Rapidly Converging Transceivers for Multiple Access ... · Hints to enabling tech. in transceiver...

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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


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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


[ ]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


{ } { }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.


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Filter Bank Perspectives

Rank Reduction: Expanding Subspaces, Filter Banks Configuration


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Rank Reduction Algorithm

Rank Reduction: The RR-CG WF Algorithm


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The Geometry of Rank Reduction

The Geometry in the Krylov SubspaceThe Krylov subspace


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


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


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Experimental Examples: Simulation Results


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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


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


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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Simulation results (good Gold codes, K=2, MR=2, Kv=6)


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Simulation Results (bad Gold codes , K=2, MR=2 Kv=6)


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Simulation Results (good Gold codes, K=4, MR=4 Kv=20)


• 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


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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Simulation Results (N=31, K=10)


{ }.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


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Code Design

Gold Sequences

Case 1: v is not included (good set)

Case 2: v is included (bad set)


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Code Design

Kasami Sequences (small set)


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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


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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)



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Numerical Results (Kasami)

Performance measurement of the RRCG-WF for MUD in CDMA systems using Kasami code (small set)



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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.


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Thanks


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