【正文】 in the munication system). At frequencies above the EHF (extremely high frequency) band, we have the infrared and visible light regions of the electromagic spectrum, which can be used to provide LOS optical munication in free space. To date, these frequency bands have been used in experimental munication systems, such as satellitetosatellite links. Underwater Acoustic Channels Over the past few decades, ocean exploration activity has been steadily increasing. Coupled with this increase is the need to transmit data, collected by sensors placed under water, to the surface of the ocean. From there, it is possible to relay the data via a satellite to a data collection center. Electromagic waves do not propagate over long distances under water 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 attenuation of electromagic waves in water can be expressed in terms of the skin depth, which is the distance a signal is attenuated by 1/r. For sea water, the skin depth 250/v7, where f is expressed in Hz and 8 is in m. For example, at 10 kHz. the skin depth is m. In contrast, acoustic signals propagate over distances of tens and even hundreds of kilometers. An underwater acoustic channel is characterized as a multipath channel due to signal reflections from the surface and the bottom of the sea. Because of wave motion, the signal multipath ponents undergo timevarying 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. The sound velocity is nominally about 1500 m/s, but the actual value will vary either above or below the nominal value depending on the depth at which the signal propagates. Ambient ocean acoustic noise is caused by shrimp, fish, and various mammals. Near harbors, there is also manmade acoustic noise in addition to the ambient noise. In spite of this hostile environment, it is possible to design and implement efficient and highly reliable underwater acoustic munication systems for transmitting digital signals over large distances. Storage Channels Information storage and retrieval systems constitute a very significant part of datahandling activities on a daily basis. Magic (ape, including digital audio tape and video tape, magic disks used for storing large amounts of puter data, optical disks used for puter data storage, and pact disks are examples of data storage systems that can be characterized as munication channels. The process of storing data on a magic tape or a magic or optical disk is equivalent to transmitting a signal over a telephone or a radio channel. The read back process and the signal processing involved in storage systems to recover the stored information are equivalent to the functions performed by a receiver in a telephone or radio munication system to recover the transmitted information. Additive noise generated by the electronic ponents and interference from adjacent tracks is generally present in the read back signal of a storage system, just as is the case in a telephone or a radio munication 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 10 bits per square inch has been recently demonstrated in an experimental magic disk storage system. (Current mercial magic storage products achieve a much lower density.) The speed ai which data can be written on a disk or tape and the speed at which it can be read back are also limited by the associated mechanical and electrical subsystems that constitute an information storage system. Channel coding and modulation are essential ponents of a welldesigned digital magic or optical storage system. In the read back process, (he signal is demodulated and the added redundancy introduced by the channel encoder is used to correct errors in the read back signal. 13 MATHEMATICAL MODELS FOR COMMUNICATION CHANNELS In the design of munication systems for transmitting information through physical channels, 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 demodulator and channel decoder at the receiver. Below, provide a brief description of the 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 munication channel is the additive noise channel, illustrated in Fig. this model, the transmitted signal s(r) is corrupted by an additive random noise process。 上面描述的三種數(shù)學(xué)模型適當(dāng)?shù)谋碚髁藢?shí)際中的絕大多數(shù)物理信道。該線性濾波器可以表征為時(shí)變信道沖激響應(yīng) c（τ； t），這里 c（τ； t）是信道在 tτ時(shí)刻加入沖激而在τ時(shí)刻的響應(yīng)。因此，如果信道輸入信號(hào)為 s（ t），那么信道輸出信號(hào)是 )()()()( tntctstr ??? ? ????? ?? )()()( tndtsc ??? 式中， )(?c 是信道的沖激響應(yīng)， ? 表示卷積。 圖 131 加性噪聲信道 2. 線性濾波器信道 在某些物理信道中，例如有線電話信道，采用濾波器來(lái)保證傳輸信號(hào)不超過(guò)規(guī)定的帶寬限制，從而不會(huì)引起相互干擾。信道的衰減很容易加入到該模型。因此，該信道的數(shù)學(xué)模型通常稱為加性高斯噪聲信道。 如果噪聲主要是由接收機(jī)中的元部件和放大器引起，那么，它可以表征為熱噪聲。在這個(gè)模型中，發(fā)送信號(hào) s（ t）被加性隨機(jī)噪聲過(guò)程 n（ t）惡化。下面，我們將簡(jiǎn)要的描述信道的模型，它們常用來(lái)表征實(shí)際的物理信道。 通信信道的數(shù)學(xué)模型 在通過(guò)物理信道傳輸信息的通信系統(tǒng)設(shè)計(jì)中，我們發(fā)現(xiàn)，建立一個(gè)能反映傳輸媒質(zhì)最重要特征的數(shù)學(xué)模型是很方便的。在回讀過(guò)程中，信號(hào)被解調(diào)。磁盤(pán)或磁帶上的數(shù)據(jù)的讀寫(xiě)速度也受到組成信息存儲(chǔ)系統(tǒng)的機(jī)械和電子子系統(tǒng)的限制。 所能存儲(chǔ)的數(shù)據(jù)量一般受到磁盤(pán)或磁帶尺寸及密度（每平方英寸存儲(chǔ)的比特?cái)?shù)）的限制，該密度是由寫(xiě) /讀電系統(tǒng)和讀寫(xiě)頭確定的?；刈x過(guò)程以及在存儲(chǔ)系統(tǒng)中恢復(fù)所存儲(chǔ)的數(shù)據(jù)的信號(hào)處理等效于在電話和無(wú)線通信系統(tǒng)中恢 復(fù)發(fā)送信號(hào)。磁帶（包括數(shù)字的聲帶和錄像帶）、用來(lái)存儲(chǔ)大量計(jì)算機(jī)數(shù)據(jù)的磁盤(pán)、用作計(jì)算機(jī)數(shù)據(jù)存儲(chǔ)器的光盤(pán)以及只讀光盤(pán)都是數(shù)據(jù)存儲(chǔ)系統(tǒng)的例子 ,它們可以表征為通信信道。盡管有這些不利的環(huán)境，還是可能設(shè)計(jì)并實(shí)現(xiàn)有效的且高可靠性的水聲通信系統(tǒng) ,以長(zhǎng)距離地傳輸數(shù)字信號(hào)。