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WSEAS PLENARY LECTURE:

The Challenges of Subspace Techniques and

their Impact on Space-Time Communications.

29th December 2004Dr Athanassios ManikasDeputy Head Comms & Signal ProcessingDepartment of Electrical & Electronic Engineering

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Outline

1. Notation

2. General Problem Formulation

3. Subspace Techniques• Signal-Subspace• Manifolds• Performance Bounds

4. Space-Time Communications

5. Conclusions

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Notation

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cont. - Notation

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cont. - Notation

Origin

bs

pL[ ]

L[ ]

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cont. - Notation

Origin

bs

pL[ ]x

L[ ] x

x

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General Problem Formulation

Condition

AWGN

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n(t)

m (t)1

m (t)2

m (t)M

+

cont. - General Problem Formulation

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cont. - General Problem Formulation

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Subspace Techniques

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cont. - Subspace Techniques

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The “Signal-Subspace” Concept

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cont. - The “Signal-Subspace” Concept

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cont. - The “Signal-Subspace” Concept

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cont. - The “Signal-Subspace” Concept

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cont. – The “Signal-Subspace” Concept

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The “Manifold” Concept

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cont. – The “Manifold” Concept

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cont. – The “Manifold” Concept

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cont. – The “Manifold” Concept

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cont. – The “Manifold” Concept

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cont. Manifold

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cont. – The “Manifold” Concept

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cont. – The “Manifold” Concept

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cont. – The “Manifold” Concept

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cont. – The “Manifold” Concept

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Performance Bounds

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Space-Time Communications

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cont. - Space-Time Communications

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cont. - Space-Time Communications

• All ‘conventional’ CDMA receivers can be modified to become Space-Time CDMA receivers

• Enhancements would result in considerable performance gains

• Enhancements are not trivial however

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cont. - Space-Time Communications

• Two classes1. ST - Single-User Rx: requires no knowledge beyond

the PN-sequence and the timing of the user it wants to demodulate/receive ('desired' user)

2. ST - Multi-User Rx: requires knowledge of the PN-sequence & the timing of every active user as well as knowledge of the received amplitudes of all users and the noise level

> Can be Optimal or Sub-optimal depending on whether the decision making criteria for symbol detection are fully met (Optimal) or partially met (Sub-optimal)

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Optimum ST-CDMA Receivers

• ST - RAKE Receiver: Optimum Single-User Receiver

• ST - MLSE Receiver: Optimum Multi-User Receiver which must take into account the PN-codes of all other CDMA users in the system. Non-linear and computationally far too complex

> Huge gap in performance and complexity between an optimum single-user and an optimum multi-user receiver

> Decorrelating MU Receiver:This is a typical sub-optimal MU Rx (but much simpler that the optimum MU Rx):

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Space-Time Channels

T xT x

T x

V IV OC h a n n el

T xT xS p a c e-T im e

R xM IV O

C h a n n e l

S p a c e-T im eR x

S p a ce -T im eT x

S p a ce -T im eT x

S p a ce -T im eT x

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+ n(t)

SIVO Channel

of 1st Source

m (t)1

SIVO Channel

of 2nd Source

SIVO Channel

of -th SourceM

VIVO Channel

Space-TimeRx

m (t)2

m (t)M

T xT x

T x

V IV OC h a n n el

T xT xS p a c e-T im e

R x

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cont. Space-Time Channels

i1 i2 iK i

S i1 S i2 S iK i

+

S p a c e-T im eR x

i1 i2-i1 i3-i2S IV O

E tc .s (t)i

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cont. Space-Time Channels

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Example – ULA of 3 elements

User1 (Desired) Path 1 Path 2 Path 3 Path 4 Path 5

Path Delay (T c ) 1 9 17 21 27

Path Direction (O ) 50 94 125 141 76Path Coefficient -0.10 + 0.26j -0.01 - 0.24j -0.31 - 0.02j -0.31 - 0.02j 0.42 - 0.35j

User2 (Interference) Path 1 Path 2 Path 3 Path 4 Path 5

Path Delay (T c ) 4 8 17 26 27

Path Direction (O ) 92 35 149 67 61Path Coefficient -0.20 + 0.56j -0.41 - 0.74j -0.39 - 0.92j -0.91 - 0.12j 0.76 - 0.00j

User3 (Interference) Path 1 Path 2 Path 3 Path 4 Path 5

Path Delay (T c ) 2 13 19 25 27

Path Direction (O ) 103 84 80 79 116Path Coefficient -0.15 + 0.27j -0.71 - 0.24j -0.11 - 0.01j -0.21 - 0.05j 0.45 - 0.55j

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Example - Channel Estimator

> Surface and contour plots shows that all 5 path delays and directions are correctly estimated

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Example - Decision Variables

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Example - SNIR Comparisons

0 5 10 15 20 25 30 35 40 45 50-20

-10

0

10

20

30

40

50Average Output SNIR Against Number of Users

Number of Users

Ave

rage

Out

put S

NIR

(in

dB

)Decorr

Proposed

ST-RAKE

Decorrelating Rx (MU) incomp.

0 5 10 15 20 25 30 35 40 45 50-20

-10

0

10

20

30

40

50

0 5 10 15 20 25 30 35 40 45 50-20

-10

0

10

20

30

40

50Average Output SNIR Against Number of Users

Number of Users

Ave

rage

Out

put S

NIR

(in

dB

)Decorr

Proposed

ST-RAKE

Decorrelating Rx (MU) incomp.

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Example – “Near-Far” Resistance

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Example – Subspace Tracking

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Conclusions:

ST Comms based on Subspace-Techniques:

– blind

– near-far resistant,

– superresolution capabilities

– The number of multipaths that can be resolved is not constrained by the number of array elements (antennas).

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