OFDM Transmission Technique SS 2013 Dr.-Ing. L. Häring
Lecture with exercises Organization Lecture: 2 SWS (90 minutes) a week Exercise: project at the end of semester Elective course Oral examination (30-45 minutes) p. 2
Preliminaries Required previous knowledge Communications 1 (System theory) Communications 2 (Statistical signal processing) Transmission Techniques (Modulation techniques) (Coding Theory) Radio Propagation Channels Recommended previous knowledge Matlab for Communications (for project) p. 3
Further references: References Scripts regarding lectures of NTS H. Rohling: OFDM A Flexible and Adaptive Air Interface for a 4G Communication System, Hamburg R. van Nee and R. Prasad: OFDM for Wireless Multimedia Communications A. Paulraj et al: Introduction to Space-Time Wireless Communications p. 4
1. Introduction 2. Radio Propagation Channels 3. OFDM Basics 4. OFDM Transmitter 5. Synchronization Mismatches 6. OFDM Receiver 7. Advanced Techniques 8. Introduction to MIMO Systems 9. Multiuser Systems 10. Case Study Outline p. 5
1 Introduction History: Transmission principle of dividing data into several bit streams more than 50 years ago Wide range of application by advanced signal processing techniques (e.g. Fast Fourier transform) Papers: 1967 by Saltzberg: Performance of an efficient parallel data transmission system 1971 by Weinstein: Data transmission by frequency-division multiplexing using the discrete Fourier transform 1990 by Bingham: Multicarrier modulation for data transmission An idea whose time has come p. 6
1 Introduction In 2008: [Source: H. Rohling: A Flexible and Adaptive Air Interface for a 4G Communication System] p. 7
1 Introduction Application areas of OFDM: UMTS LTE (downlink) p. 8
2 Radio Propagation Channel 2.1 LTI System: Multipath Propagation line-of-sight (LOS) p. 9
Frequency Domain Time Domain 2 Radio Propagation Channel 2.1 LTI System Channel Impulse Response (CIR) h c (t): number of paths path coefficient path delay Channel Transfer Function (CTF) H c ( ): p. 10
2 Radio Propagation Channels 2.1 LTI System Relation of input signal x(t) and output signal r(t) in linear, timeinvariant systems: impulse response transfer function p. 11
2 Radio Propagation Channels 2.1 LTI system Statistical properties of time-invariant CIR: Power Delay Profile (PDP) P PDP (t): coherence bandwidth Examples: IEEE 802.11a-standard (indoor) 30 Model A (small rooms) 30 Model B (large office rooms) 20 20 10 10 100 200 300 400 500 200 400 600 800 p. 12
2 Radio Propagation Channels 2.1 LTI system Discrete time representation Tapped delay line (finite impulse response filter) p. 13
2 Radio Propagation Channels 2.1 LTI system Path coefficients h c,l : often used model and independent complex Gaussian distributed (central limit theorem) variance: mean: zero non-line-of-sight (NLOS) line-of-sight (LOS) 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1-5 -4-3 -2-1 1 2 3 4 5-5 -4-3 -2-1 1 2 3 4 5 p. 14
2 Radio Propagation Channels 2.1 LTI system Rayleigh (NLOS) or Rice (LOS) pdf uniformly distributed in [0,2 ) (NLOS) Rayleigh distribution: Rice distribution with different K-factors 0.8 0.6 0.4 0.2-2 -1 1 2 3 4 0.8 0.6 0.4 0.2-2 -1 1 2 3 4 5 6 7 p. 15
2 Radio Propagation Channels 2.1 LTI system Matlab simulation example Exercise 1: Calculation of output signal variance Assumption: x i independent complex Gaussian»CN(0, x2 ) Problem: Distribution of received signal r i? p. 16
2 Radio Propagation Channels 2.2 Linear Time-Variant (LTV) system Movement of transmitter and receiver observation time delay time p. 17
2 Radio Propagation Channels 2.2 LTV system Relation of input signal x(t) and output signal r(t) in linear, timevariant systems: Linearity property: p. 18
2 Radio Propagation Channels 2.2 LTV system Example: Reaction to input signal x(t)= (t-t 0 ) p. 19
2 Radio Propagation Channels 2.2 LTV system Time correlation of path coefficients h c,l (t) often modeled by Jakes (Doppler) spectrum: with for p. 20
2 Radio Propagation Channels 2.2 LTV system Coherence time : Simulation model (time-variant coefficients) p. 21
2 Radio Propagation Channels 2.3 Narrow- and Wideband Systems Symbol duration occupied bandwidth -2-1 1 2-2 -1 1 2-4 -3-2 -1 1 2 3 4-4 -3-2 -1 1 2 3 4 p. 22
2 Radio Propagation Channels 2.3 Narrow- and Wideband Systems Narrowband channel Signal bandwidth B < coherence bandwidth B c frequency-flat frequency-nonselective No intersymbol interference (ISI) occurs Wideband channel Signal bandwidth B > coherence bandwidth B c frequency-selective Intersymbol interference (ISI) occurs p. 23
2 Radio Propagation Channels 2.3 Narrow- and Wideband Systems Frequency domain frequency-flat constant factor Time domain no intersymbol interference p. 24
2 Radio Propagation Channels 2.3 Narrow- and Wideband Systems Frequency domain frequency-selective Time domain subsequent symbols will severely overlap ISI occurs p. 25
2 Radio Propagation Channels 2.3 Narrow- and Wideband Systems Frequency-flat (B c >>B) Symbols overlap marginally (no ISI) Simple receiver sufficient Frequency-selective (B c <<B) Symbols overlap (ISI) Sophisticated time-domain receiver needed p. 26
