space time block coding for wireless communication systemsagullive/aaron.pdf · 2004. 10. 10. ·...

Space Time Block Coding for WirelessCommunication Systems

Dr. T. Aaron Gulliver

Dept. of Electrical and Computer Engineering

University of Victoria

December 11, 2003

Graduate StudentsC. Budakoglu M.A.Sc. Key Management for Mobile Ad-Hoc NetworksN. Carson Ph.D. Wavelets and Space-Time Coding for OFDMR. Chen M.A.Sc. Security in Local Area NetworksW. Chow M.A.Sc. STBC and TC for Unstructured InterferenceK. Farrahi M.A.Sc. Error Control Coding for Video TransmissionM. Khabbazian M.A.Sc. Software Elliptic Curve CryptographyO. Farooq M.A.Sc. Turbo EqualizationM. Khosravifard Ph.D. Coding for Monotone SourcesW. Li Ph.D. STBC Applications in Wireless CommunicationsC. Perez M.A.Sc. Wireless LANs and Cellular Data SystemsU. Sethakaset Ph.D. Indoor Infrared Wireless Communication SystemsY. Shi M.A.Sc. Energy Efficient Wireless Ad-Hoc NetworksJ. Swarts Ph.D. Self-Dual Codes over Finite RingsH. Zhang Ph.D. STBC and Ultrawideband CommunicationsY. Zhang M.A.Sc. Improved Routing for Ad-Hoc Networks

Recently Completed StudentsY. Abdel-Hamid M.A.Sc. Oct. 2003

On Accessing Multiple Mirror Sites in ParallelZ. Blazek Ph.D. Oct. 2003

On Lowering the Error-Floor of Low-Complexity Turbo-CodesM. Ghassemi M.A.Sc. Aug. 2003

Efficient Implementation of Turbo Decoders forSoftware Defined Radio

N. Carson M.A.Sc. May 2003Peak-to-Average Power Ratio Reduction of OFDM Symbols

J. Wong M.A.Sc. Dec. 2002Classification of Small Optimal Codes over

��

Motivation

� By the year 2005, it is projected that thenumber of wireless subscribers will exceed thatof wire-line subscribers:

� Explosive Growth in wireless services

� Rapid Convergence with the Internet

Wireless Applications

� Mobile Telephony

multimedia (3G)

� Wireless LANs (IEEE 802.11)

� Digital Broadcasting (DAB, DVB)

� Bluetooth

� Wireless Internet�

m-commerce

Wireless Challenges

� High Data Rate (multimedia traffic)

� Networking (seamless connectivity)

� Resource Allocation (quality of service-QOS)

� Mobility (rapidly changing physical channel)

� Portability (battery life)

� Privacy

Security (encryption)

Wireless Channel Impairments

� Fading (data rates depend on time, frequencyand space)

� Limited Bandwidth

� Dynamism (random access, mobility)

� Limited Power (at the mobile)

� Interference

Multipath Fading

The Current Situation

� Spectrum is limited

� Battery power is growing at a slow rate

� Terminal size is decreasing

� Processor performance is growingexponentially

� Consumers like (demand) wire-line quality

� Wire-line data rates are growing rapidly makingexpectations much higher

Conclusion

Providing high speed, high quality wirelessservices given the quality of wirelesschannels is a challenging task.

Diversity

� Deep fade � A replica of the transmittedsignal must be sent to the receiver � Diversity

� Diversity:

� Temporal Diversity (well understood)

� Frequency Diversity (well understood)

� Spatial (Antenna) Diversity

� receive antenna diversity(well understood)

� transmit antenna diversity(subject of current research)

Wireless Channel: Diversity

� In many cases the wireless channel is

� Rayleigh: requires diversity

� slowly time-varying: no temporal diversity

� non-frequency selective: no frequencydiversity

� Spatial Diversity is needed

Multiple Antenna Systems

transmit and receive antennas

� At each time,

signals are transmittedsimultaneously each from a different antenna.

