《通信原理与实验 Principles and Experiments of Communications》课程参考书：John G. Proakis Masoud Salehi《Fundamentals of Communication Systems》（Second Edition）

Section 1.3 Communication Channels and Their Characteristics 17 example,microwave radio relay systems used extensively for telephone and video trans- mission at frequencies above 1 GHz have antennas mounted on tall towers or on the top of tall buildings. At frequencies above 10 GHz,atmospheric conditions play a major role in signal propagation.In particular,heavy rain introduces extremely high propagation losses that can result in service outages(total breakdown in the communication system).For example,at 10 GHz,heavy rain results in a propagation loss of approximately 0.3 dB/km;at 30 GHz, the loss in approximately 2 dB/km;at 100 GHz,the loss is approximately 5 dB/km. At frequencies above the millimeter wave band,we have the infrared and visible light regions of the electromagnetic spectrum,which can be used to provide LOS optical com- munication in free space.To date,these frequency bands have been used in experimental communication systems,such as satellite-to-satellite links. Underwater Acoustic Channels.Over the past few decades,ocean exploration activity has been steadily increasing.Coupled with this increase in ocean exploration is the need to transmit data,which is collected by sensors placed underwater,to the surface of the ocean.From there,it is possible to relay the data via a satellite to a data collection center. Electromagnetic waves do not propagate over long distances underwater,except at extremely low frequencies.However,the transmission of signals at such low frequencies is prohibitively expensive because of the large and powerful transmitters required.The atten- uation of electromagnetic waves in water can be expressed in terms of the skin depth,which is the distance a signal is attenuated by 1/e.For seawater,the skin depth 8=250/f, where f is expressed in Hertz and 8 is in meters.For example,at 10 kHz,the skin depth is 2.5 meters.In contrast,acoustic signals propagate over distances of tens and even hundreds of kilometers. A shallow-water acoustic channel is characterized as a multipath channel due to sig- nal reflections from the surface and the bottom of the sea.Due to wave motion,the signal multipath components undergo time-varying propagation delays that result in signal fading. In addition,there is frequency-dependent attenuation,which is approximately proportional to the square of the signal frequency. Ambient ocean acoustic noise is caused by shrimp,fish,and various mammals.Addi- tionally,man-made acoustic noise exists near harbors. In spite of this hostile environment,it is possible to design and implement efficient and highly reliable underwater acoustic communication systems for transmitting digital signals over large distances. Storage Channels.Information storage and retrieval systems constitute a signif- icant part of our data-handling activities on a daily basis.Magnetic tape (including digital audio tape and video tape),magnetic disks(used for storing large amounts of computer data),and optical disks(used for computer data storage,music,and video)are examples of data storage systems that can be characterized as communication channels.The process of storing data on a magnetic tape,magnetic disk,or optical disk is equivalent to transmitting a signal over a telephone or a radio channel.The readback process and the signal process- ing used to recover the stored information is equivalent to the functions performed by a telephone receiver or radio communication system to recover the transmitted information

