The high level of technical detail included in standards specifications can make it difficult to find the correlation between the standard specifications and the theoretical results. This book aims to cover both of these elements to give accessible information and support to readers. It explains the current and future trends on communication theory and shows how these developments are implemented in contemporary wireless communication standards.

Examining modulation, coding and multiple access techniques, the book is divided into two major sections to cover these functions. The two-stage approach first treats the basics of modulation and coding theory before highlighting how these concepts are defined and implemented in modern wireless communication systems. Part 1 is devoted to the presentation of main L1 procedures and methods including modulation, coding, channel equalization and multiple access techniques. In Part 2, the uses of these procedures and methods in the wide range of wireless communication standards including WLAN, WiMax, WCDMA, HSPA, LTE and cdma2000 are considered.

• An essential study of the implementation of modulation and coding techniques in modern standards of wireless communication
• Bridges the gap between the modulation coding theory and the wireless communications standards material
• Divided into two parts to systematically tackle the topic – the first part develops techniques which are then applied and tailored to real world systems in the second part
• Covers special aspects of coding theory and how these can be effectively applied to improve the performance of wireless communications systems

Professor E. Krouk has worked in the field of communication theory and techniques for more than 30 years. His areas of interests are coding theory, the mathematical theory of communications and cryptography. He is now the Dean of the Information Systems and Data Protection Faculty of the Saint-Petersburg State University of Aerospace Instrumentation. He is author of 3 books, more than 100 scientific articles and 30 international and Russian patents.

Sergei Semenov received his Ph.D. degree from St.-Petersburg State University for Airspace Instrumentation (SUAI), Russia in 1993. Dr. Semenov joined Nokia Corporation in 1999 and is currently a Specialist in Modem Algorithm Design/Wireless Modem. His research interests include coding and communication theory and their application to communication systems.

Modulation and Coding Techniques in Wireless Communications

John Wiley & Sons

Copyright © 2011 John Wiley & Sons, Ltd
All right reserved.
ISBN: 978-0-470-74505-2

Chapter One

Channel Models and Reliable Communication

Evgenii Krouk, Andrei Ovchinnikov, and Jussi Poikonen

1.1 Principles of Reliable Communication

Ideally, design, development and deployment of communication systems aims at maximally efficient utilization of available resources for transferring information reliably between a sender and a recipient. In real systems, typically some amount of unreliability is tolerated in this transfer to achieve a predefined level of consumption of limited resources. In modern communication systems, primary resources are time, space, and power and frequency bandwidth of the electromagnetic radiation used to convey information. Given such resources, systems must be designed to overcome distortions to transmitted information caused mainly by elements within the system itself, possible external communications, and the environment through which the information propagates. To achieve efficient utilization of available resources, knowledge of the mechanisms that cause interference in a given transmission scenario must be available in designing and analyzing a communication system.

In performance evaluation of wireless communication systems, significance of the communication channel is emphasized, since the degradation of a signal propagating from a transmitter to a receiver is strongly dependent on their locations relative to the external environment. Wireless mobile communication, where either the transmitter or the receiver is in motion, presents additional challenges to channel modelling, as it is necessary to account for variation in the signal distortion as a function of time for each transmitterreceiver pair. In developing and analyzing such systems, comprehensively modelling the transmitterreceiver link is a complicated task.

In the following, distortions caused by typical communication channels to transmitted signals are described. A common property of all communication channels is that the received signal contains noise, which fundamentally limits the rate of communication. Noise is typically modelled as a Gaussian stochastic process. The additive white Gaussian noise (AWGN) channel and its effects on typical digital modulation methods are presented in Section 1.2. Noise is added to transmitted signals at the receiver. Before arriving at the receiver terminal, signals are typically distorted according to various physical characteristics of the propagation medium. These distortions attenuate the received signal, and thus increase the detrimental effect of additive noise on the reliability of communication. In Section 1.3 to 1.5 typical cases of distortion in wireless communication channels and models for the effects of such distortion on transmitted signals are presented.

1.2 AWGN

Distortions occurring in typical communication systems can be divided into multiplicative and additive components. In the following, some remarks and relevant results concerning additive distortion – also referred to simply as noise – are presented.

Additive noise is introduced to a wireless communication system both from outside sources such as atmospheric effects, cosmic radiation and electrical devices – and from internal components of the receiver hardware, which produce thermal and shot noise. Typically, additive distortion in a received signal consists of a sum of a large number of independent random components, and is modelled as additive white Gaussian noise, where the term white means that the noise is assumed to have a constant power spectral density. The Gaussian, or normal, distribution of noise is motivated by the central limit theorem (one of the fundamental theorems of probability theory), according to which the distribution of a sum of a large number of random variables approaches a normal distribution, given that these variables fulfill Lyapunov’s condition (for details, see for example).