3 OFDM Basics 3.1 Idea of multicarrier transmission Idea of multicarrier transmission: Wideband channel N narrowband channels within each subband frequency-flat p. 27
3 OFDM Basics 3.1 Idea of multicarrier transmission Comparison: Single-Carrier vs. Multi-Carrier single symbol has bandwidth: B B/N= f time duration: T S / p. 28
3 OFDM Basics 3.1 Idea of multicarrier transmission Transmitter block diagram Tx signal: p. 29
3 OFDM Basics 3.1 Idea of multicarrier transmission Receiver block diagram Rx signal: p. 30
3 OFDM Basics 3.2 OFDM as special case Orthogonal Frequency Division Multiplexing (OFDM) Special choice of pulse-shaping filter: p. 31
3 OFDM Basics 3.2 OFDM as special case Orthogonal Frequency Division Multiplexing (OFDM) Special choice of frequency spacings: p. 32
3 OFDM Basics 3.2 OFDM as special case Orthogonal Frequency Division Multiplexing (OFDM) Special choice of frequency spacings: -3-2 -1 1 2 3 4 5 6 7 8 p. 33
3 OFDM Basics 3.2 OFDM as special case Discrete time representation x(t) is sampled at t=it+kt S : p. 34
Discrete Time representation 3 OFDM Basics 3.2 OFDM as special case Receiver: Reverse operation Exercise 2: Proof p. 35
3 OFDM Basics 3.2 OFDM as special case Simplified OFDM transmission chain p. 36
Block transmission 3 OFDM Basics 3.3 Usage of cyclic prefix block 1 block 2 block 3 block 1 block 2 block 3 block 1 block 2 block 3 path 1 path 2 path L DFT window time InterBlock Interference (IBI) p. 37
3 OFDM Basics 3.3 Usage of cyclic prefix Block transmission with guard interval (GI) / cyclic prefix (CP) GI block 1 GI block 2 GI block 3 GI block 1 GI block 2 GI block 3 GI block 1 GI block 2 GI block 3 path 1 path 2 path L DFT window time no InterBlock Interference (IBI) p. 38
3 OFDM Basics 3.3 Usage of cyclic prefix Usage of guard interval / cyclic prefix IBI can be completely avoided if guard interval orthogonality interval copy p. 39
3 OFDM Basics 3.4 Transmission under ideal conditions Two-Dimensional Channel Assumptions: p. 40
3 OFDM Basics 3.4 Transmission under ideal conditions Transmission under ideal conditions Discrete-time baseband Tx signal (including cyclic prefix) with information symbols p. 41
3 OFDM Basics 3.4 Transmission under ideal conditions Signal after digital/analog conversion Tx baseband signal after pulse-shaping filter p. 43
3 OFDM Basics 3.4 Transmission under ideal conditions Transmission via radio channel with effective channel impulse response p. 44
3 OFDM Basics 3.4 Transmission under ideal conditions Receiver processing Rx baseband signal Rx signal is sampled with period T: p. 45
3 OFDM Basics 3.4 Transmission under ideal conditions block fading channel is assumed Sampled received baseband signal: p. 46
3 OFDM Basics 3.4 Transmission under ideal conditions Exercise 3: Show that holds p. 47
Overview: 3 OFDM Basics 3.4 Transmission under ideal conditions input signal (orthogonal subcarriers) linear time-(in)variant channel output signal (orthogonal subcarriers) p. 48
3 OFDM Basics 3.4 Transmission under ideal conditions Carry out DFT at receiver: Demodulated signal: p. 49
3 OFDM Basics 3.4 Transmission under ideal conditions Simplified OFDM block diagram: p. 50
3 OFDM Basics 3.4 Transmission under ideal conditions Matrix-vector representation (noise is not considered) IDFT operation where p. 51
3 OFDM Basics 3.4 Transmission under ideal conditions DFT-matrix IDFT-matrix p. 52
3 OFDM Basics 3.4 Transmission under ideal conditions Exercise 4: Show that holds p. 53
3 OFDM Basics 3.4 Transmission under ideal conditions Cyclic Prefix insertion where Last N g rows of N N identity matrix Check vector dimensions: p. 55
3 OFDM Basics 3.4 Transmission under ideal conditions Cyclic Prefix insertion p. 56
3 OFDM Basics 3.4 Transmission under ideal conditions Convolution Assumption: L=N g +1 p. 57
3 OFDM Basics 3.4 Transmission under ideal conditions Alternatively: because: by substitution: p. 58
3 OFDM Basics 3.4 Transmission under ideal conditions In matrix-vector representation: p. 59
3 OFDM Basics 3.4 Transmission under ideal conditions In matrix-vector representation: Cyclic prefix removal GI block with zero matrix p. 60
3 OFDM Basics 3.4 Transmission under ideal conditions Cyclic prefix removal Removes first N g samples p. 61
3 OFDM Basics 3.4 Transmission under ideal conditions Cyclic prefix removal influence of previous block k-1 influence of current (desired) block k p. 62
3 OFDM Basics 3.4 Transmission under ideal conditions Influence of previous block p. 63
3 OFDM Basics 3.4 Transmission under ideal conditions Cyclic prefix removal lower triangular Toeplitz matrix p. 64
3 OFDM Basics 3.4 Transmission under ideal conditions Cyclic prefix removal Exercise 4.2: Show that is circular p. 65
3 OFDM Basics 3.4 Transmission under ideal conditions Input-output relation in matrix form p. 66
3 OFDM Basics 3.4 Transmission under ideal conditions Input-output relation in set of equations circular convolution p. 67
3 OFDM Basics 3.4 Transmission under ideal conditions Cyclic prefix guarantees cyclic convolution: p. 68
3 OFDM Basics 3.4 Transmission under ideal conditions Cyclic prefix guarantees cyclic convolution: p. 69
