Presentation Thesis

Parallel Low-Complexity MIMO Detection Algorithmusing QR Decomposition and Alamouti

Space-Time Code

Maher Arar

December 16, 2009

Outline

Outline

• MIMO: definition, challenges and thesis main contribution

• MIMO capacity

• MIMO detection algorithms

• Proposed algorithm and simulation results

• Conclusion

1

MIMO: Definition, Challenges and Thesis Main Contribution

Definition

• Multiple-Input-Multiple-Output, or MIMO, is the use of multiple antennas on

the TX and RX end of the wireless link to multiply data rates and/or to

improve reliability (using same power and same RF spectrum)

• Assumptions: Flat Rayleigh Independent Block Fading

Figure 1: 4x4 MIMO System Model

2

MIMO: Definition, Challenges and Thesis Main Contribution

Challenges and Thesis Main Contribution

• RF:

– array size

– component count

– Power consumption

• Baseband:

– sub-1Gbps rates required by 4G and beyond-4G

– Power consumption

• Thesis main contribution: Propose a parallel low-complexity MIMO algorithm

3

MIMO Capacity

Instantaneous, Ergodic and Outage MIMO Capacities

•

y =

√ρ

Nt

Hs + n (1)

• Instantaneous open-loop (no feedback from RX to TX) capacity

CH =

log2 det(INr + ρ

NtHH+

)for Nr ≤ Nt

log2 det(INt + ρ

NtH+H

)for Nr > Nt,

(2)

• MIMO ergodic capacity C = E {CH} (fast fading channels)

• MIMO outage capacity Pout (CH < Cx) (block fading channels)

4

MIMO Capacity

Figure 2: Ergodic capacity of i.i.d. MIMO channel for ρ = 15dB

5

MIMO Capacity

Effect of Spatial Correlation

• Mainly caused by poor scattering, small angular spread, small spacing between

antenna elements

• Kronecker model:

H = Ψ1/2r HiidΨ

1/2t (3)

• Instantaneous capacity becomes:

CH ≈ log2

[det( ρN

HiidH+iid

)]+ log2 det(Ψt) + log2 det(Ψr)︸︷︷︸

=η(Ψt,Ψr) ≤0

(4)

• Spatial correlation reduces the achievable MIMO capacity

• Exponential correlation model

[Ψ]i,j = ψ|i−j| i, j ∈ {1, 2, ...., N} and ψ ∈ [0, 1) (5)

6

MIMO Capacity

Effect of Spatial Correlation

Figure 3: Effect of correlation on a N ×N MIMO capacity for ρ = 30 dB

7

MIMO Detection Algorithms

MIMO Algorithms Classification

• Algorithms for maximizing spatial multiplexing gain Gm: Linear detectors (ZF

or MMSE), SIC detectors (ZF or MMSE), ML and ML-like detectors, etc

• Algorithms for maximizing diversity gain Gd (Space-Time codes): STTC,

STBC, OSTBC, etc

• Hybrid algorithms: QoSTBC, GSIC, GSTTC, etc.

Figure 4: 4x4 MIMO System Model

8

MIMO Detection Algorithms: Spatial Multiplexing

Figure 5: BER comparison between various SM detection algorithms for a 4 × 4

MIMO channel with bandwidth efficiency of 8 bit/s/Hz

9

MIMO Detection Algorithms: Alamouti Code

Figure 6: BER performance of 2 × Nr Alamouti STBC with 16QAM modulation

giving a total bandwidth efficiency of 4 bit/s/Hz

10

MIMO Detection Algorithms

Summary

Algorithm Gmaxm Gmax

d Complexity

Alamouti 1 2N 0, O(N)

ZF N 1 O(N3), O(N2)

MMSE N 1 O(N3), O(N2)

ZF-VBLAST N 1 O(N4), O(N2)

MMSE-VBLAST N 1 O(N4),O(N2)

ML-like (SD) N ≈ N O(N3),≥ O(N4)

ML N N 0, O(LN)

Table 1: Comparison between various N ×N MIMO detection algorithms

• Problem definition: Find an algorithm that achieves better FER/capacity

performance than MMSE-VBLAST with same or reduced ’complexity’ keeping

in mind the need for efficient power consumption (parallel architecture)

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Proposed Architecture and Associated Algorithms

Proposed Architecture

Figure 7: Model of the proposed architecture

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New Equation

• Using QR factorization any matrix H can be decomposed as H = QR where

Q is unitary, i.e. QQ+ = I and R is upper triangular

• Equation (1) can then be rewritten as

y =

√ρ

Nt

QRs + n (6)

• By multiplying the RX vector y from the left by Q+ we get the following

transformed vector

y = Q+y =

√ρ

Nt

Rs + n (7)

• Notice that all ni still have unity variance, i.e. no noise amplification

13


Model of Transformed MIMO System

y =

√ρ

N

r11 r12 . . . r1N

0 r22 . . . r2N...

......

...

