This chapter introduces the fundamentals of the field of signal processing, which studies how signals can be synthesised, analysed and modified. Here, and for the remainder of the book, we use the term signal in a more specific sense than before, in that we take it to mean a waveform that represents a pattern of variation against time. This material describes signals in general, but serves as a precursor to the following chapters which describe the nature of speech signals and how they can be generated, manipulated and modified. This chapter uses the framework of digital signal processing, a widely adopted set of techniques used by engineers to analyse many types of signals.

Analogue signals

A signal is a pattern of variation that encodes information. Signals that encode the variation of information over time can be represented by a time waveform, which is often just called a waveform. Figure 10.1 shows an example speech waveform. The horizontal axis represents time and the vertical axis represents amplitude, hence the figure shows how the amplitude of the signal varies with time. The amplitude in a speech signal can represent diverse physical quantities: for example, the variation in air pressure in front of the mouth, the displacement of the diaphragm of a microphone used to record the speech or the voltage in the wire used to transmit the speech.

Audio and speech processing systems have steadily risen in importance in the everyday lives of most people in developed countries. From ‘Hi-Fi’ music systems, through radio to portable music players, audio processing is firmly entrenched in providing entertainment to consumers. Digital audio techniques in particular have now achieved a domination in audio delivery, with CD players, Internet radio, MP3 players and Pods being the systems of choice in many cases. Even within television and film studios, and in mixing desks for ‘live’ events, digital processing now predominates. Music and sound effects are even becoming more prominent within computer games.

Speech processing has equally seen an upward worldwide trend, with the rise of cellular communications, particularly the European GSM (Global System for Mobile communications) standard. GSM is now virtually ubiquitous worldwide, and has seen tremendous adoption even in the world's poorest regions.

Of course, speech has been conveyed digitally over long distance, especially satellite communications links, for many years, but even the legacy telephone network (named POTS for ‘Plain Old Telephone Services’) is now succumbing to digitisation in many countries. The last mile, the several hundred metres of twisted pair copper wire running to a customer's home, was never designed or deployed with digital technology in mind, and has resisted many attempts over the years to be replaced with optical fiber, Ethernet or wireless links. However with DSL (digital subscriber line – normally asymmetric so it is faster in one direction than the other, hence ADSL), even this analogue twisted pair will convey reasonably high-speed digital signals.

The design of wireless devices and networks present unique design challenges due to the combined effects of physical constraints, such as bandwidth and power, and communication errors introduced through channel fading and noise. The limited bandwidth has to be addressed through a compression operation that removes redundant information from the source. Unfortunately, the removal of redundancy makes the transmitted data not only more important but also more sensitive to channel errors. Therefore, it is necessary to complement the source compression operation with the application of an error control code to do channel coding. The goal of the channel coding operation is to add redundancy back to the source coded data that has been designed to efficiently detect and correct errors introduced in the channel. In this chapter we will study the use of cooperation to transmit multimedia traffic (such as voice or video conferencing). This involves studying the performance of schemes with strict delay constraint where user cooperation is combined with source and channel coding.

Although the source and channel codecs complement each other, historically their design had been approached independently of each other. The basic assumptions in this design method are that the source encoder will present to the channel encoder a bit stream where all source redundancy have been removed and that the channel decoder will be able to present to the source decoder a bit stream where all channel errors have been corrected.

Despite the promised gains of cooperative communication demonstrated in many previous works, the impact of cooperation at higher network levels is not yet completely understood. In the previous chapters, it was assumed that the user always has a packet to transmit, which is not generally true in a wireless network. For example, in a network, most of the sources are bursty in nature, which leads to periods of silence in which the users may have no data to transmit. Such a phenomenon may affect important system parameters that are relevant to higher network layers, for example, buffer stability and packet delivery delay. We focus on the multiple access layer in this chapter. One can ask many important questions now. Can we design cooperation protocols that take these higher layer network features into account? Can the gains promised by cooperation at the physical layer be applied to the multiple access layer? More specifically, what is the impact of cooperation on important multiple access performance metrics such as stable throughput region and packet delivery delay?

In this chapter, we try to address all of these important questions to demonstrate the possible gains of cooperation at the multiple access layer. A slotted time division multiple access (TDMA) framework in which each time slot is assigned only to one terminal, i.e., orthogonal multiple access is considered. If a user does not have a packet to transmit in his time slot, then this time slot is not utilized.

In the previous chapter, the symbol error rate performance of single-relay cooperative communications was analyzed for both the decode-and-forward and amplify-and-forward relaying strategies. This chapter builds upon the results in the previous chapter and generalizes the symbol error rate performance analysis to the multi-relay scenario.