3 OFDM Basics 3.4 Transmission under ideal conditions DFT operation: p. 70
Properties of Tx signal 4 OFDM Transmitter 4.1 Properties of Tx signal information symbols Symbols s n [k] are e.g. quadrature amplitude modulated (QAM): s n [k] = s n,r [k] + js n,i [k] zero-mean: E{s n [k]}=0 uncorrelated: E{s n [k ] (s n [k]) }= s2 k [n -n] k [k -k] p. 71
4 OFDM Transmitter 4.1 Properties of Tx signal Quadrature Amplitude Modulation Binary Phase Shift Keying (BPSK) p. 72
4 OFDM Transmitter 4.1 Properties of Tx signal 4-Quadrature Amplitude Modulation (4-QAM) / Quadrature Phase Shift Keying (QPSK) Gray coding: neighboring symbols differ only in one bit p. 73
4 OFDM Transmitter 4.1 Properties of Tx signal 16-Quadrature Amplitude Modulation (16-QAM) p. 74
4 OFDM Transmitter 4.1 Properties of Tx signal 64-Quadrature Amplitude Modulation (64-QAM) p. 75
4 OFDM Transmitter 4.1 Properties of Tx signal Probability density function (pdf) of x i [k] First moment: Second moment p. 76
4 OFDM Transmitter 4.1 Properties of Tx signal If N! 1: x i [k] Gaussian distributed (central limit theorem) x i [k]»cn(0,n s2 ) noise-like / large amplitude variations p. 77
4 OFDM Transmitter 4.1 Properties of Tx signal Example: N=256 (16-QAM frequency domain symbols) e.g., real part of signal x i p. 78
4 OFDM Transmitter 4.1 Properties of Tx signal e.g., amplitude of x i p. 79
4 OFDM Transmitter 4.1 Properties of Tx signal Large Peak-to-Average Power Ratio (PAPR) Leads to high requirements of power amplifier at Tx side Non-linear distortions For methods to reduce the PAPR see chapter 7 p. 80
4 OFDM Transmitter 4.1 Properties of Tx signal Simple models of amplifier characteristics Hard limiter: Saturation model: p. 81
Properties of Tx signal 4 OFDM Transmitter 4.1 Properties of Tx signal time-domain baseband signal Symbols s n [k] are e.g. quadrature amplitude modulated (QAM): s n [k] = s n,r [k] + js n,i [k] zero-mean: E{s n [k]}=0 uncorrelated: E{s n [k ] (s n [k]) }= s2 k [n -n] k [k -k] p. 82
4 OFDM Transmitter 4.2 Baseband modeling Relation between baseband signal x BB (t) and bandpass signal x RF (t): (see also lectures Communications 3 or Transmission and Modulation ) p. 83
4 OFDM Transmitter 4.2 Baseband modeling Block diagram: Relation between discrete-time signal x n and RF signal x RF (t): p. 84
4 OFDM Transmitter 4.2 Baseband modeling Motivation of baseband modeling: Description in RF band: p. 85
4 OFDM Transmitter 4.2 Baseband modeling Relation between baseband signals: Input signals in time and frequency: p. 86
4 OFDM Transmitter 4.2 Baseband modeling Output signal in time and frequency: Since h RF (t) is real, it holds: p. 88
4 OFDM Transmitter 4.2 Baseband modeling Equivalent baseband channel: p. 89
4 OFDM Transmitter 4.2 Baseband modeling Equivalent baseband channel: p. 90
Received signal: 4 OFDM Transmitter 4.2 Baseband modeling p. 91
4 OFDM Transmitter 4.2 Baseband modeling Narrowband assumption: X BB ( - c )=0 for <0 yields: p. 92
where: 4 OFDM Transmitter 4.2 Baseband modeling Input-output relation can be completely modeled in baseband! Complex-valued (baseband) channel impulse response p. 93
Overview: 4 OFDM Transmitter 4.2 Baseband modeling p. 94
4 OFDM Transmitter 4.2 Baseband modeling Block diagram: Relation between information signal s n [k] and RF signal x RF (t) p. 95
OFDM allows the usage of: 4 OFDM Transmitter 4.2 Baseband modeling Different modulation schemes for each subcarrier Different power for each subcarrier Overview of algorithms in chapter 7 p. 96
Tx structures: 4 OFDM Transmitter 4.3 Frame structures Broadcasting (e.g. DVB-T/C/S) Example: DVB-T p. 97
Tx structures: 4 OFDM Transmitter 4.3 Frame structures Burst-wise transmission in time division duplex mode (e.g. wireless local area networks (WLAN)) Example: IEEE 802.11a p. 98
frequency (in subcarriers) 4 OFDM Transmitter 4.3 Frame structures IEEE 802.11a frame in frequency domain time (in OFDM blocks) p. 99
4 OFDM Transmitter 4.3 Frame structures Time division duplex (TDD) Transmission in same frequency band p. 100
4 OFDM Transmitter 4.3 Frame structures Time division duplex Frequency division duplex (FDD) p. 101
Imperfections: 5 Synchronization Mismatches Nonlinear distortions (difficult to model) Thermal noise etc. Synchronization errors Time Offsets (TOs) Sampling Frequency Offsets (SFOs) Carrier Frequency Offsets (CFOs) Oscillator Phase Noise (PN) Channel Estimation errors p. 102
5 Synchronization Mismatches 5.1 Mismatch Models Time synchronization in OFDM systems Frame detection Estimation of optimal block start position 3 different cases: InterBlock Interference (IBI) ideal InterBlock Interference (IBI) p. 103
5 Synchronization Mismatches 5.1 Mismatch Models Sampling Frequency Offsets: Due to independent oscillators on transmitter and receiver side Reasons: tolerances, temperature, aging etc. Example: Sampling with different frequencies p. 104
5 Synchronization Mismatches 5.1 Mismatch Models Sampling Frequency Offsets: Definition of relative SFO: (typical values: 10-6,,10-5 ) p. 105
5 Synchronization Mismatches 5.1 Mismatch Models Sampling Frequency Offsets: Can be modeled as time-variant fractional time offset of k-th block When is time offset equal to one sample? Example: p. 106
