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This phenomenon is explained as follows: • If d < ht , signals add up constructively and path loss is proportional to 1/(d 2 + h2t ) for ht hr . 40 2 Basics of Cellular Communication Ga Gc l ht x Gb Gd hr y δ d Fig. 16 Two-ray module • If ht < d < dc , signals experience constructive and destructive interference up to a critical distance dc ≈ 4ht hr /λ . • If dc < d, signals experience destructive interference and path loss is proportional to 1/d 4 . There are several more sophisticated ray tracing models that consider more than one reflection.

Swithced-Beam Smart Antenna Systems Fig. 2 Spectral Efficiency 25 AAS MIMO Fig. 7 AAS and MIMO antennas MIMO can offer more capacity by adding more antennas and more sectors. Capacity linearly increases with number of antennas by sending different information in different spatial streams. This is preferred if the channel is strong. However, if the signal is weak, MIMO sends the same information in different spatial streams to make the signal stronger. Unlike MIMO, AAS can only increase capacity by more powerful beam.

K is unitless constant given in dBm by the following formula; K dB = 20 log10 λ . 5 for urban 7 “Diffraction loss is commonly modeled with Fresnel knife-edge diffraction, which formulates the delay and path loss. Scattering also introduces additional delay and alters the antenna gain according to geometry of the scattering object”. 5; however, it ranges between 2 and 6 for multiple floor office spaces. The values for γ are obtained from the empirical methods described next. We put more emphasis on empirical models since typically mobile communication is in complex propagation environment and can only be approximated with real data from the field.

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Asymptotic analysis of the number of comparisons in multipartition quicksort by Tan K.H.

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