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Rapidly Converging Transceivers for Multiple Access Wireless
Communication Systems
Hongya Ge
Dept. of Electrical & Computer EngineeringNew Jersey Institute of Technology
Newark, NJ, 07102, USA
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Challenges in next generation wireless systems
High Speed Multimedia Data TrafficScalability on data rate, performance, and complexityIntelligent spectrum sensing and utilizationRapidly converging transceivers
Subspace Techniques for Multiple-Access SystemsRapid converging multiuser detectors (MUDs)Fast synchronization solutionsPower control enabling rapidly converging solutionsSpreading code design for CDMA applications
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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Outline
Reduced-Rank Wiener Filter (RRWF) for MUDsSingle-rate systemMulti-rate system using STBC signature design
Rapid Synchronization in CDMA ApplicationsFast delay estimation Reduced-rank solutions demanding less training symbols
Code Design in CDMA ApplicationsTo study the eigen-sepctrum of code-set GrammianTo identify promising code-sets enabling rapidly converging transceivers for multiple access communication systems
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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Reduced-Rank Wiener Filter for MUD
1. Distributed MUD for a Desired User
Data Modela MA system with active K users, each using a distinct signatureonly the signature of the desired user is known to the terminalchip-rate MF and sampled received data vector
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
[ ]1
1 2
2
,
the matrix contains MA users' signatures; the vector contains symbol information; and the noise ( , ).
K
k k kk
K
A b
N σ
=
= + = +
=
∑y s n SAb n
S s s sbn 0 I∼
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Reduced-Rank Wiener Filter for MUD
The Linear MMSE (WF) Detector for a Desired User
Note: The test statistic is a common component for many SP applications.
High dimensionality in data, adaptive dynamic systems=> reduced-rank versions: scalable performance/complexity
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
{ } { }1
1
the -th user's BPSK symbol is estimated fromˆ sgn sgn ,
where vector = is the scaled Wiener filter for ,
and is a data correlation matrix.
T Tk k yy
yy k k
yy
k
b
b
−
−
−
= =s R y w y
w R sR
1Tk yy
−s R y
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Rank Reduction & Subspace Expansion
Rank Reduction Subspace ExpansionAim:to avoid the full matrix inversion low computation, low-complexityto achieve a fast convergence rapid adaptation
Existing Subspace Approaches:(a). Principal Component Analysis (PCA): using SVD (b). Cross Spectral Metric (CSM): using SVD (c). Multi-Stage Wiener Filter (MSWF): using matrix tri-diagonalization
techniques, or the idea of nested/iterative GSC(d). Conjugate Gradient (CG) and Conjugate Direction (CD) WF:
using the iterative matrix diagonalization techniques(e). Canonical Coordinate (CC) method: two-channel versionNote: the Eigen subspace vs. the Krylov subspace
a warp convergence exists in the Krylov subspace approach.
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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Filter Bank Perspectives
Rank Reduction: Expanding Subspaces, Filter Banks Configuration
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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Rank Reduction Algorithm
Rank Reduction: The RR-CG WF Algorithm
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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The Geometry of Rank Reduction
The Geometry in the Krylov SubspaceThe Krylov subspace
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
1( , )yy
rr yy k k yy k kK −=R s s R s R s
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Convergence Property
Convergence: General and Warp
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
2 2
1
For data , and ,
The rank- RR-WF lies in the Krylov subspace
( , ).
- For general K-user MA systems, the Krylov subspace ( , ) stops
exp
Tyy
rank Nrank Krank N
r
r l l r yy kl
r yy k
r
K
K
σ
α
−−−
=
= + = +
= ∈∑
y SAb n R SA S I
w d R s
R sanding at K-step convergence.
i.e., the steps needed for convergence = the of signal subspace . - For MA systems (signature codes & power control),
the Krylov subspace ( , )r yy k
r K Nrank
designedK
= ≤ →
S
R s
{ }stops expanding at ,
typically , and . i.e., min , # ( ) .
yy
r L K N
L K independent of K N L r dev
= ≤ ≤
= R
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Experimental Results
Experimental Examples: Simulation Results
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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Experimental Results
Experimental Examples: Simulation Results
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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RRWF for MUD: Multi-Rate Systems
2. Group-Wise MUD for User Groups with Different Data Rates
Data Model
The RR M-CG WF for the BPSK symbols of users in the desired group
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
1 2
1, 1, 1, 2, 2, 2, , , ,1 1 1
1 1 12
,1 ,2 ,
,
where , 1,2, , .
is the signature matrix of all the users in the -th group.
