Lecture Set 1: Introduction & Background (Digital Mobile Communication) PDF

Lecture Set 1 Introduction & Background Digital Mobile Communication Dr 1 Laith Danoon and Prof. Daniel So Lecture Outline Course Outline Introduction – Why Wireless? – History & Modern Development – Wireless = Mobile? – Mobile Challenge Basic Revi...

Lecture Set 1 Introduction & Background Digital Mobile Communication Dr 1 Laith Danoon and Prof. Daniel So Lecture Outline Course Outline Introduction – Why Wireless? – History & Modern Development – Wireless = Mobile? – Mobile Challenge Basic Revision – Some key concepts – Frequency translation – Different type of communications – Basics of mobile communication Digital Mobile Communication Dr 2 Laith Danoon and Prof. Daniel So Course Outline Introduction & Background Baseband digital transmissions Bandpass digital transmissions Radio propagation & Diversity Multiple access techniques Cellular network design Lecturing team – Dr Laith Danoon (Week 1 – Week 6) – Prof. Daniel So (Week 7 – Week 12) Digital Mobile Communication Dr 3 Laith Danoon and Prof. Daniel So Course Structure Lectures and surgery sessions – Lecture: :HGQHVGD\, 0(&'_$. – (DP-0Dm for Weeks 5, and 7-12, no lecture in Week 6) – Surgery and Q&As : Wednesday , MECD_2A.013 – (10am-11am for Weeks Worked Examples – Included within lectures Assessment – Two courseworks (10% + 10%) – A final exam (80%) Digital Mobile Communication Dr 4 Laith Danoon and Prof. Daniel So Course Structure Reference Books – T. Rappaport, Wireless Communications: Principles and Practice, 2nd edition, Prentice Hall, 2002. – A. F. Molisch, Wireless Communications, Wiley, 2005 – A. Goldsmith, Wireless Communications, Cambridge University Press, 2005 – S. Haykin and M. Moher, Communication Systems, Wiley, 5th edition 2010 – J. G. Proakis, Digital Communications, 4th edition, McGraw Hill, 2000 – S. Haykin, Digital Communication Systems, Wiley, 2014 – S. Lin and D. Costello, Error Control Coding, 2nd edition, Prentice Hall, 2004. Digital Mobile Communication Dr 5 Laith Danoon and Prof. Daniel So Key Notes to Learn Go through the materials for weekly asynchronous activities Try to attend synchronous lectures and surgery sessions – Ask when you don’t understand Don’t leave until the end of lecture because you won’t be able to follow the materials to come This module is highly conceptual – The maths is too complicated and will dealt with in MSc level – Understand is the key You can’t memorise all the materials in this course – Jot down side notes Digital Mobile Communication Dr 6 Laith Danoon and Prof. Daniel So Why Digital? Noise immunity Multiplexing Better security Support digital signal processing Digital Mobile Communication Dr 7 Laith Danoon and Prof. Daniel So Why Wireless? Mobility Flexibility Digital Mobile Communication Dr 8 Laith Danoon and Prof. Daniel So Wireless = Mobile? Wireless communication – Literally: Any kind of communication without wired connections e.g. Speech, hand/light signals etc – Communication between two or more objects through electromagnetic waves Can be fixed point-to-point wireless communication Mobile – Communicate wirelessly anytime and anywhere – Support mobility – A user can communicate wirelessly anytime and anywhere using a light-weight portable personalised communicator – Major focus: mobile phones & wireless networks Digital Mobile Communication Dr 9 Laith Danoon and Prof. Daniel So Modern Development (1G – 3G) – 1982 Start of GSM-specification Groupe Spéciale Mobile – 1983 Start of the American AMPS Advanced Mobile Phone System, analog system – 1992 Start of GSM Global System for Mobile communication Motorola AMPS – 1993 Start of PHS in Japan (brick) phone Personal Handyphone System – 1995 First commercial launch of CDMA (HK) – 1995 Formation of IMT-2000 for future global mobile development (3G) IMT - International Mobile Telecommunication Early GSM phones (Motorola Flip & – 1998 First satellite phone – Iridium Ericsson GH218), already a major breakthrough in size and talk & – 1999 Standardization of W-LAN 802.11a & b standby time Digital Mobile Communication Dr 10 Laith Danoon and Prof. Daniel So Modern Development (3G – 4G) – 1999 IMT-2000 decided to have more than 1 3G standard UMTS (W-CDMA), CDMA2000, FOMA First camera phone in 2000 by – 2000 Introduction of GPRS Sharp (Japan only) – 2001 Start of 3G service in Japan 2003 Launch of 3G service in UK by 3 on 3/3/2003 – 2005 Mobile TV first launched in South Korea – 2006 HSDPA (14.4Mbps) launched worldwide – 2007 HSUPA (5.7Mbps) first launched in South Korea – 2009 HSPA+ (DL/UL 42/11Mbps) planned – 2009 802.11n (max 600Mbps) standardised – 2010 (DL/UL 100/50Mbps) LTE launched in Sweden – 2013 802.11ac (> 1Gbps) standardised Digital Mobile Communication Dr 11 Laith Danoon and Prof. Daniel So Modern Development (1G – 4G) 1G 2G 3G 4G 5G Mid 1980s 1990s 2000s 2010s 2020s analog Digital voice Mobile Mobile Internet voice + Simple data broadband More & faster Courtesy of Chunyi Peng’s talk Digital Mobile Communication Dr 12 Laith Danoon and Prof. Daniel So Modern Development (5G – 1/3) – Standards for 5G The 3rd Generation Partnership Project (3GPP) unites telecommunications standard development organizations and is in charge of standardization Release 15 is termed Phase 1 of 5G, also called Non-Standalone (NSA) Release 16 is termed Phase 2 of 5G, sometimes also called New Radio (NR) Courtesy of Ericsson B5G talk Digital Mobile Communication Dr 13 Laith Danoon and Prof. Daniel So Modern Development (5G – 2/3) – What can 5G do? ITU-R Recommendation M.2083-0 Digital Mobile Communication Dr 14 Laith Danoon and Prof. Daniel So Modern Development (5G – 3/3) – The targets of 5G ITU-R Recommendation M.2083-0 Digital Mobile