Decode-and-forward relaying will be considered first, followed by the amplify-and-forward case. In both scenarios, exact and approximate expressions for the symbol error rate will be derived. The symbol error rate expressions are then used to characterize an optimal power allocation strategy among the relays and the source node.

Multi-node decode-and-forward protocol

We begin by presenting a class of cooperative decode-and-forward protocols for arbitrary N-relay wireless networks, in which each relay can combine the signal received from the source along with one or more of the signals transmitted by previous relays. Then, we focus on the performance of a general cooperation scenario and present an exact symbol error rate (SER) expressions for both M-ary phase shift keying (PSK) and quadrature amplitude modulation (QAM) signalling. We also consider an approximate expression for the SER of a general cooperation scenario that is shown to be tight at high enough SNR. Finally, we study optimal power allocation for the class of cooperative diversity schemes, where the optimality is determined in terms of minimizing the SER of the system.

In wireless communication systems with a single antenna, the channel capacity can be very low and the bit error rate high when fading occurs. Various techniques can be utilized to mitigate fading, e.g., robust modulation, coding and interleaving, error-correcting coding, equalization, and diversity. Different kinds of diversities such as space, time, frequency, or any combination of them are possible. Among these diversity techniques, space diversity is of special interest because of its ability to improve performance without sacrificing delay and bandwidth efficiency. Recently, space diversity has been intensively investigated in point-to-point wireless communication systems by the deployment of a MIMO concept together with efficient coding and modulation schemes. In recent years, cooperative communication [109] has been proposed as an alternative communication system that explores MIMO-like diversity to improve link performance without the requirement of additional antennas. However, most of existing works on MIMO systems and cooperative communications are designed based on an assumption that the receivers have full knowledge of the channel state information (CSI). In this case, the schemes must incorporate reliable multi-channel estimation, which inevitably increases the cost of frequent retraining and the number of estimated parameters to the receivers. Although the channel estimates may be available when the channel changes slowly comparing with the symbol rate, they may not be possibly acquired in a fast-fading environment. To develop practical schemes that omit such CSI requirements, we consider in this chapter differential modulations for cooperative communications.

Extending the lifetime of battery-operated devices is a key design issue that allows uninterrupted information exchange among distributed nodes in wireless networks. Cooperative communications enables and leverages effective resource sharing among cooperative nodes. This chapter provides a general framework for lifetime extension of battery-operated devices by exploiting cooperative diversity. The framework efficiently takes advantage of different locations and energy levels among distributed nodes. First, a lifetime maximization problem via cooperative nodes is considered and performance analysis for M-ary PSK modulation is provided. With an objective to maximize the minimum device lifetime under a constraint on bit error rate performance, the optimization problem determines which nodes should cooperate and how much power should be allocated for cooperation. Moreover, the device lifetime is further improved by a deployment of cooperative relays in order to help forward information of the distributed nodes in the network. Optimum location and power allocation for each cooperative relay are determined with an aim to maximize the minimum device lifetime. A suboptimal algorithm is presented to solve the problem with multiple cooperative relays and cooperative nodes.

Introduction

In many applications of wireless networks, extending the lifetime of battery-operated devices is a key design issue that ensures uninterrupted information exchange and alleviates burden of replenishing batteries. Lifetime extension of battery-limited devices has become an important issue due to the need in sensor and ad-hoc networks.

In this chapter, we will discuss shortcomings of conventional point-to-point communications that led to the introduction of the new paradigm shift for wireless communications, i.e., cooperative communications. We will define what the relay channel is, and in what aspects it is different from the direct point-to-point channel. We will also describe several protocols that can be implemented at the relay channel, and discuss the performance of these protocols which will be assessed based on their outage probability and diversity gains.

Cooperative communications

In cooperative communications, independent paths between the user and the base station are generated via the introduction of a relay channel as illustrated in Figure 4.1. The relay channel can be thought of as an auxiliary channel to the direct channel between the source and destination. A key aspect of the cooperative communication process is the processing of the signal received from the source node done by the relay. These different processing schemes result in different cooperative communications protocol. Cooperative communications protocols can be generally categorized into fixed relaying schemes and adaptive relaying schemes. In fixed relaying, the channel resources are divided between the source and the relay in a fixed (deterministic) manner. The processing at the relay differs according to the employed protocol. In a fixed amplify-and-forward (AF) relaying protocol, the relay simply scales the received version and transmits an amplified version of it to the destination.

