Approaching MIMO channel capacity with soft detection based on hard sphere decoding

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Hard sphere decoding (HSD) has well-appreciated merits for near-optimal demodulation of multiuser, block single-antenna or multi-antenna transmissions over multi-input multi-output (MIMO) channels. At increased complexity, a soft version of sphere decoding (SD), so-termed list SD (LSD), has been recently applied to coded layered space-time (LST) systems enabling them to approach the capacity of MIMO channels. By introducing a novel bit-level multi-stream coded LST transmitter along with a soft-to-hard conversion at the decoder, we show how to achieve the near-capacity performance of LSD, and even outperform it as the size of the block to be decoded (M) increases. Specifically, for binary real LST codes, we develop exact max-log-based SD schemes with M + 1 HSD steps, and an approximate alternative with only one HSD step to trade off performance for average complexity. These schemes apply directly to the real and imaginary parts of quaternary phase-shift keying signaling, and also to quadrature amplitude modulation signaling after incorporating an appropriate interference estimation and cancellation module. We corroborate our near-optimal soft detection (SoD) algorithms based on HSD (SoD-HSD) with simulations.

Original languageEnglish (US)
Pages (from-to)587-590
Number of pages4
JournalIEEE Transactions on Communications
Issue number4
StatePublished - Apr 2006

Bibliographical note

Funding Information:
Paper approved by N. C. Beaulieu, the Editor for Wireless Communication Theory of the IEEE Communications Society. Manuscript received August 5, 2003; revised December 6, 2004 and August 10, 2005. This work was supported through collaborative participation in the Communications and Networks Consortium sponsored by the U. S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD 19-01-2-0011. This paper was presented in part at the Wireless Communications and Networking ConferenceAtlanta, GA, March 2004.


  • Multi-input multi-output (MIMO) detection
  • Soft decoding
  • Sphere decoding
  • Turbo decoding


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