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**Fundamentals of Wireless Communication**

David Tse Wireless Foundations U.C. Berkeley USCD June 9-10, 2006

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1. Introduction

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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 x EV-DO, Flash OFDM.)

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**System Implementation**

Capacity limits and communication techniques Channel modelling

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**Course Outline Part I: Basics 2. The Wireless Channel Diversity**

4. Multiple Access and Interference Management 5. Capacity of Wireless Channels

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**Course Outline (2) Part II: Modern Wireless Communication**

6. Opportunistic Communication and Multiuser Diversity 7. MIMO : Spatial Multiplexing and Channel Modeling

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Assumed background: Basic signals and systems, linear algebra and proabability. Basic digital communications.

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**This course only gives an overview of the ideas.**

Full details can be found in:

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2. The Wireless Channel

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**Wireless Mulipath Channel**

Channel varies at two spatial scales: large scale fading small scale fading

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**Large-scale fading In free space, received power attenuates like 1/r2.**

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.

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**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.

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**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.

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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 time-invariant:

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**Passband to Baseband Conversion**

Communication takes place at Processing takes place at baseband

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**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.

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**Modulation and Sampling**

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**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 .

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**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 sinc(W(-i)) sampled at =l/W. Contribution is significant only when i is close to l/W.

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**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 .

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**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

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**Effective channel depends on both physical environment and bandwidth!**

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**Time Variations: 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

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**Time Variations: General**

Doppler shift of the i th path Doppler spread Coherence time

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**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.

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Types of Channels

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**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.

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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

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Correlation over Time Specified by autocorrelation function and power spectral density of fading process. Example: Clarke’s (or Jake’s) model.

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**Additive Gaussian Noise**

Complete baseband-equivalent channel model: Special case: flat fading: Will use this throughout the course.

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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.

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