Section 1.3 Communication Channels and Their Characteristics 17 example, microwave radio relay systems used extensively for telephone and video trans￾mission at frequencies above 1 GHz have antennas mounted on tall towers or on the top of tall buildings. At frequencies above 10 GHz, atmospheric conditions play a major role in signal propagation. In particular, heavy rain introduces extremely high propagation losses that can result in service outages (total breakdown in the communication system). For example, at 10 GHz, heavy rain results in a propagation loss of approximately 0.3 dB/km; at 30 GHz, the loss in approximately 2 dB/km; at 100 GHz, the loss is approximately 5 dB/km. At frequencies above the millimeter wave band, we have the infrared and visible light regions of the electromagnetic spectrum, which can be used to provide LOS optical com￾munication in free space. To date, these frequency bands have been used in experimental communication systems, such as satellite-to-satellite links. � Underwater Acoustic Channels. Over the past few decades, ocean exploration activity has been steadily increasing. Coupled with this increase in ocean exploration is the need to transmit data, which is collected by sensors placed underwater, to the surface of the ocean. From there, it is possible to relay the data via a satellite to a data collection center. Electromagnetic waves do not propagate over long distances underwater, except at extremely low frequencies. However, the transmission of signals at such low frequencies is prohibitively expensive because of the large and powerful transmitters required. The atten￾uation of electromagnetic waves in water can be expressed in terms of the skin depth, which is the distance a �ignal is attenuated by 1 / e. For seawater, the skin depth 8 = 250 / ,,JJ, where f is expressed in Hertz and 8 is in meters. For example, at 10 kHz, the skin depth is 2.5 meters. In contrast, acoustic signals propagate over distances of tens and even hundreds of kilometers. A shallow-water acoustic channel is characterized as a multipath channel due to sig￾nal reflections from the surface and the bottom of the sea. Due to wave motion, the signal multipath components undergo time-varying propagation delays that result in signal fading. In addition, there is frequency-dependent attenuation, which is approximately proportional to the square of the signal frequency. Ambient ocean acoustic noise is caused by shrimp, fish, and various mammals. Addi￾tionally, man-made acoustic noise exists near harbors. In spite of this hostile environment, it is possible to design and implement efficient and highly reliable underwater acoustic communication systems for transmitting digital signals over large distances. Storage Channels. Information storage and retrieval systems constitute a signif￾icant part of our data-handling activities on a daily basis. Magnetic tape (including digital audio tape and video tape), magnetic disks (used for storing large amounts of computer data), and optical disks (used for computer data storage, music, and video) are examples of data storage systems that can be characterized as communication channels. The process of storing data on a magnetic tape, magnetic disk, or optical disk is equivalent to transmitting a signal over a telephone or a radio channel. The readback process and the signal process￾ing used to recover the stored information is equivalent to the functions performed by a telephone receiver or radio communication system to recover the transmitted information

18 Introduction Chapter 1 Additive noise generated by the electronic components and interference from adja- cent tracks is generally present in the readback signal of a storage system. The amount of data that can be stored is generally limited by the size of the disk or tape and the density(number of bits stored per square inch)that can be achieved by the write/read electronic systems and heads.For example,a packing density of 109 bits/sq in has been achieved in magnetic disk storage systems.The speed at which data can be written on a disk or tape and the speed at which it can be read back is also limited by the associated mechanical and electrical subsystems that constitute an information storage system. Channel coding and modulation are essential components of a well-designed digital magnetic or optical storage system.In the readback process,the signal is demodulated and the added redundancy introduced by the channel encoder is used to correct errors in the readback signal. 1.4 MATHEMATICAL MODELS FOR COMMUNICATION CHANNELS While designing communication systems to transmit information through physical chan- nels,we find it convenient to construct mathematical models that reflect the most important characteristics of the transmission medium.Then the mathematical model for the channel is used in the design of the channel encoder and modulator at the transmitter and the demod- ulator and channel decoder at the receiver.Next,we provide a brief description of three channel models that are frequently used to characterize many of the physical channels that we encounter in practice. The Additive Noise Channel.The simplest mathematical model for a commu- nication channel is the additive noise channel,illustrated in Figure 1.7.In this model,the transmitted signal s(t)is corrupted by the additive random-noise process n(t).Physically, the additive noise process may arise from electronic components and amplifiers at the receiver of the communication system,or from interference encountered in transmission, as in the case of radio signal transmission. If the noise is introduced primarily by electronic components and amplifiers at the receiver,it may be characterized as thermal noise.This type of noise is characterized sta- tistically as a Gaussian noise process.Hence,the resulting mathematical model for the channel is usually called the additive Gaussian noise channel.Because this channel model applies to a broad class of physical communication channels and because it has mathemat- ical tractability,this is the predominant channel model used in the analysis and design of communication systems.Channel attenuation is easily incorporated into the model. Channel s() →r()=s()+n() n() Figure 1.7 The additive noise channel

