ENGG2310-B Principles of Communication Systems Last Lecture

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1 ENGG2310-B Principles of Communication Systems Last Lecture Wing-Kin Ma Department of Electronic Engineering The Chinese University of Hong Kong, Hong Kong November 28 29, 2017

2 Recap on ISI model: y(t) = k= a k h(t kt ) + v(t), where h(t) = g(t) }{{} transmit pulse shape c(t) }{{} channel ϕ(t) }{{} receive filter ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 1

3 Recap on ISI model (continued): y n = y(nt ) = k= a kh n k + v n, where h n = h(nt ). y n = a n h 0 + a k h n k +v n k 0 } {{ } ISI zero-isi condition: h 0 0, h n = 0 for all n 0. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 2

4 Techniques for Eliminating/Mitigating ISI narrowband case: pulse shaping. We will go through this. wideband case: channel equalization used in 2G, 3G, 4G uplink, 56kbps modem in plain old telephone lines,... orthogonal frequency division multiplexing (OFDM) a widely used scheme in the multicarrier modulation class used in 4G downlink, Wifi, broadband internet at home, digital TV broadcast,... 5G waveforms would still be multicarrier modulation, although not OFDM ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 3

5 Assumption for the Narrowband Case: Ideal Lowpass Channel a channel c(t) is said to be ideal lowpass with bandwidth B C if C(f) = A c e j2πft c, for all f B C, and for some A c > 0, t c > 0. (arguably) the ideal lowpass assumption may hold for sufficiently small B C ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 4

6 Pulse Shaping in the Narrowband Case suppose the bandwidth of g(t) is less than or equal to B C. g(t) c(t) G(f)C(f) = A c G(f)e j2πft c A c g(t t c ). pros: no pulse shape distortion! cons: B C can be (very) small... ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 5

7 Pulse Shaping in the Narrowband Case under the condition g(t) c(t) = A c g(t t c ), we may choose ϕ(t) = g( (t t c )) (good for the noisy case). assuming A c = 1, t c = 0 for convenience, h(t) = g(t) g( t) H(f) = G(f)G (f) = G(f) 2. pulse shape design: given a lowpass bandwidth B C, 1. choose a zero-isi h(t) whose bandwidth is B C or less; 2. determine g(t) by solving H(f) = G(f) 2. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 6

8 Channel Equalization: Get the Idea in One Slide suppose the ideal lowpass assumption does not hold. Or, the transmit pulse shape g(t) has been fixed. channel equalization: find a receive filter ϕ(t) such that g(t) c(t) ϕ(t) = zero-isi pulse shape. let h(t) be a desired zero-isi pulse shape. Since G(f)C(f)Φ(f) = H(f), we can do [ ] ϕ(t) = F 1 H(f) G(f)C(f) assuming such a ϕ(t) exists. remark: not as simple as it seems! Channel equalization is a topic that has been studied for decades, with numerous results. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 7

9 Digital Passband Transmission We learnt digital PAM transmission over a baseband channel; carrier modulation of an analog signal over a bandpass channel. Digital passband transmission considers digital transmission over a bandpass channel. An easy way to understand to digital passband transmission: modulate a digital baseband PAM signal by a carrier modulation scheme, such as AM, PM, FM, QAM and so forth. Aim: show you some of these baseband PAM + carrier modulation combinations. Note: digital passband transmission also has its unique characteristics, which you may learn in more advanced courses in the future. However, they are beyond the scope of this course. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 8

10 Binary Modulation Schemes: Amplitude-Shift Keying (ASK) t For the 0th symbol interval 0 t < T, s(t) = { 0, b0 = 0 A c cos(2πf c t), b 0 = 1 and the same way as above applies to the other symbol intervals. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 9

11 Binary Modulation Schemes: Phase-Shift Keying (PSK) t For the 0th symbol interval 0 t < T, s(t) = { Ac cos(2πf c t + π) = A c cos(2πf c t), b 0 = 0 A c cos(2πf c t), b 0 = 1 and the same way as above applies to the other symbol intervals. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 10

12 Binary Modulation Schemes: Frequency-Shift Keying (FSK) t For the 0th symbol interval 0 t < T, s(t) = { Ac cos(2πf 0 t), b 0 = 0 A c cos(2πf 1 t), b 0 = 1 and the same way as above applies to the other symbol intervals. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 11

13 Coherent Detection of the Binary Schemes s 0 (t) and s 1 (t) are the waveforms for 0 and 1, respectively idea: compare which one is more correlated. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 12

