Skip to main content
SpringerLink
Log in

VLSI Implementations of Sphere Detectors

  • Chapter
  • First Online:
Advanced Hardware Design for Error Correcting Codes

  • 1180 Accesses

Abstract

The multiple input multiple output (MIMO) detection problem of an uncoded system can be considered as a so-called integer least squares problem, which can be solved optimally with a hard-output maximum likelihood (ML) detector [1]. The ML detector solves optimally the so-called closest lattice point problem by calculating the Euclidean distances (EDs) between the received signal vector and points in the lattice formed by the channel matrix and the received signal, and selects the lattice point that minimizes the Euclidean distance to the received vector [2]. The ML detection problem can be solved with an exhaustive search, i.e., checking all the possible symbol vectors and selecting the closest point. The ML detector achieves a full spatial diversity with regard to the number of receive antennas; however, it is computationally very complex and not feasible as the set of possible points increases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Hassibi B, Vikalo H (2005) On the sphere-decoding algorithm I. Expected complexity. IEEE Trans Signal Process 53(8):2806–2818

    Article  MathSciNet  Google Scholar 

  2. Paulraj A, Nabar RD, Gore D (2003) Introduction to space-time wireless communications. Cambridge University Press, Cambridge

    Google Scholar 

  3. Hochwald B, ten Brink S (2003) Achieving near-capacity on a multiple-antenna channel. IEEE Trans Commun 51(3):389–399

    Article  Google Scholar 

  4. Hagenauer J (1997) The turbo principle: tutorial introduction and state of the art. In: Proceedings of the international symposium on turbo codes, Brest, France

    Google Scholar 

  5. Hagenauer J, Offer E, Papke L (1996) Iterative decoding of binary block and convolutional codes. IEEE Trans Inf Theory 42(2):429–445

    Article  MATH  Google Scholar 

  6. Robertson P, Villebrun E, Hoeher P (1995) A comparison of optimal and sub-optimal MAP decoding algorithms operating in the log domain. In: Proceedings of the IEEE international conference on communications, pp 1009–1013

    Google Scholar 

  7. Damen MO, Chkeif A, Belfiore J-C (2000) Lattice code decoder for space-time codes. IEEE Commun Lett 4(5):161–163

    Article  Google Scholar 

  8. Murugan A, Gamal HE, Damen M, Caire G (2006) A unified framework for tree search decoding: rediscovering the sequential decoder. IEEE Trans Inf Theory 52(3):933–953

    Article  MATH  Google Scholar 

  9. Anderson T (1984) An introduction to multivariate statistical analysis, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  10. Anderson J, Mohan S (1984) Sequential coding algorithms: a survey and cost analysis. IEEE Trans Commun 32(2):169–176

    Article  Google Scholar 

  11. Agrell E, Eriksson T, Vardy A, Zeger K (2002) Closest point search in lattices. IEEE Trans Inf Theory 48(8):2201–2214

    Article  MATH  MathSciNet  Google Scholar 

  12. Fincke U, Pohst M (1985) Improved methods for calculating vectors of short length in a lattice, including a complexity analysis. Math Comput 44(5):463–471

    Article  MATH  MathSciNet  Google Scholar 

  13. Pohst M (1981) On the computation of lattice vectors of minimal length, successive minima and reduced basis with applications. ACM SIGSAM Bull 15:37–44

    Article  MATH  Google Scholar 

  14. Viterbo E, Boutros J (1999) A universal lattice code decoder for fading channels. IEEE Trans Inf Theory 45(5):1639–1642

    Article  MATH  MathSciNet  Google Scholar 

  15. Damen MO, Gamal HE, Caire G (2003) On maximum–likelihood detection and the search for the closest lattice point. IEEE Trans Inf Theory 49(10):2389–2402

    Article  MATH  Google Scholar 

  16. Myllylä M, Antikainen J, Juntti M, Cavallaro J (2007) The effect of LLR clipping to the complexity of list sphere detector algorithms. In: Proceedings of the annual Asilomar conference on signals, systems, and computers, Pacific Grove, 4–7 November 2007, pp 1559–1563

