Communications IB Paper 6 Handout 5: Multiple Access
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1 Communications IB Paper 6 Handout 5: Multiple Access Jossy Sayir Signal Processing and Communications Lab Department of Engineering University of Cambridge jossy.sayir@eng.cam.ac.uk Lent Term Jossy Sayir (CUED) Communications: Handout 5 Lent Term 1 / 27
2 Outline 1 Introduction and Motivation 2 Multiple Access Techniques Frequency-Division Multiple Access Time-Division Multiple Access Code-Division Multiple Access Example: GSM 3 Course Summary Important Topics Relevant Past Tripos Questions Jossy Sayir (CUED) Communications: Handout 5 Lent Term 2 / 27
3 Introduction and Motivation So far... We have studied techniques for single user point-to-point communications. Source message Transmitter transmitted signal Channel Destination received message Receiver received signal Jossy Sayir (CUED) Communications: Handout 5 Lent Term 3 / 27
4 Introduction and Motivation Remember (Handout 4) If we have one user we have that y(t) = x(t) + z(t) x(t), y(t) are the transmitted and received signals of bandwidth B z(t) is the noise with flat power spectral density N 0 the channel capacity is given by ( C = B log P ) N 0 B Jossy Sayir (CUED) Communications: Handout 5 Lent Term 4 / 27
5 What is Multiple Access? Multiple access techniques are special modulation techniques to accommodate multiple users in a communications channel allow multiple users to share a finite amount of bandwidth Jossy Sayir (CUED) Communications: Handout 5 Lent Term 5 / 27
6 User 1 Source message Transmitter transmitted signal Multiple... Access Channel received signal Receiver Destination Modulator User K Source message Transmitter transmitted signal Jossy Sayir (CUED) Communications: Handout 5 Lent Term 6 / 27
7 Example Imagine that all of you (multiple users) have a question (which may or may not be the same) to ask me (receiver). What techniques can we use, such that I understand all questions? One after the other (time-division multiple access), each using the whole bandwidth for a fraction of the time. All at the same time, but each with a different frequency (frequency-division multiple access), using a fraction of the bandwidth all the time All at the same time using the whole bandwidth, each with a different signature (code-division multiple access), i.e., a different language (known to the receiver) Jossy Sayir (CUED) Communications: Handout 5 Lent Term 7 / 27
8 Signature Frequency Tf B Time Jossy Sayir (CUED) Communications: Handout 5 Lent Term 8 / 27
9 Example Other real-life examples include Multiple cell phones desiring to call at the same time Multiple computers accessing the internet Multiple satellites transmitting to earth Jossy Sayir (CUED) Communications: Handout 5 Lent Term 9 / 27
10 Frequency-Division Multiple Access FDMA Multiple users are multiplexed in the frequency domain, such that they do not interfere with each other, using a fraction of the total bandwidth. Essentially DSB-SC modulation for each user, such that spectrums do not overlap. User 1 User 2 User K 1 User K... f f c,1 f c,2 f c,k 1 f c,k B u B Jossy Sayir (CUED) Communications: Handout 5 Lent Term 10 / 27
11 Frequency-Division Multiple Access Signature Frequency user 1 user 2 user K Tf Bu Time B Jossy Sayir (CUED) Communications: Handout 5 Lent Term 11 / 27
12 Frequency-Division Multiple Access FDMA The time-domain signals get mixed together though... User 1 x 1 (t)... cos(2πf c,1 t)... s FDMA (t) User K x K (t) cos(2πf c,k t) Jossy Sayir (CUED) Communications: Handout 5 Lent Term 12 / 27
13 Frequency-Division Multiple Access Capacity of FDMA Assuming no overlap nor guard bands, i.e., B = KB u (see Figure) the capacity of each user is ( ) Ck FDMA = B K log P B N 0 K ( = B u log P ) N 0 B u Jossy Sayir (CUED) Communications: Handout 5 Lent Term 13 / 27
14 Time-Division Multiple Access TDMA Multiple users are multiplexed in time, so that they transmit one after the other, using the whole bandwidth B. We divide the frame duration T f into K time slots of duration T u = T f K. User 1 User 2... User K 1 User K T u T f Jossy Sayir (CUED) Communications: Handout 5 Lent Term 14 / 27
