2 The Wireless Channel Fundamentals of Wireless Communication

2: The Wireless Channel Fundamentals of Wireless Communication David Tse University of California, Berkeley Pramod Viswanath University of Illinois, Urbana-Champaign Fundamentals of Wireless Communication, Tse&Viswanath

2: The Wireless Channel 1. Introduction Fundamentals of Wireless Communication, Tse&Viswanath

2: The Wireless Channel Course Objective • Past decade has seen a surge of research activities in the field of wireless communication. • Emerging from this research thrust are new points of view on how to communicate effectively over wireless channels. • The goal of this course is to study in a unified way the fundamentals as well as the new research developments. • The concepts are illustrated using examples from several modern wireless systems (GSM, IS-95, CDMA 2000 1 x EV-DO, Flarion's Flash OFDM, Array. Comm systems. ) Fundamentals of Wireless Communication, Tse&Viswanath 2

2: The Wireless Channel System Implementation Capacity limits and communication techniques Channel modelling Fundamentals of Wireless Communication, Tse&Viswanath 3

2: The Wireless Channel Course Outline Part I: Basics 2. The Wireless Channel 3. Diversity 4. Multiple Access and Interference Management 5. Capacity of Wireless Channels Fundamentals of Wireless Communication, Tse&Viswanath 4

2: The Wireless Channel Course Outline (2) Part II: Modern Wireless Communication 6. Opportunistic Communication and Multiuser Diversity 7. MIMO I: Spatial Multiplexing and Channel Modeling 8. MIMO II: Capacity and Multiplexing Architectures 9. MIMO III: Diversity-Multiplexing Tradeoff Fundamentals of Wireless Communication, Tse&Viswanath 5

2: The Wireless Channel Assumed background: • Basic signals and systems, linear algebra and probability. • Basic digital communications. Fundamentals of Wireless Communication, Tse&Viswanath 6

2: The Wireless Channel These slides only gives an overview of the ideas. Full details can be found in: http: //www. eecs. berkeley. edu/~dtse/book. html Fundamentals of Wireless Communication, Tse&Viswanath 7

2: The Wireless Channel 2. The Wireless Channel Fundamentals of Wireless Communication, Tse&Viswanath

2: The Wireless Channel Wireless Mulipath Channel varies at two spatial scales: large scale fading small scale fading Fundamentals of Wireless Communication, Tse&Viswanath 9

2: The Wireless Channel Large-scale fading • In free space, received power attenuates like 1/r 2. • With reflections and obstructions, can attenuate even more rapidly with distance. Detailed modelling complicated. • Time constants associated with variations are very long as the mobile moves, many seconds or minutes. • More important for cell site planning, less for communication system design. Fundamentals of Wireless Communication, Tse&Viswanath 10

2: The Wireless Channel Small-scale multipath fading • Wireless communication typically happens at very high carrier frequency. (eg. fc = 900 MHz or 1. 9 GHz for cellular) • Multipath fading due to constructive and destructive interference of the transmitted waves. • Channel varies when mobile moves a distance of the order of the carrier wavelength. This is about 0. 3 m for 900 Mhz cellular. • For vehicular speeds, this translates to channel variation of the order of 100 Hz. • Primary driver behind wireless communication system design. Fundamentals of Wireless Communication, Tse&Viswanath 11

2: The Wireless Channel Game plan • We wish to understand how physical parameters such as – – – carrier frequency mobile speed bandwidth delay spread angular spread impact how a wireless channel behaves from the communication system point of view. • We start with deterministic physical model and progress towards statistical models, which are more useful for design and performance evaluation. Fundamentals of Wireless Communication, Tse&Viswanath 12

2: The Wireless Channel Physical Models • Wireless channels can be modeled as linear time-varying systems: where ai(t) and i(t) are the gain and delay of path i. • The time-varying impulse response is: • Consider first the special case when the channel is timeinvariant: Fundamentals of Wireless Communication, Tse&Viswanath 13

