Communication Systems

        We define communication as the process of information transfer across space or time. Communication across space is something we have an intuitive understanding of: for example, radio waves carry our phone conversation between our cell phone and the nearest base station, and coaxial cables (or optical fiber, or radio waves from a satellite) deliver television from a remote location to our home. However, a moment’s thought shows that that communication across time, or storage of information, is also an everyday experience, given our use of storage media such as compact discs (CDs), digital video discs (DVDs), hard drives and memory sticks. In all of these instances, the key steps in the operation of a communication link are as follows:

(a) insertion of information into a signal, termed the transmitted signal, compatible with the physical medium of interest.
(b) propagation of the signal through the physical medium (termed the channel) in space or
time;
(c) extraction of information from the signal (termed the received signal) obtained after propagation through the medium. 

        Communications systems can not only link people or systems at great distances via audio, visual, computer, or other messages, but may link the various parts within systems, and even within single semiconductor chips. They may communicate information in two directions, or only one way, and they may involve one node broadcasting to many, one node receiving from many, or a finite set of nodes communicating among themselves in a network. Even active measurement and remote sensing systems can be regarded as communications systems. In this case the transmitted signals are designed to be maxim ally sensitive to the channel characteristics, rather than insensitive, and the receiver’s task is to extract these channel characteristics knowing what was transmitted.  

        A two-node, one-way communication system consists of the channel that conveys the waves, together with a modulator and a demodulator. All communications systems can be regarded as aggregates of these basic two-node units. The modulator transforms the signal or symbol to be transmitted into the signal that is propagated across the channel; the channel may add noise and distortion. The task of the demodulator is to analyze the channel output and to make the best possible estimate of the exact symbol transmitted, accounting for the known channel characteristics and any user concerns about the relative importance of different sorts of errors. A sequence of symbols constitutes a message. A complete communications system is formed by combining many two-node, one-way systems in the desired configuration.
       Even without defining information formally, we intuitively understand that speech, audio, and video signals contain information. We use the term message signals for such signals, since these are the messages we wish to convey over a communication system. In their original form–both during generation and consumption–these message signals are analog: they are continuous time signals, with the signal values also lying in a continuum. When someone plays the violin, an analog acoustic signal is generated (often translated to an analog electrical signal using a microphone). Even when this music is recorded onto a digital storage medium such as a CD, when we ultimately listen to the CD being played on an audio system, we hear an analog acoustic signal. The transmitted signals corresponding to physical communication media are also analog. For example, in both wireless and optical communication, we employ electromagnetic waves, which correspond to continuous time electric and magnetic fields taking values in a continuum.

 Analog Communication

         Block diagram for an analog communication system. The modulator transforms the message signal into the transmitted signal. The channel distorts and adds noise to the transmitted signal. The demodulator extracts an estimate of the message signal from the received signal arriving from the channel. 

        Given the analog nature of both the message signal and the communication medium, a natural design choice is to map the analog message signal (e.g., an audio signal, translated from the acoustic to electrical domain using a microphone) to an analog transmitted signal (e.g., a radio wave carrying the audio signal) that is compatible with the physical medium over which we wish to communicate (e.g., broadcasting audio over the air from an FM radio station). This approach to communication system design, depicted in Figure 1.1, is termed analog communication. Early communication systems were all analog: examples include AM (amplitude modulation) and FM (frequency modulation) radio, analog television, first generation cellular phone technology (based on FM), vinyl records, audio cassettes, and VHS or beta videocassettes While analog communication might seem like the most natural option, it is in fact obsolete. Cellular phone technologies from the second generation onwards are digital, vinyl records and audio cassettes have been supplanted by CDs, and videocassettes by DVDs. Broadcast technologies such as radio and television are often slower to upgrade because of economic and political factors, but digital broadcast radio and television technologies are either replacing or sidestepping (e.g., via satellite) analog FM/AM radio and television broadcast. Let us now define what we mean by digital communication, before discussing the reasons for the inexorable trend away from analog and towards digital communication.

Digital Communication

        The conceptual basis for digital communication was established in 1948 by Claude Shannon, when he founded the field of information theory. There are two main threads to this theory: 

Source coding and compression: Any information-bearing signal can be represented efficiently, to within a desired accuracy of reproduction, by a digital signal (i.e., a discrete time signal taking values from a discrete set), which in its simplest form is just a sequence of binary digits (zeros or ones), or bits. This is true whether the information source is text, speech, audio or video. Techniques for performing the mapping from the original source signal to a bit sequence are generically termed source coding. They often involve compression, or removal of redundancy, in a manner that exploits the properties of the source signal (e.g., the heavy spatial correlation among adjacent pixels in an image can be exploited to represent it more efficiently than a pixel-by-pixel representation).

