Tutorial 5 - Resolution of paths Spreading and Scrambling Rake Receiver PDF

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Resolution of paths
Spreading and Scrambling
Rake Receiver...

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¨nchen Technische Universit ¨at Mu ¨ r Nachrichtentechnik Lehrstuhl fu Prof. Dr. sc. techn. Gerhard Kramer June 7th, 2017

Mobile Communications: Tutorial 5 Problem 1

Resolution of paths

A direct sequence spread-spectrum system is used to resolve the multipath signal components in a two-path radio signal propagation scenario. If the path length of the secondary path is 300 m longer than that of the direct path, determine the minimum chip rate necessary to resolve the multipath components. Is the FDD-UMTS system able to resolve the paths? What is the minimum difference of the path lengths in UMTS?

Problem 2

Spreading and Scrambling

    Two spreading signals are c1 = −1 −1 1 1 and c2 = 1 −1 −1 1 . (a) Calculate the cyclic cross correlation function CCF12 between the spreading sequence c1 and c2 . (b) Are the two spreading sequences orthogonal? (c) What are the consequences if the spreading sequences are received asynchronously? Is this typical for the uplink receiver? (d) Why are different scrambling codes applied on top of spreading sequences to separate the users on the uplink of WCDMA? (e) What is the drawback of using scrambling codes? Why is typically the same scrambling code for all users applied on the downlink of WCDMA? (f) What kind of mechanism would be needed to separate different users on the uplink of a WCDMA system only by spreading codes? Which would be the necessary accuracy in time? (g) Why do different physical channels of the same mobile station use different spreading codes?   Now the bit sequence 1 1 is spread by the spreading sequence c1 yielding the signal x1 . (h) Calculate and sketch the non-cyclic cross-correlation function between x1 and the spreading sequence c2 .

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(i) In the following x1 and c2 are composed of unit pulses beginning at t = 0 and ending at the chip length t = TC . Sketch the continuous time non-cyclic crosscorrelation function resulting in this case. In general the spreading codes used in WCDMA can have different length. (j) What is the reason for the use of spreading codes having different lengths? (k) Which condition needs to be fulfilled such that spreading codes of different length are orthogonal to each other?

Problem 3

Rake Receiver

A sequence u with 3 symbols is transmitted over a channel with two taps h0 (τ0 = 1 µs) =   0.9 and h1 (τ1 = 1.52 µs) = 0.4 using UMTS and a spreading code c = 1 −1 −1 1 , no scrambling is used. The received sequence after transmission over the channel and after adding the noise is:   y = −0.6 0.4 0.2 −0.2 −0.5 1.0 −0.2 −0.3 0.5 −2.0 −0.4 0.4 −1.0 0.3 (a) Give an estimate u ˆ of the transmitted sequence u, applying a Rake receiver! [Hint: Think about the MRC without CDMA to obtain y ˆ and then extend it by the despreading operation to obtain u ˆ.] (b) General question: Would the applied spreading code be a good solution from the auto-correlation point of view in the case of the used channel.

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