Principles of Orthogonal Frequency Division Multiplexing and Multiple Input Multiple Output Communications Systems.

Principles of Orthogonal Frequency Division Multiplexing

and Multiple Input Multiple Output Communications Systems

OFDM

OFDM Material

• Multicarrier communications

• Synchronization

• Issues– Synchronization– Sidelobes

• OFDMA

Intersymbol Interference

• Occurs when symbol period (Ts) is less than channel delay spread,

• ISI introduces an error floor to BER– Limits maximum throughput

• Solutions:– Equalization (high complexity)– Longer symbol periods (generally

means lower data rate)

+

x

+

+

+

+

+

x

x

x

x

x

10-210-4

10-3

10-2

10-1

10-1 100

BPSK QPSK OQPSK MSK

Modulation

Coherent Detection

Irre

du

cib

le B

ER

T

=delay spread

symbol period

BER Floor for various modulations

J. C.-I. Chuang, "The Effects of Time Delay Spread on Portable Radio Communications Channels with Digital Modulation," IEEE JSAC, June 1987

QPSK limit

Multicarrier communications: Longer period, same data rate

•Concept:–Divide original data stream at rate R into L lower rate (R/L) streams on different carriers to increase symbol time

•Long history–KINEPLEX–ANDEFT–KATHRYN

•Effects–High receiver complexity

• separate receiver chain per carrier

–Bandwidth due to sidebands–Each subcarrier experiences flat fading

Bc

B/L

H f

f

B

J. Andrews, A. Ghosh, R. Muhamed, Fundamentals of WiMAX, Prentice Hall, 2007

OFDM

• Much simpler to create multicarrier transmission using iFFT– Information carried in magnitude and phase of each bin– Then can be recovered by using FFT at receiver

• Inverse Fourier transform would be an infinite duration sine wave– Cut at Symbol duration Ts

– Rectangular windowing causes sinc spectrum in frequency domain with zeros at 1/Ts

– Orthogonal subcarriersFrequency

Magnitude

T0T0

Guard intervals and intersymbol interference

• If we space OFDM symbols by gaps at least as long as the delay spread, then there will be no intersymbol interference

• However, there will still be interference within the symbol

OFDM Symbol OFDM Symbol OFDM Symbol

Guard interval Guard interval

Delay Spread Delay Spread

Equalization and the DFT• While using longer symbol timing means OFDM can avoid

irreducible errors, still have interfering energy in band from multipath– Received signal is the (linear) convolution of channel impulse

response with transmitted signal

• DFT Circular Convolution Theorem– Circular convolution of two discrete vectors in time domain

– Is multiplication in the frequency domain

• Implication: If we can make the system behave like a circular convolution, equalization is trivial– complex multiplication per FFT bin at the receiver

*y h x

y x h

k k kY X H

Cyclic Prefix

• Adding a cyclic prefix at transmitter leads to circular convolution

• Note that misaligned timing still results in a circular convolution, just time shifted– Makes for phase

shifts in FFT bins– Correct that in a

momentJ. Andrews, A. Ghosh, R. Muhamed, Fundamentals of WiMAX, Prentice Hall, 2007

Comments on Cyclic Prefix• We’re transmitting redundant

bits (no information transfer)– Bandwidth penalty: L / (L + v)– Power penalty: L / (L + v)

• Penalty becomes negligible as L becomes large (but there are tradeoffs! – more later)

• Power penalty generally more important in practice where systems are interference limited

• Penalty can be avoided with zero prefix– Nothing transmitted in guard band

(zero prefix)– Receiver adds tail back to

beginning of symbol– Used in WiMedia

•Permits low complexity equalization for same data rates

•Single carrier tap# approximately bandwidth delay product–MAC

•OFDM, number subcarriers grows with bandwidth-delay product, so


Frequency Errors

• Primary sources of frequency errors– Doppler shift– Clock mismatches– Phase noise

• Effects– Reduction in amplitude

(missampling sinc)– Intercarrier

interference

O. Edfors, M. Sandell, J. van de Beek D. Landström, F. Sjöberg, “An Introduction to Orthogonal Frequency Division Multiplexing,” Sep 98,

Available online: http://epubl.luth.se/avslutade/0347-0881/96-16/esb96rc.pdf

Effects of Frequency Errors• Comments

– Impact greater for higher SNR signals

– Note 5% estimation error can lead to 5 dB effective degradation at 64-QAM like SNRs

