© Imperial College LondonPage 1 WSEAS PLENARY LECTURE: The Challenges of Subspace Techniques and their Impact on Space-Time Communications. 29 th December.

© Imperial College LondonPage 1

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


Outline

1. Notation

2. General Problem Formulation

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

4. Space-Time Communications

5. Conclusions


Notation


cont. - Notation


cont. - Notation

Origin

bs

pL[ ]

L[ ]


cont. - Notation

Origin

bs

pL[ ]x

L[ ] x

x


General Problem Formulation

Condition

AWGN


n(t)

m (t)1

m (t)2

m (t)M

+

cont. - General Problem Formulation


cont. - General Problem Formulation



Subspace Techniques


cont. - Subspace Techniques


The “Signal-Subspace” Concept


cont. - The “Signal-Subspace” Concept






cont. – The “Signal-Subspace” Concept


The “Manifold” Concept


cont. – The “Manifold” Concept








cont. Manifold










Performance Bounds


Space-Time Communications


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



• 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)


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):


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


+ 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


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


cont. Space-Time Channels




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


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

Path Delay (T c ) 2 13 19 25 27



Example - Channel Estimator

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


Example - Decision Variables


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.


Example – “Near-Far” Resistance


Example – Subspace Tracking




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).


© Imperial College LondonPage 1 WSEAS PLENARY LECTURE: The Challenges of Subspace Techniques and their Impact on Space-Time Communications. 29 th December.

Documents

user rx

optimum mu rx

active user

typical suboptimal mu

cdma users

cdma receiversenhancements

complexhuge gap

symbol detection