In some cases, the received signal is also distorted by a channel-induced superposition of different components of the useful transmission, or by signals from other transmission systems. Such distortions are called interference, and differ from additive noise in that typically some source-specific statistical characteristics of interference are known. Thus interference is not in all cases best approximated as an additive white Gaussian process. Interference effects are strongly dependent on the communication systems and transmission scenarios under consideration. Later in this chapter, interference-causing effects of wireless communication channels are considered. In the following, we focus on considering the effects of additive white Gaussian noise on complex baseband modulation symbols. Principles of digital modulation methods and the effects of noise on the reception of various types of transmitted signals will be considered in more detail in Chapter 2; the following simple examples are meant to illustrate the concept of additive noise and its effect on digital communication.

1.2.1 Baseband Representation of AWGN

In the following examples, we consider digital data which is mapped to binary phase shift keying (BPSK), quaternary phase shift keying (QPSK/4-QAM), and 16-point quadrature amplitude modulation (16-QAM) symbols. We consider complex baseband signals, that is, for our purposes the transmitted modulation symbols corresponding to a given digital modulation scheme are represented simply as complex numbers. The constellation diagrams for these examples are illustrated in Figure 1.1. The effect of an AWGN channel is to shift these numbers in the complex plane. The receiver has to decide, based on an observed shifted complex number, the most likely transmitted symbol. This decision is performed by finding which, out of the set of known transmitted symbols, is the one with the smallest Euclidian distance to the received noisy symbol. This is a rather abstract representation of digital signals and noise, but sufficient for performing error performance analyses of different modulation schemes. For a more detailed discussion on basic modulation methods and the corresponding signal forms, see Chapter 2.

As outlined above, in complex baseband signal-space representations, the effect of additive white Gaussian noise in the receiver can be described as a complex number added to each transmitted modulation symbol value. The real and imaginary parts of these complex numbers are independent and identically distributed Gaussian random variables with zero mean and variance equal to σ²_N = [bar.P].sub. N/2, where [bar.P]_N denotes the total average power of the complex noise process (that is, the power of the noise is evenly distributed into the two signalling dimensions). In the following, the orthogonal components of the noise process are denoted by a common notation X_N ~ N (0, [bar.P]_N/2).

If the absolute value of either the real or the imaginary noise component is larger than half of the Euclidian distance d between adjacent modulation symbols, a transmitted symbol may be erroneously decoded into any symbol within a complex half-plane, as illustrated in the QPSK example of Figure 1.2. The probability of one of the independent and identically distributed noise components having such values can be written as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.1)

where the final expression is given in terms of the cumulative distribution function of a normalized Gaussian random variable. Error probabilities are usually specified in this form, since the Q-function [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is widely tabulated in mathematical reference books, and easily calculated with programs such as Matlab. The expression (1.1) gives directly the probability of error for BPSK, and can be used to calculate the average probability of error for larger QAM constellations. In Figure 1.3, the principle of calculating the symbol error probability of QPSK using (1.1) is illustrated. The same principle is applied in Figure 1.4 to 16-QAM, where several different error cases have to be considered, and averaged to obtain the total probability of symbol error.

In the preceeding examples, the error probabilities are calculated in terms of the minimum distance of the constellations and the average noise power. However, it is more convenient to consider error probabilities in terms of the ratio of average signal and noise powers. For any uniform QAM constellation, the distance between any pair of neighbouring symbols (that is, the minimum distance) is easily obtained as a function of the average transmitted signal power [bar.P]_S – which is calculated as the average over the squared absolute values of the complex-valued constellation points – as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The average symbol error probability for each of the cases above is now obtained by calculating averages over demodulation error probabilities for the signal sets as a function of the average signal-to-noise ratio, given by [bar.P]_S/[bar.P]_N [??] λ. Using the equations given above, the average symbol error probabilities are obtained, following the principle outlined in the examples of Figures 1.3 and 1.4, as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

1.2.2 From Sample SNR to E_b/N₀

Assume the transmitted symbols are mapped to rectangular baseband signal pulses of duration T_symb, sampled with frequency f_sampl, with complex envelopes corresponding to the constellation points of the signal-space representation used above. These rectangular pulses are then modulated by a given carrier frequency, transmitted through a noisy channel, downconverted in a receiver and passed to a matched filter or correlator for signal detection.

