In this chapter, I introduce the main issues we will deal with in the book. In Section 2.1, I describe a multicarrier (MC) communication system. I introduce the main stages that the signals undergo in MC systems and summarize advantages and drawbacks of this technology. Section 2.2 deals with formal definitions of the main notions related to peak power: peak-to-average power ratio, peak-to-mean envelope power ratio, and crest factor. In Section 2.3, I quantify the efficiency of power amplifiers and its dependence on the power of processed MC signals. Section 2.4 introduces nonlinear characteristics of power amplifiers and describes their influence on the performance of communication systems.

Model of multicarrier communication system

The basic concept behind multicarrier (MC) transmission is in dividing the available spectrum into subchannels, assigning a carrier to each of them, and distributing the information stream between subcarriers. Each carrier is modulated separately, and the superposition of the modulated signals is transmitted. Such a scheme has several benefits: if the subcarrier spacing is small enough, each subchannel exhibits a flat frequency response, thus making frequency-domain equalization easier. Each substream has a low bit rate, which means that the symbol has a considerable duration; this makes it less sensitive to impulse noise. When the number of subcarriers increases for properly chosen modulating functions, the spectrum approaches a rectangular shape. The multicarrier scheme shows a good modularity. For instance, the subcarriers exhibiting a disadvantageous signal-to-noise ratio (SNR) can be discarded. Moreover, it is possible to choose the constellation size (bit loading) and energy for each subcarrier, thus approaching the theoretical capacity of the channel.

Multicarrier (MC) modulations such as orthogonal frequency division multiplexing (OFDM) and discrete multitone (DMT) are efficient technologies for the implementation of wireless and wireline communication systems. Advantages of MC systems over single-carrier ones explain their broad acceptance for various telecommunication standards (e.g., ADSL, VDSL, DAB, DVB, WLAN, WMAN). Yet many more appearances are envisioned for MC technology in the standards to come. A relatively simple implementation is possible for MC systems. Low complexity is due to the use of fast discrete Fourier transform (DFT), avoiding complicated equalization algorithms. Efficient performance of MC modulation is especially vivid in channels with frequency selective fading and multipath. Nonetheless, still a major barrier for implementing MC schemes in low-cost applications is its nonconstant signal envelope, making the transmission sensitive to nonlinear devices in the communication path. Amplifiers and digital-to-analog converters distort the transmit signals leading to increased symbol error rates, spectral regrowth, and reduced power efficiency compared with single carrier systems. Naturally, the transmit signals should be restricted to those that do not cause the undesired distortions. Areasonable measure of the relevance of the signals is the ratio between the peak power values to their average power (PAPR). Thus the goal of peak power control is to diminish the influence of transmit signals with high PAPR on the performance of the transmission system. Alternatives are either the complete exclusion of such signals or an essential decrease in the probability of their appearance.

In this chapter, I consider methods of decreasing peak power in MC signals. The simplest method is to clip the MC signal deliberately before amplification. This method is very simple to implement and provides essential PMEPR reduction. However, it suffers some performance degradation, as estimated in Section 8.1. In selective mapping (SLM), discussed in Section 8.2, one favorable signal is selected from a set of different signals that all represent the same information. One possibility for SLM is to choose the best signal from those obtained by inverting any of the coordinates of the coefficient vector. The method of deciding which of the coordinates should be inverted is described in Section 8.3. Further, in Section 8.4 a modification of SLM is analyzed. There the favorable vector is chosen from a coset of a code of given strength. Trellis shaping, where the relevant modification is chosen based on a search on a trellis, is described in Section 8.5. In Section 8.6, the method of tone injection is discussed. Here, instead of using a constellation point its appropriately shifted version can be used. In active constellation extension (ACE), described in Section 8.7, some of the outer constellation points can be extended, yielding PMEPR reduction. In Section 8.8, a method of finding a constellation in the frequency domain is described, such that the resulting region in the time domain has a low PMEPR. In partial transmit sequences (PTS), the transmitted signal is made to have a low PMEPR by partitioning the information-bearing vector to sub-blocks followed by multiplying by a rotating factor the coefficients belonging to the same sub-block.