    Google Scholar 

  17. Wong K, Tsui C, Cheng RK, Mow W (2002) A VLSI architecture of a K-best lattice decoding algorithm for MIMO channels. In: Proceedings of the IEEE international symposium on circuits and systems, vol 3, Scottsdale, AZ, 26–29 May 2002, pp 273–276

    Google Scholar 

  18. Guo Z, Nilsson P (2006) Algorithm and implementation of the K-best sphere decoding for MIMO detection. IEEE J Sel Areas Commun 24(3):491–503

    Article  Google Scholar 

  19. Barbero L, Thompson J (2008) Extending a fixed-complexity sphere decoder to obtain likelihood information for turbo-MIMO systems. IEEE Trans Vehicular Technol 57(5):2804–2814

    Article  Google Scholar 

  20. Li M, Bougart B, Lopez E, Bourdoux A (2008) Selective spanning with fast enumeration: a near maximum-likelihood MIMO detector designed for parallel programmable baseband architectures. In: Proceedings of the IEEE international conference on communication, Beijing, China, 19–23 May 2008, pp 737–741

    Google Scholar 

  21. Guo Z, Nilsson P (2006) Algorithm and implementation of the K-best sphere decoding for MIMO detection. IEEE J Sel Areas Commun 24(3):491–503

    Article  Google Scholar 

  22. Ketonen J, Myllylä M, Juntti M, Cavallaro JR (2008) ASIC implementation comparison of SIC and LSD receiver for MIMO-OFDM. In: Proceedings of the annual Asilomar conference on signals, systems, and computers, Pacific Grove, 25–29 October 2008, pp 1881–1885

    Google Scholar 

  23. Schnorr CP, Euchner M (1994) Lattice basis reduction: improved practical algorithms and solving subset sum problems. Math Program 66(2):181–191

    Article  MATH  MathSciNet  Google Scholar 

  24. Ketonen J, Juntti M, Cavallaro J (2010) Performance-complexity comparison of receivers for a LTE MIMO-OFDM system. IEEE Trans Signal Process 58(6):3360–3372

    Article  MathSciNet  Google Scholar 

  25. Myllylä M, Juntti M, Cavallaro JR (2007) Implementation aspects of list sphere detector algorithms. In: Proceedings of the IEEE global telecommunication conference, Washington, D.C., 26–30 November 2007, pp 3915–3920

    Google Scholar 

  26. Martin G, Smith G (2009) High-level synthesis: past, present, and future. IEEE Des Test Comput 26(4):18–25

    Article  Google Scholar 

  27. Casseau E, Gal L, Bomel P, Jego C, Huet S, Martin E (2005) C-based rapid prototyping for digital signal processing. In: Proceedings of the European signal processing conference, Antalya, Turkey, 4–8 September 2005

    Google Scholar 

  28. Cong J, Liu B, Neuendorffer S, Noguera J, Vissers K, Zhang Z (2011) High-level synthesis for FPGAs: from prototyping to deployment. IEEE Trans Comput Aided Des Integr Circuits Syst 30(4):473–491

    Article  Google Scholar 

  29. Calypto (2014) Catapult C synthesis overview. Technical report. http://calypto.com/en/products/catapult/overview

  30. Ketonen J (2012) Equalization and channel estimation algorithms and implementations for cellular MIMO-OFDM downlink. Ph.D. dissertation, Acta Univ. Oul., C Technica 423, University of Oulu, Oulu

    Google Scholar 

  31. Myllylä M (2011) Detection algorithms and architectures for wireless spatial multiplexing in MIMO–OFDM systems. Ph.D. dissertation, Acta Univ. Oul., C Technica 380, University of Oulu, Oulu

    Google Scholar 

  32. Preyss N, Burg A, Studer C (2012) Layered detection and decoding in MIMO wireless systems. In: Conference on design and architectures for signal and image processing (DASIP), Karlsruhe, Germany, 23–25 October 2012, pp 1–8