Communication Dr 15 Laith Danoon and Prof. Daniel So Visions for 6G? – Is it too early to talk about 6G? Digital Mobile Communication Dr 16 Laith Danoon and Prof. Daniel So How to develop these 1/2/3/4/5 G? Courtesy of Qualcomm Digital Mobile Communication Dr 17 Laith Danoon and Prof. Daniel So Visions for 6G Courtesy of Ericsson Digital Mobile Communication Dr 18 Laith Danoon and Prof. Daniel So Visions for 6G Courtesy of Nokia Digital Mobile Communication Dr 19 Laith Danoon and Prof. Daniel So Mobile Challenges Channel impairments – Wireless channels are varying and adversely affect performance Limited bandwidth – Bandwidth is expensive or limited in unlicensed band Transmission power – Minimise transmission power to minimise interference & power consumption Interference – Transmission causes interference to other user or system. Power consumption – Battery last the longer the better Processing power & memory – Available processing power & memory on portable is limited Digital Mobile Communication Dr 20 Laith Danoon and Prof. Daniel So Mobile Challenges In 1950s, IBM was moving a 5MB hard disk Digital Mobile Communication Dr 21 Laith Danoon and Prof. Daniel So Mobile Challenges Size – Size of the portable device must be as small as possible Security – Wireless signals can be tapped easily Robustness – Able to communicate in different environments Health issue – Radio wave causing brain damage? Goal – Engineer viewpoint Achieve the sufficient quality of service while minimising all the factors – Researcher viewpoint Achieve the best for each factor individually or jointly Digital Mobile Communication Dr 22 Laith Danoon and Prof. Daniel So Basic revision (I) Decibel (dB) – A logarithmic ratio X (dB ) = 10 log10 X – Very useful and commonly used in communications Can represent very small values in reasonable numbers (e.g. 10-10 = -100dB) Many multiplicative terms become additions – If X=a*b*c X (dB ) = 10 log10 a + 10 log10 b + 10 log10 c = a(dB) + b(dB) + c(dB) – Useful numbers Factor of 2 = addition of 3dB Factor of 1/2 = subtraction of 3dB Factor of 10 = addition of 10dB Digital Mobile Communication Dr 23 Laith Danoon and Prof. Daniel So Basic revision (II) dBW & dBm – dBW is the signal power in Watts in dB P(dBW ) = 10 log10 P(W ) 0dBW=1W – dBm is the signal power in milli-watts in dB P(dBm) = 10 log10 P(mW ) = 10 log10 (P(W ) *1000) = P(dBW ) + 30dB 1mW=0dBm=-30dBW Digital Mobile Communication Dr 24 Laith Danoon and Prof. Daniel So Basic Revision (III) Bit Error Rates – Counting the number of bit errors out of all transmitted bits Bit error occurs when bit 0 is transmitted but bit 1 is detected or vice versa – Trying to find how likely a bit will be in error – A common performance measure for digital communications Other errors rate measure exists such as symbol error rate & block error rate Signal to Noise Ratio – Ratio of signal power PS to noise power PN PS ES SNR = = PN N 0 ES is the signal energy and N0 is the noise power spectral density In digital communications, Eb/N0 is commonly used for SNR per bit – Most commonly used at the receiver to determine how good the signal is over the noise Digital Mobile Communication Dr 25 Laith Danoon and Prof. Daniel So Basic Revision (IV) Additive White Gaussian Noise (AWGN) – A very common model for noise Additive to the signal White: uncorrelated and occupies all frequencies with the same level Gaussian: the value is random & follows the Gaussian distribution – More on noise calculation will be discussed in lecture set 4 Capacity – The max data rate that can be achieved with negligible error rate If one is to transmit a higher data rate than C, error rate will become high Any data rate lower than C is fine – Bandlimited capacity for AWGN channel C = B log2 (1 + SNR ) bits / s Different for different channels Digital Mobile Communication Dr 26 Laith Danoon and Prof. Daniel So Basic Revision (V) What is the capacity for a mobile link with 10dB & 20dB SNR and 20MHz bandwidth? Digital Mobile Communication Dr 27 Laith Danoon and Prof. Daniel So Frequency Translation Shift the frequency range of a signal from one to another – Based on a Fourier transform property x(t )e j 2p f0t Û X ( f - f0 ) Why is this needed? – The message signal is often in a low frequency range (Baseband) that you are not allowed to transmit E.g., voice message is in 30 to 3kHz – Need to translate to a frequency that you have license to transmit (Bandpass signal over the Passband) E.g., LTE operates mainly in 800MHz and 2.6GHz, and some in 1.8GHz Digital Mobile Communication Dr 28 Laith Danoon and Prof. Daniel So  Digital Mobile Communication Link Block diagram of a typical digital mobile transmitter & receiver D-to-A Digital Channel Channel Baseband Channel Channel Up Channel RF Trans- Channel Converter Data Encoder Encoder Modulator Encoder Encoder Converter Encoder mission Encoder + LPF Wireless channel Output Baseband LPF + Channel Channel Channel Channel Down Channel RF Channel Data De- A-to-D Decoder Encoder Encoder Encoder Converter Encoder Reception Encoder modulator Converter – Channel encoder/decoder: correct error bits to lower BER – Baseband modulator: modulation binary data to symbols – DAC + LPF: convert digital signal to analog for RF transmission – Up/down converter: translate the baseband signal to passband – RF transmission/reception: further filtering and power amplification – LPF + ADC: convert Rx analog signal to digital for demodulation Digital Mobile Communication Dr 29 Laith Danoon and Prof. Daniel So Types of Communications Point to Point – Simplex Communication can only be made in one way (e.g., pager) – Half Duplex Communication can be made one way at a time (e.g., walkie talkie) – Full Duplex Two way communication