1. Wireless Mesh Networks
Anatolij Zubow
Orthogonal Frequency-Division Multiplexing

2. Motivation
Multi path propagation – the same transmitted symbol arrives multiple times with different amplitude and phasing at the receiver (vectorial superposition)
Symbols are distored  complex demodulation  high SER/BER
If delay spread is larger than symbol duration: inter-symbol interference
Problem:
High transmission rate  small symbol duration  high number of symbols affected by multi-path echoes

3. Elimination of Inter-Symbol Interference (ISI)
Receiver has to eliminate ISI before demodulation and detection phase.
Two strategies are possible:
Choose a symbol duration TS which is larger than the maximum delay spread  at least a part of the symbol is received undistorted  multi-carrier modulation
Adaptive equalization  single-carrier modulation
Our focus is on the first strategy (multi-carrier modulation or digital multi tone (DMT)), in particular, on Orthogonal Frequency-Division Multiplexing (OFDM)

4. DMT for Time Non-varying Channels
DMT is used for time non-varying channels with linear distortions:
Linear distortions are higher for higher frequencies
With DMT we can adapt the transmission on each sub-channel its condition:
In sub-channels with small distortions we transmit with higher data rate, i.e. more efficient modulation (e.g. 16QAM or 64QAM)
In sub-channels with high distortions a more robust modulation is used (e.g. 4PSK)
Example: ADSL, HDSL
Advantage:
Low transmitter/receiver complexity
High transmission rate

5. OFDM for Wireless Systems
Defining characteristic of the mobile wireless channel is the variations of the channel strength over time and over frequency.
We cannot predict such variations.
Therefore for the sender it is difficult to adapt the transmission to each particular sub-channel.
Thus the same modulation is used for each sub-channel (e.g. 4PSK, 16QAM)
In OFDM the sub-channels are orthogonal to each other.

6. Symbol Duration and Bandwidth
What about a trivial solution?
Multi-carrier system:
2N+1 sub-carriers are used
The symbol duration TSV is thus (at least) a factor of 2N + 1 times as long as the symbol duration TSE of the single-carrier system.
Why TSV is bounded?
Single-carrier system: symbols use the full bandwidth BCH of the channel
The bandwidth of the sub-carrier BS of the multi-carrier system, however, has a smaller (single-) bandwidth. Because they are partially overlapping, it is: BS ≥ BCH / (2N +1)
Given a bandwidth BCH both systems are able to deliver the same amount of information.
Single-Carrier System
Multi-Carrier System: 2N+1 Subcarrier

7. Multipath Echoes in Time Domain
Figure 1
E.g. echo profile (|c(t)|) of DVB-T
See Figure 1
Model case
Simplified model,
Only one active sub-carrier,
Figure illustrates the impact of echoes on the received signal,
Is similar to the single-carrier case where delay spread compared to the symbol duration is short,
The received signal consists of the main signal, 2 echoes and common-frequency channel,
See Figure 2
Figure 2

8. OFDM in Time-Domain Example: 3 active sub-carriers
Shape of the OFDM symbol is obvious
Guard interval (Cyclic prefix; repeat of the end of the symbol at the beginning)
Orthogonality –see subcarrier frequencies (1:2:3)

9. OFDM - Idealized system model
A large number of closely-spaced orthogonal sub-carriers are used to carry data.
The data is divided into several parallel data streams one for each sub-carrier.
Each sub-carrier is modulated with a conventional modulation scheme (e.g. BPSK) at a low symbol rate, maintaining total data rates similar to conventional single-carrier modulation schemes in the same bandwidth.
Transmitter:

10. OFDM - Idealized system model
Receiver:

11. Characteristics of OFDM
Orthogonality
Sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to each other
No cross-talk
Inter-carrier guard bands are not required
Simplifies the design of transmitter/receiver (in FDM a separate filter is required)
Sub-carrier spacing is Δf=k/TU [Hertz], where TU is the useful symbol duration, and k is a positive integer (typically 1).
High spectral efficiency – nearly the whole available frequency band can be utilized
'white' spectrum
Requires very accurate frequency synchronization between the receiver and the transmitter; otherwise sub-carriers will no longer be orthogonal (inter-carrier interference (ICI))

12. Characteristics of OFDM
Fast Fourier transform (FFT)
Orthogonality allows for efficient modulator and demodulator implementation using FFT on the receiver side, and inverse FFT on the sender side.
Today low-cost digital signal processing components can efficiently calculate the FFT.
Guard interval (GI)
OFDM principle: low symbol rate modulation schemes suffer less from ISI caused by multipath propagation  transmit a number of low-rate streams in parallel instead of a single high-rate stream.
Since the duration of each symbol is long, it is feasible to insert a guard interval between the OFDM symbols, thus eliminating inter-symbol interference (ISI).
Cyclic prefix (CP) is followed by the OFDM symbol TU TU

13. Characteristics of OFDM
Simplified equalization
Frequency-selective fading (due to multipath propagation) can be considered as constant (flat) over an OFDM sub-carrier.
Equalization far simpler at the receiver compared to conventional single-carrier modulation.
Some of the sub-carriers in some of the OFDM symbols may carry pilot signals for measurement of the channel conditions (equalizer gain and phase shift).
Pilot signals and training symbols are used for time synchronization (to avoid ISI) and frequency synchronization (to avoid ICI).
DVB-T frame with pilot symbols for channel estimation

