During the first years of the third millennium, considerable interest arose in complex networks such as the Internet, the world-wide web, biological networks, utility infrastructures (for transport of energy, waste, water, trains, cars and aircrafts), social networks, human brain networks, and so on. It was realized that complex networks are omnipresent and of crucial importance to humanity, whose still augmenting living standards increasingly depend on complex networks. Around the beginning of the new era, general laws such as “preferential attachment” and the “power law of the degree” were observed in many, totally different complex networks. This fascinating coincidence gave birth to an area of new research that is still continuing today. But, as is often the case in science, deeper investigations lead to more questions and to the conclusion that so little is understood of (large) networks. For example, the rather simple but highly relevant question “What is a robust network?” seems beyond the realm of present understanding. The most natural way to embark on solving the question consists of proposing a set of metrics that tend to specify and quantify “robustness”. Soon one discovers that there is no universal set of metrics, and that the metrics of any set are dependent on each other and on the structure of the network.

Any complex network can be represented by a graph. Any graph can be represented by an adjacency matrix, from which other matrices such as the Laplacian are derived.

Recent years have seen the great success of OFDM (orthogonal frequency division multiplexing) and DMT (discrete multitone) transceivers in many applications. The OFDM system has found many applications in wireless communications. It has been adopted in IEEE 802.11 for wireless local area networks, DAB for digital audio broadcasting, and DVB for digital video broadcasting. The DMT system is the enabling technology for high-speed transmission over digital subscriber lines. It is used in ADSL (asymmetric digital subscriber lines) and VDSL (very-high-speed digital subscriber lines). The OFDM and DMT systems are both examples of DFT transceivers that employ redundant guard intervals for equalization. Having a guard interval can greatly simplify the task of equalization at the receiver and it is now one of the most effective approaches for channel equalization. In this book we will study the OFDM and DMT under the framework of filter bank transceivers. Under such a framework, there are numerous possible extensions. The freedom in the filter bank transceivers can be exploited to better the systems for various design criteria. For example, transceivers can be optimized for minimum bit error rate, for minimum transmission power, or for higher spectral efficiency. We will explore all these possible optimization problems in this book.

The first three chapters describe the major building blocks relevant for the discussion of signal processing for communication and give the tools useful for solving problems in this area. Chapters 4–5 introduce the multirate building blocks and filter bank transceivers, and the basic idea of guard intervals for channel equalization. Chapter 6 gives a detailed discussion of OFDM and DMT systems. Chapters 7–10 consider the design of filter bank transceivers for different criteria and channel environments. A detailed outline is given at the end of Chapter 1. This book has been used as a textbook for a first-year graduate course at National Chiao Tung University, Taiwan, and at National Taiwan University. Most of the chapters can be covered in 16-18 weeks. Homework problems are given for Chapters 2–10.

In earlier chapters we saw that the use of redundancy in block transceivers allows us to remove ISI completely without using IIR filters. When the number of redundant samples per block v is more than the channel order L, there is no IBI, and we can further achieve zero ISI using a constant receiving matrix. The most notable example is the OFDM system studied in Chapter 6. But the use of redundant samples also decreases the transmission rate. For every M input symbols, the transmitter sends out N = M + ν samples. The actual transmission rate is decreased by a factor of N/M. There are ν redundant samples in every N samples transmitted. Reducing redundancy leads to a higher transmission rate and hence better bandwidth efficiency. At the same time, we would like the redundancy to be large enough so that the zero-forcing condition can still be satisfied without using IIR filters. A natural question to ask is: for a given channel and N, what is the smallest redundancy such that FIR transceivers exist? In other words, if we are to use an FIR transceiver that achieves zero ISI, what is the largest number of symbols that can be transmitted out of every N samples? This chapter aims to answer the question of minimum redundancy for the existence of FIR zero-forcing transceivers.

We will consider general FIR transceivers (Fig. 10.1) in which the filters are not constrained to be DFT filters as in the OFDM system. Moreover the length of the filters can be longer than the block size N. In this case the transmitting and receiving matrices are allowed to have memories, rather than constant matrices as in the OFDM case. We will see that the minimum redundancy depends on the underlying channel C(z), and it can be easily determined from the location of the zeros of the channel C(z) directly by inspection. The topic of minimum redundancy for FIR transceivers was first addressed in [182].

In this chapter we present a joint analysis of cooperation stimulation and security in autonomous mobile ad hoc networks under a game-theoretic framework. We first investigate a simple yet illuminating two-player packet-forwarding game, and derive the optimal and cheat-proof packet-forwarding strategies. We then investigate the secure-routing and packet-forwarding game for autonomous ad hoc networks in noisy and hostile environments, and derive a set of reputation-based cheat-proof and attackresistant cooperation-stimulation strategies. When analyzing the cooperation strategies, besides Nash equilibrium, other optimality criteria, such as Pareto optimality, subgame perfection, fairness, and cheat-proofing, are also considered. Both analysis and simulation studies show that the strategies discussed here can effectively stimulate cooperation among selfish nodes in autonomous mobile ad hoc networks under noise and attacks, and that the damage that can be caused by attackers is bounded and limited.

