### Abstract

The problem of designing bit-to-pattern mappings and power allocation schemes for orthogonal frequency-division multiplexing (OFDM) systems that employ subcarrier index modulation (IM) is considered. We assume that the binary source conveys a stream of independent, uniformly distributed bits to the pattern mapper, which introduces a constraint on the pattern transmission probability distribution that can be quantified using a binary tree formalism. Under this constraint, we undertake the task of maximizing the achievable rate subject to the availability of channel knowledge at the transmitter. The optimization variables are the pattern probability distribution (i.e., the bit-to-pattern mapping) and the transmit powers allocated to active subcarriers. To solve the problem, we first consider the relaxed problem where pattern probabilities are allowed to take any values in the interval [0, 1] subject to a sum probability constraint. We develop (approximately) optimal solutions to the relaxed problem by using new bounds and asymptotic results, and then use a novel heuristic algorithm to project the relaxed solution onto a point in the feasible set of the constrained problem. Numerical analysis shows that this approach is capable of achieving the maximum mutual information for the relaxed problem in low- A nd high-SNR regimes and offers noticeable benefits in terms of achievable rate relative to a conventional OFDM-IM benchmark.

Original language | English |
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Article number | 8704951 |

Pages (from-to) | 1270-1285 |

Number of pages | 16 |

Journal | IEEE Journal of Selected Topics in Signal Processing |

Volume | 13 |

Issue number | 6 |

Early online date | 2 May 2019 |

DOIs | |

Publication status | Published - 1 Oct 2019 |

Externally published | Yes |

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### Bibliographical note

This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/.### Keywords

- Modulation
- Binary trees
- Encoding
- Probability distribution
- Indexes
- OFDM
- Optimization
- binary tree
- achievable rate
- mutual information
- index modulation

### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering

### Cite this

*IEEE Journal of Selected Topics in Signal Processing*,

*13*(6), 1270-1285. [8704951]. https://doi.org/10.1109/JSTSP.2019.2914531