0 0 . . . rNN

s + n (8)

Figure 8: Transformed 4× 4 MIMO system with QR factorization

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Useful Relationships and Properties Related to R

• The magnitude square |rj,j|2 of the each diagonal entry rj,j is Chi-squared

distributed with 2(N − j + 1) degrees of freedom

P (|ri,j|2 < ε) ≈ εN−j+1 i = j (9)

P (|ri,j|2 < ε) ≈ ε i 6= j

•

Γq =

r(N−2q+1)(N−2q+1) r(N−2q+1)(N−2q+2)

0 r(N−2q+2)(N−2q+2)

, q = 1, 2, ...,N

2(10)

• SNR of qth layer is ρN||Γq||2

• Diversity provided by Γq is equal to 4q.

• Outage performance is still dominated by diversity of first layer even in

absence of error propagation

• Ordering can improve performance

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Multiple-QR version

• Note that distinct QR decompositions can be obtained by permuting the

columns of R

• Maximum number of useful permutations is limited to Nqr = N2

• To maximize capacity and when the required Nqr <N2

choice of permutations

becomes important: optimum choice is based on average SNR

Nqr = /N = 4 6 8

1 (1, 2, 3, 4) (1, 2, 3, 4, 5, 6) (1, 2, 3, 4, 5, 6, 7, 8)

2 (3, 4, 1, 2) (5, 6, 1, 2, 3, 4) (7, 8, 5, 6, 3, 4, 1, 2)

3 N/A (3, 4, 5, 6, 1, 2) (5, 6, 7, 8, 1, 2, 3, 4)

4 N/A N/A (3, 4, 1, 2, 7, 8, 5, 6)

Table 2: Optimum permutations

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Description of Multiple-QR version

Figure 9: Description of the proposed algorithm with multiple QR decompositions

17


Simulation Results: Multiple-QR 8 x 8 i.i.d

Figure 10: FER of the various versions of the proposed algorithm for a 8 × 8 i.i.d

MIMO channel and a bandwidth efficiency of 16 bits/s/Hz

18


Comparison to MMSE-VBLAST: 4× 4 i.i.d

Figure 11: FER comparison between the multiple-QR version of our proposed al-

gorithm and that of MMSE-VBLAST for varying bandwidth efficiencies. 4× 4 i.i.d

channel

19


Comparison to MMSE-VBLAST: 8× 8 i.i.d


gorithm and that of MMSE-VBLAST for varying bandwidth efficiencies. 8× 8 i.i.d

channel

20


Comparison to MMSE-VBLAST: 8× 8 correlated


gorithm and that of MMSE-VBLAST for varying bandwidth efficiencies. 8 × 8

correlated channel. ψt = 0.7 and ψr = 0.2

21


Comparison to Hybrid Algorithms: Group STTC

• All reviewed hybrid algorithms use matrix inversion (noise amplification)

• GSTTC is chosen because STTC provides SNR in addition to diversity gain

(best performance)

• STTC is used at TX in groups of two and heuristic power allocation. ML

decoding is employed at RX (HV1).

• Same as (HV1) with optimized power allocation at TX (HV2).

• HV1 uses 64-state trellis code while HV2 uses 16-state trellis code.

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Comparison to Hybrid Algorithms: 4 x 4 i.i.d

Figure 14: FER comparison between the multiple-QR version of our proposed algo-

rithm and that of HV1 and HV2 for the same bandwidth efficiency of 4 bit/s/Hz

23


Comparison to Hybrid Algorithms: 8 x 8 i.i.d

Figure 15: FER comparison between the multiple-QR version of our proposed algo-

rithm and that of HV1 and HV2 for the same bandwidth efficiency of 8 bit/s/Hz

24


Complexity Analysis

• Number of complex multiplications and additions

• CMULT=4 FLOPS, CADD=2 FLOPS

• LTE is chosen as a representative 4G standard

Algorithm N = 4 N = 6 N = 8

MMSE-VBLAST 349184 1714176 5361664

SRAB 136192 435456 1003520

Proposed Algorithm 125104 504216 1389280

Table 3: Complexity comparison between MMSE-VBLAST, SRAB and the pro-

posed algorithm (with Nqr = N2

and two iterations) to process one RB when

Nsymb = 7

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Conclusion and Suggested Future Work

• MIMO channel offers enormous capacity

• Practical algorithms do not attain MIMO capacity

• MMSE-VBLAST offers a compromise between performance and complexity

• Alamouti offers linear processing but limited to the use of two TX antennas

• Proposed an algorithm that combines low-complexity benefits of QR

decomposition and Alamouti coding/decoding

• Algorithm’s complexity is comparable to a reduced-complexity version of

MMSE-VBLAST with the added advantage of having a parallel architecture

and does not need knowledge of variance

• Suggested future work:

- Replace Alamouti by full-diversity full-rate codes such as Golden code

- Leave some symbols uncoded

- Investigate effects of LOS and mobility

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Presentation Thesis