18 Introduction Chapter 1 Additive noise generated by the electronic components and interference from adja￾cent tracks is generally present in the readback signal of a storage system. The amount of data that can be stored is generally limited by the size of the disk or tape and the density (number of bits stored per square inch) that can be achieved by the write/read electronic systems and heads. For example, a packing density of 109 bits/sq in has been achieved in magnetic disk storage systems. The speed at which data can be written on a disk or tape and the speed at which it can be read back is also limited by the associated mechanical and electrical subsystems that constitute an information storage system. Channel coding and modulation are essential components of a well-designed digital magnetic or optical storage system. In the readback process, the signal is demodulated and the added redundancy introduced by the channel encoder is used to correct errors in the readback signal. 1.4 MATHEMATICAL MODELS FOR COMMUNICATION CHANNELS While designing communication systems to transmit information through physical chan￾nels, we find it convenient to construct mathematical models that reflect the most important characteristics of the transmission medium. Then the mathematical model for the channel is used in the design of the channel encoder and modulator at the transmitter and the demod￾ulator and channel decoder at the receiver. Next, we provide a brief description of three channel models that are frequently used to characterize many of the physical channels that we encounter in practice. The Additive Noise Channel. The simplest mathematical model for a commu￾nication channel is the additive noise channel, illustrated in Figure 1. 7. In this model, the transmitted signal s(t) is corrupted by the additive random-noise process n(t). Physically, the additive noise process may arise from electronic components and amplifiers at the receiver of the communication system, or from interference encountered in transmission, as in the case of radio signal transmission. If the noise is introduced primarily by electronic components and amplifiers at the receiver, it may be characterized as thermal noise. This type of noise is characterized sta￾tistically as a Gaussian noise process. Hence, the resulting mathematical model for the channel is usually called the additive Gaussian noise channel. Because this channel model applies to a broad class of physical communication channels and because it has mathemat￾ical tractability, this is the predominant channel model used in the analysis and design of communication systems. Channel attenuation is easily incorporated into the model. Channel s (t) 1----1--,..._ r(t) = s(t) + n (t) n (t) Figure 1.7 The additive noise channel

Section 1.4 Mathematical Models for Communication Channels 19 When the signal undergoes attenuation in transmission through the channel,the received signal is r(t)=as()+n(t), (1.4.1) where a represents the attenuation factor. The Linear Filter Channel.In some physical channels,such as wireline tele- phone channels,filters are used to ensure that the transmitted signals do not exceed spec- ified bandwidth limitations;thus,they do not interfere with one another.Such channels are generally characterized mathematically as linear filter channels with additive noise,as illustrated in Figure 1.8.Hence,if the channel input is the signal s(r),the channel output is the signal r(t)=s(t)*h(t)+n(t) =h(t)s(t-r)dr+n(t), (1.4.2) Jo where h(t)is the impulse response of the linear filter and denotes convolution. The Linear Time-Variant Filter Channel.Physical channels,such as underwa- ter acoustic channels and ionospheric radio channels,which result in time-variant multipath propagation of the transmitted signal,may be characterized mathematically as time-variant linear filters.Such linear filters are characterized by the time-variant channel impulse response h(r;t),where h(t;t)is the response of the channel at time t,due to an impulse applied at time t-t.Thus,t represents the "age"(elapsed time)variable.The linear time- variant filter channel with additive noise is illustrated in Figure 1.9.For an input signal s(t),the channel output signal is s(t) Linear filter →r)=s()*h(0+n() h(t) n() Channel Figure 1.8 The linear filter channel with additive noise. s() Linear time-variant r(0 filter h(;t) n() Channel Figure 1.9 Linear time-variant filter channel with additive noise