14 M-ary Modulation Schemes: M-ary QAM For the 0th symbol interval 0 t < T, s(t) = a I 0 A c cos(2πf c t) a Q 0 A c sin(2πf c t) = A c Re[a 0 e j2πf ct ] where a 0 = a I 0 + ja Q 0 is a complex-valued symbol. In particular, 4-ary QAM: a I 0 { 1, +1}, a Q 0 16-ary QAM: a I 0 {±1, ±3}, a Q 0 { 1, +1} {±1, ±3} 64-ary QAM: a I 0 {±1, ±3, ±5, ±7}, a Q 0. {±1, ±3, ±5, ±7} same as applying two baseband PAM signals to the in-phase and quadrature-phase components of QAM. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 13

15 An Example of Bits-to-Symbol Mapping in M-ary QAM Q 0 Q (a) 4-ary QAM I (b) 16-ary QAM I ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 14

16 M-ary Modulation Schemes: M-ary PSK For the 0th symbol interval 0 t < T, s(t) = A c cos(2πf c t + θ 0 ), where { 2πm θ 0 M }. m = 0, 1,..., M 1 2-ary PSK: θ 0 {0, π} 4-ary PSK: θ 0 { 0, π 2, π, } 3π 2 8-ary PSK: θ 0 { 0, π 4, π 2, 3π 4, π,..., } 7π 4. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 15

17 An Example of Bits-to-Symbol Mapping in M-ary PSK Q 0 Q (a) 4-ary PSK I (b) 8-ary PSK I ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 16

18 Communications: What s Next? we have dealt with transmission and reception of message signals, both analog and digital. but we didn t touch much on the information asepcts. aim: give you a quick tour on information. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 17

19 A System Diagram for Digital Communications source coding: compress data, reduce redundancy in information channel coding: protect data against noise, detect and correct errors in data and do so by adding a suitable amount of redundancy in data ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 18

20 Source Coding Example: Variable-Length Coding Conversion of characters to binary codewords 1. Do you see fixed codeword length? 1 The picture here and some hereafter were obtained from the Internet. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 19

21 Source Coding Example: Variable-Length Coding Morse code. Do you see variable codeword length? E, which is used more frequently, has a short code length, while Z has a long code length. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 20

22 Source Coding Example: Variable-Length Coding An illustration of the Huffman code. assigned shorter codewords. Characters with higher probabilities are ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 21

23 Source Coding Example: Image Compression Source coding is also important for audio, image and video we need it desperately. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 22

Channel Coding Example: Parity Check the picture above assumes even parity bit; i.e., the parity bit is 0 if the number of 1 s in the data block is odd, and 1 if the number of 1 s is even.

24 Channel Coding Example: Parity Check the picture above assumes even parity bit; i.e., the parity bit is 0 if the number of 1 s in the data block is odd, and 1 if the number of 1 s is even. with one parity bit we can detect one error. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 23

25 Channel Coding Example: Repetition Coding consider sending one bit by repeating it three times: by the following decoding rule we can correct one error. received codeword decoded bit ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 24

26 Channel Coding Example: Linear Block Codes Linear block codes are a class of error correcting code schemes; repetition is an example. It can correct more error bits if the code rate k/n is lower. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 25

Information Theory and Shannon s Channel Capacity question: what is the maximum transmission rate for error-free communication over a noisy channel?

27 Information Theory and Shannon s Channel Capacity question: what is the maximum transmission rate for error-free communication over a noisy channel? Shannon s channel capacity (1949): C = log 2 (1 + SNR) bits/s/hz. Zero ISI and Gaussian noise are assumed. Claude Shannon, a key implication: it s impossible to transmit faster than C bits/s/hz. further question: can we transmit at the limit, C bits/s/hz? it s not until late 1990 s to early 2000 s we found solutions to approaching Shannon s capacity practically and it s by some powerful channel codes. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 26

Information Theory and Shannon s Channel Capacity ENGG2310-B, 2017 18 Term 1. W.-K.

28 Information Theory and Shannon s Channel Capacity ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 27

Information Costello and Theory Forney: Channel Coding: androadshannon s to Channel Capacity Channel Capacity Costello and Forney: Channel Coding: Road to Channel Capacity Source: D. J.

Performance of rate-1/2 turbo code with interleaver length N ¼ 2 16, compared to NASA standard concatenated code and relevant Shannon limits for ¼ 1. IEEE, 2007.

