Digital communications: Principles and systems
A worldwide digital and wireless communication revolution has taken place in the last 20 years which has created a high demand in industry for graduates with indepth expertise in digital transmission techniques and a sound and complete understanding of their core principles. Digital communications: Principles and systems recognises that although digital communications is developing at a fast pace, the core principles remain the same. It therefore concentrates on giving the reader a thorough understanding of core principles and extensive coaching in the solution of practical problems drawn from various application areas. The intention is that after studying the material presented, the student will have a solid foundation free of knowledge gaps, and will be fully equipped to undertake digital communication systems analysis, design and computer simulations, and to deal with specialised applications and follow advances in the technology. Topics covered include: overview of digital communication; linear and nonlinear channels and systems; sampling of baseband and bandpass signals; quantisation and PCM; source coding and lossless data compression; line codes and modulation; transmission through bandlimited AWGN channels; transmitted digital signals; error control coding; link analysis and design. Many works on emerging digital transmission techniques are largely confined to academic research papers. This book will give postgraduate students and practicing engineers a sound mastery of the subject.
Inspec keywords: quantisation (signal); digital communication; bandlimited communication; AWGN channels; source coding; radio links; error correction codes; pulse code modulation; signal sampling; nonlinear systems
Other keywords: base band signal sampling; digital transmission link analysis; error control coding; noise impact; lossless data compression; nonlinear systems; band limited AWGN channels; digital communication; source coding; digital signal transmission; line codes; linear channels; PCM; band pass signal sampling; quantisation
Subjects: Codes; General electrical engineering topics; Textbooks; Radio links and equipment; Signal processing and detection
 Book DOI: 10.1049/PBTE058E
 Chapter DOI: 10.1049/PBTE058E
 ISBN: 9781849196116
 eISBN: 9781849196123
 Page count: 514
 Format: PDF

Front Matter
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1 Overview of digital communication
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This chapter presents an overview of digital communications and lays a crucial foundation on which we will build further knowledge of the subject in later chapters. It deals with the building blocks, signal processing and features of digital communications, and is a nonmathematical introduction to a modern digital communication system. Design considerations are emphasised, including performance objectives and system resource utilisation. We discuss the building blocks of a communication system and the signal processing tasks usually carried out at the sending and receiving ends of a digital communication system. We also justify the digital revolution that has taken place in telecommunications by outlining the advantages and disadvantages of modern digital communication compared to analogue communication.

2 Linear channels and systems
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Analysis of linear systems in the time and frequency domains. The concepts of impulse response, transfer function, gain response and phase response of linear timeinvariant systems and how they are employed to model system effects and determine system output in response to an arbitrary input are discussed. The various effects of multipath radio propagation in general and analysed in detail the special case of a radio channel in which multipath propagation arises due to the existence at the receiver of a primary signal received directly from the transmitter. The distortions present in the signal can be minimized by connecting a suitably designed equalisation filter.

3 Nonlinear systems
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The principle of superposition does not hold in nonlinear systems where response to one input is modified in the presence of other inputs. So we are unable to determine the response of this system to an arbitrary input signal based on its response to an impulse or a sinusoid. We may however employ the system's transfer characteristic, which gives its output as a polynomial function of input over a specified range. In so doing we find that nonlinearity not only distorts the wanted signal, but it also introduces harmonic and intermodulation products into the output, and these may interfere with other signals in adjacent channels or frequency bands. This is undesirable in transmission channels and must be minimised by ensuring that HPA operations are linear, for example by using a larger (and heavier) HPA than necessary and employing sufficient input power backoff to set its operating point within the linear region. In the next chapter we begin an indepth study of the efficient representation of digital signals for transmission, and explore how the conflicting goals of minimising transmission bandwidth requirement and maintaining high fidelity with the source signal are achieved in practice.

4 Sampling of base band and band pass signals
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This chapter deals in complete detail with the first two steps involved in converting an analogue signal in to a sequence of binary numbers (called bit stream), specifically the processes of antialias filtering and sampling.The sampling theorem that governs distortionfree sampling can only be obeyed in strictly band limited signals that have no frequency components outside a bandwidth B. However, most naturally occurring analogue signals are not strictly band limited in the sense that they do contain stray frequency components outside the bandwidth B. In that case alias distortion is unavoidable and the design goal is to reduce this distortion to a negligible level in order to allow a signal of acceptable quality to be reconstructed from samples even when the original signal is not strictly band limited. This and other issues to do with the sampling of base band and band pass signals as well as measures to mitigate practical constraints and distortions have been discussed in full.

5 Quantisation and PCM
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Logarithmic nonuniform quantisation that delivers a constant signaltoquantisation noise ratio (SQNR) across all input signal levels. The benefit and price of nonuniform quantisation are also quantified in terms of companding gain and companding penalty.A comprehensive treatment of Alaw and mlaw PCM source coding standards, including derivation of the standards from the ideal logarithmic compression curve through piecewise linear approximations, detailed SQNR analysis, and performance comparisons with linear ADC. Lossy data compression: A brief overview highlighting various categories of low bit rate speech coding, namely waveform coders, vocoders and hybrid coders. The discussion particularly focuses on speech quality measures and tradeoffs in low bit rate speech coding, and on differential quantisation, linear prediction and various special cases of bit rate reduction, including ADPCM, ADM and LPC10.