2: The Wireless Channel Passband to Baseband Conversion • Communication takes place at • Processing takes place at baseband Fundamentals of Wireless Communication, Tse&Viswanath 14

2: The Wireless Channel Complex Baseband Equivalent Channel • The frequency response of the system is shifted from the passband to the baseband. • Each path is associated with a delay and a complex gain. Fundamentals of Wireless Communication, Tse&Viswanath 15

2: The Wireless Channel Modulation and Sampling Fundamentals of Wireless Communication, Tse&Viswanath 16

2: The Wireless Channel Multipath Resolution Sampled baseband-equivalent channel model: where hl is the l th complex channel tap. and the sum is over all paths that fall in the delay bin System resolves the multipaths up to delays of 1/W. Fundamentals of Wireless Communication, Tse&Viswanath 17

2: The Wireless Channel Sampling Interpretation • hl is the l th sample of the low-pass version of the channel response hb(¢). • Contribution of the i th path is the projection of aib ( - i) onto sinc(W -l). Fundamentals of Wireless Communication, Tse&Viswanath 18

2: The Wireless Channel Flat and Frequency-Selective Fading • Fading occurs when there is destructive interference of the multipaths that contribute to a tap. Delay spread Coherence bandwidth single tap, flat fading multiple taps, frequency selective Fundamentals of Wireless Communication, Tse&Viswanath 19

2: The Wireless Channel Effective channel depends on both physical environment and bandwidth! Fundamentals of Wireless Communication, Tse&Viswanath 20

2: The Wireless Channel Time Variations Doppler shift of the i th path Doppler spread Coherence time Fundamentals of Wireless Communication, Tse&Viswanath 21

2: The Wireless Channel Two-path Example v= 60 km/hr, fc = 900 MHz: direct path has Doppler shift of -50 Hz reflected path has shift of +50 Hz Doppler spread = 100 Hz Fundamentals of Wireless Communication, Tse&Viswanath 22

2: The Wireless Channel Doppler Spread Doppler spread is proportional to: • the carrier frequency fc; • the angular spread of arriving paths. where i is the angle the direction of motion makes with the i th path. Fundamentals of Wireless Communication, Tse&Viswanath 23

2: The Wireless Channel Fundamentals of Wireless Communication, Tse&Viswanath 24

2: The Wireless Channel Types of Channels Fundamentals of Wireless Communication, Tse&Viswanath 25

2: The Wireless Channel Typical Channels are Underspread • Coherence time Tc depends on carrier frequency and vehicular speed, of the order of milliseconds or more. • Delay spread Td depends on distance to scatterers, of the order of nanoseconds (indoor) to microseconds (outdoor). • Channel can be considered as time-invariant over a long time scale. Fundamentals of Wireless Communication, Tse&Viswanath 26

2: The Wireless Channel Statistical Models • Design and performance analysis based on statistical ensemble of channels rather than specific physical channel. • Rayleigh flat fading model: many small scattered paths Complex circular symmetric Gaussian. Squared magnitude is exponentially distributed. • Rician model: 1 line-of-sight plus scattered paths Fundamentals of Wireless Communication, Tse&Viswanath 27

2: The Wireless Channel Correlation over Time • Specified by autocorrelation function and power spectral density of fading process. • Example: Clarke’s (or Jake’s) model. Fundamentals of Wireless Communication, Tse&Viswanath 28

2: The Wireless Channel Additive Gaussian Noise • Complete baseband-equivalent channel model: • Special case: flat fading: • Will use this throughout the course. Fundamentals of Wireless Communication, Tse&Viswanath 29

2: The Wireless Channel Summary • We have understood how time and frequency selectivity of wireless channels depend on key physical parameters. • We have come up with statistical channel models that are useful for analysis and design. Fundamentals of Wireless Communication, Tse&Viswanath 30