Digital information transfer: Once the source encoding is done, our communication task reduces to reliably transferring the bit sequence at the output of the source encoder across space or time, without worrying about the original source and the sophisticated tricks that have been used to encode it. The performance of any communication system depends on the relative strengths of the signal and noise or interference, and the distortions imposed by the channel. Shannon showed that, once we fix these operational parameters for any communication channel, there exists a maximum possible rate of reliable communication, termed the channel capacity. Thus, given the information bits at the output of the source encoder, in principle, we can transmit them reliably over a given link as long as the information rate is smaller than the channel capacity, and we cannot transmit them reliably if the information rate is larger than the channel capacity. This sharp transition between reliable and unreliable communication differs fundamentally from analog communication, where the quality of the reproduced source signal typically degrades gradually as the channel conditions get worse.

        A block diagram for a typical digital communication system based on these two threads is shown in Figure 1.2. We now briefly describe the role of each component, together with simplified examples of its function.

Source Encoder

As already discussed, the source encoder converts the message signal into a sequence of information bits. The information bit rate depends on the nature of the message signal (e.g., speech, audio, video) and the application requirements. Even when we fix the class of message signals, the choice of source encoder is heavily dependent on the setting. For example, video signals are heavily compressed when they are sent over a cellular link to a mobile device, but are lightly compressed when sent to an high definition television (HDTV) set. A cellular link can support a much smaller bit rate than, say, the cable connecting a DVD player to an HDTV set, and a smaller mobile display device requires lower resolution than a large HDTV screen. In general, the source encoder must be chosen such that the bit rate it generates can be supported by the digital communication link we wish to transfer information over. Other than this, source coding can be decoupled entirely from link design (we comment further on this a bit later).

Example: A laptop display may have resolution 1024×768 pixels. For a grayscale digital image, the intensity for each pixel might be represented by 8 bits. Multiplying by the number of pixels gives us about 6.3 million bits, or about 0.8 Mbyte (a byte equals 8 bits). However, for a typical image, the intensities for neighboring pixels are heavily correlated, which can be exploited for significantly reducing the number of bits required to represent the image, without noticeably distorting it. For example, one could take a two-dimensional Fourier transform, which concentrates most of the information in the image at lower frequencies and then discard many of the high frequency coefficients. There are other possible transforms one could use, and also several more processing stages, but the bottomline is that, for natural images, state of the art image compression algorithms can provide 10X compression (i.e., reduction in the number of bits relative to the original uncompressed digital image) with hardly any perceptual degradation. Far more aggressive compression ratios are possible if we are willing to tolerate more distortion. For video, in addition to the spatial correlation exploited for image compression, we can also exploit temporal correlation across successive frames.

Channel encoder 

The channel encoder adds redundancy to the information bits obtained from the source encoder, in order to facilitate error recovery after transmission over the channel. It might appear that we are putting in too much work, adding redundancy just after the source encoder has removed it. However, the redundancy added by the channel encoder is tailored to the channel over which information transfer is to occur, whereas the redundancy in the original message signal is beyond our control, so that it would be inefficient to keep it when we transmit the signal over the channel.

Example: The noise and distortion introduced by the channel can cause errors in the bits we send over it. Consider the following abstraction for a channel: we can send a string of bits (zeros or ones) over it, and the channel randomly flips each bit with probability 0.01 (i.e., the channel has a 1% error rate). If we cannot tolerate this error rate, we could repeat each bit that we wish to send three times, and use a majority rule to decide on its value. Now, we only make an error if two or more of the three bits are flipped by the channel. It is left as an exercise to calculate that an error now happens with probability approximately 0.0003 (i.e., the error rate has gone down to 0.03%). That is, we have improved performance by introducing redundancy. Of course, there are far more sophisticated and efficient techniques for introducing redundancy than the simple repetition strategy just described.

