The main objective of a communication system is the transfer of information over a channel. By its nature, the message signal that is to be transmitted is best modeled by a random signal. This is due to the fact that any signal that conveys information must have some uncertainty in it, otherwise its transmission is of no interest. When a signal is transmitted through a communication channel, there are two types of imperfections that cause the received signal to be different from the transmitted signal. One type of imperfection is deterministic in nature, such as linear and nonlinear distortions, intersymbol interference (ISI), etc. The second type is nondeterministic, such as addition of noise, interference, multipath fading, etc. For a quantitative study of these nondeterministic phenomena, a random model is required.

This chapter is concerned with the methods used to describe and characterize a random signal, generally referred to as a random process and also commonly called a stochastic process. Since a random process is in essence a random variable evolving in time we first consider random variables.

Random variables

Sample space and probability

The fundamental concept in any probabilistic model is the concept of a random experiment. In general, an experiment is called random if its outcome, for some reason, cannot be predicted with certainty. Examples of simple random experiments are throwing a die, flipping a coin, and drawing a card from a deck.

Introduction

Up to now we have considered only the detection (or demodulation) of signals transmitted over channels of infinite bandwidth, or at least a large enough bandwidth that any signal distortion is negligible and can be ignored. Though in some situations this assumption is reasonable, satellite communications is a common example, bandlimitation is also common. The classical example is the telephone channel where the twisted-pair wires used as the transmission medium have a bandwidth on the order of kilohertz. But even a medium such as optical fiber exhibits a phenomenon called dispersion which results in an effect very analogous to bandlimitation.

It is important to realize that bandlimitation depends not only on the channel medium but also on the source, specifically the source rate, Rs (symbols/second). One common measure of the bandwidth needed or occupied by a source is W = 1/Ts = Rs (hertz). As source rates keep increasing to accommodate more data eventually any channel starts to look bandlimited. Bandlimitation can also be imposed on a communication system by regulatory requirements. A user is usually allotted only so much bandwidth in which to transmit her/his information.

The general effect of bandlimitation on a transmitted signal of finite time duration, Ts seconds, is to disperse it or to spread it out. Therefore the signal transmitted in a particular time slot (or symbol interval) will interfere with signals in other time slots resulting in what is called intersymbol interference (each signal represents a data symbol) or ISI.

Introduction

As pointed out in the previous chapter, binary digits (or bits) “0” and “1” are used simply to represent the information content. They are abstract (intangible) quantities and need to be converted into electrical waveforms for effective transmission or storage. How to perform such a conversion is generally governed by many factors, of which the most important one is the available transmission bandwidth of the communication channel or the storage media.

In baseband data transmission, the bits are mapped into two voltage levels for direct transmission without any frequency translation. Such a baseband data transmission is applicable to cable systems (both metallic and fiber optics) since the transmission bandwidth of most cable systems is in the baseband. Various baseband signaling techniques, also known as line codes, have been developed to satisfy a number of criteria. Typical criteria are:

1. (i) Signal interference and noise immunity Depending on the signal sets, certain signaling schemes exhibit superior performance in the presence of noise as reflected by the probability of bit error.

2. (ii) Signal spectrum Typically one would like the transmitted signal to occupy as small a frequency band as possible. For baseband signaling, this implies a lack of high-frequency components. However, it is sometimes also important to have no DC component. Having a signaling scheme which does not have a DC component implies that AC coupling via a transformer may be used in the transmission channel.

3. (iii) […]

The previous two chapters have reviewed and discussed the various characteristics of signals along with methods of describing and representing them. This chapter begins the discussion of transmitting the signals or messages using a digital communication system. Though one can easily visualize messages produced by sources that are inherently digital in nature, witness text messaging via the keyboard or keypad, two of the most common message sources, audio and video, are analog, i.e., they produce continuous time signals. To make them amenable for digital transmission it is first required to transform the analog information source into digital symbols which are compatible with digital processing and transmission.

The first step in this transformation process is to discretize the time axis, which involves sampling the continuous time signal at discrete values of time. The sampling process, primarily how many samples per second are needed to exactly represent the signal, practical sampling schemes, and how to reconstruct, at the receiver, the analog message from the samples is considered first. This is followed by a brief discussion of three pulse modulation techniques, a sort of half-way house between the analog modulation methods of AM and FM and the various digital modulation–demodulation methods which are the focus of the rest of the text.

Though time has been discretized by the sampling process the sample values are still analog, i.e., they are continuous variables.

