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From the Book:PREFACE: Outline After the introductory focus in this part, the rest of this book covers (i) unequalized systems, (ii) equalizers, (iii) OFDM, and (iv) Rake receivers. All these four parts are self-contained, so they can be read in arbitrary sequence. PART II - UNEQUALIZED SYSTEMS by Molisch discusses those systems at the boundary between wideband and narrowband where the time dispersion is smaller, but not much smaller, than the symbol duration (slightly time-dispersive systems) and do not contain equalizers. Typically, those systems were originally designed as true narrowband systems, where it later turned out that under some circumstances time dispersion can play a role, or where equalizers were simply too expensive. After a brief introduction, Chapter 7 gives a generic system description for both transmitter and receiver. The most important modulation formats, namely, phase-shift keying, quadrature amplitude modulation, and continuous-phase frequency shift keying are described mathematically, together with the standard detection methods (coherent, differentially coherent, and incoherent). Chapter 8 then describes various mathematical methods for computing the bit error probability (BER) of unequalized systems under the influence of time-dispersive signals. Although most textbooks on mobile radio describe the standard approach for flat-fading, namely, first computing the BER for AWGN channels and then averaging over the distribution of channel attenuation, this approach is no longer possible for time-dispersive channels. Methods that circumvent these problems are, e.g., based on certain properties of quadratic forms ofGaussianvariables, probability density functions of the angles between Gauss-distributed vectors, or the group delay distributions of the channel. Unfortunately, none of these can be considered to be a master approach that is optimum for all possible cases. Methods based on Gaussian variables are usually the simplest but always require the channel to be Rayleigh- or Rice-fading, and encounter problems, e.g., in Nakagami channels. Within this group, the method based on quadratic forms can most easily include arbitrary time dispersion but cannot easily be extended to multilevel modulation formats, e.g., A -ary PSK, which can be better treated by pdfs of Gaussian vectors or the two-path equivalent matrix method. Chapter 8 describes the different methods in sufficient detail for the reader to judge what is needed to solve a specific problem, but details are covered only in a few examples. Closed-form equations and figures of the performance of standard systems are the contents of Chapter 9. The influence of modulation format, delay spread, shape of the power delay profile, sampling instant, and other parameters are presented. In Chapter 10, the author describes special modulation formats and receiver structures that are used for the reduction of ISI-induced errors (error floor). Some modulation formats try to actually exploit the time dispersion and thus approach the performance of an equalized system in a time-dispersive environment. The penalty paid for this approach lies in a higher bandwidth requirement, which precludes these formats from application in cellular systems, but the technique might be interesting for wireless LANs and cordless applications. Some receiver structures, on the other hand, try just to reduce the error floor by eliminating the ISI before detection, thus making the performance comparable to a true flat-fading channel. These stay within the framework of standard modulation formats and thus usually have only a penalty in the form of a slightly more complex receiver structure (but still much simpler than an equalizer). A technique that also has these properties is adaptive sampling, more exactly, the adaptive choice of the sampling instant according to the channel constellation. Adaptive sampling is described in Chapter 11. Chapter 12 describes antenna diversity. Although antenna diversity is usually known to reduce noise-induced errors, it was also shown to be an effective countermeasure for ISI-induced errors. After a description of the different ways to combine the diversity signals, the mathematical methods of Chapter 8 are modified to include the diversity effects. Those methods are useful not only for conventional multidimensional diversity, but also for the performance of Rake receivers, since these use the time-delayed echoes of the original signal as diversity signals that are combined with maximum-ratio combining. Subsequently, the performance with the diversity antennas is presented in some examples. A summary (Chapter 13) concludes this part. PART III - EQUALIZERS by Vitetta, Hart, Mammela, and Taylor focuses on the equalization techniques for single-carrier, unspread digital signals transmitted over multipath fading channels and is organized as described below. Some preliminary topics are presented in Chapter 14, where the mathematical models of the transmitted signal and of the wireless channel are illustrated. An optimal receiver must not discard useful information present in the continuous time received signal; digital processing, however, is an inevitable