Information-bearing noncoherently modulated pilots for MIMO training

Yingqu Yu, Georgios B. Giannakis, Nihar Jindal

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this correspondence, we deal with noncoherent communications over multiple-input-multiple-output (MIMO) wireless links. For a Rayleigh flat block-fading channel with M transmit- and N receive-antennas and a channel coherence interval of length T, it is well known that for T ≫ M, or, at high signal-to-noise-ratio (SNR) p ≫ 1 and M ≤ min {N, {⌊T/2cg⌋}, unitary space-time modulation (USTM) is capacity-achieving, but incurs exponential demodulation complexity in T. On the other hand, conventional training-based schemes that rely on known pilot symbols for channel estimation simplify the receiver design, but they induce certain SNR loss. To achieve desirable tradeoffs between performance and complexity, we propose a novel training approach where USTM symbols over a short length TT (< T) are used as pilots which carry information to the receiver, and coherent communication is used for the remainder of the block. This new approach considerably reduces the receiver complexity when T is a small fraction of T, and recovers part of the SNR loss experienced by the conventional training-based schemes. When p → ∞ and T ≥ TT ≥ 2M = 2N → ∞, but the ratios α = M/T, α1 = TT/T are fixed, we obtain analytical expressions of the asymptotic SNR loss for both the conventional and new training-based approaches, serving as a guideline for practical designs.

Original languageEnglish (US)
Pages (from-to)1160-1168
Number of pages9
JournalIEEE Transactions on Information Theory
Issue number3
StatePublished - Mar 2007

Bibliographical note

Funding Information:
Manuscript received May 11, 2005; revised September 13, 2006. This work was supported in part by the ARL/CTA under Grant DAAD19-01-2-0011. This work was prepared 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 DAAD19-01-2-0011. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon.


  • Capacity
  • Channel estimation
  • Coherent detection
  • Multiple antennas
  • Noncoherent detection
  • Unitary space-time modulation

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