lect17 - Wireless Communication Technologies Lecture 17...

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Wireless Communication Technologies Lecture 17 & 18 Sandeepa Mukherjee Page 1 of 18 Wireless Communication Technologies 16:332:559 (Advanced Topics in Communications) Lecture #17 and #18 (April 1, April 3, 2002) Instructor Prof. Narayan Mandayam Summarized by Sandeepa Mukherjee (smdatta@ece.rutgers.edu) This lecture note is about multiuser CDMA systems and we study in detail about the performance of such systems.
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Wireless Communication Technologies Lecture 17 & 18 Sandeepa Mukherjee Page 2 of 18 1.1Multiuser BPSK CDMA System Let’s assume that we have a CDMA system with K users indexed as j =1,2…K and each user transmits BPSK modulated signal waveforms simultaneously. Then the transmitted signal of one such user j can be represented as, (1) where, ( 29 = -∞ = - = n n c T n j j nT t p c t c c ) ( ) ( { } 1 , 1 ) ( + - n j c ( 29 = -∞ = - = n n T n j j nT t p b t b ) ( ) ( { } 1 , 1 ) ( + - n j b T = NT c N = Processing Gain The received signal at the receiver can be represented as, (2) where, j t = relative time offset φ j = phase offset η (t) ) 2 , 0 ( o N N In general signal from the various users are received at various propagation delays, τ j ] , 0 [ T and φ j ] 2 , 0 [ p Receiver in the multiuser scenario can be modeled as figure below:
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Wireless Communication Technologies Lecture 17 & 18 Sandeepa Mukherjee Page 3 of 18 Figure 1: Received signal in multiuser scenario 1.1.2 Single User Reception Focusing on user 1, we try to look at the demodulation of bit stream of user 1. Assume the receiver is synchronized to user 1. So, without loss of generality we can say, τ 1 = 0 and φ 1 = 0. We will consider demodulation of a single bit of user 1, which is bit b 1 (0). The matched filter receiver matched to user 1 is illustrated in the following figure, The output of the matched filter corresponding to user 1 is given as, (3) 1 1 0 1 1 ) cos( ) cos( ) ( ) ( ) ( 2 h w f w t t + + - - = = K j T c j c j j j j j dt t t t b t c t c P z where, τ 1 τ 2 τ K S 1 (t) S 2 (t) S K (t) Σ η (t) Rx x r(t) C 1 cos ϖ c t Z 1 (t)
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Wireless Communication Technologies Lecture 17 & 18 Sandeepa Mukherjee Page 4 of 18 = T c dt t t c t 0 1 1 ) cos( ) ( ) ( w h h Neglecting all double frequency terms, [ ] 1 2 1 , ) 0 ( 1 , ) 1 ( ) 0 ( 1 1 1 cos ) ( ˆ ) ( 2 2 h f t t + + + = = - K j j j j j j j j j R b R b P Tb P z (4) We introduce continuous time partial cross-correlation functions, - = t t t 0 1 1 , ) ( ) ( ) ( dt t c t c R j j (5) - = T j j dt t c t c R t t t ) ( ) ( ) ( ˆ 1 1 , T t 0 Thus, in one bit interval of the desired user i.e. user 1, there would be effectively two bits of every interferer j, by assuming that the signals of the interferers are delayed by not more than one bit interval. This is illustrated in the following figure: T b 1 (0) b 1 (t) b j (0) b j (-1) b j (t) T
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Wireless Communication Technologies Lecture 17 & 18 Sandeepa Mukherjee Page 5 of 18 Case of Synchronous users For the case of synchronous system,
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lect17 - Wireless Communication Technologies Lecture 17...

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