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Coded Modulation for Coded Modulation for Multiple Antennas Multiple Antennas

over Fading Channelsover Fading Channels

Israfil Bahçeci

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OutlineOutline Signaling over Wireless Channels

Fading Channels Diversity techniques Channel Coding, Space-time Coding for Multiple Antenna Systems

Space-time architectures

Turbo- and Trellis-Coded Space-Time Modulation

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IntroductionIntroduction

multipathmultipath propagationpropagation and time variations fafadidingng

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Time selective fading (due to Doppler spread)

Space selective fading

(due to delay spread)

abcdefghijklmnopq

Frequencyselective fading(due to delay spread)

Fading in Time, Frequency and Space

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Frequencyselective fading(due to delay spread)

Signaling over Fading Wireless channels

Frequencydiversity

Time diversity:Channel codingandinterleaving.

Antenna diversity

diversity techniques

aeimqbfjncskodhlp

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Channel coding

Different techniques : linear block codes (Hamming, Hadamard, Golay, BCH, etc.) • convolutional codes • code concatenation (parallel, serial, product codes, etc.)

• turbo codes• trellis coded modulation • turbo coded modulation

A sophisticated form of time diversity

Combined space and time diversity

• multiple transmit and receive antennas are used.• robust to variations of the channel. • high spectral efficiencies can be achieved.

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Multiple antennas at the transmitter and the receiver

NNMMN wHsM

x 111

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Capacity Results for known CSI

HH

MIEC HN

detlog

• memoryless channel, Rayleigh flat fading

• C ~ roughly linear with the smaller of the number of the

transmitter and receiver antennas.

i.e., if , the capacity increases m bits/s/Hz for every 3 dB increase in signal-to-noise ratio (SNR).

NMm ,min

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Space-time Codes :

• Combination of channel coding/modulation with multiple

antennas.• Encoder generates M elementary signals to be transmitted simultaneously.

If CSI is available

• Space-time trellis codes• Space-time block codes• Turbo coded modulation with antenna diversity• Layered Space-Time Codes, i.e., BLAST

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Space-Time Trellis Codes

• Diversity order is Nr, where r is minimum rank of B=S-Ŝ over the set of two tuples of distinct codewords.

• Coding gain is (λ1 λ2 …λr)1/r, where λi are non-zero eigenvalues of BBH.

QPSK constellation M=2, N=1, R=2 b/s/Hz,

4-PSK, 4-states, Diversity order is 2.

Code construction ML Decoding

Branch metric at time t

N

n

M

m

mtmn

nt shx

1

2

1

Viterbi algorithm is then usedto find the path with the Lowest accumulated metric.

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BLAST (Bell Labs Layered Space-Time)

•As M and N increase, complextity with ML decoding increase•Suboptimal design but still achieving most of the capacity•Layered space-time codes, processing higher dimensional signals with the use of 1-D codes.

11 99 1717 2525 3333 4141 4949 5757 6565 7373

22 1010 1818 2626 3434 4242 5050 5858 6666

33 1111 1919 2727 3535 4343 5151 5959

44 1212 2020 2828 3636 4444 5252

55 1313 2121 2929 3737 4545

66 1414 2222 3030 3838

77 1515 2323 3131

88 1616 2424

Ante

nnas

Transmission time

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nulling

cancellation

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Capacity Results for no CSI case• Block fading channel, T: coherence time of the channel.

• Capacity does not increase as number of transmit antennas increases beyond the coherence time!

• Capacity achieving signals have considerable structures:

Isotropically distributed random vectors x Diagonal random matrix

• For M=N, the capacity increases by K(1-K/T) bits/s/Hz for every 3 dB SNR increase where K= min(r, T/2).

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• Unitary Space-Time modulation

• Differential Space-Time Modulation schemesi.e., differential encoding of Group Codes (comprising of matrices), similar to the ordinary DPSK modulation for single antenna trasnmission.

Space-Time Codes when CSI is not available

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• Block Rayleigh fading

Unitary Space-Time Modulation

NTNMMTNT WHSM

X

HT

MH

SSM

I

ITS

,

• Information is carried on the subspace spanned by orthonormal signals that are sent to transmit antennas.

• Large signal constellations can be generated systematically.

• Unitary space-time (UST) signals achieves capacity.

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Turbo Coded Unitary Space-Time Modulation

Block diagram of turbo coded modulation

Block diagram of turbo code

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Block diagram for decoder.

Decoding

Find the likelihood values for transmitted bits and use them as if they are observations from BPSK modulation over AWGN channel

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0,:/

/1

1

1,:/

/1

1

log

|0Pr

|1Prlog

l

HH

l

HH

bbfSTS

XXTM

tr

bbfSTS

XXTM

tr

l

ll

e

e

Xb

Xbb

b/s/Hz. ,log ed. transmittis 221 RLTRbbbb TR

L = number of signals in the constellation

CSIP seminarsT=8, L=256, M=2, N=1, R= 7/8 b/s/Hz

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T=5, L= 32, 1024, M=2, N=1, R= 1 b/s/Hz

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Trellis Coded Unitary Space-Time Modulation

8-state encoder and L = 8 USTM and uncoded L = 4 USTM schemes

{0,1,…7} denote the UST signals

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1

0

maxargK

ii

Hii

Hi

Sopt XXtrS

Optimal Decoding

• can be implemented using Viterbi algorithm

where is the received signal.

iX

• Set Partitioning (similar to Ungerboeck Rules)

• small larger separation between signal pairs and

where s.t. are singular values of

Parallel transitions should be assigned to members of the lowest level partition.

Adjacent transitions should be assigned the next available partition.

Code Design• Given the constellations

M

iidM 1

21i j

id kHi

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•example, L = 8 USTM

0.38350.3835770.38350.383533

0.37860.3786660.37860.378622

0.38350.3835550.38350.383511

0.35360.3536441.0001.00000

ikik i-k mod Li-k mod Likik i-k mod Li-k mod L

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M=2, N=1, R=1/4 b/s/Hz. 8-state L=8 USTM schemes compared with uncoded L=4 USTM.

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M=2, N=1, R=1 b/s/Hz. 256-state L=512 TCM compared with L=256 uncoded modulation.

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Conclusions

• Multiple antennas have great potential to provide large transmission rates, particularly required by multimedia applications.• Space-time coding technology with other techniques such as array processing, OFDM, CDMA, etc. promise large performance improvement.• Further research on space-time coding for various channel models needs.