14. Characteristics of OFDM
Channel coding and interleaving
OFDM is invariably used in conjunction with channel coding (FEC), and almost always uses frequency and/or time interleaving to avoid error bursts
Frequency (subcarrier) interleaving increases resistance to frequency-selective channel conditions such as fading – bits are spread out over sub-carriers
Time interleaving ensures that bits that are originally close together in the bit-stream are transmitted far apart in time.
Problems with interleaving:
Time interleaving  slowly fading channels (stationary reception)
Frequency interleaving  narrowband channels that suffer from flat-fading
Typical error correction coding in OFDM: Convolutional + Reed-Solomon coding

15. Characteristics of OFDM
Adaptive transmission
If channel information is available (e.g. sent over a return-channel)
Based on this feedback information, adaptive modulation, channel coding and power allocation may be applied across all sub-carriers, or individually to each sub-carrier.
If a particular range of frequencies suffers from interference or attenuation the carriers within that range can be disabled or made to run slower (more robust MCS or FEC).
Discrete multitone modulation (DMT) is an OFDM based systems that adapt the transmission to the channel conditions individually for each sub-carrier (bit-loading)  ADSL
OFDM for multiple access
OFDM can be combined with multiple access using time, frequency or coding separation of the users  Orthogonal Frequency Division Multiple Access (OFDMA)

16. Advantages of OFDM
The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe channel conditions:
E.g., attenuation of high frequencies in a long copper wire, narrowband interference and frequency-selective fading due to multipath (without complex equalization filters).
Channel equalization is simplified because OFDM may be viewed as using many slowly-modulated narrowband signals rather than one rapidly-modulated wideband signal.
The low symbol rate makes the use of a guard interval between symbols affordable, making it possible to handle time-spreading and eliminate intersymbol interference (ISI).

17. Applications of OFDM Cable Wireless
ADSL and VDSL broadband access via POTS copper wiring.
Power line communication (PLC).
Wireless
The wireless LAN radio interfaces IEEE a, g, n and HIPERLAN/2.
The digital radio systems DAB/EUREKA 147, DAB+, Digital Radio Mondiale, HD Radio, T-DMB and ISDB-TSB.
The terrestrial digital TV system DVB-T.
The cellular communication systems Flash-OFDM
The mobile broadband 3GPP Long Term Evolution air interface named High Speed OFDM Packet Access (HSOPA)
The Wireless MAN / Fixed broadband wireless access (BWA) standard IEEE (or WiMAX).
The Mobile Broadband Wireless Access (MBWA) standards IEEE , IEEE e (Mobile WiMAX) and WiBro.
The wireless Personal Area Network (PAN) Ultra wideband (UWB) IEEE a implementation suggested by WiMedia Alliance.

18. Standard name
DAB Eureka 147
DVB-T
DVB-H
DMB-T/H
IEEE a
Ratified year
1995
1997
2004
2006
1999
Frequency range of today's equipment (MHz)
470 – 862
Channel spacing B (MHz)
1.712
8, 7, 6,
8, 7, 6 & 5 8 20
Number of subcarriers N
192, 384, 768 or 1536
2K mode: K mode: 6817
1705, 3409, 6817
1 (single-carrier) 3780 (multi-carrier) 52
Subcarrier modulation scheme
DQPSK
QPSK[4], 16QAM or 64QAM
4QAM[4], 4QAM-NR,[5] 16QAM, 32QAM and 64QAM.
BPSK, QPSK[4], 16QAM or 64QAM
Useful symbol length TU (μs)
2K mode: 224 8K mode: 896
224, 448, 896
500 (multi-carrier)
3.2
Additional guard interval TG (Fraction of TU)
1/4, 1/8, 1/16, 1/32
1/4, 1/6, 1/9
1/4
Subcarrier spacing Δf = 1/(TU) ≈ B/N (Hz)
2K mode: K mode: 1116
4464, 2232, 1116
8 M (single-carrier) 2000 (multi-carrier)
312.5K
Net bit rate R (Mbit/s)
(typically 24)
6 - 54
Link spectral efficiency R/B (bit/s/Hz)
Inner FEC
Conv coding with code rates 1/4, 3/8 or 1/2
Conv coding with code rates 1/2, 2/3, 3/4, 5/6 or 7/8
LDPC with code rates 0.4, 0.6 or 0.8
Conv coding with code rates 1/2, 2/3 or 3/4
Outer FEC (if any)
None
RS(204,188,t=8)
RS(204,188,t=8) + MPE-FEC
BCH code (762,752)
Maximum travelling speed (km/h)
depends on transmission frequency
Time interleaving depth (ms)
385
Adaptive transmission (if any)
Multiple access method (if any)
Typical source coding
192 kbit/s MPEG2 Audio layer 2
Mbit/s Standard - HDTV H.264 or MPEG2
Not defined (MPEG-2 or H.264 w/MP2)

19. Why OFDM in Broadcast? Enables Single Frequency Network (SFN)
Multiple transmit antennas geographically separated
Several adjacent transmitters send the same signal simultaneously at the same frequency, as the signals from multiple distant transmitters may be combined constructively, rather than interfering as would typically occur in a traditional single-carrier system.
Enables same radio/TV channel frequency throughout a country
Creates artificially large delay spread – OFDM has no problems!
20km

20. Resources
TFH Berlin, "Digitale Funksysteme“,

21. Channel examples
Example of a frequency selective, slowly changing (slow fading) channel for a user at 35 km/h

22. Channel examples …
Example of a frequency selective, fast changing (fast fading) channel for a user at 35 km/h