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Transcript of 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
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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)
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MIMO Capacity
Effect of Spatial Correlation
Figure 3: Effect of correlation on a N ×N MIMO capacity for ρ = 30 dB
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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
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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
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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
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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
12
Proposed Architecture and Associated Algorithms
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
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Proposed Architecture and Associated Algorithms
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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Proposed Architecture and Associated Algorithms
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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Proposed Architecture and Associated Algorithms
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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Proposed Architecture and Associated Algorithms
Description of Multiple-QR version
Figure 9: Description of the proposed algorithm with multiple QR decompositions
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Proposed Architecture and Associated Algorithms
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
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Proposed Architecture and Associated Algorithms
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
Proposed Architecture and Associated Algorithms
Comparison to MMSE-VBLAST: 8× 8 i.i.d
Figure 12: FER comparison between the multiple-QR version of our proposed al-
gorithm and that of MMSE-VBLAST for varying bandwidth efficiencies. 8× 8 i.i.d
channel
20
Proposed Architecture and Associated Algorithms
Comparison to MMSE-VBLAST: 8× 8 correlated
Figure 13: FER comparison between the multiple-QR version of our proposed al-
gorithm and that of MMSE-VBLAST for varying bandwidth efficiencies. 8 × 8
correlated channel. ψt = 0.7 and ψr = 0.2
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Proposed Architecture and Associated Algorithms
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.
22
Proposed Architecture and Associated Algorithms
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
Proposed Architecture and Associated Algorithms
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
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Proposed Architecture and Associated Algorithms
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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