Introduction

OFDM, also known as simultaneous MFSK, has been widely implemented in high-speed digital communications in delay-dispersive environments. It is a multicarrier modulation (MCM) technique. OFDM was first proposed by Chang in 1966. Chang proposed the principle of transmitting messages simultaneously over multiple carriers in a linear band-limited channel without ISI and ICI. The initial version of OFDM employed a large number of oscillators and coherent demodulators. In 1971, DFT was applied to the modulation and demodulation process by Weinstein and Ebert. In 1980, Peled and Ruiz introduced the notion of cyclic prefix to maintain frequency orthogonality over the dispersive channel. The first commercial OFDM-based wireless system is the ETSI DAB standard proposed in 1995.

A wide variety of wired and wireless communication standards are based on the OFDM or MCM technology. Examples are

• digital broadcasting systems such as DAB, DVB-T (Terrestrial DVB), and DVB-H;

• home networking such as digital subscriber line (xDSL) technologies;

• wireless LAN standards such as HyperLAN/2 and IEEE 802.11a/g/n;

• wireless MANs such as IEEE 802.16a/e (WiMAX), ETSI HiperACESS, IEEE 802.20 (mobile-Fi), WiBro, and HiperMAN2;

• wireless WANs such as 3GPP LTE and 3GPP2 UMB;

• powerline communications such as HomePlug;

• wireless PANs such as UWB radios (IEEE 802.15.3a/3c/4a).

It is commonly deemed that OFDM is a major modulation technique for beyond-3G wireless multimedia communications.

Features of OFDM technology

In OFDM technology, the multiple carriers are called subcarriers, and the frequency band occupied by the signal carried by a subcarrier is called a sub-band.

Introduction

Analog input signals are converted into digital signals for digital processing and transmission. The analog-to-digital (A/D) converter (ADC) performs this functionality using two steps: the sample-and-hold (S/H) operation, followed by digital quantization. The ADC is primarily characterized by the sampling rate and resolution. A sampling rate of above twice the Nyquist frequency is a must; otherwise, aliasing occurs and the result is not usable. A higher sample rate leads to a more accurate result, but a more complex system. The successive-approximation ADC successively increases the digital code by digitizing the difference until a match is found. The successive-approximation ADC is the most popular type of ADC. The sigma-delta (Σ-Δ) ADC uses oversampling and noise shaping to significantly attenuate the power of quantization noise in the band of interest.

The digital-to-analog (D/A) converter (DAC) is used to convert the processed digital signal back to an analog signal by comparing it to the input voltage. This chapter introduces ADCs and DACs that are used in wireless communication systems.

Sampling

Ideal and natural sampling

An analog signal x(t), bandlimited to fmax, can be transformed into digital form by periodically sampling the signal at time nT, where T is the sampling period.

In the last three decades, the explosive growth of mobile and wireless communications has radically changed the life of people. Wireless services have migrated from the conventional voice-centric services to data-centric services. The circuit-switched communication network is now being replaced by the all-IP packet-switched network. Mobile communications have also evolved from the first-generation (1G) analog systems to the third-generation (3G) systems now being deployed, and the fourth-generation (4G) systems are now under development and are expected to be available by 2010. The evolution of wireless networking has also taken place rapidly during this period, from low-speed wireless local-area networks (LANs) to broadband wireless LANs, wireless metropolitan area networks (MANs), wireless wide-area networks (WANs), and wireless personal-area networks (PANs). Also, broadband wireless data service has been expanded into broadcasting service, leading to satellite TV broadcasting and wireless regional-area networks (RANs) for digital TV. The data rate has also evolved from the 10 kbits/s voice communications to approximately 1 Gbit/s in the 4G wireless network. In addition, the 4G wireless network will provide ubiquitous communications.

Scope and Purpose

A complete wireless system involves many different areas. However, most existing textbooks on wireless communications focus only on the fundamental principles of wireless communications, while many other areas associated with a whole wireless system, such as digital signal processing, antenna design, microwave and radio frequency (RF) subsystem design, speech coding, video coding, and channel coding, are left to other books.

Conception of software-defined radio

Conception of software-defined radio (SDR) started in the early 1990s, and has now become a core technology for future-generation wireless communications. In 1997, the U.S. DoD recommended replacing its 200 families of radio systems with a single family of SDRs in the programmable modular communications system (PMCS) guideline document. An architecture outlined in this document includes a list of radio functions, hardware and software component categories, and design rules. The ultimate objective of SDR is to configure a radio platform like a freely programmable computer so that it can adapt to any typical air interface by using an appropriate programming interface. SDR is targeted to implement all kinds of air interfaces and signal processing functions using software in one device. It is the basis of the 3G and 4G wireless communications.

Proliferation of wireless standards has created the dramatic need for an MS architecture that supports multiband, multimode, and multistandard low-power radio communications and wireless networking. SDR has become the best solution. By using a unified hardware platform, the user needs only to download software of a radio and run it, and immediately shift to a new radio standard for a different environment. The download of the software can be over the air or via a smart card. For example, several wireless LAN standards, including IEEE 802.11, IEEE 802.15, Bluetooth, and HomeRF, use the 2.4 GHz ISM band, and they can be implemented in one SDR system.

