In this chapter we review probability and statistics. We define the ideas of probability, the probability density function, and the cumulative density function. We introduce Bayes’ theorem that relates prior, marginal, posterior, and conditional probability densities, which allows us to define the maximum a posterior and the maximum likelihood estimators. We discuss central moments of distributions. We review multivariate probability distributions including the correlated multivariate complex circularly symmetric Gaussian distributions. We also review a set of useful distributions, including Rayleigh, exponential, χ2, and Rician. Finally, we discuss random processes.

Users in a social network are usually confronted with decision-making under uncertain network states. While there are some works in the social learning literature on how to construct belief in an uncertain network state, few studies have focused on integrating learning with decision-making for the scenario in which users are uncertain about the network state and their decisions influence each other. Moreover, the population in a social network can be dynamic since users may arrive at or leave the network at any time, which makes the problem even more challenging. In this chapter, we introduce a dynamic Chinese restaurant game to study how a user in a dynamic social network learns about the uncertain network state and makes optimal decisions by taking into account not only the immediate utility, but also subsequent users’ influence. We introduce a Bayesian learning-based method for users to learn the network state and discuss a multidimensional Markov decision process-based approach for users to make optimal decisions. Finally, we apply the dynamic Chinese restaurant game to cognitive radio networks and use simulations to verify the effectiveness of the scheme.

In this chapter, we consider how to map bits to a sequence of voltages or signal levels at complex baseband. We introduce the idea of a constellation, which defines a lattice of allowed baseband signaling voltages. We provide a discussion of modulation-specific capacities. We introduce the idea of pulse shaping that we use to reduce the spectral spread of our signals. We discuss channel estimation and compensation. We evaluate the raw bit error rate of BPSK and symbol error rates of QPSK modulations. We discuss demodulation and consider both hard decisions and soft decisions, which involves estimating likelihoods of possible symbols.

In this chapter we discuss analog radio techniques. Nearly all modern systems employ digital communications. However, for historical reasons, we review these legacy approaches. We introduce linear and angle modulation techniques. Linear modulation approaches include

In this chapter, we discuss the effects of channel dispersion, or equivalently, the effects of resolvable multipath, and techniques for enabling communications in these environments. We introduce the model for delay spread that is the source of dispersion. We relate the time-domain and frequency-domain representations of the propagation channel. We introduce the approach of adaptive equalization, including zero-forcing and Weiner filtering. We provide an example of finite-sample Weiner filtering. We also introduce the orthogonal frequency-division multiplexing (OFDM) approach to compensate for dispersive channels. We describe OFDM’s processing chain. We determine the waveform characteristics and spacing of the subcarriers used to construct OFDM. Finally, we discuss models for dispersive channels.

While peer-to-peer (P2P) video streaming systems have achieved promising results, they introduce a large number of unnecessary traverse links, leading to substantial network inefficiency. To address this problem, we discuss how to enable cooperation among“group peers,” which are geographically neighboring peers with large intragroup upload and download bandwidths. Considering the peers’ selfish nature, we formulate the cooperative streaming problem as an evolutionary game and introduce, for every peer, the evolutionarily stable strategy (ESS). Moreover, we discuss a simple and distributed learning algorithm for the peers to converge to the ESSs. With the discussed algorithm, each peer decides whether to be an agent who downloads data from the peers outside the group or a free-rider who downloads data from the agents by simply tossing a coin, where the probability of the coin showing a head is learned from the peer’s own past payoff history. Simulation results show that compared to the traditional noncooperative P2P schemes, the discussed cooperative scheme achieves much better performance in terms of social welfare, probability of real-time streaming, and video quality.