Modulator 

The modulator maps the coded bits at the output of the channel encoder to a transmitted signal to be sent over the channel. For example, we may insist that the transmitted signal fit within a given frequency band and adhere to stringent power constraints in a wireless system, where interference between users and between co-existing systems is a major concern. Unlicensed WiFi transmissions typically occupy 20-40 MHz of bandwidth in the 2.4 or 5 GHz bands. Transmissions in fourth generation cellular systems may often occupy bandwidths ranging from 1-20 MHz at frequencies ranging from 700 MHz to 3 GHz. While these signal bandwidths are being increased in an effort to increase data rates (e.g., up to 160 GHz for emerging WiFi standards, and up to 100 MHz for emerging cellular standards), and new frequency bands are being actively explored (see the epilogue for more discussion), the transmitted signal still needs to be shaped to fit within certain spectral constraints.

Example: Suppose that we send bit value 0 by transmitting the signal s(t), and bit value 1 by transmitting −s(t). Even for this simple example, we must design the signal s(t) so it fits within spectral constraints (e.g., two different users may use two different segments of spectrum to avoid interfering with each other), and we must figure out how to prevent successive bits of the same user from interfering with each other. For wireless communication, these signals are voltages generated by circuits coupled to antennas, and are ultimately emitted as electromagnetic waves from the antennas.

The channel encoder and modulator are typically jointly designed, keeping in mind the anticipated channel conditions, and the result is termed a coded modulator.

Channel 

The channel distorts and adds noise, and possibly interference, to the transmitted signal. Much of our success in developing communication technologies has resulted from being able to optimize communication strategies based on accurate mathematical models for the channel. Such models are typically statistical, and are developed with significant effort using a combination of measurement and computation. The physical characteristics of the communication medium vary widely, and hence so do the channel models. Wireline channels are typically well modeled as linear and time-invariant, while optical fiber channels exhibit nonlinearities. Wireless mobile channels are particularly challenging because of the time variations caused by mobility, and due to the potential for interference due to the broadcast nature of the medium. The link design also depends on system-level characteristics, such as whether or not the transmitter has feedback regarding the channel, and what strategy is used to manage interference.

Example: Consider communication between a cellular base station and a mobile device. The electromagnetic waves emitted by the base station can reach the mobile’s antennas through multiple paths, including bounces off streets and building surfaces. The received signal at the mobile can be modeled as multiple copies of the transmitted signal with different gains and delays. These gains and delays change due to mobility, but the rate of change is often slow compared to the data rate, hence over short intervals, we can get away with modeling the channel as a linear time-invariant system that the transmitted signal goes through before arriving at the receiver.

Demodulator 

The demodulator processes the signal received from the channel to produce bit estimates to be fed to the channel decoder. It typically performs a number of signal processing tasks, such as synchronization of phase, frequency and timing, and compensating for distortions induced by the channel.

Example: Consider the simplest possible channel model, where the channel just adds noise to the transmitted signal. In our earlier example of sending ±s(t) to send 0 or 1, the demodulator must guess, based on the noisy received signal, which of these two options is true. It might make a hard decision (e.g., guess that 0 was sent), or hedge its bets, and make a soft decision, saying, for example, that it is 80% sure that the transmitted bit is a zero. There are a host of other aspects of demodulation that we have swept under the rug: for example, before making any decisions, the demodulator has to perform functions such as synchronization (making sure that the receiver’s notion of time and frequency is consistent with the transmitter’s) and equalization (compensating for the distortions due to the channel).

Channel decoder 

The channel decoder processes the imperfect bit estimates provided by the demodulator, and exploits the controlled redundancy introduced by the channel encoder to estimate the information bits.

Example: The channel decoder takes the guesses from the demodulator and uses the redundancies in the channel code to clean up the decisions. In our simple example of repeating every bit three times, it might use a majority rule to make its final decision if the demodulator is putting out hard decisions. For soft decisions, it might use more sophisticated combining rules with improved performance.

While we have described the demodulator and decoder as operating separately and in sequence for simplicity, there can be significant benefits from iterative information exchange between the two. In addition, for certain coded modulation strategies in which channel coding and modulation are tightly coupled, the demodulator and channel decoder may be integrated into a single entity. 

Source decoder 

The source decoder processes the estimated information bits at the output of the channel decoder to obtain an estimate of the message. The message format may or may not be the same as that of the original message input to the source encoder: for example, the source encoder may translate speech to text before encoding into bits, and the source decoder may output a text message to the end user.