g
l
KK K
k k k k k k g k g k g kk k k
g
l l lldesired group
l l l l K
A b A b A b
l g
l
= = =
=
= + + + +
= + +
= =
∑ ∑ ∑
∑
y s s s n
S A b S A b n
S s s s …
{ } { }1ˆ sgn , with rank_r_approx ( , )Td d d yy d r yy dK−= = ∈b W y W R S R S
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RRWF for MUD: Multi-Rate Systems
QO-STBC signature for user groups with different ratesSignature matrix for the k-th group users is designed as
Signature matrix can also be designed as for user groups
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
1 2R
2 1
, O -S T B C d es ig n , M = 2d
= −
g gS
g g
3 41 21 2
4 32 1
1 2R
2 1
, = ,
, QO-STBC design, M =4d
= −−
= −
g gg gG G
g gg g
G GS
G G
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Experimental Results
Simulation results (good Gold codes, K=2, MR=2, Kv=6)
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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Experimental Results
Simulation Results (bad Gold codes , K=2, MR=2 Kv=6)
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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Experimental Results
Simulation Results (good Gold codes, K=4, MR=4 Kv=20)
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
• HR users -- Good codes in use •HR users -- Bad codes in use
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Rapid Synchronization Application
Data Model
Maximum Likelihood Estimate
Krylov Subspace Reduced-rank Solution
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
1( ) ( ) ( ) ( )
K
k k k ki k
y t A b i s t iT n tτ=
= − − +∑ ∑
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1
( ) ( )
1 1
ˆˆ ( )ˆ arg max ( ) arg max ,ˆ( ) ( )
1 1ˆˆ ˆ ˆwith [ ], [ ] [m]- , and ( ) ( ) ( )
Tk
k Tk k
M MT T L R
k k km m
J
m mM M
τ τ
ττ τ
τ τ
τ τ τ
−
−
= =
= =
= = ⋅ ⋅ = +∑ ∑
m Q u
u Q u
m y Q y y m m u u u
2( )( )
( )
( )
1
ˆ ( )ˆ arg m ax ( ) arg m ax ,
( ) ( )ˆw ith vector ( ) { , ( )} being a rank-r
ˆapprox im ation o f the ( ) ( )
k
k
k
k
T rr
k T rk
rr k
k
J
K
τ τ
ττ τ
τ τ
τ τ
τ τ−
= =
∈
=
u
u
u
u
m wu w
w Q u
w Q u
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Experimental Results
Simulation Results (N=31, K=10)
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
{ }.2ˆPr - ,5sig acq cP Tτ τ τ τ= ≤ ∆ ∆ =
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Code Design Enabling A Warp Convergence
The convergence step of the RRCG-WF is determined by the number of distinct eigenvalues of the code-set Gramming (or the cross-correlation matrix of the code-set) under perfect power control.
-- [Ge, Lundberg, and Scharf, 2004]
Orthogonal Codes
m-sequences
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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Code Design
Gold Sequences
Case 1: v is not included (good set)
Case 2: v is included (bad set)
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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Code Design
Kasami Sequences (small set)
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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Numerical Results (Gold)
Performance measurement of the RRCG-WF for MUD in CDMA applications using Gold code (with good cross-correlation)
N=15, K=8, SNR1=11dB, SNRk=SNR1+NFR Convergence Step: 2
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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Numerical Results (Gold)
Performance measurement of the RRCG-WF for MUD in CDMA systems using Gold code (with bad cross-correlation)
N=31, K=10, SNR1=11dB, SNRk=SNR1+NFR Convergence Step: 4
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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Numerical Results (Kasami)
Performance measurement of the RRCG-WF for MUD in CDMA systems using Kasami code (small set)
N=63, K=3, SNR1=11dB, SNRk=SNR1+NFR Convergence Step: 2
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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Conclusions
Subspace techniques provide effective solutions to
rapidly converging MUDs (distributed MUD for mobile users; centralized MUD for base-station; and group-wise MUD for users with different rates), for designed wireless systems
proper power control and intelligent signature design enables a warp convergence in MUDs, meaning RR-MUD converges to the MUD much earlier (in rsteps), irrespective of the user number K and spreading gain N.
The warp convergence is observed in group-wise MUD involving users with different groups of data-rate.
rapid timing synchronization for MA system (requiring much less number of training symbols than the traditional ML approaches)
Hints to enabling tech. in transceiver design with scalable complexity.
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT
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Thanks
Rapidly Converging Transceivers for Multiple Access Wireless Communication Systems, Hongya Ge, NJIT