can be made at the same time (e.g., landline) Point to Multi-Point – Broadcast One single source is transmitted to all receivers (e.g., radio, TV) – Multicast One single source is transmitted to a group of receivers (e.g., mobile TV) Digital Mobile Communication Dr 30 Laith Danoon and Prof. Daniel So Types of Communications Multi-Point to Multi-Point – Allow multiple source to transmit to multiple receivers – Multiplexing Multiple sources are available locally (e.g., telephone exchange) E.g., Frequency Division Multiplexing (FDM) – Each source is allowed to transmit its message at different frequencies Digital Mobile Communication Dr 31 Laith Danoon and Prof. Daniel So Types of Communications – Multiplexing (contd) E.g., Time Division Multiplexing (TDM) – Multiple Access Multiple sources are separated geographically (e.g., mobile phone) Since mobiles are separated, multiple access is the common term in mobile communication – E.g., FDMA, TDMA, CDMA, OFDMA etc Will be covered in more detail in lecture set 6 Digital Mobile Communication Dr 32 Laith Danoon and Prof. Daniel So Mobile Communications Bidirectional communication Downlink Base station Mobile (Node B) (User Equipment) Uplink – Downlink or Forward link: From BS to UE – Uplink or Reverse link: From UE to BS Duplex techniques – Mobile communications require full duplex for real time comms – Frequency Division Duplex (FDD) Transmit and receive at different frequencies but at the same time – Time Division Duplex (TDD) Transmit and receive at different times but at the same frequency Digital Mobile Communication Dr 33 Laith Danoon and Prof. Daniel So Summary Module details Brief introduction on the background of wireless systems Challenges in mobile communications Course outline in context Basic revisions Different types of communications Basics of mobile communications Digital Mobile Communication Dr 34 Laith Danoon and Prof. Daniel So  Lecture Set 2 Baseband Digital Transmission – Part I 1 a =0 a =0.5 0.8 a =1 0.6 0.4 p(t) 0.2 0 -0.2 -3 -2 -1 0 1 2 3 Normalised time Digital Mobile Communication Dr 1 Laith Danoon & Prof. Daniel So Lecture Aims Part I – Introduction to error control (types of errors, error control, codes, etc) – Examples of block codes (array code, Hamming code) – Mathematical structure of linear block codes (generator matrix, parity check matrix, syndrome) – LDPC – Convolutional codes (concepts, encoding, decoding, etc) – Turbo codes References – Lin & Costello Ch 2-4 – Haykin & Moher Ch 8 – Haykin Ch 6.10 & 8 Digital Mobile Communication Dr 2 Laith Danoon & Prof. Daniel So Wireless System Block Diagram Digital Mobile Communication Dr 3 Laith Danoon & Prof. Daniel So Error Control – Introduction (1/2) Baseband binary digits need to be encoded – to better withstand the effect of various channel impairment, such as noise, fading and jamming I/P O/P CHANNEL Channel coding is also termed error control coding, FEC, etc. – Reduce the probability of error – Reduce the effective data rate – Not just used for communications but also for (distributed) storage Digital Mobile Communication Dr 4 Laith Danoon & Prof. Daniel So Error Control – Introduction (2/2) Types of error control – Forward error correction and detection – Automatic request for Retransmission (ARQ) Types of errors – Random – Burst Types of codes – Block – Convolutional Digital Mobile Communication Dr 5 Laith Danoon & Prof. Daniel So Error Control Coding – Definitions (1/2) Block length of code: n No. of information digits: k No. of parity check bits: r = n-k Hamming distance: d – The number of positions in which a pair of n-tuples differs – Minimal Hamming distance: the minimal value of the pair-wise distance The efficiency of a code: R = k/n No. of errors that a code can detect: e = d-1 No. of errors that a code can correct: t = êê úú d -1 ë 2 û Linear codes: the parity check bits are modulo – 2 sums of information bits Digital Mobile Communication Dr 6 Laith Danoon & Prof. Daniel So Error Control Coding – Definitions (2/2) Example for (minimum) Hamming distance Consider two codewords: U–100101101 V– 0 1 1 1 1 0 1 0 0 d(U,V)=6 is the Hamming distance between the two codewords In a codebook, there are many codewords Minimal Hamming distance is the smallest distance between all pairs. Digital Mobile Communication Dr 7 Laith Danoon & Prof. Daniel So Error Control Coding – Example 1 (1/2) n=3 000 001 010 011 100 101 110 111 Digital Mobile Communication Dr 8 Laith Danoon & Prof. Daniel So Channel Coding – Example 1 (2/2) All possible codewords 000 001 010 011 100 101 110 111 No Redundancy No Error Correction or Detection Information Rate: R=1 Minimum Hamming Distance: dmin=1 Digital Mobile Communication Dr 9 Laith Danoon & Prof. Daniel So Channel Coding – Example 2 (1/3) n=3 000 011 101 110 Digital Mobile Communication Dr 10 Laith Danoon & Prof. Daniel So Channel Coding – Example 2 (2/3) n=3 All possible codewords 000 011 101 110 This code provides – Single error detection – No error correction Information Rate: R=2/3 Minimum Hamming Distance: dmin=2 Digital Mobile Communication Dr 11 Laith Danoon & Prof. Daniel So Channel Coding – Example 2 (3/3) How does it work? k=2 K1 K2 r r=1 n=K+r=3 0 0 0 d=2 0 1 1 N = 2k = 4 1 0 1 r = K1 Å K2 1 1 0 Linear This code is called “single parity check code (SPC)” How does it detect errors? Why cannot it correct errors? Digital Mobile Communication Dr 12 Laith Danoon & Prof. Daniel So Channel Coding – Example 3 (1/2) n=3 000 111 Digital Mobile Communication Dr 13 Laith Danoon & Prof. Daniel So Channel Coding – Example 3 (2/2) n=3 All possible codewords 000 111 How many errors can it detect? How many errors can it correct? Information Rate: R=???? Minimum Hamming Distance: dmin=??? Digital Mobile