helps to appreciate their practical implications. Let us note that while writing Eq.(1.5), we assumed that x(t) is an energy signal so that its Fourier transform exists. With this setting, if we assume that x(t) has no appreciable frequency component greater than W Hz and if fs 2W, then Eq.(1.5) implies that Xs(f), the Fourier Transform of the sampled signal xs(t) consists of infinite number of replicas of X(f), centered at discrete frequencies n.fs, -∞ n ∞ and scaled by a constant fs= 1/Ts Fig. 1.2.1 indicates that the bandwidth of this instantaneously sampled wave xs(t) is infinite while the spectrum of x(t) appears in a periodic manner, centered at discrete frequency values n.fs. Part – I of the sampling theorem is about the condition fs 2.W i.e. (fs – W) W and (– fs + W) – W. As seen from Fig. 1.2.1, when this condition is satisfied, the spectra of xs(t), centered at f = 0 and f = ± fs do not overlap and hence, the spectrum of x(t) is present in xs(t) without any distortion. This implies that xs(t), the appropriately sampled version of x(t), contains all information about x(t) and thus represents x(t). The second part suggests a method of recovering x(t) from its sampled version xs(t) by using an ideal lowpass filter. As indicated by dotted lines in Fig. 1.2.1, an ideal lowpass filter (with brick-wall type response) with a bandwidth W ≤ B (fs – W), when fed with xs(t), will allow the portion of Xs(f), centered at f = 0 and will reject all its replicas at f = n fs, for n ≠ 0. This implies that the shape of the continuous time signal xs(t), will be retained at the output of the ideal filter. 12 www.annauniversityplus.com Einstein College of Engineering Sampling of Band Pass Signals: Consider a band-pass signal g(t) with the spectrum shown in figure 2.2: G(f) B B Band width = B Upper Limit = f u Lower Limit = f -f -f 0 f f f l u l l u Fig 2.2: Spectrum of a Band-pass Signal The signal g(t) can be represented by instantaneous values, g(kTs) if the sampling rate fs is (2f /m) where m is an integer defined as u ((f / B) -1 ) m ≤ (f / B) u u If the sample values are represented by impulses, then g(t) can be exactly reproduced from it‟s samples by an ideal Band-Pass filter with the response, H(f) defined as H(f) = 1 f f f l u 0 elsewhere If the sampling rate, fs ≥ 2fu, exact reconstruction is possible in which case the signal g(t) may be considered as a low pass signal itself. f s 4B 3B 2B B 0 B 2B 3B 4B 5B f u Fig 2.3: Relation between Sampling rate, Upper cutoff frequency and Bandwidth. 13 www.annauniversityplus.com Einstein College of Engineering Example-1 : Consider a signal g(t) having the Upper Cutoff frequency, f = 100KHz and the u Lower Cutoff frequency f = 80KHz. l The ratio of upper cutoff frequency to bandwidth of the signal g(t) is f / B = 100K / 20K = 5. u Therefore we can choose m = 5. Then the sampling rate is f = 2f / m = 200K / 5 = 40KHz s u Example-2 : Consider a signal g(t) having the Upper Cutoff frequency, f = 120KHz and the u Lower Cutoff frequency f = 70KHz. l The ratio of upper cutoff frequency to bandwidth of the signal g(t) is f / B = 120K / 50K = 2.4 u Therefore we can choose m = 2. ie.. m is an integer less than (f /B). u Then the sampling rate is f = 2f / m = 240K / 2 = 120KHz. s u Quadrature Sampling of Band – Pass Signals: This scheme represents a natural extension of the sampling of low – pass signals. In this scheme, the band pass signal is split into two components, one is in-phase component and other is quadrature component. These two components will be low–pass signals and are sampled separately. This form of sampling is called quadrature sampling. Let g(t) be a band pass signal, of bandwidth „2W‟ centered around the frequency, fc, (fcW). The in-phase component, g (t) is obtained by multiplying g(t) with I cos(2πfct) and then filtering out the high frequency components. Parallelly a quadrature phase component is obtained by multiplying g(t) with sin(2πfct) and then filtering out the high frequency components.. The band pass signal g(t) can be expressed as, g(t) = g (t). cos(2πfct) – g (t) sin(2πfct) I Q The in-phase, g (t) and quadrature phase g (t) signals are low–pass signals, having band I Q limited to (-W f W). Accordingly each component may be sampled at the rate of 2W samples per second. 