© imperial college londonpage 1 wseas plenary lecture: the challenges of subspace techniques and...
TRANSCRIPT
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© 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
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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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