In this chapter I collect the basic mathematical tools which are used throughout the book. Most of them are given with rigorous proofs. I mainly concentrate here on results and methods that do not appear in the standard engineering textbooks and omit those that happen to be common technical knowledge. On the other hand, I have included some material that is not directly used in further arguments, but I feel that it might prove useful in further research on peak power control problems. It should be advised that the chapter is mainly for reference purposes and may be omitted in the first reading.

The chapter is organized as follows. Section 3.1 deals with harmonic analysis. In Section 3.1.1 I describe the Parseval equality and its generalizations. Section 3.1.2 introduces some useful trigonometric relations. Chebyshev polynomials and interpolation are described in Section 3.1.3. Finally, in Section 3.1.4, I prove Bernstein's inequality relating the maximum of the absolute value of a trigonometric polynomial and its derivative. In Section 3.2 I deal with some notions related to probability. I prove the Chernoff bound on the probability of deviations of values of random variables. In Section 3.3, I introduce tools from algebra. In Section 3.3.1 groups, rings, and fields are defined. Section 3.3.2 describes exponential sums in finite fields and rings. A short account of results from coding theory is presented in Section 3.4. Section 3.4.1 deals with properties of the Hamming space. In Section 3.4.2, definitions related to error-correction codes are introduced. Section 3.4.3 deals with the distance distributions of codes. In Section 3.4.4, I analyze properties of Krawtchouk polynomials playing an important role in the Mac Williams transform of the distance distributions.

In many situations it is beneficial to deal with a discrete-time “sampled” version of multicarrier signals. This reduction allows passing from the continuous setting to an easier-to-handle discrete one. However, we have to estimate the inaccuracies stemming from the approach. In this chapter, I analyze the ratio between the maximum of the absolute value of a continuous MC signal and the maximum over a set of the signal's samples. We start with considering the ratio when the signal is sampled at the Nyquist frequency, i.e. the number of sampling points equals the number of tones. In this case I show that the maximum of the ratio over all MC signals grows with the number of subcarriers (Theorem 4.2). However, if one computes a weighted sum of the maximum of the signal's samples and the maximum of the signal derivative's samples the ratio already is, at most, a constant (Theorem 4.5). I further show that actually the ratio depends on the maximum of the signal; the larger the maximum is the smaller is the ratio (Theorem 4.6). An even better strategy is to use over sampling. Then the ratio becomes constant tending to 1 when the over sampling rate grows (Theorems 4.8, 4.9, 4.10, and 4.11). Furthermore, I tackle the case when we have to use the maximum estimation, projections on specially chosen measuring axes instead of the absolute values of the signal (Theorem 4.14). Finally, I address the problem of relation between the PAPR and the PMEPR and show that the PMEPR estimates the PAPR quite accurately for large values of the carrier frequency (Theorem 4.19).

Chapter 2 kicks off the presentation with an overview of the standard metrics and methodologies followed by a description of specialized tools employed for obtaining subjective voice-quality scores through genuine opinion surveys and via computer modeling emulating human perceptive evaluation of speech quality. It then relates voice-quality scores obtained via surveys or computer evaluations to the perception of worth. It elaborates on the relationships between opinion scores and the potential return on investment in voice-quality technology. It examines results of voice-quality studies with reference to the three popular GSM codecs – full rate (FR), enhanced full rate (EFR) and half rate (HR). The presentation includes a discussion of the effect of noise and transmission errors on the relative performance of these codecs.