requirement of any modern receiver. Therefore, filtering and discretizing of the received signal are discussed. Notations for the various scalar and matrix quantities needed in the remainder of the Part are given; in particular, matrix representations for the received signal samples are provided to simplify the derivation of equalization algorithms. Finally, reduced complexity channel models, i.e., parsimonious representations or parameterizations of the channel impulse response, are introduced to simplify the channel estimation problem and the equalizer design. In particular, the authors focus on the Karhunen-Loeve expansion, on the complex exponential parameterization, and on the power series models. Any equalization algorithm processes the received signal, producing a set of real quantities, known as metrics, that are evaluated by the receiver to make decisions on the transmitted data. In Chapter 15 we derive, interpret and analyze the performance of the metrics computed by optimal detectors under the assumption that the CIR (or some equivalent quantity) is known, estimated, or averaged over for the doubly selective wireless channel and its special cases: the frequency-flat and frequency-selective channels. Both the maximum likelihood (ML) and maximum a posteriori (MAP) methods are discussed as optimality criteria, and their application to bits, symbols and sequences of symbols is illustrated. In particular MAP bit detectors (MAPBDs), MAP symbol detectors (MAPSDs) and ML sequence detectors (MLSDs) are considered. In addition, performance bounds for both the ML and MAP detectors are provided; they represent useful tool to assess their error performance in some situations. In Chapter 16, we describe various equalization algorithms corresponding to different ways of implementing the computation of the derived metrics, ranging from optimal to highly suboptimal. Again the primary division into sections is related to how the CIR is treated. Within each section, the structure, complexity, and performance measures of each type of equalizer are described. In particular, in Section 16.1 we begin by assuming that the CIR is known exactly a priori, and we derive five important classes of equalizers: MLSDs, MAPSDs and MAPBDs, reduced complexity sequence detectors, decision feedback equalizers (DFEs), and linear equalizers (LEs). The aim of Section 16.2 is twofold. First, we show some mathematical tools for channel estimation and we discuss blind equalization techniques. Secondly, we illustrate equalization techniques incorporating channel estimation strategies, like adaptive MLSDs and adaptive MAPBD/MAPSDs. Adaptive LEs and DFEs and pilot-based detection techniques for frequency-flat fading channels are also considered. Equalization when the CIR is averaged-over is investigated in Section 16.3. MLSDs and MAPSDs are developed and are related to their adaptive counterparts. Finally, various equalization/detection strategies for FF fading channels are illustrated. PART IV - OFDM by May and Rohling describes orthogonal frequency division multiple access (OFDM), also known as multicarrier modulation. Chapter 17 introduces OFDM and describes its historical evolution. Chapter 18 describes the basic transmission/reception technique, both in a time-continuous formulation that is intuitively appealing and in a time-discrete formulation that illuminates the important relation to discrete Fourier transforms. The shaping of the basic pulses is discussed. In a conventional system, rectangular pulses are used as a basis for constructing the total signal, but this might not be optimum in dispersive channels. Chapter 19 then treats frame, timing, and carrier frequency synchronization. Chapters 20 and 21 are devoted to modulation and demodulation. Many aspects are identical to those of single-carrier systems, but there are also some specific points that are unique to OFDM systems. When, for example, using differential modulation/demodulation, we have a choice whether we take the difference with the previous symbol (in time) or the adjacent symbol (in frequency). For coherent demodulation, the design of the pilot tones also plays a vital role. Trade-offs between the quality of the channel estimation and the spectral efficiency loss because of the insertion of non-information-carrying symbols must be considered. An OFDM system can really exploit its advantages in wideband channels only when appropriate coding (discussed in Chapter 22) is used. Transmission on carriers in fading dips will always result in a high bit-error rate, and only appropriate interleaving and coding can recover the information in such a way that the frequency diversity of the wideband transmission is really exploited. Soft-decision demodulation is also one major aspect and realizes large gains compared to hard decisions. Convolutional codes, possibly concatenated, and trellis-coded modulation are additional performance-enhancing methods. In contrast to conventional modulation methods, which are usually constant-envelope, OFDM can exhibit a high Crest factor. The reason is that an OFDM signal is a sum of many (hundreds or thousands) partial signals whose phase is determined by the data sequence to be transmitted. For some data, these