5 Synchronization Mismatches 5.1 Mismatch Models Carrier Frequency Offsets: Simple model in baseband: phase rotation in time domain Definition of CFO normalized to subcarrier spacing p. 107
5 Synchronization Mismatches 5.1 Mismatch Models Carrier Frequency Offsets: Usually baseband oscillator also generates wave at carrier frequency In addition: Doppler effect Different carrier frequencies at Tx and Rx side OFDM very sensitive to CFOs because: Desired signal part will be damped Orthogonality between subcarriers is destroyed Crosstalk between subcarrier signals InterCarrier Interference (ICI) p. 108
Influence of CFOs 5 Synchronization Mismatches 5.1 Mismatch Models Spectrum superposition sampling simple correction of (ideal) presence single of spectra possible subcarriers of CFOs p. 109
Phase noise: 5 Synchronization Mismatches 5.1 Mismatch Models Caused by imperfections of oscillators In baseband modeled by phase fluctuations F(t) F(t) usually non-stationary p. 110
5 Synchronization Mismatches 5.1 Mismatch Models Lorentzian/Wiener model Random walk with phase difference Autocorrelation function of complex envelope m(t)=e jf(t) p. 111
5 Synchronization Mismatches 5.1 Mismatch Models Autocorrelation function of complex envelope m(t)=e jf(t) p. 112
5 Synchronization Mismatches 5.1 Mismatch Models Determination of variance of phase difference (only if instantaneous frequency noise is stationary and white, i.e. Relation between instantaneous frequency and phase difference linear system with transfer function H F ( ) p. 113
5 Synchronization Mismatches 5.1 Mismatch Models Transfer function H F ( ) Power spectral density of F(t) p. 114
5 Synchronization Mismatches 5.1 Mismatch Models Variance of F(t) p. 115
5 Synchronization Mismatches 5.1 Mismatch Models Autocorrelation function of complex envelope Power spectral density of phase noise p. 116
5 Synchronization Mismatches 5.1 Mismatch Models p. 117
5 Synchronization Mismatches 5.1 Mismatch Models Example: One realization of random process with g =2 50 Hz p. 118
5 Synchronization Mismatches 5.2 Transmission under realistic conditions Transmission chain including all synchronization mismatches p. 119
5 Synchronization Mismatches 5.2 Transmission under realistic conditions Examples with Matlab Effect of CFO: Linear increasing phase Intercarrier interference p. 120
5 Synchronization Mismatches 5.2 Transmission under realistic conditions Blockwise phase rotation due to CFO 10 10 10 5 5 5 0 0 0-5 -5-5 -10-10 -5 0-10 5-10 L. Häring 10-5 0-105 -10 10-5 0 5 10 OFDM - Orthogonal Frequency Division Multiplexing p. 121
5 Synchronization Mismatches 5.2 Transmission under realistic conditions Intercarrier interference due to CFO 10 10 10 5 5 5 0 0 0-5 -5-5 -10-10 -5 0-105 -10 L. Häring 10-5 0-10 5-10 10-5 0 5 10 OFDM - Orthogonal Frequency Division Multiplexing p. 122
5 Synchronization Mismatches 5.2 Transmission under realistic conditions Effects of phase noise: Time-variant frequency deviation (similarity to effect of CFO) Common phase error (CPE) blockwise random phase rotation (instead of linear phase rotation as for CFOs) Intercarrier interference p. 123
5 Synchronization Mismatches 5.2 Transmission under realistic conditions Constellation diagram with phase noise (single OFDM block) 10 5 0-5 Two effects: CPE (rotation) & ICI ( noise -like) -10-10 -5 0 5 10 p. 124
Synchronization Time/Frame start detection Carrier Frequency/Sampling Frequency Channel Estimation Preamble-based Pilot subcarrier-based Equalization MAP/ML Linear techniques 6 OFDM Receiver p. 125
6 OFDM Receiver mod. bit source channel coding S/P IFFT P/S interleaving preamble cyclic prefix mod. OFDM transmitter pilots radio channel OFDM receiver channel estimation and equalization AWGN demod bit sink channel decod. deinterleaving S/P demod FFT P/S CP removal time and freq. synch. p. 126
6 OFDM Receiver 6.1 Time and frequency synchronization Classification: Training-based/data-aided (preamble/pilot subcarriers) Blind (e.g. cyclic prefix, guard subcarriers) Combination of both p. 127
6 OFDM Receiver 6.1 Time and frequency synchronization Data-aided: Algorithm by Moose (1994): Preamble: repeated signal parts Received signal (including CFO, ideal channel) Idea: correlation of signal values at distance N TS : p. 128
6 OFDM Receiver 6.1 Time and frequency synchronization Blind: Maximum-Likelihood Estimation: Joint estimation of block start position and CFO Recall: repeated sequences due to guard interval guard interval orthogonality interval copy p. 129
6 OFDM Receiver 6.1 Time and frequency synchronization Signal model at Tx side: Signal model at Rx side (AWGN channel): CFO time offset p. 130
6 OFDM Receiver 6.1 Time and frequency synchronization Correlation of received samples: Further assumption: data symbols are Gaussian distributed uncorrelated p. 131
6 OFDM Receiver 6.1 Time and frequency synchronization ML estimators of time and frequency are: with Autocorrelation term Energy term p. 132
6 OFDM Receiver 6.1 Time and frequency synchronization Overview of cost functions p. 133