Introduction

It is widely agreed that the most vital element affecting the performance of voice quality in wireless networks is the type of codec used in the communication session. It is also well known that spectrum is the most expensive (per channel) building block contributing to the viability of wireless infrastructure. Yet most European GSM wireless operators, throughout the nineties and the first half of the following decade, have opted to restrict their service offerings to full-rate (FR) or enhanced full-rate (EFR), rather than embracing the half-rate (HR) option, which could cut their spectrum consumption in half and save them millions of dollars in operating expenses.

Introduction

Chapter 6 is dedicated to the subject of level-control optimization. The presentation is divided into three parts and an introduction. The chapter starts the ball rolling in the introduction by defining standard methodologies for measuring and quantifying signal levels. The first part deals with automatic level control (ALC), how it works, and its placement within the network. The second part describes the adaptive level control, a.k.a. noise compensation (NC), how it works under different codecs, and where it is placed in the network. The third part describes the high-level compensation procedure along the same outline.

Basic signal-level measurements and definitions

One of the most critical speech-quality attributes is the perceived-speech level. When it is too loud, it may either overload or hurt the eardrum. When it is too soft, the listener or even the codec may have difficulties picking up words. There are several different measures and metrics used to measure speech levels. The common thread linking them together to a standardized scale is the unit of measurement defined as decibel and abbreviated as dB.

The human auditory system has a dynamic range of 100,000,000,000,000 (1014) intensity units. This dynamic range is better represented by a logarithmic scale, as a ratio of two intensities, P1 and P2. The expression “log(P1/P2)” is labeled a bel. The resulting number is still too large so, instead, the measure employed is one tenth of a bel or a decibel (dB).

Chapter 3 provides an overview of echo in telecommunications networks, its root causes, and its parameters. It follows the presentation with the methods used for controlling electrical echo, including network loss, echo suppression, linear convolution, non-linear processing, and comfort noise injection. The chapter covers the application of echo cancelation in wireless communications. And, in view of the fact that today's wireless networks include long-distance circuit switched, VoIP, and VoATM infrastructures (specifically as part of third-generation architectures), the chapter covers echo cancelation in long-distance and voice-over-packet applications.

Electrical echo

Many people have never experienced echo on a telephone call. They either never made calls outside their vicinity, or never encountered a malfunctioning echo canceler on their long-distance or wireless calls. In reality, echo does exist in the network. It accompanies every call involving an analog PSTN phone, but in most cases it either gets canceled before reaching its listening ear or it arrives too quickly with little delay, so it can sneak in undetected.

To hear an echo, we must first generate a sound. Then the sound must travel over a substantial distance or a slow terrain (a.k.a. complex processing) to accumulate delay. Next, the sound must be reflected and then travel back towards us. Finally, when the reflected sound reaches our ear, it must be loud enough to be heard. In addition, the amount of delay that the original sound signal incurs influences our perception of “reverberated echo” (i.e., increasing delay produces a greater echo effect).

Most people view sleep as a biological necessity designed to rejuvenate and invigorate body and mind so that human beings can function effectively when they are awake. While awake we tend to eat, dispose of waste, spawn the new generation, and take care of business, so that when the day is over we can go back to sleep.

When asked: “What is life's purpose?” we immediately think of life as the time we spend on earth while being awake.

Now let's reverse the paradigm. Let's pretend for a brief moment that life's purpose is a good sleep, and that all of the energetic activities above are designed to sustain our ability to go back and “live” (while asleep) the next day (see Figure 16.1).

I know. This is a weird thought, but let's see if we can apply the concept to voice-quality engineering in wireless networks, so that it makes sense.

Voice-quality systems are designed to operate on voice and to disable themselves on detection of data transmission. In other words, when turning on the VQS, voice-enhancement applications are enabled automatically while the system goes on guard, watching for any data that might require a disabling action.

Now let's reverse the paradigm. Let's disable all or a particular VQ application upon system turn-on, and continue to monitor the channel until voice is detected. When this occurs, the system enables the VQ application, and then puts it back to sleep when the monitored signal no longer looks like voice.