Introduction

The main objective of a communication system is the reliable transfer of information over a channel. Typically the information is represented by audio or video signals, though one may easily postulate other signals, e.g., chemical, temperature, and of course text, i.e., the written word which you are now reading. Regardless of how the message signals originate they are, by their nature, best modeled as a random signal (or process). This is due to the fact that any signal that conveys information must have some uncertainty in it. Otherwise its transmission would be of no interest to the receiver, indeed the message would be quite boring (known knowns so to speak). Further, when a message signal is transmitted through a channel it is inevitably distorted or corrupted due to channel imperfections. Again the corrupting influences such as the addition of the ever present thermal noise in electronic components, the multipath fading experienced in wireless communications, are unpredictable in nature and again best modeled as nondeterministic signals or random processes.

However, in communication systems one also utilizes signals that are deterministic, i.e., completely determined and therefore predictable or nonrandom. The simplest example is perhaps the carrier used by AM or FM analog modulation. Another common example is the use of test signals to probe a channel's characteristics. Channel imperfections can also be modeled as deterministic phenomena: these include linear and nonlinear distortion, intersymbol interference in bandlimited channels, etc.

Anytime, anywhere, anything can be taken as the motto and objective of digital communications. Anytime means that one can communicate on a 24/7 basis; anywhere states this communication can take place in any geographical location, at minimum one no longer is tied to being close to one's land line; anything implies that not only traditional voice and video but also other messages can be transmitted over the same channel, principally text, and not only individually but in combination. In large part digital communication systems over the past three decades have achieved the three objectives. Text messaging in all its forms, such as email, internet access, etc., is a reality. Webcasting and podcasting are becoming common. All parts of the globe are connected to the world wide communication system provided by the Internet.

Perhaps, and arguably just as important, a fourth “any” can be added, anybody. Though perhaps not as well developed as the first three, digital communication has the potential to make communication affordable to everyone. One feature of digital circuitry is that its cost, relative to its capability, keeps dropping dramatically. Thus though analog communication could achieve the above objectives, digital communications, due to this increasingly low cost, flexibility, robustness, and ease of implementation, has become the preferred technology.

This text is an introduction to the basics of digital communication and is meant for those who wish a fundamental understanding of important aspects of digital communication design.

This chapter looks at three important modulation paradigms. Trellis-coded modulation (TCM) is considered first. Developed in the late 1970s as a method to conserve bandwidth without sacrificing error performance it has become an extremely important modulation.

The second technique is called code-division multiple access (CDMA). It falls within the broad class of multiple access methods and is an administrator's favorite. It makes the addition (or deletion) of new users essentially transparent, easing the administrator's work. However, the technique does have technical merits that warrant its study by communication engineers. It forms the basis for the so-called 3G (third generation) and beyond wireless communication systems. In contrast to TCM, CDMA is a very wideband modulation technique.

The last modulation method studied uses space-time codes which provide diversity gain for the fading channel through the use of multiple transmit antennas. The important Alamouti's space-time block code (STBC) is discussed in some detail. It was first described in 1998, almost at the same time Tarokh et al. published their paper on space-time trellis codes.

Trellis-coded modulation (TCM)

By now one can appreciate that over an AWGN channel, the basic idea in digital communications is to find signal constellations with as large a distance between signals as possible without increasing the energy Eb (joules) expended per bit inordinately and with as small a bandwidth as possible.

Introduction

A successful communication system must establish synchronization, in addition to utilizing the modulation and demodulation techniques discussed so far. Synchronization is required at several levels. At the physical-layer level the receiver needs to know or estimate three parameters: (i) the incoming carrier frequency, fc (hertz); (ii) for coherent demodulation any phase shift or phase drift, θ(t) (radians), introduced during transmission; (iii) the bit (symbol) timing, i.e., where on the time axis do the kTb (or kTs) (seconds) ticks occur. How to obtain estimates of these parameters is the subject of this chapter.

The reader should realize, however, that one needs to establish other levels of synchronization. After detection of the transmitted bit sequence the sequence needs to be segmented or parsed into “words.” The best example of this is perhaps voice where the bit sequence needs to be segmented typically into eight-bit words, each word representing a voice sample. If error coding has been used, the sequence needs to be parsed properly into codewords for error decoding. Another example occurs in time-division multiple access where the communication channel is time shared. In this case the time slots need to be properly segmented to route the information from the different users properly. Such synchronization is typically called frame synchronization.