6 OFDM Receiver 6.1 Time and frequency synchronization Implementation structure of synchronization unit based upon correlation metric J 3,i p. 134
6 OFDM Receiver 6.1 Time and frequency synchronization Illustrative example of correlation metric J 3,i in AWGN channel correlation correlation sum correlation small sum increases maximal sum sum decreases small p. 135
6 OFDM Receiver 6.1 Time and frequency synchronization Matlab example: AWGN channel 1.0 0.5 p. 136
6 OFDM Receiver 6.1 Time and frequency synchronization Problem: Timing metrics designed for AWGN channel Application to radio propagation channel possible? Signal model in frequency-selective channels: CFO time offset p. 137
6 OFDM Receiver 6.1 Time and frequency synchronization Example: p. 138
6 OFDM Receiver 6.1 Time and frequency synchronization Time shift of maximum depends strongly on channel realization h i Performance degrades in frequency-selective fading channels By exploiting channel knowledge, timing relation can be interpreted correctly Optimal: Joint synchronization and channel estimation or Iterative synchronization and channel estimation Suboptimal (but fast and simple): statistical approaches p. 139
6 OFDM Receiver 6.1 Time and frequency synchronization Idea of suboptimal approach: Relation between expected timing metric and power delay profile (assumed to be known) p. 140
6 OFDM Receiver 6.1 Time and frequency synchronization Idea of suboptimal approach: Optimal start position is: Usually, (i opt -i Peak ) is taken by rule of thumb Using average shape of timing metrics, (i opt -i Peak ) can be stated more precisely p. 141
6 OFDM Receiver 6.2 Channel Estimation mod. bit source channel coding S/P IFFT P/S interleaving preamble cyclic prefix mod. OFDM transmitter pilots radio channel OFDM receiver channel estimation and equalization AWGN demod bit sink channel decod. deinterleaving S/P demod FFT P/S CP removal time and freq. synch. p. 142
6 OFDM Receiver 6.2 Channel estimation Training information: Preamble (midambles etc.) Initial estimation in burst-transmission Precise Pilot symbols on selected subcarriers Often used for tracking Precision depends on number of pilot subcarriers p. 143
6 OFDM Receiver 6.2 Channel estimation Preamble-based: training sequences Designed in conjunction with synchronization Repetitive structure Constraints: correlation properties, PAPR etc. Example: IEEE 802.11a p. 144
6 OFDM Receiver 6.2 Channel estimation Example: IEEE 802.11a p. 145
6 OFDM Receiver 6.2 Channel estimation Pilot structures p. 146
6 OFDM Receiver 6.2 Channel estimation Estimation on pilot subcarriers Methods: Zero-Forcing (ZF) p. 147
6 OFDM Receiver 6.2 Channel estimation Minimum-Mean Squared Error (MMSE) Linear approach: Exercise 5: Show that solution is p. 148
6 OFDM Receiver 6.2 Channel estimation Comparison ZF $ MMSE Expected value: Expected power of estimation error p. 149
6 OFDM Receiver 6.2 Channel estimation ZF special case of MMSE MMSE tends to ZF for large SNR values p. 150
6 OFDM Receiver 6.2 Channel estimation Interpolation in time and frequency direction p. 151
6 OFDM Receiver 6.2 Channel estimation Interpolation techniques Polynomial interpolation of mth order typically: m=1,2,3 (linear, quadratic, cubic) Wiener filtering knowledge about second-order statistics required Spline interpolation Lagrange interpolation p. 152
6 OFDM Receiver 6.2 Channel estimation Alternative: decision-directed channel estimation Feedback of symbol decisions Problems: Very sensitive to decision errors Definition of reliability regions p. 153
6 OFDM Receiver 6.3 Equalization and Detection mod. bit source channel coding S/P IFFT P/S interleaving preamble cyclic prefix mod. OFDM transmitter pilots radio channel OFDM receiver channel estimation and equalization AWGN demod bit sink channel decod. deinterleaving S/P demod FFT P/S CP removal time and freq. synch. p. 154
6 OFDM Receiver 6.3 Equalization and Detection Detection problem Similar to estimation problem Limited to finite possible decision set p. 155
6 OFDM Receiver 6.3 Equalization and Detection Key advantage in OFDM: Equalization and detection on each subcarrier independently For each OFDM block: p. 156
6 OFDM Receiver 6.3 Equalization and Detection Maximum-Likelihood detection Typically very complex! suboptimal schemes Here: if noise is Gaussian distributed with zero-mean p. 157
6 OFDM Receiver 6.3 Equalization and Detection Linear equalization and detection Filtering followed by decision stage Q( ) Closest neighbor p. 158
6 OFDM Receiver 6.3 Equalization and Detection Zero-forcing equalizer (also see 6.2) Problem: noise enhancement on faded subcarriers p. 159
6 OFDM Receiver 6.3 Equalization and Detection Minimum-Mean-Square Error equalizer (see also 6.2) Approach: Solution: p. 160
6 OFDM Receiver 6.4 Bit-Interleaved CODFM mod. bit source channel coding S/P IFFT P/S interleaving preamble cyclic prefix mod. OFDM transmitter pilots radio channel OFDM receiver channel estimation and equalization AWGN demod bit sink channel decod. deinterleaving S/P demod FFT P/S CP removal time and freq. synch. p. 161