14 www.annauniversityplus.com Einstein College of Engineering g(t)cos(2πfct) ½ g (t) ½ g (nT ) I I s LPF sampler g(t) cos (2πfct) g(t) sin(2πfct) ½g (t) -½ g (nT ) Q Q s LPF sampler sin (2πfct) Fig 2.4: Generation of in-phase and quadrature phase samples G(f) -fc 0 fc f  2W- a) Spectrum of a Band pass signal. G (f) / G (f) I Q -W 0 W f b) Spectrum of g (t) and g (t) I Q Fig 2.5 a) Spectrum of Band-pass signal g(t) b) Spectrum of in-phase and quadrature phase signals 15 www.annauniversityplus.com Einstein College of Engineering RECONSTRUCTION: From the sampled signals g (nTs) and g (nTs), the signals g (t) and g (t) are I Q I Q obtained. To reconstruct the original band pass signal, multiply the signals g (t) by I cos(2πfct) and sin(2πfct) respectively and then add the results. g (nT ) I s Reconstruction Filter + Cos (2πf t) g(t) c Σ - g (nT ) Q s Reconstruction Filter Sin (2πf t) c Fig 2.6: Reconstruction of Band-pass signal g(t) Sample and Hold Circuit for Signal Recovery. In both the natural sampling and flat-top sampling methods, the spectrum of the signals are scaled by the ratio τ/Ts, where τ is the pulse duration and Ts is the sampling period. Since this ratio is very small, the signal power at the output of the reconstruction filter is correspondingly small. To overcome this problem a sample-and-hold circuit is used . SW AMPLIFIER Input Output g(t) u(t) a) Sample and Hold Circuit 16 www.annauniversityplus.com Einstein College of Engineering b) Idealized output waveform of the circuit Fig: 2.7 Sample Hold Circuit with Waveforms. The Sample-and-Hold circuit consists of an amplifier of unity gain and low output impedance, a switch and a capacitor; it is assumed that the load impedance is large. The switch is timed to close only for the small duration of each sampling pulse, during which time the capacitor charges up to a voltage level equal to that of the input sample. When the switch is open , the capacitor retains the voltage level until the next closure of the switch. Thus the sample-and-hold circuit produces an output waveform that represents a staircase interpolation of the original analog signal. Natural Sampling: In this method of sampling, an electronic switch is used to periodically shift between the two contacts at a rate of fs = (1/Ts ) Hz, staying on the input contact for C seconds and on the grounded contact for the remainder of each sampling period. The output x (t) of the sampler consists of segments of x(t) and hence x (t) can be s s considered as the product of x(t) and sampling function s(t). x (t) = x(t) . s(t) s Fig: 2.8 Natural Sampling – Simple Circuit. 17 www.annauniversityplus.com Einstein College of Engineering Fig: 2.9 Natural Sampling – Waveforms. Applying Fourier transform FT Using x(t) X(f) x(t) cos(2πf t) ½ X(f-f ) + X(f+f ) 0 0 0 Xs(f) = Co.X(f) + C X(f-f ) + X(f+f ) + C X(f-f ) + X(f+f ) + ... … 1 0 0 2 0 0 n≠0 1 X(f) f -W 0 +W Message Signal Spectrum Xs(f) C 0 C C C C 2 1 1 2 f -2f -f -W 0 +W f 2f s s s s Sampled Signal Spectrum (f 2W) s 18 www.annauniversityplus.com Einstein College of Engineering Fig:2.10 Natural Sampling Spectrum The signal x (t) has the spectrum which consists of message spectrum and repetition of s message spectrum periodically in the frequency domain with a period of f . But the s message term is scaled by „Co”. Since the spectrum is not distorted it is possible to reconstruct x(t) from the sampled waveform x (t). s Quantization: The process of transforming Sampled amplitude values of a message signal into a discrete amplitude value is referred to as Quantization. The quantization Process has a two-fold effect: 1. the peak-to-peak range of the input sample values is subdivided into a finite set of decision levels or decision thresholds that are aligned with the risers of the staircase, and 2. the output is assigned a discrete value selected from a finite set of representation levels that are aligned with the treads of the staircase.. A quantizer is memory less in that the quantizer output is determined only by the value of a corresponding input sample, independently of earlier analog samples applied to the input. Analog Signal Discrete Samples ( Quantized ) 0 Ts 2Ts 3Ts Time 19 www.annauniversityplus.com Einstein College of Engineering Fig:2.11 Typical Quantization process. Types of Quantizers: 1. Uniform Quantizer 2. Non- Uniform Quantizer Uniform Quantizer: In Uniform type, the quantization levels are uniformly spaced, whereas in non- uniform type the spacing between the levels will be unequal and mostly the relation is logarithmic. Types of Uniform Quantizers: ( based on I/P - O/P Characteristics) 1. Mid-Rise type Quantizer 2. Mid-Tread type Quantizer In the stair case like graph, the origin lies the middle of the tread portion in Mid –Tread type where as the origin lies in the middle of the rise portion in the Mid-Rise type. Mid – tread type: Quantization levels – odd number. Mid – Rise type: Quantization levels – even number. 20 www.annauniversityplus.com

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