5.1. Small-Scale Multipath Propagation5.1.1. Factors Influencing Small-Scale Fading5.1.2. Doppler Shift5.2. Impulse Response Model of a Multipath Channel5.2.1. Relationship Between Bandwidth and Received Power5.3. Small-Scale Multipath Measurements5.3.1. Direct RF Pulse System5.3.2. Spread Spectrum Sliding Correlator Channel Sounding5.3.3. Frequency Domain Channel Sounding5.4. Parameters of Mobile Multipath Channels5.4.1. Time Dispersion Parameters5.4.2. Coherence Bandwidth5.4.3. Doppler Spread and Coherence Time5.5. Types of Small-Scale Fading5.5.1. Fading Effects Due to Multipath Time Delay Spread5.5.1.1. Flat fading5.5.1.2. Frequency Selective Fading5.5.2. Fading Effects Due to Doppler Spread5.5.2.1. Fast Fading5.5.2.2. Slow Fading5.6. Rayleigh and Ricean Distributions5.6.1. Rayleigh Fading Distribution5.6.2. Ricean Fading Distribution5.7. Statistical Models for Multipath Fading Channels5.7.1. Clarke’s Model for Flat Fading5.7.1.1. Spectral Shape Due to Doppler Spread in Clarke’s Model5.7.2. Simulation of Clarke and Gans Fading Model5.7.3. Level Crossing and Fading Statistics5.7.4. Two-ray Rayleigh Fading Model5.7.5. Saleh and Valenzuela Indoor Statistical Model5.7.6. SIRCIM and SMRCIM Indoor and Outdoor Statistical Models5.8. Theory of Multipath Shape Factors for Small-Scale Fading Wireless Channels5.8.1. Introduction to Shape Factors5.8.1.1. Multipath Shape FactorsAngular Spread, ΛAngular Constriction, γAzimuthal Direction of Maximum Fading, θmax5.8.1.2. Fading Rate Variance RelationshipsComplex Received Voltage,Received Power, P(r)Received Envelope, R(r)5.8.1.3. Comparison to Omnidirectional Propagation5.8.2. Examples of Fading Behavior5.8.2.1. Sector Channel Model5.8.2.2. Double Sector Channel Model5.8.2.3. Ricean Channel Model5.8.3. Second-Order Statistics Using Shape Factors [Dur00]5.8.3.1. Level-Crossing Rates and Average Fade Duration5.8.3.2. Spatial Autocovariance5.8.3.3. Coherence Distance5.8.4. Applying Shape Factors to Wideband Channels5.8.5. Revisiting Classical Channel Models with Shape Factors5.9. Summary5.10. Problems