6 OFDM Receiver 6.4 Bit-Interleaved CODFM Motivation: Why is channel coding needed? Bit error ratio (BER): 4-QAM, frequency-selective channel 10 0 10-1 mainly determined by errors in faded subchannels 10-2 10-3 10-4 0 5 10 15 20 25 30 35 p. 162
6 OFDM Receiver 6.4 Bit-Interleaved CODFM Example: p. 163
6 OFDM Receiver 6.4 Bit-Interleaved CODFM Burst-errors: p. 164
6 OFDM Receiver 6.4 Bit-Interleaved CODFM Idea to overcome lack of frequency diversity: Spread errors to all subcarriers by interleaving Correct errors by channel (de-)coding Gain in frequency diversity Bit-Interleaved Coded OFDM (COFDM) p. 165
6 OFDM Receiver 6.4 Bit-Interleaved CODFM Interleaving techniques (on bit level) Block interleaver read write p. 166
6 OFDM Receiver 6.4 Bit-Interleaved CODFM Channel coding techniques See lecture Coding Theory Block coding (e. g. LDPC codes) Convolutional coding Typically used in mobile communications: Efficient decoder: Viterbi Turbo coding etc. p. 167
6 OFDM Receiver 6.4 Bit-Interleaved CODFM Example: BER comparison OFDM vs. BiCOFDM 10 0 uncoded coded, R c =0.5 10-1 interleaved, coded, R c =0.5 10-2 10-3 10-4 0 5 10 15 20 25 30 35 p. 168
7 Advanced Techniques 7.1 PAPR Reduction Peak-to-Power Average Ratio: Often used performance measure: Probability that PAPR exceeds threshold p. 169
7 Advanced Techniques 7.1 PAPR Reduction PAPR under ideal assumptions: Number of subcarriers large Central limit theorem applicable Real and imaginary part of time-domain signal Gaussian distributed with mean 0 and variance ½ p. 170
7 Advanced Techniques 7.1 PAPR Reduction Cumulative distribution function of instantaneous sample power CDF of data block with N samples p. 171
7 Advanced Techniques 7.1 PAPR Reduction Complementary CDF 10 0 10-1 10-2 10-3 10-4 0 2 4 6 8 10 12 p. 172
7 Advanced Techniques 7.1 PAPR Reduction PAPR Reduction Algorithms: Amplitude clipping and filtering Coding Partial transmit sequence Selected mapping Interleaving Tone reservation Tone injection Active constellation mapping p. 173
7 Advanced Techniques 7.1 PAPR Reduction Criteria for algorithm design: PAPR reduction capability Power increase of transmit signal BER increase at the receiver Loss in data rate Computational complexity p. 174
7 Advanced Techniques 7.1 PAPR Reduction Amplitude clipping and filtering Clipping noise Inband and outband noise/distortion Filtering can reduce out-of-band radiation Repeated clipping-and-filtering p. 175
7 Advanced Techniques 7.1 PAPR Reduction Coding Select code words with minimum PAPR Simple example: 4 subcarrier, BPSK modulation data block PAPR [db] [1,1,1,1] 6.0 [1,1,1,-1] 2.3 [1,1,-1,1] 2.3 [1,1,-1,-1] 3.7 p. 176 Department of
7 Advanced Techniques 7.1 PAPR Reduction Idea: avoid sequences with high PAPR Block coding Disadvantages: Exhaustive search required (especially for large number of subcarriers) Does not address error correction (combined coding schemes even more sophisticated) p. 177 Department of
7 Advanced Techniques 7.1 PAPR Reduction Partial Transmit Sequence (PTS) Block diagram Data source Partition into blocks and S/P Division into subblocks IDFT IDFT Optimization for b p. 178 Department of
7 Advanced Techniques 7.1 PAPR Reduction Complex phase vectors Optimization problem to minimize PAPR Usually, b m limited to finite number of elements Exhaustive search for phase vectors p. 179 Department of
7 Advanced Techniques 7.1 PAPR Reduction Selective Mapping (SM) Block diagram Data source Partition into blocks and S/P IDFT IDFT Select one with minimum PAPR p. 180 Department of
7 Advanced Techniques 7.1 PAPR Reduction Phase sequences b (u) Unmodified data block by b (u) =[1,1,,1] Simple: select sequence with smallest PAPR Reverse operations at the receiver Disadvantage: Amount of PAPR reduction varies blockwise Transmission of side information required (loss in effective data rate) p. 181 Department of
7 Advanced Techniques 7.1 PAPR Reduction Interleaving Very similar to SMT Set of M interleaver instead of phase sequences with one-to-one mapping {n}!{ (n)} M possible candidates Select sequence with minimum PAPR p. 182 Department of
7 Advanced Techniques 7.1 PAPR Reduction Tone Reservation (TR) Introduce redundancy via reserved subcarrier symbols p. 183 Department of
7 Advanced Techniques 7.1 PAPR Reduction Idea: one single subcarrier influences the whole time-domain signal Optimization problem: Transmission of side information not needed Simple receiver processing: neglect reserved tones Average transmit power increases: performance loss in power efficiency p. 184 Department of
7 Advanced Techniques 7.1 PAPR Reduction Tone Injection (TI) Main idea: increase constellation size Substitute modulation symbols to equivalent points in expanded constellation Active Constellation Extension (ACE) Similar to TI technique Outer signal constellation points are dynamically extended towards the outside of the original constellation Increase of transmit power p. 185 Department of
7 Advanced Techniques 7.1 PAPR Reduction Example for QPSK: p. 186 Department of