Introduction

Node cooperation is a very important issue in order for ad hoc networks to be successfully deployed in an autonomous way. In addition to many schemes that have been studied to stimulate node cooperation in ad hoc networks, ARCS was considered in the previous chapter to simultaneously stimulate cooperation among selfish nodes and defend against various attacks.

Introduction

The purpose of digital demodulation is to recover the information (bits, symbols) carried by the digitally modulated signals. This process can be achieved via coherent or noncoherent demodulation. The former requires a local reference carrier to be matched exactly in frequency and phase to the received signal. The latter requires only a match in frequency. Both types of demodulation involve two steps. In the first step, a signal processor is employed to convert the received signal that represents a bit (binary modulation) or a symbol (M-ary modulation) into a decision sample at maximum signal-to-noise ratio for the case of coherent demodulation. For noncoherent demodulation, the signal processor converts the received signal into a nonnegative decision sample independent of its unknown initial phase, which is cleverly discarded. Since the phase information is not employed, a loss in the signal-to-noise ratio for the decision sample results. The coherent signal processors are the matched filter and the correlator, both are equivalent at the time the decision sample is taken. The noncoherent signal processors are the matched filter-envelope detector (also known as noncoherent matched filter) and the quadrature correlator-square law detector (also known as noncoherent correlator), both are also equivalent at the time the decision sample is obtained. Binary demodulation employs one or two signal processors depending on the type of modulation.

In practical communication systems, the transmitter usually sends out training symbols to the receiver, based on which the channel can be estimated at the receiver. It is therefore reasonable to assume that the channel is known to the receiver. When the channel state information is also known to the transmitter, we can optimize the transmitter to better the system performance. Having this knowledge available to the transmitter requires the receiver to send back the information, which takes time. For wireless transmission, the channel varies rapidly. By the time the transmitter receives the channel profile, the channel may have changed. Therefore, for wireless applications it is often desirable to have a transmitter that is channel-independent. In such a channel-independent transmitter, there is no bit/power allocation. Having a channel-independent transmitter is also of vital importance for broadcasting applications, where there are many receivers with different transmission paths. The OFDM system has the much desired feature that the transmitter is channel-independent and furthermore the channel-dependent part of the transceiver is only a set of M scalars at the receiver. Moreover, the main processing at the transmitter (receiver) is M-point IDFT (DFT), which can be implemented efficiently using fast algorithms, and the complexity is in the order of M log2M instead of M2.

The discussion in Chapter 6 suggests that the OFDM system can be severely affected by channel spectral nulls. For high SNR the error rate is usually limited by those subchannels that have low SNRs. One method that prevents the performance being dominated by a few bad subchannels is to have a precoder. Figure 7.1 shows an OFDM transmission system with a precoder at the transmitter and a post-coder at the receiver. We have seen earlier that when the precoder is the DFT matrix, the precoder DFT matrix will cancel out the IDFT at the transmitter and the precoded system becomes the SC-CP system shown in Fig. 6.10. The SC-CP system illustrates that having a precoder can alter the BER behavior of the system, although the total output mean squared error is unchanged in this case.

From Chapter 6, we know that an OFDM system converts an LTI channel into a set of parallel subchannels. When the channel is frequency-selective, these subchannels can have very different subchannel gains. The system performance can be severely limited by a few bad subchannels. One solution to this problem is to use a precoder as demonstrated in Chapter 7. In many applications, the transmission environment does not change frequently. These applications include most wired transmission schemes, such as ADSL and VDSL systems, and many wireless transmission schemes, such as fixed wireless access systems and wireless LAN system where the end users are not mobile. Under these environments, if the channel state information is known at the transmitter, one can exploit this information to carry out bit allocation. By optimally assigning the bits to the subchannels, the system performance can be substantially improved, especially when the channel is highly frequency-selective. In this chapter, we will derive the optimal zero-forcing transceivers when there is bit allocation at the transmitter.

Zero-forcing block transceivers

The DFT-based transceivers studied in Chapter 6 employ either DFT or IDFT operations at the transmitter and receiver. The filter bank formulation shows that their polyphase matrices are constant matrices related to the DFT/IDFT operations. In this chapter, we study general block transceivers where the polyphase matrices can be arbitrary constant matrices. Figure 8.1 shows a block transceiver system. The M × 1 input vector s is processed by the N × M transmitting matrix G0 to produce an N × 1 output vector

х = G0s.

which is converted to a sequence x(n) and transmitted over the channel. At the receiver, the received sequence is blocked into vectors of size N. The N × 1 received vector r is then processed by the M × N receiving matrix So to obtain the M × 1 output vector

ŝ = S0r.