� Signals transmitted from different antennasundergo independent fading.

� The signal at each receive antenna is a linearsuperposition of the transmitted signalsperturbed by noise (and interference).

Capacity of MIMO Systems

� Telatar, and independently Foschini and Gans,determined that for a multiple antenna systemwith

transmit and � �

receive antennas

The Capacity Increases Linearlyas a function of as .

� How to exploit this capacity?

Space-Time Codes!

Notation

� Codewords are written as a matrix:

� ��

��

� � � � � � � � � � � � � � � �

......

. . . . . . . . ....

��

� To send codeword�

, at time

� � ��

��

, wesend �� simultaneously fromtransmit antennas

��

, respectively.

Space-Time Block Codes

� A simple example for two transmit antennas:

� Suppose the signal constellation has

� �

elements, i.e. BPSK, QPSK, 8-PSK, 16-QAM

� At time

�� ,

� �

bits arrive at the encoder andpick up constellation symbols � � and �

� The transmission matrix is then:

� �

��

� � � � ��

Space Time Block Code Example (2x2)

� �

�� Symbol

Calculation

� Transmit

Antennas

��

Ant1 Ant2

Transmitter Block Diagram

Capacity of STBC over Fading Channels

� Rayleigh/Ricean/Nakagami-m fading withPAM/PSK/QAM modulation

� Closed form expressions for Shannon Capacity

� � �� SNR�

bits/s/Hz

For a Ricean channel

� � � � � � � � �� bits/s/Hz

�� ! "# $

% � �& � � % �� & ��' " # ( ) * �� +� � � ,�

� �

First closed form expressions for STBC ShannonCapacity with PAM/PSK/QAM and fading

Capacity of STBC with QPSK in RayleighFading

−15 −10 −5 0 5 10 15 20 25 300

SNR (dB)

z2T1R x G22T2R x G22T4R x G22T1R x G42T2R x G42T4R x G42T1R x H42T2R x H42T4R x H4

Probability of Error Analysis for STBC

� SER of STBC over Rayleigh/Ricean/Nakagami-mfading channels (given below for Ricean)

� �

��

� � �� ! " # $% � � & � �

� � ��

� � & ��

� �,

� First exact closed form probability of errorexpressions for STBC over fading channels

BER of STBC with QPSK in Rayleigh Fading

−5 0 5 10 15 20 25 30 3510

10−5

10−4

10−3

10−2

10−1

SNR (dB)

yG2−1RxG2−2RxG3−1RxG3−2RxH3−1RxH3−2RxG4−1RxG4−2RxH4−1RxH4−2Rx

STBC in a DS-CDMA System

Capacity of DS-CDMA with BPSK and STBCin Rayleigh Fading

5 10 15 20 250.3

Number of User − K

z2T1R x G22T2R x G22T4R x G24T1R x G44T2R x G44T4R x G44T1R x H44T2R x H44T4R x H4

Performance of DS-CDMA wth BPSK and �

in Rayleigh Fading

� � � ��

0 1 2 3 4 5 6 7 8 9

10−4

10−3

10−2

10−1

SNR (dB)

y1Rx2Rx3Rx4Rx

Correlated Channels

� Channel correlation occurs when antennasare not separated sufficiently

� On small wireless devices, receive antennasmust be close together

� This correlation results in a diversity loss andperformance degradation

BER of STBC over Correlated Channels

� BER for Correlated Rayleigh Channels

� � �

��

� � ��

� � � � ��

� � ��

� � � � ��

� BER for Correlated Ricean and Nakagamifading channels

� �

��

�' �

�� ,�

BER of STBC with BPSK in UncorrelatedRicean Fading

� � ��

0 1 2 3 4 5 6 7 8 9 1010

10−4

10−3

10−2

10−1

SNR (dB)

RSISO−(1TX,1RX)ALAMOUTI−(2TX,1RX)ALAMOUTI−(2TX,2RX)