7 Advanced Techniques 7.1 PAPR Reduction Algorithm Tx processing Rx processing Clipping and filtering Amplitude clipping, filtering none Coding Encoding or table search Decoding or table search PTS M IDFTs, vector sums Side information extraction, inverse PTS SLM U IDFTs Side information extraction, inverse SLM Interleaving K IDFTs, (K-1) interleavings Side information extraction, inverse interleaving TR IDFTs, find value of PRCs Ignore non-data-bearing subcarriers TI ACE IDFTs, search for maximum point in time, tones to be modified IDFTs, projection onto shaded area Reverse tone modification none p. 187 Department of
7 Advanced Techniques 7.2 Adaptive Modulation Flexibility of OFDM offers bit and power loading 64-QAM 16-QAM 4-QAM BPSK null Main idea: Good subcarriers: higher-order modulation schemes Bad subcarriers: robust modulation schemes p. 188
Different strategies Constant bit rate 7 Advanced Techniques 7.2 Adaptive Modulation Constant link quality (in terms of BER) Different optimization approach Maximization of channel capacity Minimization of error probability Minimization of complexity! p. 189
Simulation example 7 Advanced Techniques 7.2 Adaptive Modulation 10 0 AM, uncoded AM, coded 10-1 no AM, coded no AM, uncoded 10-2 10-3 10-4 0 5 10 15 20 25 30 p. 190
7 Advanced Techniques 7.2 Adaptive Modulation Challenge: Transmitter must have channel state information! CSI via feedback (requires very large coherence time) Step 1) MS carries out channel estimation in DL Step 2) MS sends CSI to BS Step 3) BS applies adaptive modulation scheme for DL p. 191
7 Advanced Techniques 7.2 Adaptive Modulation CSI in Time-Division Duplex (TDD)-systems (requires large coherence time and reciprocity of up- and downlink) Step 1) BS carries out channel estimation in UL Step 2) BS applies adaptive modulation scheme for DL p. 192
Further challenge: Receiver must know BAT as well Conventional solution: signaling channel Amount of signaling information (worst-case): 5 different modulation schemes 0, 1, 2, 4, 6 bit/subcarrier no subcarrier grouping code rate 1/2 BPSK modulation of signaling bits 7 Advanced Techniques 7.2 Adaptive Modulation 6 OFDM blocks overhead Automatic Modulation Classification? f t null 64QAM 16-QAM 4-QAM BPSK p. 193
8 Introduction to MIMO Systems Tx Rx Single-Input Single-Output (SISO) Tx Rx Single-Input Multiple-Output (SIMO) Tx Rx Multiple-Input Single-Output (MISO) Tx Rx Multiple-Input Multiple-Output (MIMO) p. 194
8 Introduction to MIMO Systems 8.1 Capacity Capacity in AWGN SISO channels 10 8 6 4 2-10 -5 5 10 15 20 25 30 p. 195
8 Introduction to MIMO Systems 8.1 Capacity Capacity in AWGN MIMO channels 40 30 20 10 min(m t,m r )=4 min(m t,m r )=2 M t =M r =1-10 -5 5 10 15 20 25 30 p. 196
8 Introduction to MIMO Systems 8.2 MIMO Schemes Exploiting multiple antennas Diversity gain Increase reliability Spatial multiplexing Increase data rate Array gain Enhance SNR Interference reduction Suppress interfering signals beamforming p. 197
8 Introduction to MIMO Systems 8.2 MIMO Schemes MIMO signal model for flat-fading channels Rx Tx p. 198
8 Introduction to MIMO Systems 8.2 MIMO Schemes In OFDM: MIMO signal model for each subcarrier n Throughout chapter 8: Subcarrier index n neglected p. 199
8 Introduction to MIMO Systems 8.2.1 Diversity Receive diversity SIMO Tx Rx p. 200
8 Introduction to MIMO Systems 8.2.1 Diversity Rx processing: Maximum Ratio Combining (MRC) Diversity gain (diversity order: M r ) Exercise 6: Show that SNR at receiver is No channel knowledge needed at Tx p. 201
8 Introduction to MIMO Systems 8.2.1 Diversity p. 202
8 Introduction to MIMO Systems 8.2.1 Diversity p. 203
8 Introduction to MIMO Systems 8.2.1 Diversity Transmit diversity MISO Tx Rx Two cases Channel knowledge available at transmitter Channel knowledge not available at transmitter p. 204
8 Introduction to MIMO Systems 8.2.1 Diversity With channel knowledge at Tx side: Similar to SIMO Tx Rx Tx processing: weighting vector Tx Rx Transmit MRC: same performance as SIMO p. 205
8 Introduction to MIMO Systems 8.2.1 Diversity Without channel knowledge at Tx side Tx Rx Special case: M t =2 (Alamouti) Transmit sequence p. 206
8 Introduction to MIMO Systems 8.2.1 Diversity Rx processing: form vector r=(r 1,r 2 ) Orthogonalize p. 207
8 Introduction to MIMO Systems 8.2.1 Diversity p. 208
8 Introduction to MIMO Systems 8.2.1 Diversity Diversity gain (diversity order M t =2) No SNR gain p. 209
8 Introduction to MIMO Systems 8.2.1 Diversity Transmit and receive diversity MIMO Tx Rx Two cases Channel knowledge available at transmitter Channel knowledge not available at transmitter p. 210
8 Introduction to MIMO Systems 8.2.1 Diversity With channel knowledge at Tx side: Tx Rx Dominant eigenmode transmission p. 211
8 Introduction to MIMO Systems 8.2.1 Diversity Singular value decomposition (SVD) unitary matrix (eigenvectors) diagonal matrix (eigenvalues) unitary matrix (eigenvectors) Optimal pre- and post-vectors w and g: input and output eigenvector corresponding to largest eigenvalue max Equivalent signal model p. 212
8 Introduction to MIMO Systems 8.2.1 Diversity Without channel knowledge at Tx side: Tx Rx Alamouti scheme combined with receive MRC p. 213
8 Introduction to MIMO Systems 8.2.1 Diversity Rx processing: form vector r=(r 1T,r 2H ) T Orthogonalize by matched filtering p. 214
