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A stack based tree searching method for the implementation of the List Sphere Decoder

A stack based tree searching method for the implementation of the List Sphere Decoder. ASP-DAC 2006 paper review Presenter : Chun-Hung Lai. Abstract.

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A stack based tree searching method for the implementation of the List Sphere Decoder

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  1. A stack based tree searching method for the implementation of the List Sphere Decoder ASP-DAC 2006 paper review Presenter : Chun-Hung Lai

  2. 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.

  3. Outline • What’s the problem • Introduction • Introduction and analysis of LSD algorithm • Proposed tree searching architecture for LSD • Conclusions • My comments

  4. What’s the Problem • Existing decoding algorithms for the Maximum likelihood (ML) detection is either high complexity or low efficiency • High complexity are hardly tobeimplemented • 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

  5. 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 incursperformance 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

  6. 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 …….. (1) m

  7. 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

  8. Operation numbers with no factorization • Operation numbers to select candidates in LSD with equation (1) 1

  9. Operation numbers with factorization • Operation numbers to select candidates in LSD with equation (4) • Multi-stage sequential decoding methodology (4) has smaller operation 4

  10. Operation sequence of LSD algorithm • The following is a 2*2 QPSK example(Nrx=2 and Ntx=2) Chosen from constellation value Number of constellation valueis 2 : Received vector : Candidate vector

  11. 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 chosen bysi(entry of candidate vector ) is ignored i=4 for s4 i=3 for s3 …. i=1 for s1

  12. Operation described by tree searching structure • Tree for the 2*2 QPSK MIMO system • Possible number of constellation value which are chosen bysiare 2 • Formal candidate vector= [-0.707 -0.707 -0.707 -0.707] Parallelizable -0.707 +0.707

  13. 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

  14. Tree searching sequence in 2*2 QPSK mode Proposed method parallelized calculation • 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 calculation Number of formal candidate vector to be selected is equal to 4

  15. Stack operation for tree searching sequence

  16. 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

  17. 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.

  18. 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 * * * * * * * * * *

  19. My comments • Low originality • List sphere decoder (LSD) uses multi-stage sequential decoding 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 chapter • Contribution • This paper is the first one to propose the hardware implementation of LSD algorithm I am inclined to reject this paper

  20. 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 Entry of received vector Constellation value If 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

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