    Google Scholar 

  33. Mohan S, Anderson JB (1984) Computationally optimal metric-first code tree search algorithms. IEEE Trans Commun 32(6):710–717

    Article  MATH  Google Scholar 

  34. Dijkstra EW (1959) A note on two problems in connexion with graphs. In: Numerische Mathematik, vol 1. Mathematisch Centrum, Amsterdam, pp 269–271

    Google Scholar 

  35. Knuth D (1997) The art of computer programming. Volume 3: sorting and searching, 3rd edn. Addison-Wesley, Reading

    Google Scholar 

  36. Baro S, Hagenauer J, Witzke M (2003) Iterative detection of MIMO transmission using a list-sequential (LISS) detector. In: Proceedings of the IEEE international conference on communications, vol 4, pp 2653–2657

    Google Scholar 

  37. Xu W, Wang Y, Zhou Z, Wang J (2004) A computationally efficient exact ML sphere decoder. In: Proceedings of the IEEE global telecommunication conference, vol 4, 29 November – 3 December 2004, pp 2594–2598

    Google Scholar 

  38. Hagenauer J, Kuhn C (2007) The list-sequential (LISS) algorithm and its application. IEEE Trans Commun 55(5):918–928

    Article  Google Scholar 

  39. Studer C, Burg A, Bolcskei H (2008) Soft-output sphere decoding: algorithms and VLSI implementation. IEEE J Sel Areas Commun 26(2):290–300

    Article  Google Scholar 

  40. Burg A, Borgmanr M, Wenk M, Studer C, Bolcskei H (2006) Advanced receiver algorithms for MIMO wireless communications. In: Proceedings of the design, automation and test in Europe (DATE’06), vol 1, March 2006, 6 pp

    Google Scholar 

  41. Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Introduction to algorithms. MIT Press, Cambridge

    MATH  Google Scholar 

  42. Ullman J (1994) Computational aspects of VLSI. Computer Science Press, Rockville

    Google Scholar 

  43. Bajwa RS, Owens R, Irwin M (1994) Area time trade-offs in micro-grain VLSI array architectures. IEEE Trans Comput 43(10):1121–1128

    Article  MATH  Google Scholar 

  44. Sun Y, Cavallaro JR (2009) High throughput VLSI architecture for soft-output MIMO detection based on a Greedy graph algorithm. In: ACM great lakes symposium on VLSI design, May 2009, pp 445–450

    Google Scholar 

  45. Sun Y, Cavallaro JR (2012) High-throughput soft-output MIMO detector based on path-preserving trellis-search algorithm. IEEE Trans Very Large Scale Integr (VLSI) Syst 20(7):1235–1247

    Article  Google Scholar 

  46. Sun Y, Cavallaro JR (2012) Trellis-search based soft-input soft-output MIMO detector: algorithm and VLSI architecture. IEEE Trans Signal Process 60(5):2617–2627

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Communications Engineering, University of Oulu, Oulu, Finland

    Johanna Ketonen

  2. Nokia Networks, Nokia, Oulu, Finland

    Markus Myllylä

  3. ECE Department, Rice University, 6100 Main St., Houston, TX, 77005, USA

    Yang Sun & Joseph R. Cavallaro

Authors
  1. Johanna Ketonen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Markus Myllylä
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yang Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Joseph R. Cavallaro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joseph R. Cavallaro .

Editor information

Editors and Affiliations

  1. Université de Bretagne Sud, Lorient, France

    Cyrille Chavet

  2. Université de Bretagne Sud, Lorient, France

    Philippe Coussy

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Ketonen, J., Myllylä, M., Sun, Y., Cavallaro, J.R. (2015). VLSI Implementations of Sphere Detectors. In: Chavet, C., Coussy, P. (eds) Advanced Hardware Design for Error Correcting Codes. Springer, Cham. https://doi.org/10.1007/978-3-319-10569-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-10569-7_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10568-0

  • Online ISBN: 978-3-319-10569-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation