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# Multipath channels

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### Multipath channels

1. 1. Parameters of Multipath channels <ul><ul><ul><ul><ul><li>M.Vignesh pandi </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>A.Vijayasekhar </li></ul></ul></ul></ul></ul>
2. 2. Coherence Bandwidth <ul><li>It is a measure of range frequencies over which the channel is considered flat. </li></ul><ul><li>Otherwise it is range frequencies over which two frequency component have a strong potential for amplitude correlation. </li></ul>
3. 3. <ul><li>It is used to characterize the channel in the frequency domain </li></ul><ul><li>It is inversely proportional to the rms delay spread </li></ul><ul><li>B c =1/ σ ז </li></ul><ul><li>Two sinusoidal with frequency separation greater than Bc are affected quite differently by the channel. </li></ul><ul><li>If the frequency correlation function is above 0.9, than the correlation bandwidth is </li></ul><ul><li>B c =1/50 σ ז </li></ul><ul><li>If the frequency correlation function is above 0.5 than the coherence bandwidth is approximately B c =1/5 σ ז </li></ul>
4. 4. <ul><li>Doppler spread and coherence time are parameters are describes the time varying nature of the channel in a small- scale region. </li></ul><ul><li>It is defined as the range of frequency over which the received Doppler spectrum is essentially non-zero </li></ul><ul><li>Doppler spread and Doppler frequency: </li></ul><ul><li>Doppler spread B d is defined as the range of frequencies over which the received Doppler spectrum is essentially non-zero. </li></ul>Doppler spread and coherence time
5. 5. <ul><li>The maximum Doppler frequency f d is give by </li></ul><ul><li>f d =v/ λ </li></ul><ul><li>λ =c/f </li></ul><ul><li>f d =v/ λ = v/(c/f) </li></ul><ul><li>f d =vf/c </li></ul><ul><li>Where </li></ul><ul><li>C-velocity of light </li></ul><ul><li>V-speed of the mobile, including the speed of the mobile environment in m/s </li></ul><ul><li> λ - wavelength of the radio signal in meters and </li></ul><ul><li>F- radio frequency </li></ul><ul><li>When a pure sinusoidal tone of frequency fc is transmitted the received signal spectrum, will have components in the range fc-fd to fc+fd </li></ul><ul><li>where fd is the Doppler shift. </li></ul>
6. 6. Coherence Time (T c ) <ul><li>Coherence time is the time duration over which two received signal have a strong potential for amplitude correlation </li></ul><ul><li>Distortion is occurred at the receiver, if the reciprocal bandwidth of signal is greater than the coherence time for the channel </li></ul><ul><li>The Doppler spread & coherence time are inversely proportional to each other </li></ul><ul><li>T c ≈1/f m </li></ul>
7. 7. <ul><li>If the time correlation function is above 0.5 than the coherence time is given as </li></ul><ul><li> T c ≈9/(16 π f m ) </li></ul><ul><li>where </li></ul><ul><li>f m =maximum Doppler shift </li></ul><ul><li>f m =v/ λ </li></ul><ul><li>If the digital transmission system is used,than the coherence time as geometric mean of above two equation </li></ul><ul><li>T c =√(9/(16 π f m 2 )) </li></ul>
8. 8. <ul><li>THE END </li></ul>