Communication Dr 14 Laith Danoon & Prof. Daniel So Error Control Coding Block error control (also termed linear coding) – Array codes – Hamming codes – Cyclic codes Convolutional coding – Convolutional encoding – Convolutional decoding Digital Mobile Communication Dr 15 Laith Danoon & Prof. Daniel So Array Codes (1/2) Array codes m 1 - Generalized SPC HORIZONTAL 1´ m 1xm CHECKS R= (l + 1)(m + 1) l INFORMATION DIGITS n=(l+1)(m+1) 1 CHECKS E.G. 1 = 2, m = 3 VERTICAL CHECKS ON CHECKS m = 3, n = 12 R = 0.5, 1 1 1 1 All single errors can be corrected 1 0 0 1 All single, double and triple errors can be 0 1 1 0 detected Digital Mobile Communication 16 Prof. Zhiguo Ding & Prof. Daniel So Array Codes (1/2) Structure of the (16,9) Array Code x x x o C= x x x o EXAMPLE: x x x o 1 0 1 0 0 0 0 0 o o o o 1 1 1 1 X - represents information digit; 0 1 0 1 O - represents parity check digit Digital Mobile Communication Dr 17 Laith Danoon & Prof. Daniel So Hamming Codes – Concept (1/3) For any positive integer m>=3, there exists a Hamming code with the following parameters: Code length: n=2m-1 Number of information bits: k = 2m-1 - m Number of parity check bits: m Error correcting capability: t=1 (dm=3) Hamming codes form a class of single error correcting codes Digital Mobile Communication Dr 18 Laith Danoon & Prof. Daniel So Hamming Codes – Concept (2/3) How to generate Hamming codes 1. Select the block length n 2. Write down the binary no. from 1 to n. (each one corresponding to the position in the n-digit codeword) 3. Place parity checks in the positions which are power of 2, i.e., 1, 2, 4, 8, … 4. The parity check equation for r1 is determined by the digits in those positions for which the least significant digits is of the position no. expressed in binary contains one (examples to be shown in the next slides) 5. Similarly r2 can be determined by the next significant digits , and so on. Digital Mobile Communication Dr 19 Laith Danoon & Prof. Daniel So Hamming Codes – Concept (3/3) r3 r2 r 1 POSITION NO. An example with m=3 0 0 1 1 20 r1 0 1 0 2 21 r2 r1= K1Å K2 Å K4 0 1 1 3 K1 r2= K1Å K3 Å K4 1 0 0 4 22 r3 r3= K2 ÅK3 ÅK4 1 0 1 5 K2 1 1 0 6 K3 1 1 1 7 K4 Digital Mobile Communication Dr 20 Laith Danoon & Prof. Daniel So Hamming Codes – Decoding (1/2) At the receiver, recalculate the parity checks from the observations Compare, and add (mod-2) the received parity checks and the recalculated checks – Syndrome If the syndrome is all zero, no error happens – Otherwise read in reverse order to correct the error An example: r1 r 2 K1 r 3 K2 K3 K4 TRANSMITTED CODE WORD 1 1 1 1 1 1 1 ERROR SEQUENCE 0 0 0 0 0 1 0 RECEIVED CODE WORD 1 1 1 1 1 0 1 Digital Mobile Communication Dr 21 Laith Danoon & Prof. Daniel So Hamming Codes – Decoding (2/2) r1 = K 1 K 2 K4 = 1 r2 = K 1 K 3 K4 = 0 RECALCULATE P.C. 1 0 0 r3 = K 2 K 3 K4 = 0 PERCEIVED P.C. 1 1 1 SYNDROME 0 1 1 SYNDROME REVERSE 1 1 0 =6 Digital Mobile Communication Dr 22 Laith Danoon & Prof. Daniel So Fundamentals to Design a Code To Synthesis a code with desired redundancy or error detection/control property To find a simple decoder To make the overall coding system as efficient as possible – Minimal amount of redundant information is injected – The codewords form an Abelian group under digit-by-digit modulo- 2 addition; that is, the sum of two codewords is another codeword. r1 r2 k1 r3 k2 1 0 0 1 1 r1 = k1 Å k2 1 1 1 0 0 r2 = k1 0 1 1 1 1 r3 = k2 Digital Mobile Communication Dr 23 Laith Danoon & Prof. Daniel So General Linear Codes – Encoding (1/2) Hamming codes belong to a general framework, termed linear codes (focusing systematic forms of generator/PC matrices) A linear code can be generated by using a generator matrix k r 1 0 0 × × × 0 g11 g12 × × × g1,n - k 0 1 0 0 g 21 g 22 × × × g 2, n - k 0 0 1 0 g 31 g 32 × × × g1,n - k × × × × × × k × × × × × × × G= × × × × × × × 0 0 0 × × × 1 g k1 g k 2 × × × g k ,n - k n The encoded vector can be obtained as follows: X = K* G Digital Mobile Communication Dr 24 Laith Danoon & Prof. Daniel So General Linear Codes – Encoding (2/2) Example 1: é1 0 1ù ê ú SPC G = êê0 1 ú 1ûú ë [0 0] [G ] = 0 0 0 [0 1] [G ] = 0 1 1 [x ] = [K ][G ] Þ= [1 0] [G ] = 1 0 1 [1 1] [G ] = 1 1 0 Example 2: é1 0 0 1 1 0ù FOR K = [1 1 1] G = ê0 1 0 1 0 1ú x = KG = [1 1 1] [G ] ê ú êë0 0 1 0 1 1úû =1 1 1 0 0 0 Digital Mobile Communication 25 Prof. Zhiguo Ding & Prof. Daniel So General Linear Codes – Decoding (1/3) Parity check matrix, H = r [g t I ] n é g11 g 21 ! gk 1 0 0 0.. 0ù ê g g 22 ! gk2 0 1 0 0.. 0ú ê 12 ú ê ú ê ú ê ú ê ú ê ú êëg 1, n - k g 2 , n - k g k , n - k 0 0..... 1ú û Why X [H T ] = 0 ? Digital Mobile Communication Dr 26 Laith Danoon & Prof. Daniel So General Linear Codes – Decoding (2/3) A more formal definition for syndrome [X] - Transmitted codeword; [e] - error vector; [Y] - received vector, such that Then: [Y] = [X] + [e] [Y] éêH T ùú = [X ] éH T ù + [e] éH T ù ë û êë úû êë úû = 0 + [e] éêH T ùú = [S] ë û If s=0, no error is detected, otherwise, check the error table. Digital Mobile Communication Dr 27 Laith Danoon & Prof. Daniel So General Linear Codes – Decoding (3/3) Example – Hamming code ék1 k 2 k3 k4 r1 r2 r3 ù r1 = k1 + k 2 + k 4 ê1 1 0 1 1 0 0ú r2 = k1 + k 3 + k 4 H=ê ú ê1 0 1 1 0 1 0ú r3 = k 2 + k 3 + k 4 ê ú ë0 1 1 1 0 0 1û é1 1 0ù If : K = (1111) ê1 0 1ú ê ú Then : X = (1111111) ê0 1 1ú If : e = (0 0 1 0 0 0 0) ê ú H T = ê1 1 1ú Y = (1 1 0 1 1 1 1) ê1 0 0ú ê ú S = Y * H T = (0 1 1) ê0 1 0ú êë0 0 1úû This corresponds to an error in the third position Digital Mobile Communication Dr 28 Laith Danoon & Prof. Daniel So Implementation of Block Encoding 1 - UP FOR INFORMATION DIGITS TO THE CHANNEL [K ] K-STAGE S.R. 1 P.C.SUM Å Å Å O/P 2 R-STAGE S.R. 2 - DOWN FOR CHECK DIGITS TO THE CHANNEL Digital