Introduction

The previous chapter shows that there are benefits to be gained when M-ary (M = 4) signaling methods are used rather than straightforward binary signaling. In general, M-ary communication is used when one needs to design a communication system that is bandwidth efficient. It is based on the observation that as the time duration of a signal, Ts, increases, the bandwidth requirement decreases. See Examples 2.11, 2.16, and Problem 2.38, which illustrate this. Typically, unlike QPSK and its variations in the previous chapter, the gain in bandwidth is accomplished at the expense of error performance. M-ary modulation is also a natural choice when the source is inherently M-ary, for example, the transmission of the English alphabet or when error control coding is used.

However, even when the source is inherently M-ary, the usual scenario is that the M messages are mapped to a sequence of bits, e.g., the ASCII code used for text. Therefore, even in these situations the final source output is binary and from the perspective of the modulator looks like a binary source. The typical application of M-ary modulation is one where a binary source has its bit stream blocked into groups of λ bits. The number of different bit patterns is 2λ, which means M = 2λ, where each bit pattern is mapped (modulated) into a distinct signal.

Introduction

In baseband transmission the transmitted signal power lies at low frequencies, typically around zero. It is desirable in many digital communication systems, for the same reasons as in analog communication systems, for the transmitted signal to lie in a frequency band toward the high end of the spectrum. As an example satellite communication is normally conducted in the 6–8 gigahertz band, while mobile phones systems are implemented in the 800 megahertz–2.0 gigahertz band.

The digital information is encoded as a variation of the parameters of a sinusoidal signal, called the carrier signal. Typically, as for analog modulation systems, the carrier frequency is much higher than the highest frequency of the modulating signals (or messages). Digital passband modulation is based on variation of the amplitude, phase, or frequency of the sinusoidal carrier, or some combination of these parameters.

Amplitude-shift keying (ASK) was probably the first type of digital modulation to be practically applied. In its simplest form it has been used for radio telegraphy transmission in Morse code. Another name for ASK is “on–off keying” (OOK), since a binary “1” corresponds to the sinusoid being transmitted while a binary “0” suppresses the carrier. Phase-shift keying (PSK) is an efficient, in terms of signal power, digital modulation method. It is widely used in modern digital communication systems, such as satellite links, wideband microwave radio relay systems, etc. The digital information is encoded in the phase function of a constant-amplitude carrier signal.

Introduction

Up to now we have assumed that the transmitted signal is only degraded by AWGN. Even when it is subjected to filtering, as in the previous chapter, the filtering characteristics are known precisely by the receiver. This knowledge is exploited in the design of the modulator/ demodulator by employing Nyquist's criterion to avoid intersymbol interference (ISI), or by allowing a certain amount of ISI as in the case of partial response systems, or by using a maximum likelihood sequence detection based on the unavoidable ISI.

In practice, however, there arise communication channels where the received signal is not subjected to a known transformation or filtering. In particular the gain and/or phase of a digitally modulated transmitted signal is not known precisely at the receiver. These parameters can be modeled as either unknown but fixed over the period of transmission or as random. In the former case, one could transmit a known signal briefly at the beginning of transmission to estimate the parameter(s) and then use the estimate(s) for the remainder of the transmission, which would be the message of interest. However, in the more typical application, the parameters do change in time, so though they may remain reasonably constant over a bit interval, or several bit intervals, they do change over the course of the entire message transmission, typically unpredictably.

In the preceding chapter we showed that meshes were good for extending coverage beyond the existing network edge, without requiring additional infrastructure – a sufficient number of user nodes, in the right places, was all that was required. We also implied that this meant that obstacles to propagation such as buildings in the line-of-sight might be less of a problem, given that a mesh could hop around them in a way which cellular systems cannot. We even dropped a small application hint that the structure of a mesh can be quite similar to a grid of downtown city streets. In this chapter we look more closely at linking a number of useful application scenarios with the relevant attributes of a mesh.

We now propose that there are, at heart, only two worthwhile motivations for mesh networks. These are

1. coverage improvement,

2. lack of infrastructure.

All successful examples of meshing or multi-hopping known to us embody one or both of these core mesh attributes.

To support this conclusion, we now spend some time considering application scenarios. Overall, from a technology standpoint, we found it hard to envisage any new services which only a mesh could support, although vehicle ad hoc networks and wireless sensor networks are probably the closest – but even here a mesh is the best rather than the only solution. Rather it seems more likely that a mesh would contribute by delivering services in a new way. Six suitable application areas are identified below where mesh adoption is thought to be most likely. In hindsight, it is easy to see that all six applications are based on a mesh network's valuable attributes of coverage and/or reduced reliance on infrastructure.