– Big frequency impact is why OFDM was originally for fixed deployments

• Techniques– Data aided– Non data aided– Cyclic prefix

Fading ChannelAWGN

O. Edfors, M. Sandell, J. van de Beek D. Landström, F. Sjöberg,

“An Introduction to Orthogonal Frequency Division Multiplexing,”

Sep 98, Available online: http://epubl.luth.se/avslutade/0347

-0881/96-16/esb96rc.pdf

Solution Techniques

• Clipping– Eliminate signals above a certain

level or ratio• Peak windowing

– Filter peaks• Linear block code

– Select only those codewords with small PAPR

– Can also provide error correction• Peak Cancellation

– Subtract signals from high peaks– Need to be similar bandwidth to

limit out-of-band interfernce• Symbol Scrambling

Spectral Effects of Windowing and Clipping

Peak Cancellation, Clipping, PAPR = 4dB

Time Domain Frequency Synchronization

• Complex baseband model of passband signal

• ftx is transmitter carrier frequency, Ts is symbol period, sn is transmitted signal

• Received

Time Domain Frequency Synchronization

• Evaluate sum of products of time-delayed and conjugated repeated symbols

Estimator

• Frequency offset estimator

• Ambiguity limit

• When D = Ts

• In AWGN, this is the maximum likelihood detector with variance proportional to

Frequency domain (post-FFT)

• Similar estimator evaluated on Fourier Transformed signal

• So same performance, but much more complex as the DFT has to be calculated for both repeated symbols.

Channel Estimation

• Channel assumed static for duration of symbol, though frequency/phase varying over bandwidth

• Solution, embed pilot symbols at regular intervals in the symbol– Used closest pilot– Interpolate

H f

From IEEE Std 802.16-2004

More synchronization

• Need to detect beginning of packet– Energy detect

• Measure energy, see when it exceeds threshold

– Packet detection• Correlate with known sequence

– Delay and correlate

• Symbol timing– No problem to be off by a fraction of the guard interval from

perspective of DFT– Bad timing does get ISI though from cyclic prefixes– Better to be early (low ISI) than late

Synchronization all together

• Steps:– Detect packet beginning– Align symbol boundary– Perform coarse frequency/timing synchronization– Perform fine frequency/timing synchronization– Track changes in channel as needed

802.11a FramingIdentical symbols

Peak-to-Average Power Ratio

• Sum of large number of (somewhat) independent subcarriers leads to signal distribution that is somewhat Gaussian

• Implications– long tails for amplitude distribution– Possibly large ratios of peak-to-

power ratios• Long tails can drive amplifiers

into nonlinear region– Introduces harmonics and

significant out-of-band spectral energy

0 2 4 6 8 10 12 14 1610

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10-5

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10-1

100

PAPR[dB]

log

(CD

F)

(a )N=16 (b) N=32 (c) N=64 (d) N=128 (e) N=256 (f) N=1024

(f)

(e)

(d)

(c)

(b)

(a)

PAPR CDF for Varying # Subcarriers

11

11

MDSMDS

P1dB,out

P1dB,in

1dBP1dB,out

P1dB,in

1dB

Noise FloorNoise Floor

Fund

amen

tal

Fund

amen

tal

Fund

amen

tal

Input Power (dBm)

Output Power (dBm)

Input Power (dBm)

Output Power (dBm)

BDRBDR

Adaptive Modulation

• Different subcarriers experience different flat fades

• Means different SINR• Adapting modulation

scheme of each subcarrier to its SINR allows the system to approach Shannon capacity

Bc

B/L

H f

f

B

B/L


OFDMA

• Multiple user access with OFDM

• Lots of flexibility possible when splitting up OFDM symbols and frames– Assign different subcarriers

to different users– Assign different time slots

to different users– Vary modulation and

coding– Vary powers– More options available with

antenna arrays

• Allocation algorithms– Maximum Sum Rate– Proportional fairness– Proportional rates

constraints


Antenna Array Algorithms and MIMO

Antenna Array Principles• The use of multiple antennas provide two forms of diversity:–Diversity gain

• Exploit multiple independent channels created by multipath diversity

• Works with uncorrelated antennas–Array gain

• Coherently combine energy from antennas• Works even with perfectly correlated antennas

as received SNR increases linearly with the number of receive antennas

• Adding additional transceiver chains is expensive (SWAP and cost), but can provide tremendous (though competing) gains

– Increase the system reliability (decrease the bit or packet error rate)– Increase the achievable data rate and hence system capacity– Increase the coverage area– Decrease the required transmit power

0 200 400 600 800 1000-10

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10

Samples

Fa

din

g E

nve

lop

es

[dB

]

Receive Diversity

• Oldest and simplest diversity technique

• Receiver leverages independence of fades on antennas– Selection Combining (SC)

• Choose antenna with maximum SINR• Lowest complexity

– Equal Gain Combining (EGC)• Phase align and sum signals across

antennas

– Maximum Ratio Combining (MRC)• Weight signals by SINR• Best performance (system SINR is

sum of antenna SINRs)

...