Mobile Communication Dr 29 Laith Danoon & Prof. Daniel So Implementation of Block Decoding UP FOR INFORMATION FROM k - stage S.R. Å CHANNEL 1 Å Å Å Combinational K [y] 2 S logic circuit stage or store S DOWN C-stage S.R. R FOR CHECKS Digital Mobile Communication Dr 30 Laith Danoon & Prof. Daniel So Block Error Control - Cyclic Codes In cyclic codes, all the cyclic translates of every codeword are also codewords. A cyclic translate of a codeword is the new sequence formed by cyclically shifting all the digits in the code used by one or more digits. EXAMPLE: SPC Code is cyclic code because: 000 has no distinct translates 011 has translates 101 and 110 101 has translates 011 and 110 110 has translates 011 and 101 Reed-Solomon code is a special case of cyclic codes Digital Mobile Communication Dr 31 Laith Danoon & Prof. Daniel So Block Error Control - LDPC LDPC ( Low Density Parity Check ) codes are a class of linear bock code. LDPC codes were first introduced by R. Galager in his PhD thesis in 1960 and soon forgotten due to the implementation issues with limited technological knowhow at that time. The LDPC codes were rediscovered in mid 90s by R. Neal and D. Mackay at the Cambridge University. How important it is? – LDPC code is arguably the best error correction codes in existence at present. – It is the code to be used in 5G. Digital Mobile Communication Dr 32 Laith Danoon & Prof. Daniel So LDPC – Recap for Parity Check (1/3) A binary parity check code is a block code: i.e., a collection of binary vectors of fixed length n. Each codeword of length n can contain (n-r)=k information digits and r check digits. The symbols in the code satisfy r=n-k parity check equations of the form: Digital Mobile Communication Dr 33 Laith Danoon & Prof. Daniel So LDPC – Recap for Parity Check (2/3) What is a parity check matrix? – A parity check matrix is an r-row by n-column binary matrix. Remember k=n-r. – The rows represent the equations. – There is a 1 in the i-th row and j-th column if and only if the i-th code digit is contained in the j-th equation. Digital Mobile Communication Dr 34 Laith Danoon & Prof. Daniel So LDPC – Recap for Parity Check (3/3) Example: Hamming Code with n=7, k=4, and r=3 Can you write the parity check equations? ék1 k 2 k3 k4 r1 r2 r3 ù ê1 1 0 1 1 0 0ú H=ê ú ê1 0 1 1 0 1 0ú ê ú ë0 1 1 1 0 0 1û Digital Mobile Communication Dr 35 Laith Danoon & Prof. Daniel So LDPC – Encoding (1/4) The percentage of 1’s in the parity check matrix for a LDPC code is low. A regular LDPC code has the property that: – every code digit is contained in the same number of equations, – each equation contains the same number of code symbols. An irregular LDPC code relaxes these conditions. Digital Mobile Communication Dr 36 Laith Danoon & Prof. Daniel So LDPC – Encoding (2/4) The Equations for A Simple LDPC Code with n=12 There are actually only 9 independent equations so there are 9 parity digits. Digital Mobile Communication Dr 37 Laith Danoon & Prof. Daniel So LDPC – Encoding (3/4) The Parity Check Matrix for the Simple LDPC Code Note that each code symbol is contained in 3 equations and each equation involves 4 code symbols. Digital Mobile Communication Dr 38 Laith Danoon & Prof. Daniel So LDPC – Encoding (4/4) Can you provide the parity check matrix for a simple irregular LDPC code with following parity check equations (n=6)? c1 Å c2 Å c5 = 0 c1 Å c4 Å c6 = 0 c1 Å c2 Å c3 Å c6 = 0 Can you provide the parity check matrix? Digital Mobile Communication Dr 39 Laith Danoon & Prof. Daniel So LDPC – Tanner Graph (1/4) Tanner graph is a graphical representation of the parity check matrix specifying parity check equations. The graph has two types of nodes: bit nodes and parity nodes. Each bit node represents a code symbol and each parity node represents a parity equation. There is a line drawn between a bit node and a parity node if and only if that bit is involved in that parity equation. Decoding of LDPC codes is best understood by such a graphical description. Digital Mobile Communication Dr 40 Laith Danoon & Prof. Daniel So LDPC – Tanner Graph (2/4) Digital Mobile Communication Dr 41 Laith Danoon & Prof. Daniel So LDPC – Tanner Graph (3/4) Entire Graph for the Simple LDPC Code Note that each bit node has 3 lines connecting it to parity nodes and each parity node has 4 lines connecting it to bit nodes. Digital Mobile Communication Dr 42 Laith Danoon & Prof. Daniel So LDPC – Tanner Graph (4/4) Draw the Tanner graph for the following LDPC code é1 1 0 0 1 0ù H = êê1 0 0 1 0 1úú êë1 1 1 0 0 1úû Digital Mobile Communication Dr 43 Laith Danoon & Prof. Daniel So Convolutional Codes A convolutional code is described by the following parameters: k – No. input digits n – No. of outputs digits K – Constraint length R – coding rate (k/n) Differences from block codes: – The encoder has memory – The constraint length is varied to control the redundancy (coding rate) Digital Mobile Communication Dr 44 Laith Danoon & Prof. Daniel So Convolutional Codes – Encoding + U1 OUTPUT INPUT WORD U2 BIT m + RATE R = 1/2 K=3 Digital Mobile Communication Dr 45 Laith Danoon & Prof. Daniel So Convolutional Codes – Encoding t=1 × INPUT U1 U2 1 0 0 1 1 BIT m × RATE R = 1/2 K= 3 m=101 t=2 × INPUT U1 U2 0 1 0 1 0 BIT m × Digital Mobile Communication Dr 46 Laith Danoon & Prof. Daniel So Convolutional Codes – Encoding t=3 × INPUT U1 U2 1 0 1 0 0 BIT m × RATE R = 1/2 K= 3 m=101 t=4 INPUT × U1 U2 0 1 0 1 0 BIT m × Digital Mobile Communication Dr 47 Laith Danoon & Prof. Daniel So Convolutional Codes – Encoding t=5 U1 U2 INPUT 0 0 1 1 1 RATE R = 1/2 BIT m K=3 m= 101 t=6 INPUT U1 U2 0 0 0 0 0 BIT m OUTPUT SEQUENCE: 11 10 00 10 11 00 Digital Mobile Communication Dr 48 Laith Danoon & Prof. Daniel So Convolutional Codes – Encoding A trellis representation of convolutional encoding t1 t2 t3 t4 t5 t6 STATE × × × × × × 00 00 00 00 00 00 11 11 11 11 × 11 × × × × × 11 11 11 10 00 00 00 10 × × × 10 × 10 × × 10 01 01 01 01 01 × × × ×01 × 01 ×01 11 10 10 10 LEGEND: INPUT BIT 0 INPUT BIT 1 Digital Mobile Communication 49 Prof. Zhiguo Ding & Prof. Daniel So Convolutional Codes – Encoding Find a trellis representation for the following encoder: + U1 OUTPUT INPUT WORD U2 BIT m + RATE R = 1/2 K=3 Digital Mobile Communication Dr 50 Laith Danoon & Prof. Daniel So Convolutional Codes – Viterbi Decoding LET: m = 1 1 0 1 1 1 1 Tx u: 11 01 01 00 01 10 10 LET RECEIVED SEQUENCE BE 01 01 01 00 01 10 10 t1 × × t2 STEP 1: STATE 00 1 PATH METRIC: 00 d=1 × × 11 1 d=1 10 01 × × 11 × × Digital Mobile Communication 51 Prof. Zhiguo Ding & Prof. Daniel So Convolutional Codes – Viterbi Decoding AT SECOND STAGE: RECEIVED SYMBOLS: 01 STEP 2: PATH METRIC: t1 t2 STATE × t3 1 × 1 × d=2 00 × 1 × 1 × d=2 10 × × 2 × d=3 01 × × 0 × d=1 11 Digital Mobile Communication 52 Prof. Zhiguo Ding & Prof. Daniel So Convolutional Codes – Viterbi Decoding STEP 3: RECEIVED SYMBOLS: 01 PATH METRIC: t1 t2 t3 t4 t1 t2 t3 t4 × × × 1 1 1 ×3 × × 1 × 1 × 1 d=3 1 1 4 × × × 1 1 ×3 × × 1 × 1 × 1 d=3 4 × × × 2 2 4 × × × × × 0 1 0 d=1 × × 0 0 × 2 2 3 × × × × 0 × d=2 Digital Mobile Communication 53 Prof. Zhiguo Ding & Prof. Daniel So Convolutional Codes – Viterbi Decoding STEP 4: RECEIVED SYMBOLS: 00 × t1 1 t2 × 1 × t3 × × 3 t4 0 t5 3 2 3 × 1 × × 3 × ×1 2 0 5 × × 1 × × × 1 4 0 1 1 3 × × × 2 × 1 × 4 3 ×t1 t2 t3 t4 t5 PATH METRIC: 1 × × × × d=3 × 1 × × × × d=1 × × × × × d=3 0 0 × × × × × d=3 Digital Mobile Communication 54 Prof. Zhiguo Ding & Prof. Daniel So Convolutional Codes – Viterbi Decoding RECEIVED SYMBOLS: 01 STEP 5: t1 × ×t2 t3 × t4 × ×t5 t6 4× d=3 4 × × × × d=1 × × 4 4 × × × × d=3 × × 3 3 d=3 × × × × × ×× 1 5 PATH METRIC: t1 × t2 × ×t3 t4 × ×t5 t6 × d=4 × × × × × × d=4 × × × × × × d=3 × × × × × × d=1 Digital Mobile Communication 55 Prof. Zhiguo Ding & Prof. Daniel So Convolutional Codes – Viterbi Decoding STEP 6: RECEIVED SYMBOLS: 10 × t1 t2 × t3 × t4 × t5 × × t6 t7 5 × 4 × × × × × × × 5 4 × × × × × × × 4 3 × × × × × × × 6 1 PATH METRIC: t1 t2 × ×t3 t4 × t5 × × t6 × t7 5 d=4 4 × × × × × × × 5 d=4 4 × × × × × × × 4 3 d=3 × × × × × × × d=1 6 1 Digital Mobile Communication 56 Prof. Zhiguo Ding & Prof. Daniel So Convolutional Codes – Viterbi Decoding STEP 7: RECEIVED SYMBOLS: 10 t1 × ×t2 ×t3 t4 × ×t5 × t6 × 4 t7 × 5 t8 4 × × × × × × 4 × ×5 4 × × × × × × 3 × 4 × 3 × × × × × × × 4 × 1 1 t1 × ×t2 ×t3 t4 × ×t5 × t6 × t7 × t8 1 × × × × × × × × 1 1 1 × × × × × × × × 0 × × × × × × 1 × 1 × Digital Mobile Communication 57 Prof. Zhiguo Ding & Prof. Daniel So Turbo Codes – History A brief introduction for coding theory C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., July 1948. Digital Mobile Communication Dr 58 Laith Danoon & Prof. Daniel So Turbo Codes – History A brief introduction for coding theory – The early days – M. J. E. Golay codes (1949) – Richard W. Hamming (1950) – Cyclic Codes, Eugene Prange (1957) – BCH – Reed-Solomon (1960) – LDPC – Gallager (1963) – Convolutional codes – Viterbi decoding (1967) – Until 1993, coding theorists worked hard for a few decades But the found codes are far away from achieving Shannon’s limit “Coding is dead” (The first IEEE Comm. Theory Workshop) – 1970s Digital Mobile Communication Dr 59 Laith Danoon & Prof. Daniel So Turbo Codes – History IEEE International Comm. Conf. (ICC)1993 in Geneva Berrou, Glavieux. Thitimajshima, ‘Near Shannon Limit Error-Correcting Coding : Turbo codes’ Provided virtually error free communication at data date/power efficiencies beyond most expert thought Double data throughput at a given power Or work with half the power The three men were not known, “most were thinking that they are wrong in calculation” How important it is? – Used by 3G, 4G, NASA, etc. Digital Mobile Communication Dr 60 Laith Danoon & Prof. Daniel So Turbo Codes – Key Concepts Parallel encoding involving two encoders Using an interleaver to avoid correlation between two encoders X RSC Input Y1 Interleaver random Systematic codeword RSC Y2 Digital Mobile Communication Dr 61 Laith Danoon & Prof. Daniel So Turbo Codes – Encoding (© IEEE Spectrum) Digital Mobile Communication Dr 62 Laith Danoon & Prof. Daniel So Turbo Codes – Decoding (© IEEE spectrum) Digital Mobile Communication Dr 63 Laith Danoon & Prof. Daniel So Other Types of Error Control Automatic Repeat Request (ARQ) Purpose: To pass to the receiver every frame correctly Bad things can happen: Error, arbitrary delay, out-of-order arrival, or loss. What happens if there are excessive errors? – Recall that forward error correction codes can recover a small number of errors ARQ simply asks the transmitters to resend packets. – Assume that errors can be detected (parity check, cyclic redundancy check – CRC, etc) – ACKs (positive acknowledgments) – NAKs (negative acknowledgments) Digital Mobile Communication Dr 64 Laith Danoon & Prof. Daniel So Other Types of Error Control – H-ARQ ARQ and forward error correction codes have been introduced separately. – The forward error correction codes are to correct a subset of all errors that may occur – ARQ methods are used as a fall-back to correct errors that are un- correctable using only the redundancy sent in the initial transmission The combination of the two yields Hybrid-ARQ – Chase combining – Incremental redundancy Digital Mobile Communication Dr 65 Laith Danoon & Prof. Daniel So Other Types of Error Control Interleaving Example Interleaving: O/P 1101 (5,1) Without Interleaving Rep. I/P: 1 0 1 1 O/P 11111 00000 11111 11111 Error 0 0 111 00000 00000 00000 Rx Signal 1 1 0 0 0 00000 11111 11111 Data