On an achievable rate of large rayleigh block-fading MIMO channels with no CSI

Keigo Takeuchi, Ralf R. Muller, Mikko Vehkaperä, Toshiyuki Tanaka

Research output: Contribution to journalArticleScientificpeer-review

27 Citations (Scopus)


Training-based transmission over Rayleigh block-fading multiple-input multiple-output (MIMO) channels is investigated. As a training method a combination of a pilot-assisted scheme and a biased signaling scheme is considered. The achievable rates of successive decoding (SD) receivers based on the linear minimum mean-squared error (LMMSE) channel estimation are analyzed in the large-system limit, by using the replica method under the assumption of replica symmetry. It is shown that negligible pilot information is best in terms of the achievable rates of the SD receivers in the large-system limit. The obtained analytical formulas of the achievable rates can improve the existing lower bound on the capacity of the MIMO channel with no channel state information (CSI), derived by Hassibi and Hochwald, for all SNRs. The comparison between the obtained bound and a high-SNR approximation of the channel capacity, derived by Zheng and Tse, implies that the high-SNR approximation is unreliable unless quite high SNR is considered. Energy efficiency in the low-SNR regime is also investigated in terms of the power per information bit required for reliable communication. The required minimum power is shown to be achieved at a positive rate for the SD receiver with no CSI, whereas it is achieved in the zero-rate limit for the case of perfect CSI available at the receiver. Moreover, numerical simulations imply that the presented large-system analysis can provide a good approximation for not so large systems. The results in this paper imply that SD schemes can provide a significant performance gain in the low-to-moderate SNR regimes, compared to conventional receivers based on one-shot channel estimation.
Original languageEnglish
Article number6532317
Pages (from-to)6517-6541
JournalIEEE Transactions on Information Theory
Issue number10
Publication statusPublished - 25 Sept 2013
MoE publication typeA1 Journal article-refereed


  • Biased signaling
  • large-system analysis
  • linear minimum mean-squared error (LMMSE) channel estimation
  • multiple-input multiple-output (MIMO) systems
  • noncoherent capacity
  • Rayleigh block-fading channels
  • replica method
  • successive decoding (SD)
  • training-based transmission


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