Section 1 .4 M athematical Models for Communication Channels 19 When the signal undergoes attenuation in transmission through the channel, the received signal is r (t) = as(t) + n(t), ( 1.4. l) where a represents the attenuation factor. The Linear Filter Channel. In some physical channels, such as wireline tele￾phone channels, filters are used to ensure that the transmitted signals do not exceed spec￾ified bandwidth limitations; thus, they do not interfere with one another. Such channels are generally characterized mathematically as linear filter channels with additive noise, as illustrated in Figure 1.8. Hence, if the channel input is the signal s(t), the channel output is the signal r (t) = s(t) * h(t) + n (t) = l:xo h(r)s(t - r) dr + n(t), ( 1.4.2) where h(t) is the impulse response of the linear filter and * denotes convolution. The Linear Time-Variant Filter Channel. Physical channels, such as underwa￾ter acoustic channels and ionospheric radio channels, which result in time-variant multipath propagation of th� transmitted signal, may be characterized mathematically as time-variant linear filters. Such linear filters are characterized by the time-variant channel impulse response h ( r; t), where ,; ( r; t) is the response of the channel at time t, due to an impulse applied at time t - r. Thus, r represents the "age" (elapsed time) variable. The linear time￾variant filter channel with additive noise is illustrated in Figure 1.9. For an input signal s(t), the channel output signal is r----------------- --- 1 I I I I s(t) 1 Linear 1 _ ___, i,.......;� filter >-- 1---i � r(t) = s(t) * h(t) + n(t) : h(t) I I : �0 I 1 Channel : l--------------------� r-------------------- 1 I I I I () 1 Linear 1 _s_t_i-.. time-variant >-- 1---, � r(t) filter h ( r; t) : I Figure 1.8 The linear filter channel with additive noise. n (t) : Channel I l--------------------� Figure 1.9 Linear time-variant filter channel with additive noise

20 Introduction Chapter 1 r(I)=s(t)*h(t;)+() 00 =h(;t)s(t-t)dr+n(t) (1.4.3) Let us consider signal propagation through a multipath channel,such as the iono- sphere(at frequencies below 30 MHz)and mobile cellular radio channels.For such chan- nels,a good model for the time-variant impulse response has the form L h(r:0=∑a()(x-t). (1.4.4) k=1 where the (ak(t))represents the possibly time-variant attenuation factor for the L multipath propagation paths.If Equation (1.4.4)is substituted into Equation (1.4.3),the received signal has the form L r)=∑a)s-)+n). (1.4.5) k=1 Hence,the received signal consists of L multipath components,where each component is attenuated by (ak)and delayed by () The three mathematical models previously described characterize a majority ofphys- ical channels encountered in practice.These three channel models are used in this text for the analysis and design of communication systems. 1.5 SUMMARY AND FURTHER READING Following a brief historical review of telecommunication developments over the past two centuries,we presented an introduction of the basic elements of analog and digital commu- nication systems and described several important advances in the development of digital communications in the first 60 years of the twentieth century.The second part of this chapter focused on the characteristics of different types of wireline and wireless commu- nication channels,including their mathematical models which are used in the design and performance analysis of communication systems. We have already cited several historical books on radio and telecommunications pub- lished in the past century.These include the books by McMahon (1984),Ryder and Fink (1984),and Millman (1984).In addition,the classical works of Nyquist (1924),Hartley (1928),Kotelnikov (1947),Shannon (1948),and Hamming (1950)are particularly impor- tant because they lay the groundwork of modern communication systems engineering