Example: For the example of a digital image considered earlier, the compressed image can be translated back to a pixel-by-pixel representation by taking the inverse spatial Fourier transform of the coefficients that survived the compression. We are now ready to compare analog and digital communication, and discuss why the trend towards digital is inevitable.

Comparing the block diagrams for analog and digital communication, respectively, we see that the digital communication system involves far more processing. However, this is not an obstacle for modern transceiver design, due to the exponential increase in the computational power of low-cost silicon integrated circuits. Digital communication has the following key advantages.

Optimality 

For a point-to-point link, it is optimal to separately optimize source coding and channel coding, as long we do not mind the delay and processing incurred in doing so. Due to this source-channel separation principle, we can leverage the best available source codes and the best available channel codes in designing a digital communication system, independently of each other. Efficient source encoders must be highly specialized. For example, state of the art speech encoders, video compression algorithms, or text compression algorithms are very different from each other, and are each the result of significant effort over many years by a large community of researchers. However, once source encoding is performed, the coded modulation scheme used over the communication link can be engineered to transmit the information bits reliably, regardless of what kind of source they correspond to, with the bit rate limited only by the channel and transceiver characteristics. Thus, the design of a digital communication link is source-independent and channel-optimized. In contrast, the waveform transmitted in an analog communication system depends on the message signal, which is beyond the control of the link designer, hence we do not have the freedom to optimize link performance over all possible communication schemes. This is not just a theoretical observation: in practice, huge performance gains are obtained from switching from analog to digital communication.

Scalability 

While a single digital communication link between source encoder and decoder, under the source-channel separation principle, there is nothing preventing us from inserting additional links, putting the source encoder and decoder at the end points. This is because digital communication allows ideal regeneration of the information bits, hence every time we add a link, we can focus on communicating reliably over that particular link. (Of course, information bits do not always get through reliably, hence we typically add error recovery mechanisms such as retransmission, at the level of an individual link or “end-to-end” over a sequence of links between the information source and sink.) Another consequence of the source-channel separation principle is that, since information bits are transported without interpretation, the same link can be used to carry multiple kinds of messages. A particularly useful approach is to chop the information bits up into discrete chunks, or packets, which can then be processed independently on each link. These properties of digital communication are critical for enabling massively scalable, general purpose, communication networks such as the Internet.

Such networks can have large numbers of digital communication links, possibly with different characteristics, independently engineered to provide “bit pipes” that can support data rates. Messages of various kinds, after source encoding, are reduced to packets, and these packets are switched along different paths along the network, depending on the identities of the source and destination nodes, and the loads on different links in the network. None of this would be possible with analog communication: link performance in an analog communication system depends on message properties, and successive links incur noise accumulation, which limits the number of links which can be cascaded.

The preceding makes it clear that source-channel separation, and the associated bit pipe abstraction, is crucial in the formation and growth of modern communication networks. However, there are some important caveats that are worth noting. Joint source-channel design can provide better performance in some settings, especially when there are constraints on delay or complexity, or if multiple users are being supported simultaneously on a given communication medium. In practice, this means that “local” violations of the separation principle (e.g., over a wireless last hop in a communication network) may be a useful design trick. Similarly, the bit pipe abstraction used by network designers is too simplistic for the design of wireless networks at the edge of the

Internet 

physical properties of the wireless channel such as interference, multi path propagation and mobility must be taken into account in network engineering.

Why analog design remains important??

While we are interested in transporting bits in digital communication, the physical link over which these bits are sent is analog. Thus, analog and mixed signal (digital/analog) design play a crucial role in modern digital communication systems. Analog design of digital-to-analog converters, mixers, amplifiers and antennas is required to translate bits to physical wave-forms to be emitted by the transmitter. At the receiver, analog design of antennas, amplifiers, mixers and analog-to-digital converters is required to translate the physical received wave-forms to digital (discrete valued, discrete time) signals that are amenable to the digital signal processing that is at the core of modern transceivers. Analog circuit design for communications is therefore a thriving field in its own right, which this textbook makes no attempt to cover. However, the material in Chapter 3 on analog communication techniques is intended to introduce digital communication system designers to some of the high-level issues addressed by analog circuit designers. The goal is to establish enough of a common language to facilitate interaction between system and circuit designers. While much of digital communication system design can be carried out by abstracting out the intervening analog design (as done in Chapters 4 through 8), closer interaction between system and circuit designers becomes increasingly important as we push the limits of communication systems, as briefly indicated in the epilogue.