15 Time-Division Multiple Access Signature user K Frequency user 1 user 2 Tu Tf B Time Jossy Sayir (CUED) Communications: Handout 5 Lent Term 15 / 27
16 Time-Division Multiple Access Capacity of TDMA Assuming no overlap nor guard intervals, i.e., T f = KT u (see Figure) and users transmit with power KP when active (so that the average power per user is P), the capacity of each user is C TDMA k = 1 K B log 2 ( 1 + PK N 0 B = B u log 2 ( 1 + P N 0 B u = C FDMA k ) ) Jossy Sayir (CUED) Communications: Handout 5 Lent Term 16 / 27
17 Code-Division Multiple Access CDMA Multiple users are multiplexed in code or signature, and transmit using the whole bandwidth B over the whole time frame of duration T f.... but what is a signature? A signature is a signal characteristic to each user, and known to the receiver. We denote the K signatures by c k (t) for k = 1,..., K. Jossy Sayir (CUED) Communications: Handout 5 Lent Term 17 / 27
18 Code-Division Multiple Access Signature user 1 c1(t) Signature user 2 c2(t) +1 t t +1 t t Signature user 3 c3(t) Signature user 4 c4(t) Jossy Sayir (CUED) Communications: Handout 5 Lent Term 18 / 27
19 Code-Division Multiple Access User 1 x 1 (t) s 1 (t)... c 1 (t)... cos(2πf c t) K s CDMA (t) = c k (t)x k (t) cos(2πf c t) k=1 User K x K (t) s K (t) c K (t) cos(2πf c t) Jossy Sayir (CUED) Communications: Handout 5 Lent Term 19 / 27
20 Code-Division Multiple Access Orthogonal Signatures The received CDMA signal is given by K y(t) = c k (t)x k (t) cos(2πf c t) + z(t) k=1 where z(t) is the noise signal. Assuming we have no noise (i.e., z(t) = 0) and perfect carrier demodulation we have K ỹ(t) = c k (t)x k (t) k=1 where ỹ(t) is the demodulated signal. Jossy Sayir (CUED) Communications: Handout 5 Lent Term 20 / 27
21 Code-Division Multiple Access Orthogonal Signatures If we chose the signatures to be orthogonal, i.e., c k (t), c j (t) = 1 { T 0 j k c k (t)c j (t)dt = T 0 1 j = k we can recover the transmitted information by each user, by simply performing the following operations for all j = 1,..., K (assuming that x k (t) are rectangular pulses) ỹ(t), c j (t) = 1 T = 1 T T 0 T 0 ỹ(t)c j (t)dt K c k (t)x k (t)c j (t)dt = k=1 assuming x k (t) does not vary within the period T. { 0 j k x k (t) j = k Jossy Sayir (CUED) Communications: Handout 5 Lent Term 21 / 27
22 Code-Division Multiple Access Orthogonal Signatures: Summary If we chose the signatures to be orthogonal, the signals can overlap in both time and frequency and we are still able to recover the information of each user. Jossy Sayir (CUED) Communications: Handout 5 Lent Term 22 / 27
23 Code-Division Multiple Access Signature user 1 user 2 Frequency Tf user K B Time Jossy Sayir (CUED) Communications: Handout 5 Lent Term 23 / 27
24 Example: GSM GSM GSM uses a combination of both TDMA and FDMA, and assigns a time slot and a frequency carrier to each. GSM In order to minimise the distortion due to fading (mobility, multipath propagation) GSM changes the time-frequency allocations assigned to different users during transmission. Jossy Sayir (CUED) Communications: Handout 5 Lent Term 24 / 27
25 Example: GSM Signature user 1 user 2 user K Frequency Tu Tf Bu Time B Jossy Sayir (CUED) Communications: Handout 5 Lent Term 25 / 27
26 Course Summary Important Topics 1 Communications Channels Convolution Noise Multipath and Doppler (coherence bandwidth and time) 2 Analogue Modulation AM, DSB-SC, SSB-SC (properties, differences, spectrum, power) FM: Carson s rule 3 Digitisation Sampling Quantisation (quantisation noise) Representation of digital signals and spectrum 4 Digital modulation ASK, FSK, BPSK (spectrum, error probability) 5 Channel capacity Concept of rate and channel coding Channel capacity 6 Multiple-Access (FDMA, TDMA, CDMA) Jossy Sayir (CUED) Communications: Handout 5 Lent Term 26 / 27
27 Course Summary Relevant Past Tripos Questions 2012 Paper 6, Questions 5 and Paper 6, Questions 5 and Paper 6, Questions 5 and Paper 6, Questions 5 and Paper 6, Questions 5 and Paper 6, Questions 4 and Paper 6, Question Paper 6, Question Paper 6, Question Paper 6, Question 5 excluding the final two lines of part (d) Paper 6, Question Paper 6, Question 6 except part (c) Paper 6, Question 6 Jossy Sayir (CUED) Communications: Handout 5 Lent Term 27 / 27
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