20 Introduction Chapter 1 r(t) = s(t) * h(r; t) + n(t) = 1: h(r; t)s(t - r) dr + n(t). ( l.4.3) Let us consider signal propagation through a multipath channel, such as the iono￾sphere (at frequencies below 30 MHz) and mobile cellular radio channels. For such chan￾nels, a good model for the time-variant impulse response has the form L h(r; t) = I >k(t)o(r - rk), ( l.4.4) k=I where the { ak (t)} represents the possibly time-variant attenuation factor for the L multipath propagation paths. If Equation (l.4.4) is substituted into Equation (l.4.3), the received signal has the form L r(t) = L ak(t)s(t - Tk) + n(t). ( l.4.5) k=I Hence, the received signal consists of L multipath components, where each component is attenuated by { ak} and delayed by { rk}. The three mathematical models previously described characterize a majority of phys￾ical channels encountered in practice. These three channel models are used in this text for the analysis and design of communication systems. 1.5 SUMMARY AND FURTHER READING Following a brief historical review of telecommunication developments over the past two centuries, we presented an introduction of the basic elements of analog and digital commu￾nication systems and described several important advances in the development of digital communications in the first 60 years of the twentieth century. The second part of this chapter focused on the characteristics of different types of wireline and wireless commu￾nication channels, including their mathematical models which are used in the design and performance analysis of communication systems. We have already cited several historical books on radio and telecommunications pub￾lished in the past century. These include the books by McMahon ( 1984), Ryder and Fink ( 1984), and Millman ( 1984). In addition, the classical works of Nyquist ( 1924), Hartley ( 1928), Kotelnikov ( 1947), Shannon ( 1948), and Hamming ( 1950) are particularly impor￾tant because they lay the groundwork of modern communication systems engineering

CHAPTER Signals and Linear Systems In this chapter,we will review the basics of signals and linear systems.The motivation for studying these fundamental concepts stems from the basic role they play in modeling various types of communication systems.In particular,signals are used to transmit infor- mation over a communication channel.Such signals are usually called information-bearing signals.Speech signals,video signals,and the output of an ASCII terminal are examples of information-bearing signals. When an information-bearing signal is transmitted over a communication channel, the shape of the signal is changed,or distorted,by the channel.In other words,the output of the communication channel,which is called the received signal,is not an exact replica of the channel input due to many factors,including channel distortion.The communication channel is an example of a system,i.e.,an entity that produces an output signal when excited by an input signal.A large number of communication channels can be modeled closely by a subclass of systems called linear systems.Linear systems arise naturally in many practical applications and are rather easy to analyze. 2.1 BASIC CONCEPTS In this book,we generally deal with communication signals that are functions of time, i.e.,time is the independent variable.Examples of such signals are audio signals(speech, music),video signals,and data signals.Such signals are represented as mathematical func- tions of the form s(t),or x(t),or f(r).As an example,a sample waveform of a speech signal is shown in Figure 2.1. 2.1.1 Basic Operations on Signals Basic operations on signals involve time shifting,time reversal(flipping),and time scaling. In this section,we describe the effect of these operations on signals. Time Shifting.Shifting,or delaying,a signal x(t)by a given constant time to results in the signal x(t-to).If to is positive,this action is equivalent to a delay of to;thus, 21

Signals and Linear Systems In this chapter, we will review the basics of signals and linear systems. The motivation for studying these fundamental concepts stems from the basic role they play in modeling various types of communication systems. In particular, signals are used to transmit infor￾mation over a communication channel. Such signals are usually called information-bearing signals. Speech signals, video signals, and the output of an ASCII terminal are examples of information-bearing signals. When an information-bearing signal is transmitted over a communication channel, the shape of the signal is changed, or distorted, by the channel. In other words, the output of the communication channel, which is called the received signal, is not an exact replica of the channel input due to many factors, including channel distortion. The communication channel is an example of a system, i.e., an entity that produces an output signal when excited by an input signal. A large number of communication channels can be modeled closely by a subclass of systems called linear systems. Linear systems arise naturally in many practical applications and are rather easy to analyze. 2.1 BASIC CONCEPTS In this book, we generally deal with communication signals that are functions of time, i.e., time is the independent variable. Examples of such signals are audio signals (speech, music), video signals, and data signals. Such signals are represented as mathematical func￾tions of the form s(t), or x(t), or f(t). As an example, a sample waveform of a speech signal is shown in Figure 2.1. 2.1.1 Basic Operations on Signals Basic operations on signals involve time shifting, time reversal (flipping), and time scaling. In this section, we describe the effect of these operations on signals. Time Shifting. Shifting, or delaying, a signal x (t) by a given constant time to results in the signal x (t - t0). If to is positive, this action is equivalent to a delay of t0; thus, 21