Stephen B. Weinstein

Automatic and Adaptive Equalization

Up to this point in the text, we have made two key assumptions in discussing the structures described in Chapter 7: we have assumed arbitrary receiver complexity and we have also assumed that the channel characteristics are known at the receiver. For the maximum likelihood sequence estimation receiver, implemented via the Viterbi algorithm, the number of states was allowed to grow without bound and the observables used to compute the transition metrics are outputs of a (presumed known) filter matched to the channel. In the optimum linear receiver, the matched filter appears again along with a tapped delay line equalizer of arbitrary length. In the optimum linear receiver which does not use a matched filter, the tap weights are dependent on the channel covariance matrix. In practice, the channel characteristics are generally not known. If a dialed telephone line is used, the channel is different on each call. Even for private or leased channels, the characteristics may be known only within certain limits. For many channels, such as fading radio systems, phase perturbations and other time-varying channel variations are present, requiring constant tracking to avoid deterioration of performance. The optimum receivers we have described in the preceding chapters would be of academic interest only if it were not possible to adapt the parameters appearing in their structures to accurately model the actual channel or a function of the channel, such as its inverse.

Synchronization: Carrier and Timing Recovery

The theme of this chapter might well be “…timing is everything.” In the course of our discussion in Chapter 4, we saw that the detection of a baseband digital data sequence presumed proper timing at the receiver. (See Section 4.10, particularly.) The same requirement for timing is present in the detection of passband signals; however, as we saw in Section 5.2, carrier phase coherency is also necessary. The roles of each of these synchronization subsystems are shown in Figure 6.1a. The carrier tracking system provides an estimate of the received carrier phase θ^, while the timing recovery system provides an estimate of the proper sampling epoch to the receiver sampling system A^. The effect of a poorly designed carrier loop will be to increase the dispersion of the received symbols about their nominal values, bringing the received points considerably closer to the decision boundaries and decreasing the margin against an error (caused say by a noise burst); of course, large phase perturbations can cause errors without any noise. In Figure 6.1b we show how the transmitted symbol s 1 is rotated by phase jitter to the point u, and then further distorted by noise to the point z; note that the received point is within the decision region associated with s 2 so that an error will be made. Similarly, timing phase errors will cause the receiver to sample away from the maximum eye opening, and reduce the margin for error. It is the purpose of this chapter to present the various aspects of synchronization.

Passband Data Transmission

Modulation is the process by which a baseband information signal is converted into a passband signal that can transit a passband channel constrained in bandwidth and possibly other ways. In order to conserve bandwidth, it is convenient to impress the information signal onto a sinusoidal carrier signal. Spread spectrum systems, on the other hand, effectively modulate information signals onto wideband carriers. We shall restrict attention here to digital modulation formats that are spectrally efficient, that is, the breadth of spectrum taken up by the modulated waveform is the same or not much more than that taken up by the baseband signal.

Error Correcting and Detecting Codes

As we have seen in Section 2.5, information theory provides theoretical upper bounds on the information rates that can be obtained over physical channels. While these bounds can be computed for a wide range of channels, the theory gives little indication of how they may be attained. It is fortuitous that, about the same time information theory was conceived, a theory of error correcting and detecting codes emerged. By the systematic injection of redundant bits into the encoding of information, the reliability of transmission could be improved. Hopes that codes achieving the bounds could be easily obtained proved to be illusionary; however, the theory has steadily developed so that codes have become indispensable components of many communications systems yielding considerable performance gains. The remarkable series of pictures that have been received from deep-space probes attest to the power of coding. A recent breakthrough, trellis coding, which is a direct outgrowth of the theory and which will be covered in Section 5.8, has put the Shannon bound within reach for bandlimited channels.

