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Unformatted text preview: E4703 Wireless Communications Lecture 4 Outline Summary of last lecture. Information theory Capacity in AWGN (no fading). Capacity with flat fading (narrowband). Channel Distribution Information (CDI). Receiver Channel State Information (CSI): Shannon capacity. Outage capacity. Transmitter & receiver CSI. Constant transmit power. Adapted transmit power. Shannon capacity. Channel Inversion. Truncated channel inversion. Comparisons Capacity with frequencyselective fading (wideband). Time invariant. Time variant. Summary Summary Stochastic smallscale channel modeling under local stationarity (fixed path loss and shadow fading). Linear timevarying impulse response with or without LOS component. Because of motion, frequency experiences Doppler spread. A tone at f c gives rise to tones on an interval [ f c f D , f c + f D ] where f D = v f c /c. Reciprocal of f D gives the coherence time. Because the multipaths have different lengths (and thus delays), the signal is also spread in time. The rms delay spread characterizes the extent of this spread. Classification into narrowband (frequency flat) or wideband (frequency selective) depending on how delay spread relates to symbol period. Equivalently, how coherence bandwidth relates to signal bandwidth. Narrowband: fading amounts to a scaling. Wideband: ISI distortion. If number of multipath components is large, fading process is approximately Gaussian. Characterized by mean and autocorrelation. Amplitude is Rayleigh. With LOS component, it becomes Rician. In narrowband case, particular insight with Clarke Jakes model. Multipath channel also randomizes signal polarization. Announcement Midterm next week (March 9 th ). Same location and time of lecture. Duration: 2 hours. No Homework this week. Well post the solutions to some textbook problems on the material covered today. Information Theory Discipline born in 1948, with the publication of A mathematical theory of communication, a landmark paper by Claude Shannon (a Bell Labs researcher). Revolutionary work, arguably one of the greatest scientific contributions of the XX century, marking the birth of the information age. Before Shannon, it was believed that the only way to reduce the error probability was by either increasing the power or reducing the data rate. Shannon proved that, at a given rate and power, the error probability can be made as small as desired through coding as long as the rate is below the channel capacity for that power level. Coding entails introducing controlled redundancies and dependencies in the data. Conversely, he proved that the error probability is always bounded away from 0 when the capacity is exceeded....
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This note was uploaded on 08/05/2008 for the course ELEN E4702 taught by Professor Lazano during the Summer '08 term at Columbia.
 Summer '08
 LAZANO

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