Chapter 0. Overview. 0.1 Digital communication systems

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1 Chapter 0 Overview Our goal is to acquire a basic understanding of digital communications. To do so, we study the basic design and analysis principles of digital communication systems. This set of notes is written for the purpose. It can be divided into two parts. The rst part describes, in detail, some common digital modulation and demodulation techniques, which form the basis of digital communications. The second part presents a survey of various advanced topics, such as synchronization, equalization, diversity reception, and error control coding. The combination of the two parts aims to provide a solid introduction to modern digital communication theory. 0.1 Digital communication systems A digital communication system conveys information in digital form from a source to one or more destinations through a communication channel. Figure 0.1 gives the block diagram of a typical digital communication system. The standard components shown in Figure 0.1 include (in the order of the ow of information): 1. information source or input transducer 2. source encoder 3. encryptor 4. channel encoder 0.1

2 0.2 Figure 0.1: Block diagram of a typical digital communication system Information Source Source Encoder Analog/Digital Information Source Sink Decoder Encryptor Transmitter Receiver Decryptor Channel Encoder Digital Channel Decoder Digital Modulator Timing & Carrier Synchronizer Digital Demodulator Commun. Channel Analog Wong & Lok: Theory of Digital Communications

3 5. digital modulator 6. communication channel 7. timing and carrier synchronizer 8. digital demodulator 9. channel decoder 10. decryptor 11. source decoder 12. information sink or output transducer The rst ve components, which are pertinent to the transmission of information, form the transmitter of the communication system. The last six components, which are pertinent to the reception of information, make up the receiver of the communication system. We point out that some of the components above may not be found in some digital communication systems. However, any digital communication system should contain a modulator, a demodulator, and a synchronizer. Our main focus is on these three components. Later in the notes, we will brie y introduce the concept of channel coding (error control coding). Source coding and encryption are not covered here. To facilitate the design and evaluation of communication systems, we need to establish a measure of performance. For a digital communication system, a common performance measure is the probability of the event that an error 1 occurs at the receiver. There are many such error events, at various stages of the reception, we can employ to set up our performance measure. In most of the discussions followed, we use the average symbol error probability (or the average bit error probability in the cases of binary symbols) at the output of the demodulator as our performance measure. This is the probability that the symbol estimate given by the demodulator does not correspond to the transmitted symbol. In a (channel) coded system, we also use the average symbol error probability at the output of the (channel) decoder as a measure of performance. We again would like to point out that the average symbol error probability may not be the most meaningful performance indicator in some systems. For example, 1 An error occurs when the information output by the receiver does not match the transmitted information 0.3

4 the quality of the received speech may be a more meaningful performance measure in a voice communication system. Nevertheless, due to its simplicity and generality, we (and most communication researchers) adopt the average symbol error probability as the performance measure based on which we evaluate and design digital communication systems. With this in mind, we study some common analysis techniques to obtain the average symbol error probabilities of different communication systems. Our primary design objective is to minimize the average symbol error probability of a digital communication system. 0.2 Communication channels The communication channel provides a connection through which the information-bearing signal propagates. It is perhaps the most important component of a communication system. The design of all other components in Figure 0.1 depends heavily on the characteristics of the communication channel. There are many different types of physical communication channels, such as: 1. wireline channels 2. wireless channels 3. ber optic channels 4. underwater acoustic channels 5. storage channels Different kinds of channels can have very different characteristics. In order to design an ef cient digital communication system over a speci c communication channel, we need to study the characteristics of the channel extensively and carefully. Unfortunately, this is impractical for our general treatment on digital communication theory. Instead, we adopt a model-based approach here, i.e., we construct a generic mathematical channel model to represent a typical communication channel. For this purpose, our channel model describes the physical communication channel as well as the properties of the equipments, such as antennas and ampli ers, necessary to access the channel. The model 0.4

5 not only needs to be general enough to approximate most of the physical channels described above, but also simple enough to facilitate the analysis and design of the communication system. To this end, we notice that the major characteristic of a communication channel we are interested in is how the channel distorts the information-bearing signal. We start by listing out some common channel defects: 1. thermal noise in the electronic devices 2. signal attenuation 3. amplitude and phase distortion 4. multipath distortion 5. nite-bandwidth (lowpass lter) distortion 6. impulsive noise Based on knowledge of these channel defects, we construct the generic channel model. Suppose we use the symbol s(t) to denote the transmitted signal at the output of the modulator, then it is found that the following linear lter model (see Figure 0.2) suf ciently approximates the behaviors of many typical communication channels: r(t) = c(τ; t)s(t τ)dτ + n(t), (1) where r(t) represents the received signal at the input of the demodulator, n(t) is a random process which models the thermal and impulsive noises, and c(τ,t) is a linear time-varying lter 2 which models the other channel distortions listed above. We note that the linear (time-varying) channel model in (1) is very general and we work with simpli cations of this model in many cases. Among the various common simplications of the general model, the additive white Gaussian noise (AWGN) model is perhaps the most studied and important. In the AWGN model, c(τ,t)=δ(τ) and (1) reduces to r(t) =s(t)+n(t), (2) 2 We note that c(τ,t) can be deterministic or random depending on the channel it models. 0.5

6 s(t) c( τ;t) r(t) n(t) Communication channel Figure 0.2: Linear lter channel model where n(t) is a zero-mean wide-sense stationary Gaussian random process with autocorrelation function R n (τ) = N 0 2 δ(τ). The factor N 0 /2 is called the two-sided noise spectral density of the noise n(t). This model is primarily employed to represent the situation in which the only channel defect is the thermal noise in the electronic devices of a communication system. Although AWGN channels are rare in practice (except in deep space communications), because of its simplicity, we use the AWGN model as the cornerstone of our introduction to digital communications. 0.3 More information Check the course homepage at eel6535/ 0.6