Non-Coherent Multi-Level Index Modulation

Ali Fazeli, Ha H. Nguyen, Hoang Duong Tuan, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


This paper develops a non-coherent index modulation (IM) system in which activation patterns are characterized by multi-level block codes. We analyze performance of such a system under the maximum-likelihood (ML) receiver and when the set of activation patterns follows a multi-level code generated from asymptotically optimal alphabets. An asymptotic analysis of the pair-wise error probability (PEP) shows that the system can exploit a diversity order that is determined by the distance of the worst codeword pair in the $l_{1}$ metric, known as the Manhattan norm. We then explore the rate-diversity tradeoff for the developed non-coherent IM system as a function of the code length. Specifically, Gilbert-style bounds on the data rates for systems based on binary and ternary codes are obtained that can ensure a given diversity order. We approach the problem of packing in the l1 metric by partitioning codes into permutation modulation codes (PMCs) and obtaining Gilbert-style bounds on PMCs. Several achievable rates for non-coherent binary and ternary IM systems, as well as a tradeoff between the information rate and codeword error probability (CEP) are also derived. Finally, simulation results are provided to corroborate the theoretical analysis.

Original languageEnglish (US)
Pages (from-to)2240-2255
Number of pages16
JournalIEEE Transactions on Communications
Issue number4
StatePublished - Apr 1 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


  • Achievable rate
  • Diversity order
  • Index modulation
  • Non-coherent communication


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