Receiver

Comparator

Short-TermAverage

PresetThreshold

Antenna

Selection Diversity

Average SNR Improvements

SN

R (

dB)

Antennas

SC

EGC

MRC

Open Loop Transmit Diversity (1/2)• Transmitter sends multiple

signals (possibly copies)– These interfere at the receiver,

but if coded properly, the receiver can recover the signal

• Simplest implementation is orthogonal space time block codes or Alamouti codes1

– Assumes flat constant channel over two symbol periods (may not be true for high mobility)

– Requires channel knowledge at receiver

– No change in rate required

• Receiver Alamouti Operation

• Output SNR 2x1 Alamouti

1. S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE Journal on Selected Areas in Communications, vol 16 pp.1451–1458, Oct 1998

TX Encoder

RX Decoder

h1

h2

Open Loop Transmit Diversity (2/2)

• 2x2 STBC (same transmit encoder) SINR

– Note number of h terms maximized when Nt = Nr for a fixed number of antennas

– Also full-diversity, orthogonal STBCs exist only for certain combinations of Nt and Nr.

• Can also use space-time trellis codes for added 1-2 dB, but those have exponential complexity order

Comparison of STBC and MRC

A 4x2 Stacked Alamouti System


Space-Time Trellis Coding• Convolutional code applied to space and time domain• Each antenna output is mapped into modulation symbol• Maximum likelihood sequence estimator ( Viterbi algorithm)

Encoder structure for two antennasExample) Delay Diversity (by Wittneben [4])

Generator matrix form

Modular-4addition

(u1,u2)a1 a2 a3 a4

Output to ANT2

Output to ANT1

g11 g21 g31 g41

g12 g22 g32 g42

QPSK mapping

[a1 a2 a3 a4]

Closed Loop Systems• Transmit selection diversity

–Antenna(s) chosen which maximizes SINR–Equivalent to receiver selection diversity–Not as good as beamforming–Little bandwidth required–Makes most sense in in deployments with small bandwidths and small delay spreads (low range)

• Linear diversity precoding– Feedback channel state information to transmit encoder– Transmit encoder then attempts to fine encoding matrix which maximizes SNR

at the receiver– Higher SNR than STBC

– Typically use some sort of codebook to reduce feedback bandwidth

Beamforming Systems

0.5

1

1.5

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180 0

desiredsignal

interferer

Narrowband adaptive array or linear combiner

w1

w2

wM

x1(t)

x2(t)

xM(t)

... y(t)

• The weight vector is adjusted to improve the reception of some desired signal

– Angle of arrival• MUSIC, ESPRIT

– Eigenbeamforming• No physical interpretation, but useful in multipath

environment• Minimize some cost function

• Useful for interference rejection, multipath fading mitigation, and increased antenna gain

Adaptive Beamforming• Narrowband beamforming is equivalent to spatial filtering

–By choosing appropriate sensor coefficients, it is possible to steer the beam in the desired direction

–By varying the sensor coefficients (spatial filter taps) adaptively, the interference is reduced

• Wideband beamforming requires joint space-time processing

–Phase shift at the antennas is frequency dependent

–Frequency-dependent response is required (filter)• Common algorithms

–Maximum Signal to Interference and Noise Ratio (MSINR)

–Minimum Mean Squared Error–Least Mean Squares–Minimum Variance Distortionless Response (MVDR)–Recursive Least Squares–Similar to linear precoding, but may account for interferers

Performance Comparison

• MRT refers to maximum ratio transmission – the choice of antenna

weights that maximize received SNR

• With optimal eigenbeamformer, canceling an interferer is equivalent to dropping and antenna element

3 dB

Modified from: J. Andrews, A. Ghosh, R. Muhamed, Fundamentals of WiMAX, Prentice Hall, 2007

Spatial Multiplexing• In rich scattering environments, independent data signals

transmitted from different antennas can be uniquely decoded to yield an increase in channel capacity

Source SinkModulation &

CodingDemodulation& Decoding

......