29 Information Costello and Theory Forney: Channel Coding: androadshannon s to Channel Capacity Channel Capacity Costello and Forney: Channel Coding: Road to Channel Capacity Source: D. J. Costello and G. D. Forney, Channel coding: The road to channel capacity, Proc. ig. 7. P s ðeþ versus SNR norm for uncoded QAM, compared to Shannon limits on SNR norm with and without shaping. Fig. 12. Performance of rate-1/2 turbo code with interleaver length N ¼ 2 16, compared to NASA standard concatenated code and relevant Shannon limits for ¼ 1. IEEE, This baseline performance curve of P s ðeþ versus with n!1and therefore incorporates 1.53 db of shaping NR norm for uncoded QAM transmission is plotted in gain (over an uncoded square QAM that constellation). an erasure channel, In the 13 decoding linear codes is design LDPC codes that can approach capacity arbitrarily ig. 7. For example, in order to achieve a symbol error bandwidth-limited regime, coding essentially without a matter shapingof can solving linear equations and closely, in the limit as n!1. The erasure channel is robability of P s ðeþ 10 5,wemusthaveSNR norm 7 therefore get only to within 1.53becomes db of the very Shannon efficientlimit; if it can be reduced to solving a the only channel for which such a result has been.5 db) for uncoded Left: QAM transmission. error probabilitythe performance remaining 1.53 db can be obtained without by shaping channel and only coding. Right: series of equations, each of which involves a single proved. error probability We recall from Section II that the Shannon limit by shaping. unknown variable. An important general discovery that arose from this n SNR norm isperformance 1 (0 db), so the gap to capacity withis about channel We docoding. not have space to discuss shaping schemes in.5 db at P s ðeþ 10 5 work was the superiority of irregular LDPC codes. In a. Thus, the maximum possible this paper. It turns out that obtaining shaping gains on regular LDPC code, such as the one shown in Fig. 13, oding gain is somewhat smaller in the bandwidth-limited the order of 1 db is not very all hard, symbol so nodes nowadays havemost the same degree (number of incident edges), andgaussian so do all check nodes. Luby et al. gime than in the power-limited regime. Furthermore, practical schemes for the bandwidth-limited s we will discuss next, in the bandwidth-limited regime channel incorporate shaping. [106], For example, [107] foundthethat V.34 by using irregular graphs and e Shannon limit on SNR norm with no shaping is e=6 modem (see Section V-D) incorporates optimizinga 16-dimensional the degree sequences (numbers of symbol ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong db), so the maximum possible coding gain with no Bshell mapping[ shaping scheme andwhose check nodes shaping of gain each is degree), they could approach aping at P s ðeþ 10 5 is only about 7 db. These two about 0.8 db. the capacity of the erasure channel, i.e., achieve small mits are also shown on Fig. 7. The performance curve of error any probabilities practical at coding code rates of nearly 1 p, where

Okay, so anymore with Communications? yes, a lot more if I want to; e.g., cellular networks, communications as a resource management problem, enabling technology for 4G and the future 5G,.

30 Okay, so anymore with Communications? yes, a lot more if I want to; e.g., cellular networks, communications as a resource management problem, enabling technology for 4G and the future 5G,... Distributed antennas Optical fibre Cloud centre I will talk these two (briefly): OFDM, multiple-input multiple-output (MIMO). ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 29

31 Orthogonal Frequency Division Multiplexing A very intuitive explanation of how OFDM works (warning: technically innaccurate!): Trick 1: chop a wideband channel into many narrowband channels each subchannel may be have zero or little ISI if the subchannel bandwidth is small enough example: 4G supports a maximum of 2048 subchannels, with freq. spacing 15kHz ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 30

32 Orthogonal Frequency Division Multiplexing Trick 2: adapt the channel adaptive power allocation, modulation and coding over subchannels is key to high-rate transmission ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 31

33 Orthogonal Frequency Division Multiplexing Trick 3: allow spectral overlaps between subchannels while overlapping in frequency, the subchannels do not interfere each other. why? Careful multicarrier modulation-demodulation design. Also, correlation and orthogonality concepts play a key role. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 32

send only one symbol stream 2 2 MIMO: can send two symbol streams in parallel, data rate 2 4 4 MIMO: can send four symbol streams

34 Multiple-Input Multiple-Output (MIMO) can we increase the transmission rate without increasing the bandwidth? yes, we may if the transmitter and receiver are equipped with multiple antennas very roughly speaking, 1 1 single-in single-out: send only one symbol stream 2 2 MIMO: can send two symbol streams in parallel, data rate MIMO: can send four symbol streams in parallel, data rate 4. ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 33

35 MIMO in a Massive Scale Current research talks about hundreds of antennas. Source: ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 34

36 Epilogue As a first course on communications, we learnt analog and digital communication schemes at the signal or physical-layer level. Particularly, key concepts are bandwidth as a resource (very precious in real life or communications industry), how different modulation schemes work, their pros and cons, bit rates (how fast we can transmit) and its relation with bandwidth. For those who wish to pursue further, there are a lot more to study, e.g., signal processing, random processes and probability, signal compression and source coding, channel coding, information theory. Hope you found communications an interesting subject! ENGG2310-B, Term 1. W.-K. Ma, Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kong 35

Handout 13: Intersymbol Interference

ENGG 2310-B: Principles of Communication Systems 2018 19 First Term Handout 13: Intersymbol Interference Instructor: Wing-Kin Ma November 19, 2018 Suggested Reading: Chapter 8 of Simon Haykin and Michael