Figure 1.5 shows an example of two BPSK symbols transmitted and received as described above. In this example, the signal-to-noise ratio per sample is defined as SNR = A²/σ_n², where σ_n² is the sample variance of the real-valued noise process. It can be seen that, based on any individual sample of the received signals, the probability of error is quite large. However, calculating the averages (plotted with dashed lines in Figure 1.5) of the signals over their entire durations (0.1 s, containing 100 samples) gives values for the signal envelopes that are very close to the correct values –1 and 1, thus reducing the effect of the added noise considerably. It is clear that in this case, the sample SNR is no longer enough to determine the probability of error at the receiver. The relevant question is how should the sample SNR be scaled to obtain the correct error probability? We study this using BPSK as an example.

As above, the probability of symbol (bit) error based on the signal-space representation for BPSK over an AWGN channel is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where N is a normally distributed random variable with standard deviation σn and zero mean, and it is assumed (without loss of generality) that the signal amplitude A₁ > 0 (corresponding to a 1 being sent). This can be thought of as transmitting a single sample of the signal envelope. Sampling a received signal envelope S(t) + N(t) at k points produces a sequence of samples S(i*middot;T_sampl) + N(i*middot;T_sampl), where T_sampl = 1/f_sampl, and i = 1 … k. A correlator receiver for BPSK may use the following test statistic to decide whether a 1 was most likely to be transmitted:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Assuming that a 1 was indeed sent, a false decision will be made if:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

or

[bar.N] <–A₁

denoting the sample mean of the noise as [bar.N]. We note that the expression is the same as for the single sample case, only with the normal random variable replaced by the sample mean of k samples from a normal distribution. Basic results of statistics state that this sample mean is also normally distributed, in this case with mean zero and standard deviation σ_[bar.N] = σ_n/[square root of k]. We thus find that the error probability in this example is determined by the ratio k · (σ^2>_s/σ^2> _s), or k times the sample SNR.

It should be noted that although we used BPSK as an example to simplify the relevant expressions, the above result is not restricted only to BPSK. In fact, the obtained expression k · (σ^2>_s/σ ^2>_s) is generally used in a form derived as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

In the above, N₀ is the noise power spectral density and B_n is the noise bandwidth. Note that the signal energy E_S = [bar.P]_S · T_symb, and that B_n = f_sampl (this is based on the Shannon-Nyquist sampling theorem applied for complex samples). Note also that here it is implicitly assumed that the signal bandwidth corresponds to the Nyquist frequency; if the signal is oversampled, care should be taken in performance analysis to include only the noise bandwidth which overlaps with the spectrum of the signal. Finally, the ratio of energy per bit to noise power spectral density E_b /N₀, very commonly used as a measure for signal quality, is obtained as:

E_b/N₀ = 1/n_b E_s/N₀

where n is the number of bits per transmitted symbol.

1.3 Fading Processes in Wireless Communication Channels

Additive noise is present in all communication systems. It is a fundamental result of information theory that the ratio of signal and noise powers at the receiver determines the capacity, or maximum achievable rate of error-free transmission of information, of a channel. Generally, multiplicative effects of a communication channel, or fading, can be represented as a convolution of the transmitted signal with the channel impulse response, as illustrated in Figure 1.6. A general effect of fading is to reduce the signal power arriving at the receiver. Since the noise power at the receiver is independent of the useful signal, and the noise component does not experience fading, a fading channel generally reduces the ratio of the signal power to the noise power at the receiver, thus also reducing the transmission capacity.

The distortion, or noise, caused by a communication channel to the transmitted signal can be divided into multiplicative and additive components; the latter was considered above. Multiplicative noise, or fading, can be defined as the relative difference between the powers contained in corresponding sections of the transmitted and received signals. Factors that typically contribute to the fading in wireless communication systems are the transmitter and receiver antenna and analog front-end characteristics, absorption of the signal power by the propagation media, and reflection, refraction, scattering and diffraction caused by obstacles in the propagation path. The receiver experiences the combined effect of all these physical factors, which vary according to the positions of the receiver and transmitter within the propagation environment. It should be noted that it is generally possible to describe the effects of a communication channel entirely by its impulse response as illustrated in Figure 1.6. However, it is typical that estimation of the average power conveyed by a transmission channel is performed separately from the modelling of the channel’s impulse response, which is then power-normalized. We also apply this principle in the following discussion on fading processes in wireless channels.

Fading in wireless channels is in literature typically characterized as a concatenation or superposition of several types of fading processes. These processes are often classified using the qualitative terms path loss, shadowing, and multipath fading, which is also often referred to as fast fading. However, these fading processes cannot in general be considered fully independent of each other, and indeed in many references (for example in) path loss and shadowing are not considered as separate processes. Justification for this will be subsequently considered in more detail. In the following, fading is primarily classified according to the typical variation from the mean attenuation over a spatial region of given magnitude. The terms large-scale, medium-scale, and small-scale fading are thus used.

(Continues…)

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