BER of STBC with BPSK in Correlated RiceanFading

� � ��

� �

0 1 2 3 4 5 6 7 8 9 1010

10−3

10−2

10−1

SNR (dB)

BER of STBC with BPSK in Correlated RiceanFading

� � ��

� �

0 1 2 3 4 5 6 7 8 9 1010

10−2

10−1

SNR (dB)

BER of STBC with BPSK in CorrelatedNakagami Fading

� � � ��

� �

0 1 2 3 4 5 6 7 8 9 1010

10−5

10−4

10−3

10−2

10−1

SNR (dB)

STBC with Turbo Codes in UnstructuredInterference

� STBC and Turbo Codes (TC) are used for highdata-rate wireless communications (3G, 4G)

� Industry measurements show that surroundingelectronics cause noise in STBC receiversleading to poor performance

� Solution: use a robust STBC receiver forunknown interference suppression

Space-Time Block Coding with CyclicMaximum-Likelihood Detection

� Received signal in matrix form

��

� = Transmit energy � normalized by

= Channel between each transmit-receive antenna pair

= Transmitted signal matrix

= AWGN noise at the receiver

= External localized interference

Concatenated STBC and TC System Model

Data Bit

Source

Space-Time Block

Encoder

AWGN Noise

Space-Time Block Decoder

AWGN Noise Localized Noise

Channel &

Noise Covariance

Estimator

Estimated Data Bits

Encoder

Turbo Decoder

} ,..., { 1 t

} ˆ ,..., ˆ { 1 t

} ,..., { 1 t

} ˆ ,..., ˆ { 1 t

} ,..., { 1 , 1 , 1 t

s s TX Antenna 1

RX Antenna 2

RX Antenna 1

TX Antenna 2

} ,..., { 2 , 2 , 1 t s s

} ,..., { 1 , 1 , 1 t

} ,..., { 2 , 2 , 1 t

} ˆ ,..., ˆ { 1 , 1 , 1 t s s

} ˆ ,..., ˆ { 2 , 2 , 1 t s s

} ˆ ,..., ˆ { 1 , 1 , 1 t

Maximum-Likelihood Detection and CML

� Detection of received frame of codewordmatrices incorporating noise statistics� �

� ��

�� +

� � �

� � ��

� i � � ��

� CML obtains and refines initial channel

andnoise estimates based on training data

Interference Suppression

0 5 10 15 20 2510

10−3

10−2

10−1

SNR (dB)

2x2−Known H and Q2x2−TWML2x2−TCML2x2−1 Iter Cyclic WML2x2−1 Iter Cyclic CML

Interference Suppression with Coding

2 4 6 8 10 12 14 16

10−4

10−3

10−2

10−1

SNR (dB)

1 Iter WML and 1 Iter TC1 Iter WML and 4 Iter TC1 Iter CML and 1 Iter TC1 Iter CML and 4 Iter TC1 Iter CML and uncoded

Differential Space Time Modulation

0 2 4 6 8 10 12 14 16 18 2010

10−4

10−3

10−2

10−1

SNR (dB)

OSTBC with H and QDSTM with known QTML1 Iter WML1 Iter CML2 Iter WML2 Iter CML

Performance versus Training

1 2 3 4 5 6 7 8 9 1010

10−5

10−4

10−3

10−2

10−1

Number of DSTM Training Matrices

OSTBC with known H and QDSTM with known QTWMLTCML1 Iter WML1 Iter CML2 Iter WML2 Iter CML

Impact of Doppler Fading

0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.0510

10−2

10−1

Normalized Doppler Frequency (Fd*Ts)

OSTBC with Known H and QTML1 Iter WML1 Iter CML2 Iter WML2 Iter CML

Coherent versus Noncoherent

3 4 5 6 7 8 9 10 11 12 13 14

10−4

10−3

10−2

10−1

SNR(dB)