Wireless communications technologies have seen a remarkably fast evolution in the past two decades. Each new generation of wireless devices has brought notable improvements in terms of communication reliability, data rates, device sizes, battery life, and network connectivity. In addition, the increase homogenization of traffic transports using Internet Protocols is translating into network topologies that are less and less centralized. In recent years, ad-hoc and sensor networks have emerged with many new applications, where a source has to rely on the assistance from other nodes to forward or relay information to a desired destination.

Such a need of cooperation among nodes or users has inspired new thinking and ideas for the design of communications and networking systems by asking whether cooperation can be used to improve system performance. Certainly it means we have to answer what and how performance can be improved by cooperative communications and networking. As a result, a new communication paradigm arose, which had an impact far beyond its original applications to ad-hoc and sensor networks.

First of all, why are cooperative communications in wireless networks possible? Note that the wireless channel is broadcast by nature. Even directional transmission is in fact a kind of broadcast with fewer recipients limited to a certain region. This implies that many nodes or users can “hear” and receive transmissions from a source and can help relay information if needed.

The idea of using multiple transmit and receive antennas in wireless communication systems has attracted considerable attention with the aim of increasing data transmission rate and system capacity. A key issue is how to develop proper transmission techniques to exploit all of the diversities available in the space, time, and frequency domains. In the case of narrow-band wireless communications, the channel fading is frequency non-selective (flat) and diversities are available only in the space and time domains. The modulation and coding approach that is developed for this scenario is termed space–time (ST) coding, exploiting available spatial and temporal diversity.

In this chapter, we first describe the MIMO communication system architecture with frequency-non-selective fading channels, which are often termed as narrow-band wireless channels, and discuss design criteria in achieving the full space–time diversity. Then, we introduce several well-known ST coding techniques that can be guaranteed to achieve full space–time diversity.

System model and performance criteria

Assume that the MIMO systems have Mt transmit and Mr receive antennas. Channel state information (CSI) is assumed to be known at the receiver, but not at the transmitter. In narrowband transmission scenario, the fading channel is frequency-non-selective or flat, and is assumed to be quasi-static, i.e., the channel stays constant during one codeword transmission and it may change independently from one codeword transmission to another. In this case, diversity is available only in the space and time domains.

In this chapter, we consider single relay cooperative communications in wireless networks. We focus on the discussion of symbol error rate (SER) performance analysis and optimum power allocation for uncoded cooperative communications with either an amplify-and-forward (AF) or a selective decode-and-forward (DF) cooperation protocol. In this chapter and the rest of this book, we simply call the selective DF cooperation protocol a DF protocol without confusing it with the fixed DF relaying protocol.

The chapter is organized as follows. First, we briefly describe a system model for cooperative communications with either DF or AF cooperation protocols. Second, we analyze the SER performance for DF cooperation systems, in which a closed-form SER formulation is obtained explicitly for systems with M-PSK and M-QAM modulations. An SER upper bound as well as an approximation are provided to reveal the asymptotic performance of the cooperative system. Based on the tight SER approximation, we can determine an asymptotic optimum power allocation for DF cooperation systems. Third, we consider the SER performance for AF cooperation systems, in which we first derive a simple closed-form moment-generating function (MGF) expression for the harmonic mean of two independent exponential random variables. Then, based on the simple MGF expression, closed-form SER formulations are given for AF cooperation systems with M-PSK and M-QAM modulations. We also provide a tight SER approximation to show the asymptotic performance of AF cooperation systems and to determine an optimum power allocation.

In Chapter 13 we argued that cooperation can benefit the layers of the communication stack that are above the physical layer, where the idea was approached through the study of distributed cooperative routing. In Chapter 14 cooperation was studied as combined with source and channel coding, which extends the use of cooperation with the higher application layer. In fact, when considering that the benefits of cooperation come from the degree of diversity it provides, it is important to also recognize that diversity is not exclusive to implementations at the physical layer. Diversity can also be formed when multiple channels are provided to the application layer, where they are exploited through the use of multiple description source encoders. In multiple description coding different descriptions of the source are generated with the property that they can each be individually decoded or, if possible, be jointly decoded to obtain a reconstruction of the source with lower distortion. More importantly, a multiple description stream provides diversity that can be exploited by sending each description through an independent channel. This form of diversity has been called source coding diversity. Similarly, if we consider channel coding instead of source coding as the originator of diversity, we would be generating channel coding diversity. This chapter focuses on studying systems that exhibit three forms of diversity: source coding diversity, channel coding diversity, and cooperation.