Multipe-Symbol Sphere Decoding for Space-

Time Modulation

Vincent HagMarch 7th 2005

Why MIMO?

• Limited radio resources• Need for higher data rate (3G services and beyond)

Make the best possible use of the spectrum in order to further increase throughput as well as user-capacity

MIMO antennas is a key technology

Why Multiple-Symbol Detection?

N received symbols are jointly processed to estimate N-1 symbols

Better evaluation of the channel statistics yields improved performances

Why Non-coherent Detection?

Phase estimation difficult or costly

Develop (de)modulation techniques that do not require CSI

Extend DPSK to MIMO systems

Problem Formulation

Performance(exploit space and time dimensions)

Complexity

(exponential in space and time dimensions)

Need for fast-algorithm based detection

Talk Outline

Transmission

Channel Model

Reception: Sphere Decoder

Simulation Results

Conclusions and Further Works

Transmission

Non-coherent Detection Differential Transmission

Diagonal codes (= extension of DPSK signals to STC)

Differential Encoding

klV

0 0

1k k k

l l

l l l

S VS V S

Code matrices are differentially encoded such as

Diagonal Codes

11tNu u

12

2

0 0

0 0 time

0 0

space

k

k

Nt

lj u

L

l

j u

L

Ve

e

Channel Model

• AWGN• Rayleigh fading• Multi-channel action:

1 1 1 10 0

0 0

0 0N N N N

R S H W

R S H W

Communication link

Catch-up slide

fast detection scheme

MIMO systems

Multiple-Symbol Sphere Decoding

for

Space-Time Modulation

Talk Outline

Transmission

Channel Model

Reception: Sphere Decoder

Simulation Results

Conclusions and further Works

Reception: Metric

Metric:

2

arg max Pr |

arg min

N

N

MLS C

MLS C

S R S

S US

ML decision rule:

Sphere Decoding: Concept

Fix and examine signals such that

2 2US

S

Search of signals lying inside a sphere of radius instead of the whole space

Sphere Decoding

i N?2 2 2

NN N N NU S d S

2

11 1 120

0 0

N

NN N

U U S

U S

with U upper triangular

NS 1SS can be determined component-wise,

starting from and tracking up to

Sphere Decoding

1i N

?22 2 2

1 1 1 1 1 1N N N N N N N N Nd U S U S d S

2

11 1 120

0 0

N

NN N

U U S

U S

Sphere Decoding

choose that minimizes to keep it as small as possible:

Partial distance criterion:

2

2 21

1

N

i i ii i ij jj i

d d U S U S

2

1

arg mini

N

i ii i ij jS C

j i

S U S U S

iS id

Sphere Decoding

1i

S

radius updated to U S

Then, restart the sphere decoding algorithm with the new radius value

Sphere Decoding

• Phase ambiguities:

1NS fix and start sphere decoding at

• Search strategy:

Zigzag procedure: hypothetical symbols(examined for the ith component) are ordered according monotically increasing distance

1i N

iS

id

Zigzag for 8-PSK constellation

Representation in a tree

DFDD

Attractive low-complexity algorithm performing differential detection

Linear predictor making decision onbased on and

klV

-( -1), , k k NR R ( 1, , 2)k ilV i N

Talk Outline

Transmission Channel ModelReception: Sphere DecoderSimulation ResultsConclusions and further Works

Simulation Results

• Simulation setup

• BER performances

• Computational Complexity

• BER vs. Complexity

Simulation Setup

• bit/channel use,

• Spatially independent Rayleigh continuous fading channels

• Detect at least 1000 bit errors to assess the BER at any SNR

• Number of multiplications as a measure of the complexity

2R 0.03dB T

BER performances

Error floor removed

Single Antenna System

BER performances

MSDSDvs

DFDD

3tN

BER performances

Mismacth of the Doppler rate

4dB shiftRobust?

Computational Complexity

Average Number of Real Multiplicationsdone to estimate a 10-length sequence

Computational Complexity

( ) log ( )c NE N ANMB

BER vs Complexity

Restrict the number of multiplications for practical reasons

BER vs Complexity

Conclusion

• SD outperforms DFDD, a good low-complexity algorithms

• Excellent performance versus complexity trade-off:

• ML performances

• But orders of magnitudes below that of brute-force search (ML detection)

• Gains in power efficiency almost for free

Further Works

• Investigate other STC, possibly with other search strategy for PDP

• Take interference into account

Questions?