partial signals can add up in such a way that the output signal has a huge instantaneous amplitude. Amplifiers for the transmission of such signals would have to have a large dynamic range, which is difficult to implement. There are thus intensive investigations, described in Chapter 23, on how to reduce the Crest factor. Solution proposals range from insertion of redundancy, application of correcting functions, to special coding. Nonlinearities of the transmission amplifier are also one reason for out-of-band emissions. Also, the shaping of the basis pulses, as discussed for Chapter 18, plays a role. In any case, these out-of-band transmissions must be eliminated as much as possible, since especially in a cellular system, adjacent channel interference requirements are very strict. This reduction is usually achieved by filtering, which in turn increases intersymbol interference. The trade-off between these two considerations is the focus of Chapter 24. Chapter 25 relates conventional OFDM systems to multicarrier OFDM, where information symbols are spread over several carriers, and to single-carrier transmission with frequency-domain equalization. All of these systems can be viewed as special cases of a generic OFDM system; this viewpoint facilitates comparisons of the various advantages and disadvantages. PART V - CDMA by Goiser (Chapters 26-28), Win and Chrisikos (Chapter 29), and Glisic (Chapters 30-33) describes how CDMA systems exploit the time-delay diversity that is inherent in multipath propagation. This exploitation is achieved by the so-called Rake receiver, which with its several "fingers" detects several time-delay replicas of the original signal and then adds them coherently. Chapter 26 introduces direct-sequence spread spectrum, which forms the basis for CDMA systems. It describes how the information is spread by multiplication with a spreading sequence from a bandwidth A to a bandwidth A equal to B where A is the processing gain and A is the chip duration of a chip in a spreading sequence. This chapter also explains some basic trade-offs in the design of a CDMA network, including trade-offs between number of users, spreading gain, achievable BER, etc. Since the chip duration is quite short, a lot of echoes can be resolved by a receiver. The correlation between the received signals and the spreading sequence thus exhibits several peaks, each corresponding to one echo. The Rake receiver now adds up the largest echoes with the correct phases. This technique exploits the path diversity inherent in the wideband channel. Chapter 27 compares the performance of such a Rake receiver to a simpler MUW receiver that receives only one echo and suppresses the other echoes. Simulation curves show the gain that is possible by the Rake receiver in different channels for a single-user environment. Chapter 28 describes a receiver concept known as D-Rake (decorrelating Rake receiver) that is especially suitable for a multiuser environment, as always occurs in a multiuser environment. This receiver not only exploits the multiple echos but also suppresses the signals from other users very efficiently. Interference from other users is always present because the used codes are never orthogonal in a multipath environment and the power control has only a finite accuracy and dynamic. Thus, interference from users in the same cell is usually the capacity limit. Chapter 29 explores the theoretical performance of a Rake receiver with a finite number of fingers. Such a receiver selects the echoes that have the highest instantaneous energy. The authors introduce a technique that allows a closed-form computation of the resulting SNR and BER. One of the most important practical aspects of Rake receivers is code synchronization, which consists of acquisition and tracking. Code acquisition is treated in Chapter 30. After the description of performance analysis tools, especially the signal flow graph method, the performance of acquisition methods in quasi-synchronous and asynchronous networks are computed for different multipath channel models. Chapter 31 then treats code tracking. First, three different types of code tracking loops are explained: the baseband full-time early-late tracking loop, the full time early-late noncoherent tracking loop, and the tau-dither early-late non-coherent tracking loop. After this, the influence of a wideband channel on the tracking loop performance is computed. Chapter 32 treats the problem of channel estimation, especially with a subspace-based method, which is explained in detail and shown to give good results in channels with near/far effect. Chapter 33 treats the capacity of CDMA networks. This is an especially important subject since high capacity is one of the key arguments for the use of CDMA in mobile radio. After describing the system model, some general equations for the capacity are given. Then, the effect of power control, and the influence of the Rake receiver and interference-cancelling receivers are shown. In general, Rake receivers with many fingers should give higher capacity than those with few fingers. However, due to channel estimation errors, there can actually be also a decrease. An appendix with mathematical background material concludes Part V.