The wireless age

Subsequent to the mathematical theory of electromagnetic waves formulated by James Clerk Maxwell in 1873 and the demonstration of the existence of these waves by Heinrich Hertz in 1887, Guglielmo Marconi made history by using radio waves for transatlantic wireless communications in 1901. In 1906, amplitude modulation (AM) radio was invented by Reginald Fessenden for music broadcasting. In 1913, Edwin H. Armstrong invented the superheterodyne receiver, based on which the first broadcast radio transmission took place at Pittsburgh in 1920. Land-mobile wireless communication was first used in 1921 by the Detroit Police Department. In 1929, Vladimir Zworykin performed the first experiment of TV transmission. In 1933, Edwin H. Armstrong invented frequency modulation (FM). The first public mobile telephone service was introduced in 1946 in five American cities. It was a half-duplex system that used 120 kHz of FM bandwidth. In 1958, the launch of the SCORE (Signal Communication by Orbital Relay Equipment) satellite ushered in a new era of satellite communications. By the mid-1960s, the FM bandwidth was cut to 30 kHz. Automatic channel trunking was introduced in the 1950s and 1960s, with which full-duplex was introduced. The most important breakthrough for modern mobile communications was the concept of cellular mobile systems by AT&T Bell Laboratories in the 1970s.

Roadmap of cellular communications

First-generation systems

The 1G mobile cellular systems were analog speech communication systems. They were mainly deployed before 1990. They are featured by FDMA (frequency division multiple access) coupled with FDD (frequency division duplexing), analog FM (frequency modulation) for speech modulation, and FSK (frequency shift keying) for control signaling, and provide analog voice services. The 1G systems were mainly deployed at the frequency bands from 450 MHz to 1 GHz. The cell radius is between 2 km and 40 km.

The AMPS (Advanced Mobile Phone Services) technique was developed by Bell Labs in the 1970s and was first deployed in late 1983. Each channel occupies 30 kHz. The speech modulation is FM with a frequency deviation of ±12 kHz, and the control signal is modulated by FSK with a frequency deviation of ±8 kHz. The control channel transmits the data streams at 10 kbits/s. AMPS was deployed in the USA, South America, Australia, and China. In 1991, Motorola introduced the N-AMPS to support three users in a 30 kHz AMPS channel, each with a 10 kHz channel, thus increasing the capacity threefold.

The European TACS (Total Access Communication System) was first deployed in 1985. TACS is identical to AMPS, except for the channel bandwidth of 25 kHz. Speech is modulated by FM with a frequency deviation of ±12 kHz, and the control signal is modulated by FSK with a frequency deviation of ±6.4 kHz, achieving a data rate of 8 kbits/s.

Random variables

Probability is an essential idea in both information theory and quantum mechanics. It is a highly developed mathematical and philosophical subject of its own, worthy of serious study. In this brief appendix, however, we can only sketch a few elementary concepts, tools, and theorems that we use elsewhere in the text.

In discussing the properties of a collection of sets, it is often useful to suppose that they are all subsets of an overall “universe” set U. The universe serves as a frame within which unions, intersections, complements, and other set operations can be described. In much the same way, the ideas of probability exist with a frame called a probability space Σ. For simplicity, we will consider only the discrete case. Then Σ consists of an underlying set of points and an assignment of probabilities. The set is called a sample space and its elements are events. The probability function, or probability distribution, assigns to each event e a real number P(e) between 0 and 1, such that the sum of all the probabilities is 1.

The probability P(e) is a measure of the likelihood that event e occurs. An impossible event has P(e) = 0 and a certain event would have P(e) = 1; in other cases, P(e) has some intermediate value.

The probability space itself contains all possible events that may occur, identified in complete detail, which makes it too elaborate for actual use. Suppose we flip a coin.

Beyond state vectors

We cannot always assign a definite state vector |ψ〉 to a quantum system Q. It may be that Q is part of a composite system RQ that is in an entangled state |Ψ(RQ)〉. Or it may be that our knowledge of the preparation of Q is insufficient to determine a particular state |ψ〉. Consider, for instance, a qubit sent from Alice to Bob during the BB84 key distribution protocol from Section 4.4. The state of this qubit could be |0〉, |1〉, |+〉 or |−〉, each with equal likelihood. In either case – whether Q is a subsystem of an entangled system, or the state of Q is determined by a probabilistic process – we cannot specify a quantum state vector |ψ〉 for Q.

Nevertheless, in either case we are in a position to make statistical predictions about the outcomes of measurements on Q. In this chapter we describe the mathematical machinery for doing this.

Mixtures of states

Suppose the state of Q arises by a random process, so that the state |ψα〉 is prepared with probability pα. The possible states |ψα〉 need not be orthogonal (as you can see in the BB84 example above). We call this situation a mixture of the states |ψα〉, or a mixed state for short.

One way to interpret a mixed state is to return to the idea of an ensemble of systems, which we introduced in Section 3.3.