Detected 0 0 1 1 error Digital Mobile Communication Dr 66 Laith Danoon & Prof. Daniel So Other Types of Error Control I/P 1 0 1 1 O/P 11111 00000 11111 11111 With Interleaving 11111 Modified 00000 To 11111 11111 Reading as 1 0 11 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 Error 0 0 11 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Rx = Signal 1000 0011 1011 1011 1011 Re-arrange 10111 00000 01111 01111 Digital Mobile Communication Dr 67 Laith Danoon & Prof. Daniel So Other Types of Error Control 10111 00000 01111 01111 Data 1 0 1 1 Rx Burst errors can be corrected Digital Mobile Communication Dr 68 Laith Danoon & Prof. Daniel So  Applications of Error Correcting Codes (1/2) Deep Space Mission Code Mariner ’69 ’71 Reed Muller (1,5) Voyager 1+2 ’77 (Saturn Concatenated Convolutional And Jupiter) coding CCSDS Turbo/LDPC Other – including adaptive Application Code/ DVB Turbo codes H.261/H.263 video compression Cyclic Optical transmission i.e. Shortened Hamming submarines Fading Channel applications Turbo/LDPC, Hamming, (e.g. Mobile comms) Cyclic 3G UMTS Turbo 4G LTE Turbo 5G data channel LDPC 5G control channel Polar codes Digital Mobile Communication Dr 69 Laith Danoon & Prof. Daniel So  Applications of Error Correcting Codes (2/2) Data Storage Storage Device Code used Tape Drive IBM 3850 Cyclic Magnetic Disks IBM 3370 RS Optical IBM Cypress RS CD-ROM/ Cross interleaved RS code) DRAM Hamming codes Adaptive – mainly computer networking COMSAT ATM Link (terrestrial or Variable RS Satellite computer network link) Adaptive Multicasting (one to many Variable RS Computer network transmission) Digital Mobile Communication Dr 70 Laith Danoon & Prof. Daniel So Summary Error correction coding – Introduction to error control – Linear block codes (array code, Hamming code, LDPC) – Convolutional codes (concepts, encoding, decoding, Turbo, etc) Digital Mobile Communication Dr 71 Laith Danoon & Prof. Daniel So  Lecture Set 2 Baseband Digital Transmission – Part II 1 a =0 a =0.5 0.8 a =1 0.6 0.4 p(t) 0.2 0 -0.2 -3 -2 -1 0 1 2 3 Normalised time Digital Mobile Communication Dr 1 Laith Danoon & Dr. Daniel So Lecture Aims Know how to design a pulse shaping filter Understand the concept of matched filtering Know how to detect digital signals References – Lin & Costello Ch 2-4 – Haykin & Moher Ch 8 – Haykin Ch 6.10 & 8 Digital Mobile Communication Dr 2 Laith Danoon & Dr. Daniel So Baseband transmission Original signal could be analog – For digital transmission, samples of the signal must be taken Remember sampling theorem and Nyquist rate? Sampling frequency must be at least 2 times the source frequency – The samples are then converted into binary digits Remember Pulse Code Modulation? It maps a value into binary digits E.g., 3 bit PCM – 000, 001, 010, 011, 100, 101, 110, 111 These binary digits are in the baseband – Baseband signal: signals with frequency band that are close to that of the original signal Have a lowpass characteristics and centered around the origin of the frequency domain (i.e., |f| < W) E.g., square pulse -> sinc function in the frequency domain Comparative term to the Bandpass signal which is a modulated signal at a higher carrier frequency Digital Mobile Communication Dr 3 Laith Danoon & Dr. Daniel So Line Coding (I) Binary digits need to be represented by actual voltage for transmission – A 1 or 0 has to be represented by a signal – Line coding is the electrical representation of the encoded binary streams Various line coding types – Unipolar Non-Return-to-Zero (NRZ) Transmit voltage A for bit 1, and 0 for bit 0 (aka On-Off signalling) – Polar NRZ Transmit voltage A for bit 1, and -A for bit 0 Digital Mobile Communication Dr 4 Laith Danoon & Dr. Daniel So Line Coding (II) – Unipolar Return-to-Zero (RZ) Voltage A for half the symbol period only if bit 1 – Bipolar RZ +A and –A are used alternately for bit 1, and return to zero after half the symbol period No pulse for bit 0 Also known as Alternate Mark Inversion (AMI) – Manchester code Invented in this university for the Manchester Mark 1 computer Bit 1: +A for half a symbol and then –A for the other half Bit 0: Reverse of bit 1 (i.e., -A first and then +A) Was used for Mark 1, and still used for RFID, NFC, etc., Digital Mobile Communication Dr 5 Laith Danoon & Dr. Daniel So Line Coding (III) Digital Mobile Communication Dr 6 Laith Danoon & Dr. Daniel So Example Draw the signalling diagram of all line coding schemes for bit stream [1 0 1 1 1 0] Digital Mobile Communication Dr 7 Laith Danoon & Dr. Daniel So More Insight of Line Coding (extra) Line coding signals can be understood better by studying power spectral density (PSD) of these signals – PSD describes the distribution of signal power over frequency – PSD and autocorrelation are a Fourier transform pair How to find PSD for line coding pulses? We consider line coding pulses as a pulse train constructed from a basic pulse p(t) repeating at intervals of T with relative strength ak for the pulse starting at t=kT such that the k-th pulse in this pulse train y(t) is ak p(t-kT). The PSD of y(t) is the product of the PSD of the basic pulse and the PSD of the impulse train sequence x(t) containing ak Digital Mobile Communication Dr 8 Laith Danoon & Dr. Daniel So More Insight of Line Coding The PSD of the basic pulse can be easily obtained by applying FT For NRZ For RZ The PSD of the impulse train is where Digital Mobile Communication Dr 9 Laith Danoon & Dr. Daniel So More Insight of Line Coding The PSD of the line coding signals is PSD of polar NRZ/RZ – Since ak and ak+n are independent and equally likely Digital Mobile Communication Dr 10 Laith Danoon & Dr. Daniel So More Insight of Line Coding The PSD of polar NRZ and RZ Digital Mobile Communication