### 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 |
---|---|

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

**Binary-Tree Encoding for Uniform Binary Sources in Index Modulation Systems.** / Coon, Justin; Badiu, Mihai-Alin; Liu, Ye; Yarkin, Ferhat; Dang, Shuping.

Research output: Contribution to journal › Article

*IEEE Journal of Selected Topics in Signal Processing*, vol. 13, no. 6, 8704951, pp. 1270-1285. https://doi.org/10.1109/JSTSP.2019.2914531

}

TY - JOUR

T1 - Binary-Tree Encoding for Uniform Binary Sources in Index Modulation Systems

AU - Coon, Justin

AU - Badiu, Mihai-Alin

AU - Liu, Ye

AU - Yarkin, Ferhat

AU - Dang, Shuping

N1 - This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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.

AB - 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.

KW - Modulation

KW - Binary trees

KW - Encoding

KW - Probability distribution

KW - Indexes

KW - OFDM

KW - Optimization

KW - binary tree

KW - achievable rate

KW - mutual information

KW - index modulation

UR - http://www.scopus.com/inward/record.url?scp=85065436319&partnerID=8YFLogxK

U2 - 10.1109/JSTSP.2019.2914531

DO - 10.1109/JSTSP.2019.2914531

M3 - Article

VL - 13

SP - 1270

EP - 1285

JO - IEEE Journal on Selected Topics in Signal Processing

JF - IEEE Journal on Selected Topics in Signal Processing

SN - 1932-4553

IS - 6

M1 - 8704951

ER -