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A stack based tree searching method for the implementation of the List Sphere Decoder
ASP-DAC 2006 paper reviewPresenter : Chun-Hung Lai
112/04/19 A stack based tree searching method for the implementation of the List Sphere Decoder 2/20
Abstract
Maximum likelihood (ML) detection is an optimal solution for the MIMO communication system. List Sphere detector (LSD) is attractive to approach the performance of the ML detector. This paper proposed a VLSI architecture of the tree searching block, which is an essential part of the LSD. The implemented result with 0.25 cell library is 276270 equivalent gates for the 4*4 64QAM. And the area for this design is 3741358 um.
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Outline
What’s the problem Introduction Introduction and analysis of LSD algorithm Proposed tree searching architecture for LSD Conclusions My comments
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What’s the Problem
Existing decoding algorithms for the Maximum likelihood (ML) detection is either high complexity or low efficiency High complexity are hardly to be implemented
Area cost and power consumption are inefficient
So, a practical VLSI architecture with low complexity and high performance becomes the key issues for the lattice decoding point of view
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Introduction
Several VLSI architectures are proposed for the ML detection Sphere Decoder (SD)
Computationally efficient, but high complexity K-best architecture
Reduces SD’s high hardware resource usages, but incurs performance degradation
Recently, List Sphere Decoding (LSD) algorithm is proposed Both low complexity and high performance
This paper proposed An VLSI architecture of tree searching method used in the LSD
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Linear model of MIMO system The received vector in the MIMO system can be represented y= Hs + n
( H is Nrx * Ntx channel matrix) Nrx: the number of receive antennas Ntx: the number of transmit antennas ( s=[s1 s2 …sNtx] is the Ntx dimensional transmitted signal vector)
The entries of s are chosen from some complex constellation
( n is the additive noise vector) An optimal method to minimize error of the transmitted signal
Using ML detection at the receiver
Q is the set of all possible transmitted vector Needs an exhaustive search and complexity grow exponentially
Ex: In 2*2 MIMO system with 16-QAM modulation
16*16*16*16=65536 transmitted vector need to be considered
m…….. (1)
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LSD model for the MIMO system
The List Sphere Decoding (LSD) avoids exhaustive search and examining only those points that lie inside a sphere
Using QR factorization of channel matrix H=QU equation (2) can be rewritten to equation (3)
Matrix U is the QR factorized upper-triangular matrix
If the number of transmit antennas is equal to receive antennas
…….. (2)
…….. (3)Further writing
…….. (4)
is equal to 0
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Operation numbers with no factorization Operation numbers to select candidates in LSD with
equation (1)
1
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Operation numbers with factorization Operation numbers to select candidates in LSD with e
quation (4)
Multi-stage sequential decoding methodology (4) has smaller operation
4
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Operation sequence of LSD algorithm The following is a 2*2 QPSK example (Nrx=2 and Ntx=2)
: Received vector
: Candidate vector
Chosen from constellation value
Number of constellation value is 2
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Multi-stage sequential decoding
4 steps in 2*2 QPSK mode
The distance is calculated at each step and compared with r If the condition is not satisfied, this constellation value which are chos
en by si (entry of candidate vector ) is ignored
i=4 for s4
i=3 for s3
i=1 for s1
….
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Operation described by tree searching structure Tree for the 2*2 QPSK MIMO system
Possible number of constellation value which are chosen by si are 2
Formal candidate vector = [-0.707 -0.707 -0.707 -0.707]
Parallelizable
-0.707 +0.707
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Block diagram of proposed tree searching method
If the calculated distance at the last step is stall smaller than the expected radius, this formal candidate vector is moved to the mem_ctl block
8 parallelized calculation units
Each unit calculates the distance of candidates for the specific step
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Tree searching sequence in 2*2 QPSK mode
The number in each circle represents the depth and order of the constellation
The latency to select all formal candidate vector Parallelized calculation: 6 Non-parallelized calculation: 12
Non-parallelized calculationProposed method
parallelized calculation
Number of formal candidate vector to be selected is equal to 4
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Stack operation for tree searching sequence
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Accumulated operations in the stack for the worst case
Analyzed for the case of 4*4 64QAM MIMO system There are 8 constellation values The calculation step is 2Nrx=2*4=8
Worst case Popped one operation and pushed 8 operations at each step So, the required depth of stack is about 50
Increase 7 at each step
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Conclusions
Proposed a stack based tree searching architecture for the LSD algorithm Two main characteristics
Parallelization Reduced the latency of searching sequence
Memory based Made the design very simple
The implemented codes are synthesized with 0.25 cell library. It has 276270 gates and 3741358 um area.
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Grade to my review paper
Excellent good average not-good unacceptable
A. Overall score B. Overall technical contents
B.1 originality, novelty B.2 significance of results B.3 readability
C. Overall presentation C.1 English usage C.2 clarity C.3 adequacy of references
D. Confidence on your decision
**
*****
**
*
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My comments
Low originality List sphere decoder (LSD) uses multi-stage sequential dec
oding are proposed by [10] Illustration and explanation is insufficient
Many figures are ambiguous to understand, however the writer does’t explain in detail
Many errors Misspell in grammar, index error in formula, index error in c
hapter Contribution
This paper is the first one to propose the hardware implementation of LSD algorithm
I am inclined to reject this paper
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Visualization of the List Sphere Decoding 16 constellation value within 16-QAM modulation
The entry of candidate vector [s1 s2…sNtx] are chosen from those constellation value
Constellation valueIf the distance between the received vector and the candidate vector is less than the expected radius r then this constellation value are really considered by the formal candidate vector
Entry of received vector