Dr 11 Laith Danoon & Dr. Daniel So More Insight of Line Coding PSD of unipolar NRZ/RZ – R0 is 1/2 because half the time the signals are 1 and half the time they are 0. – The issue is with all the higher order terms. If we look at Rn, 1/4 of the time two bits separated by n are both 1, 1/2 the time one is one and one is zero, and 1/4 the time they are both zero. The autocorrelation is then – Therefore, the PSD of unipolar NRZ is – So unipolar NRZ/RZ contains DC Digital Mobile Communication Dr 12 Laith Danoon & Dr. Daniel So More Insight of Line Coding The PSD of unipolar NRZ and RZ Advantage of RZ – possibility to extract clock information Disadvantage of RZ – larger bandwidth Digital Mobile Communication Dr 13 Laith Danoon & Dr. Daniel So More Insight of Line Coding PSD of bipolar RZ (AMI) – If the data sequence {ak} consists of equally likely and independent 0’s and 1s, then the autocorrelation function of the sequence is for R0 is – For R±1 there are four possibilities, 11, 01, 10, and 00. Since the signs change for successive 1’s, and all the others have autocorrelations of zero, – For n = 2, the various permutations of 1’s and 0’s are either zero, or cancel out and give R2 = 0. This continues for n > 2. Digital Mobile Communication Dr 14 Laith Danoon & Dr. Daniel So More Insight of Line Coding PSD of bipolar RZ (AMI) – Therefore – This PSD falls off faster than than P(f) – The PSD has a null at DC, which aids in transformer coupling. Digital Mobile Communication Dr 15 Laith Danoon & Dr. Daniel So The PSD of Line Coding Signals Digital Mobile Communication Dr 16 Laith Danoon & Dr. Daniel So Pulse Shaping (I) Line coding approach is good for wired transmission – In frequency domain, square pulse is a sinc function that occupies wide bandwidth Digital Mobile Communication Dr 17 Laith Danoon & Dr. Daniel So Pulse Shaping (II) Line coding approach is good for wired transmission – In frequency domain, square pulse is a sinc function that occupies wide bandwidth For wireless transmissions – Transmission using large bandwidth is expensive and inefficient – If multiple users transmit at adjacent channels, it will create interference Adjacent channel interference – Interference coming from signals in the neighbouring channels – Can significantly degrade the signal quality Digital Mobile Communication Dr 18 Laith Danoon & Dr. Daniel So Pulse Shaping (III) Quite often an operator is given a spectral mask to fit their signals into – A range of frequency band for the main signals – Some leakage allowed on the side with restricted power level Reduce adjacent channel interference – E.g., 802.11n 20MHz mask – Need to design a signal that fits into the spectral mask Pulse Shaping – Instead of using square pulse, different pulse shape should be used to fit the spectral mask Multiply the filter response to the signal frequency response Digital Mobile Communication Dr 19 Laith Danoon & Dr. Daniel So Pulse Shaping (IV) How to design a pulse? – A pulse with sharp edges will have high frequency components E.g., square pulse in frequency domain is sinc function, which has lots of high frequency components. This implies wider bandwidth – Pulses are transmitted continuously and hence should not interfere with each other Pulse shape design principles – Smooth shape to avoid high frequency components – Must not cause interference to the neighbouring symbols i.e., No Inter-Symbol Interference (ISI) Digital Mobile Communication Dr 20 Laith Danoon & Dr. Daniel So Pulse Shaping (V) Nyquist criterion for zero ISI – The criterion to ensure zero ISI for a pulse – Since sampling occurs at the receiver, the only requirement is that a pulse signal exists at the corresponding sampling instance, and zero at all other sampling instances I.e., Anything occurs between the sampling points are irrelevant 1 for 𝑖 = 𝑘 𝑝 𝑖𝑇! − 𝑘𝑇! = ' 0 for 𝑖 ≠ 𝑘 where Tb is the sampling time, i is the transmitted instance, and k is the sampling instance Digital Mobile Communication Dr 21 Laith Danoon & Dr. Daniel So Pulse Shaping (VI) Raised Cosine Spectrum – One of the most common pulse shaping spectrum – Has a raised cosine shape – Allows some leakage into adjacent band to reduce interference in time – Frequency spectrum: 1/2𝑊 0 ≤ 𝑓 ≤ 𝑓" 1 𝜋 𝑃 𝑓 = 1 + 𝑐𝑜𝑠 𝑓 − 𝑓" 𝑓" ≤ 𝑓 ≤ 2𝑊 − 𝑓" 4𝑊 2𝑊𝛼 0 𝑓 ≥ 2𝑊 − 𝑓" α is the roll-off factor and 𝑓" = 𝑊(1 − 𝛼) – Time domain signal cos(2𝜋𝛼𝑊𝑡) 𝑝 𝑡 = 𝑠𝑖𝑛𝑐(2𝑊𝑡) 1 − 16𝛼 # 𝑊 # 𝑡 # Digital Mobile Communication Dr 22 Laith Danoon & Dr. Daniel So  Pulse Shaping (VII) Raised cosine pulse – Frequency domain Time domain 1 1 a =0 a =0 0.9 a =0.5 a =0.5 a =1 0.8 0.8 a =1 0.7 0.6 0.6 2WP(f) 0.4 0.5 p(t) 0.4 0.2 0.3 0 0.2 0.1 -0.2 0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -3 -2 -1 0 1 2 3 Normalised time f/W – A larger α occupies wider bandwidth, but has a smoother pulse – Small α will have high distortion if sampling time is not precise Digital Mobile Communication Dr 23 Laith Danoon & Dr. Daniel So Matched Filter (I) Now a pulse has been transmitted, how do we detect the signal at the receiver? Option 1: Take a sample at the peak of the pulse – However such a sample cannot guarantee best SNR At a certain time, the noise can be very large and severely distort the sample Option 2: Integrate the signal over a symbol period – The effect of noise can be averaged over a symbol period leading to a better SNR Noise power is still the same. Only avoided instantaneously large variations – Consider integrating a square pulse " 1 1 1 C 𝑑𝑡 = 𝑡 E = 1 $ 0 t t 1 1 Integrate & dump Square pulse Digital Mobile Communication Dr 24 Laith Danoon & Dr. Daniel So Matched Filter (II) Now consider the convolutional between two square pulses ' 𝑦 𝑡 = C 𝑟𝑒𝑐𝑡 𝜏 𝑟𝑒𝑐𝑡 𝑡 − 𝜏 𝑑𝜏 1 0≤𝑡≤1 𝑟𝑒𝑐𝑡 𝜏 = ' %& 0 𝑡>1 0 𝑡