Theoretical Foundations of Digital Communications

The generic communications system of interest in this book is depicted in Figure 2.1. This model contains most of the elements which will be discussed in this and subsequent chapters. The output of an information source* is first encoded into a digital, usually binary, data stream. The encoding operation may involve several steps. If the source is analog, sampling and quantization by an analog-to-digital (A/D) converter are involved. The next step may be source coding in the form of redundancy removal. Huffman coding and the Lempel-Ziv algorithm, discussed in Section 2.5, are examples of this operation. Redundancy in the form of parity bits may be added in order to guard against channel errors. We shall be discussing redundancy encoding in Chapter 3. Once a digital stream is available, the operation of the encoder may also involve encryption for security. The digital stream may also be scrambled to provide randomization of the transmitted signal to facilitate adaptive equalization and timing recovery in the receiver. Scrambling is discussed in Section 6.7. The function of the modulator is to put the digital data stream into a form which is suitable for transmission over the physical channel. This may involve simply translating a sequence of binary digits into a sequence of pulses. This step may also involve baseband pulse encoding to combat intersymbol interference (see Section 4.6). In the case of passband systems, the data sequence may be used to modulate a carrier, thereby placing the signal into the passband of the channel (see Chapter 5). The receiver reverses the operations performed at the transmitter.

Baseband Pulse Transmission

The foregoing chapters have given an overview of data communications, and reviewed topics in statistical communication theory, coding, and computer communication relevant to data communications analysis and systems design. Chapter 2 in particular described detection techniques for isolated pulse signaling. This chapter begins a detailed examination of signaling techniques for pulse trains. Such techniques constitute the art of conveying digital information through analog channels, which means essentially all channels, since every meaningful physical channel is analog. They include telephone channels, twisted-pair subscriber access lines, magnetic recording channels, shared coaxial media, and optical fiber channels. Not all of the discussion is analytical, for signal design is to some extent a collection of clever techniques developed over time, but there are some unifying theoretical foundations.

Topics in Digital Communications

In this chapter we discuss several advanced topics in digital communications. These concepts are advanced from two perspectives: (1) they represent a synthesis and/or an extension of material that has been discussed earlier in this text; (2) the work is very timely in the technical literature and for product applications, and has not yet appeared in texts. With regard to the first item, the foundation technologies that have been described in earlier chapters are the basic building blocks used for the design and analysis of communications systems. Although several of the subjects we consider could have been treated in earlier chapters, we have chosen to collect them here so that we can draw on the foundation that has been developed.

Optimum Data Transmission

In Chapter 4, we examined signal design for baseband pulse transmission, and described the compromises among the bandwidth of the transmitted signal, noise immunity, and mitigation of intersymbol interference inherent in any design. Peak and mean-square intersymbol interference were defined, and it was shown how linear channel distortion can degrade performance. This chapter describes system structures that are optimum, either with respect to maximizing the probability that a sequence of symbols is correctly received or minimizing the output mean-square error; these receivers are primarily designed to correct the degradation caused by noisy channels and linear distortion. It is not possible, except in certain singular cases, to achieve the performance of an impairment-free system, or that of a system which attains the matched filter bound (which is equivalent to the transmission of isolated pulses). A further limitation discussed in Chapter 2 was the assumption of pulse-by-pulse (i.e. symbol-by-symbol) detection, which is optimum only in the absence of intersymbol interference. In the case of partial response signaling, we described precoding operations that eliminated the intentional intersymbol interference, but with a penalty in noise immunity. This penalty can be avoided if pulse-by-pulse detection is replaced by a process (the maximum likelihood receiver) that uses the entire received sequence for detection. This technique, the Viterbi algorithm, was applied to the decoding of convolutional codes in Chapter 3 and to the decoding of trellis codes in Chapter 5. In this chapter, the same technique will be applied to the detection of a sequence of amplitude-modulated pulses.

Introduction to Data Communications

Data communication has been with us for a long time. Smoke signals, drum beats, and semaphore signals are examples that are commonly given; indeed, semaphore relay may be regarded as the first modern communication network [1]. But the most remarkable example must surely be alphabetical writing. The concept of conveying information by successive choices from a finite alphabet is the very essence of both writing and digital data communication [2]. In fact, many of the ideas of linguistics carry over to information theory, communications, and pattern recognition. It is the purpose of this first chapter, in a book devoted to the principles of data communications, to provide a perspective on the technology of data communications, and to highlight the broad applicability of the foundation technologies of modulation/demodulation, equalization, coding, and synchronization. In this text we will demonstrate the communication-theoretic origin and the broad application of these technologies to a variety of communication media, including the telephone channel, twisted pairs, radio, magnetic recording, and optical fiber.