6 Source coding and lossless data compression
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This chapter treats in some detail the subject of lossless data compression, the aim of which is to minimise the number of bits needed to exactly represent a given source message. To understand how this is done and the challenges and constraints that face in compressing a message, information theory is discussed to introduce the concepts of information content of a character drawn at random from a discrete source and the entropy of such a source. Then three methods of lossless compression are discussed generally described as entropy coding since they aspire to match average codeword length to the entropy of the source. The methods discussed include Huffman coding, LempelZiv coding and arithmetic coding.

7 Line codes
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Line codes for application in digital base band transmission systems are intended to satisfy a number of features some of which contain elements of mutually conflicting requirements. The desirable characteristics include spectral content and shape that are suited to the transmission channel, no DC content, small bandwidth, guaranteed timing content, transparency and bit sequence independence, error detection and performance monitoring capability, high code efficiency, low error probability, and low codec complexity. No one code in the world has all these features so a decision on which code to use must be guided by the priorities of the particular application. The purpose of this chapter was to equip the reader with the tools needed to analyse the performance of line codes and to make informed decisions on their suitability for a desired application.

8 Transmission through band limited AWGN channels
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This chapter deals with the constraints set on symbol rate (i.e. how many pules we transmit per second) by the finite bandwidth of the transmission system or channel, and with the constraints set on bit rate and signal power by the noisiness of the transmission channel. We carefully quantify the challenges at hand and then explore practical measures that can be taken at the transmitter to minimise intersymbol interference (ISI) and at the receiver to maximise correct detection of incoming symbols in the presence of noise.

9 Transmitted digital signals
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This chapter deals with the geometric and complex representations of transmitted signals and noise in digital communications, and the correlation of signals. Working carefully through the material presented here will give you a thorough grounding in these vital concepts which have extensive applications in communication systems design and analysis, as highlighted at various points throughout the chapter. Computer simulation has now become an indispensable tool in the design of a communication system and the analysis of its performance. This chapter also aims to equip you with an excellent understanding of how transmitted signals and noise are represented for simulation purposes.

10 Noise impact in digital transmission
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Noise is inherent in all communications systems and the system designer does not need to incur huge system costs in pursuit of a goal of system noise reduction. In fact a zeronoise goal is not only unattainable; it is absolutely unnecessary. Given the right knowledge and skills, we can design very reliable transmission systems through noisy channels. In this chapter we have learnt the salient points about the statistical characterisation of random signals in general and AWGN in particular. We have also learnt how to quantify the noisiness of devices and systems and have applied this knowledge to communication system receivers, particularly radio reception systems, and have been able to calculate noise power per unit bandwidth at thereference point of such systems. We also learnt how to calculate signal power at the same point and hence to determine the ratio between carrier signal power and noise power C/N as well as the ratio between signal energy per bit and the noise power per unit bandwidth Eb/No. We also performed extensive analysis of the impact of noise on various digital transmission systems and derived expressions for the BER of such systems when coherent symbol detection is employed. We found that in each system BER depends entirely on Eb/No and it monotonically decreases asEb/No increases.

11 Error control coding
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Error control coding has been an area of intense research for more than 50 years and a vast array of techniques has been developed, which cannot all be covered even in a book devoted exclusively to coding. In this chapter, we primarily focus on imparting a clear understanding of the principles involved in error control coding in general, and on the parameters and design constraints that govern their use in communication system design. We also discuss linear binary block coding and the nonbinary ReedSolomon code, including a few worked examples to fully explain their coding and decoding algorithms.

12 Digital transmission link analysis and design
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The purpose of this brief concluding chapter is to introduce a useful tool called the link power budget, and to summarise the steps and considerations involved in communications link design and analysis.

Appendix A: Character codes
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Appendix B: Trigonometric identities
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This paper discusses trigonometric identities involved in digital communications. The paper begins with compound angle relations and goes on to discuss various identities.

Appendix C: Fourier transform
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A statement of the Fourier theorem is that any periodic signal gT(t) of period T, such as shown in Fig. C.1(a), can be expressed as the sum of sinusoids with frequencies at integer multiples (called harmonics) of the fundamental frequency, and with appropriate amplitudes and phases. Thus we have the Fourier series expression for gT(t): 1 X gT tÞ 1/4 Ao þ Ancos2nnfot þ ψnÞ n1/41 1 X Ao þ n1/41 1 Xancos2nnfotÞ þ n1/41 bn sin 2nnfotÞ 1 fo 1/4 C.1Þ T The coefficients in Eq. (C.1) are obtained as follows: Integrating both sides of Eq. (C.1) over an interval of one period Tyields the average value (or DC component) Ao of the periodic signal. First multiplying both sides by cos(2nmfot) before integrating over one period yields the mth cosine coefficient am; and multiplying first by sin(2nmfot) before integrating over one period gives the mth sine coefficient bm: Ao 1/4 an 1/4 T/2 1 ( TJ g tÞ dt T/2 T/2 2 ( TJ g tÞcos2nnfotÞ dt T/2 T/2 _ 2 bn T An 1/4 g tÞsin2nnfotÞ dt T/2 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2n þ b2 Amplitude of nth harmonic component n , ψn 1/4 arctan n/anÞ, Phase of nth harmonic component C.2Þ Employing Euler's formula exp(j2nnfot) 1/4 cos(2nnfot) þjsin(2nnfot) in Eq. (C.1) leads to the exponential form of Fourier series: where 1 X g tÞ 1/4 n1/41 Cnej2nnfot T/2 11 Cn 1/4 2an  jbnÞ 1/4 T gtÞe_j2nnfotdt T/2

Appendix D: Tables and constants
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Back Matter
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