Channel

x1

xM

y1

xN

h11

h1M

hN1

hNM

Spatial Multiplexing Techniques•Open loop (Unknown channel)

–Maximum likelihood• Little gain, except at low SNR

–Zero-forcing• Evaluates pseudo-inverse of H• Can dramatically increase noise power

–MMSE• Minimizes distortion• Like Zero-forcing at high SNR, but

without the instability at low SNR–BLAST

• Layers & codes transmissions across antennas

• Effectively linear receiver with successive interference cancellation

• Receiver iterates through transmission streams using MMSE or ZF

• Works better in lab than real-world due to high SNR requirement

•Closed loop (known channel)–Singular Value Decomposition

• Computationally complex• Capacity (assuming waterfilling)

• For large SNR, capacity grows linearly with rank of H, approximately min{Nt, Nr}

–Approximations guided by• information capacity, • error probability • detection MSE• received SNR

–Can tradeoff multiplexing for diversity

Relative Capacity as function of Antenna Array Technique

• 19 BS, 3 sectors, spaced 2.8 km, mix of users

• Proportional Fair scheduling

Source: WiMAX Forum

Cooperative Antenna Arrays• Concept:

– Leverage other radios to effect an antenna array

• Applications:– Extended vehicular coverage– Backbone comm. for mesh

networks– Range extension with

cheaper devices

• Issues:– Timing, mobility– Coordination– Overhead

source

destination

Transmit Diversity

Cooperative MIMO

Source Cluster Relay cluster

First Hop Second Hop


First Hop


First Hop


First Hop


First Hop


First Hop

Destination Cluster

Correlation/Coupling Effects

• Spacing between antennas influence correlation and coupling

• Multipath components can act like interference for beamforming which reduces antenna gain

http://www.ngwnet.ac.uk/files/wspres/mimo2.thompson.pdf[Ref. D. Figueiredo, WPMC’04]

4x4, SNR = 20 dB, 30 AS Beamforming BER

Diversity vs. BeamformingDiversity Combining

• Combine signals from different antenna elements using various algorithms

• Signal from each element is processed separately

• Signals have to be uncorrelated for maximum performance

• Mitigates fading• Increases gain• Can improve polarization match• No interference rejection

capabilities

Adaptive beamforming• Focus the antenna’s gain in the

direction of the desired signal– Achieved by manipulating the

weights associated with each element

• Antenna elements have to be separated by /2 to attain a certain phase difference in the signals– Signals are correlated

• All advantages of diversity combining

• Has interference rejection capabilities– Typically > 20 dB

OFDM/MIMO Summary

OFDM Summary

• OFDM overcomes even severe intersymbol interference through the use of the IFFT and a cyclic prefix.

• Limiting factor is frequency offset– Correctable via simple algorithm when preambles

used• Two key details of OFDM implementation are

synchronization and management of the peak-to-average ratio.

• OFDMA provides a lot of flexibility to a system’s resource allocation– Permits exploitation of multi-user diversity

MIMO Summary• Spatial diversity offers incredible

improvements in reliability, comparable to increasing the transmit power by a factor of 10–100.

• These diversity gains can be attained with multiple receive antennas, multiple transmit antennas, or a combination of both.

• Beamforming techniques are an alternative to directly increase the desired signal energy while suppressing, or nulling, interfering signals.

• In contrast to diversity and beamforming, spatial multiplexing allows multiple data streams to be simultaneously transmitted using sophisticated signal processing.

• Since multiple-antenna techniques require channel knowledge, the MIMO-OFDM channel can be estimated, and this channel knowledge can be relayed to the transmitter for even larger gains.

• It is possible to switch between diversity and multiplexing modes to find a desirable reliability-throughput operating point; multiuser MIMO strategies can be harnessed to transmit to multiple users simultaneously over parallel spatial channels.


Useful References

• O. Edfors, M. Sandell, J. van de Beek, D. Landström, F. Sjöberg, “An introduction to orthogonal frequency division multiplexing,” Sep 1996.

• A. Bahai, B. Saltzbeg, M. Ergen, Multi-Carrier Digital Communications Theory and Applications of OFDM, Springer 2nd edition, 2004.

• J. Andrews, A. Ghosh, R. Muhamed, Fundamentals of WiMAX, Prentice Hall, 2007

Principles of Orthogonal Frequency Division Multiplexing and Multiple Input Multiple Output Communications Systems.

Documents

channel delay

longer symbol timing

effects of time delay

symbol period ts

bandwidth delay productmacofdm

bandwidthdelay product

data rateconcept

circular convolutionnote