8 Introduction to MIMO Systems 8.2.1 Diversity Diversity gain (diversity order M t M r =4) SNR gain p. 215
8 Introduction to MIMO Systems 8.2.1 Diversity Other schemes: Space-Time (block) coding Space-Frequency (block) coding etc. p. 216
8 Introduction to MIMO Systems 8.2.2 Spatial multiplexing Spatial multiplexing Increase data rate Transmit data in parallel MIMO signal model: Tx Rx p. 217
8 Introduction to MIMO Systems 8.2.2 Spatial multiplexing ML receiver Noise is zero-mean uncorrelated Gaussian Brute-force search through entire vector constellations High complexity (exponentially increasing with M t ) Algorithms to reduce complexity: sphere decoding etc. p. 218
8 Introduction to MIMO Systems 8.2.2 Spatial multiplexing Linear receivers Zero-forcing (M r M t ) Pseudo-inverse Assuming full rank channel matrix Cancels stream-interference completely Problem: noise enhancement p. 219
8 Introduction to MIMO Systems 8.2.2 Spatial multiplexing Minimum Mean Square Error (M r M t ) Optimization criterion: Solution: Converges to ZF for high SNR (ZF special case of MMSE) p. 220
8 Introduction to MIMO Systems 8.2.2 Spatial multiplexing Successive Interference Cancellation (SIC) Idea: symbol streams are decoded and subtracted layer by layer Loop with respect to transmitted stream M t 1. step: equalize and detect m t -th transmitted signal 2. step: subtract interference of m t -th transmitted symbol Ordered SIC (e.g. V-BLAST): Detection order from strongest to weakest p. 221
8 Introduction to MIMO Systems 8.2.2 Spatial multiplexing Linear Pre- and Decoding (proposed in UMTS LTE) No channel knowledge at Tx Idea if channel knowledge is available at Tx: design W and F in a jointly optimized way p. 222
8 Introduction to MIMO Systems 8.2.3 Beamforming Beamforming ( Smart Antenna ) Idea: steer into direction of desired user while suppress interfering signals p. 223
8 Introduction to MIMO Systems 8.2.3 Beamforming Signal model (receive beamforming) p. 224
8 Introduction to MIMO Systems 8.2.3 Beamforming Rx signal at i-th array element Rx signal at (i+1)-th array element (narrowband assumption) p. 225
8 Introduction to MIMO Systems 8.2.3 Beamforming Rx signal at antenna array with steering vector (uniform linear array) p. 226
8 Introduction to MIMO Systems 8.2.3 Beamforming Sampled baseband signal with interference p. 227
8 Introduction to MIMO Systems 8.2.3 Beamforming Concept of beamforming (receive mode) Goal: Maximize signal-to-interference plus noise power ratio (SINR) p. 228
8 Introduction to MIMO Systems 8.2.3 Beamforming SINR at receiver with spatial covariance matrix p. 229
8 Introduction to MIMO Systems 8.2.3 Beamforming Maximization of SINR Extension: desired signal with angular spread eigenvector to largest eigenvalue of characteristic equation: p. 230
8 Introduction to MIMO Systems 8.2.3 Beamforming Example: 90 90 desired path 120 60 desired path 120 60 10dB 10dB 150 0dB -10dB 30 150 0dB -10dB 30-20dB -20dB -30dB -30dB -40dB -40dB 180 0 180 0 210 330 210 330 240 300 240 300 270 number of array elements: 4 270 number of array elements: 8 p. 231
9 Multiuser Systems 9.1 Cellular Systems Hexagonal cells Intercell interference Intracell interference desired MS undesired MS considered BS p. 232
9 Multiuser Systems 9.2 Multiple Access Schemes Classical multiple access schemes: Time Division Multiple Access (TDMA) Users are allocated to different time slots (e.g. in GSM) Code Division Multiple Access (CDMA) Users are separated by different codes (e.g. in UMTS) Frequency Division Multiple Access (FDMA) Users are allocated to different frequency bands (e.g. in WIMAX), can be combined with OFDM: Orthogonal Frequency Division Multiple Access (OFDMA) p. 233
9 Multiuser Systems 9.2 Multiple Access Schemes Division of resources Radio Channel : TDMA CDMA FDMA p. 234
9 Multiuser Systems 9.2 Multiple Access Schemes Enabled by using antenna arrays: Space Division Multiple Access (SDMA) users separated solely by different locations user 2 user 1 p. 235
9 Multiuser Systems 9.2 Multiple Access Schemes OFDM-TDMA p. 236
9 Multiuser Systems 9.2 Multiple Access Schemes OFDM-FDMA (e.g. UMTS LTE downlink) p. 237
10 Case Study 10.1 MIMO Audio Demonstrator Receiver 8 Microphones Transmitter 2 or 4 Loudspeaker Amplifier p. 238
10 Case Study 10.2 Project: Receiver Design OFDM transmission Frame structure Tx 1: TS data data data data data Tx 2: TS data data data data data Tx 3: TS data data data data data Tx 4: TS data data data data data time p. 239
10 Case Study 10.2 Project: Receiver Design Transmitted preamble in time-domain: Chu sequence x i =e j2 i2 /N Transmitted information: ASCII text OFDM parameters: N=64 N g =64 f c =8kHz T a =1/8kHz etc. p. 240
10 Case Study 10.2 Project: Receiver Design Link to Matlab code of transmitter p. 241
10 Case Study 10.2 Project: Receiver Design p. 242
10 Case Study 10.2 Project: Receiver Design Project: Design receiver to recover transmitted data Time synchronization (CP correlation technique) Channel estimation (preamble-based ZF technique) Equalization and Detection (ZF technique) Source Decoding into ASCII symbols Good luck! p. 243
10 Case Study 10.2 Project: Receiver Design Any suggestions to improve? p. 244