ROSTBC − 1 Iter CML and 1 Iter TCOSTBC − 1 Iter CML and 4 Iter TCDSTM − 2 Iter CML and 1 Iter TCDSTM − 2 Iter CML and 4 Iter TCDSTM − 2 Iter CML and uncoded

Future Work

� Successive Interference Cancellation with STBC

� Space Time Multilevel Codes

� Space Time Turbo Codes

� Performance and Capacity of MC-CDMA andOFDM systems with STBC

� Wavelet OFDM (Multicarrier Modulation)

� STC for PAPR reduction in OFDM

� PAPR estimation and reduction techniques forOFDM

A New STBC Cellular System Structure - 1

� This Structure consists of edge-excited cells

� Each base station covers part of the cells withSDMA

� Eliminates channel correlation

� Reduces interference between users

User 2

User 1

0 2 4 6 8 10−5

Eb/No (dB)

Log 10

SDMA+CDMA 5 User/Cell SDMA+CDMA 3 User/Cell SDMA+CDMA 2 User/Cell SDMA+CDMA+STBC 5 User/CellSDMA+CDMA+STBC 3 User/CellSDMA+CDMA+STBC 2 User/CellSDMA+CDMA+STBC COR 5 User SDMA+CDMA+STBC COR 3 User SDMA+CDMA+STBC COR 2 User

Wavelets

� DSP tool used for analysis of signals

� Wavelets are simultaneously scalable in timeand frequency

� Lower complexity than FFT

� Provides high temporal and frequencyresolution

� Can be used for partial removal of AWGN

Wavelets

Wavelet transformFourier transform

Multilevel STBC

Space Time Turbo Code with Bit Selection

The Error MatrixFor two distinct codewords

� � +� +�� + �� + ��

� � ��

the error matrix

� � � � +� � �� +� � ��

� + �� & � �� + ��

has full rank � diversity!

Properties

� Simple decoding: Each symbol is decodedseparately using only linear processing.

� Maximum diversity: Same performance astwo-level maximum ratio combining.

Is it possible to design similar codes for morenumber of transmit antennas?

Orthogonal Designs

� What is the reason for these properties?

� �

��

� � � � ��

� The columns of

are orthogonal

� � � ��

� We call such an

an orthogonal design.

Existence of Real Orthogonal Designs

A real orthogonal design exists if and only if

� � ��

��

� ��

��

� ��

� � � � ��

��

Example

��

� ��

� � � ��

� ��

� � � ��

� � � � � ��

� � � � � � � � ��

��

Existence of Complex Orthogonal Designs

Given a complex orthogonal design of size � , wereplace each complex variable

� � � � � � � � � � � � � , � � by the

� � �

real matrix

��

� � � � � � �In this way � � �is represented by

��

� � � � � �

Existence of Complex Orthogonal Designs

� The

�� matrix formed in this way is a realorthogonal design of size

�� .

� Result: A complex orthogonal design of size �

exists only if � � �

How can we design space-time block codes forhigher number of transmit antennas?

Generalized Orthogonal Designs

� Instead of orthogonal designs that are squarematrices, we construct generalized orthogonaldesigns that are rectangular matrices.

� We only allow linear combinations of symbols(linear processing at the transmitter).

� This leads to space-time block coding.

Example

� � �

� � ��

��

� ��

� � � � ��

� ��

� � ��

��

Example

� � �

� � ��

��

� ��

� � � � ��

� ��

� � ��

��

Example

� � �

� � ��

��

� � ��

� ��

� � ��

��

STBC for MIMO wireless channels

� Space-time block codes from orthogonaldesigns can provide maximum diversity.

� Real space-time block codes can providemaximum diversity and rate for any number oftransmit antennas,

� Rate half complex space-time block codescan provide maximum diversity for any numberof transmit antennas,

� Rate 3/4 complex space-time block codes canprovide maximum diversity for

� � ��

, andrate one code for

� � �

space time block coding for wireless communication systemsagullive/aaron.pdf · 2004. 10. 10. ·...

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