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In this paper, we investigate new signal constellation pairs for mapping active subcarriers of the zero-padded trimode orthogonal frequency division multiplexing with index modulation (ZTM-OFDM-IM) systems. In the presented system, one of a constellation pair is the same as the one used in the previous work, and the other is a constellation larger than the one used in the previous work. It increases the minimum Euclidean distance between the subblocks of the ZTM-OFDM-IM system with new constellation pairs under the constraint of the same spectral efficiency. Computer simulation in AWGN and frequency-selective fading channels shows that the new ZTM-OFDM-IM system has a much lower bit error rate than OFDM-IM and dual-mode OFDM-IM and slightly outperforms the system with conventional constellation pairs. Since the proposed constellation pairs prove the error performance improvement of the system, it is considered that a further study on generalized design of the constellation pair for the ZTM-OFDM-IM system is necessary in the future.

Due to its large capacity, high spectral efficiency, and robustness against frequency-selective fading [

To accommodate the requirements for high spectral and energy efficiencies, a lot of studies on index modulation (IM) have been carried out. In the IM scheme, a part of indexed resources are activated and used for data transmission [

As a compromise between spectral efficiency and energy efficiency, the zero-padded trimode OFDM-IM (ZTM-OFDM-IM) system has been proposed in [

In this paper, we introduce new constellation pairs to improve error performance of the ZTM-OFDM-IM system. Here, one of the two mappers used to map active subcarriers uses the same signal constellation as the one used in the previous work, while the other uses a larger constellation than the one used in [

The rest of this paper is organized as follows. The transceiver models of the OFDM systems with the IM scheme are briefly introduced in Section II. In Section III, the new pairs of constellations are discussed in detail. Performance of the proposed ZTM-OFDM-IM system is analyzed in Section IV. Finally, some conclusions are provided in Section V.

There are three typical index modulation schemes for the OFDM system. The OFDM-IM and DM-OFDM-IM can be considered as special cases of the ZTM-OFDM-IM system. The typical transmitter structure of the ZTM-OFDM-IM is shown in Figure

The transmitter structure of the ZTM-OFDM-IM system.

The

According to the

Each

The index selector uses

Except for the subcarrier indexing method, the OFDM-IM and the DM-OFDM-IM have the same functional structures as the ZTM-OFDM-IM. In the OFDM-IM scheme, only one constellation is used to generate active subcarriers. It is equivalent to the ZTM-OFDM-IM system with

The OFDM system with an index modulation scheme also performs

Suppose that the transmission environment is a frequency-selective Rayleigh fading channel of which the impulse response is

The maximum likelihood (ML) detector is used to minimize the Euclidean distance between the estimated subblocks and the received subblocks. The estimation of the

When an ML detector is exploited, error performance of the ZTM-OFDM-IM system depends largely on the MED between different OFDM subblocks. The Euclidean distance between two subblocks can be defined as

The constellation pair proposed in this paper is compared with the one in [

The constellation pair with

The new constellation pair with

Supposed that the number of subcarriers

The parameters for IM schemes when

Modulation | Constellation | |||||||
---|---|---|---|---|---|---|---|---|

ZTM-OFDM-IM | Previous (Figure | 2 | 2 | 4 | 2 | 1 | 6 | 2.309 |

Proposed (Figure | 2 | 4 | 4 | 1 | 1 | 6 | 2.667 | |

DM-OFDM-IM | 2 | 2 | 4 | 2 | 2 | 6 | 1.633 | |

IM-OFDM-IM | 16-QAM | 4 | 6 | 1.461 |

When the spectral efficiency is 2.222 bit/s/Hz, a constellation pair shown in Figure

The previous constellation pair with

The new constellation pair with

The parameters for IM schemes when

Modulation | Constellation | |||||||
---|---|---|---|---|---|---|---|---|

ZTM | Previous (Figure | 4 | 8 | 4 | 2 | 1 | 10 | 1.812 |

Proposed (Figure | 4 | 8 | 4 | 2 | 1 | 10 | 1.886 | |

DM | Figure | 4 | 4 | 4 | 2 | 2 | 10 | 1.371 |

IM | 16-QAM | 4 | 10 | 1.333 |

To evaluate performance of the proposed constellation pairs for the ZTM-OFDM-IM system, computer simulation has been carried out. The parameters presented in Tables

BERs of the OFDM systems with the IM scheme in the AWGN and frequency-selective Rayleigh fading channels are plotted in Figures

BERs in the AWGN channel when

BERs in the Rayleigh fading channel when

As a result, the ZTM-OFDM-IM system with the recommended constellation pair shows better error performance than the previous system. When the signal-to-noise ratio (SNR) is lower than 8.5 dB in the AWGN environment, it can be observed that the DM-OFDM-IM system has better error performance than other systems as shown in Figure

In the Rayleigh fading channel, both ZTM-OFDM-IM systems have almost the same BER. However, it can be observed that those systems still have a performance gain of about 3.0 dB and 5.5 dB, respectively, compared to the DM-OFDM-IM and OFDM-IM systems at a reference BER of

When the spectral efficiency is increased to 2.222 bit/s/Hz, the simulation results in the AWGN and Rayleigh fading channels are plotted in Figures

BERs in the AWGN channel when

BERs in the Rayleigh fading channel when

Similar to Figure

This paper introduces new signal constellation pairs which improve the error performance of the ZTM-OFDM-IM system. In the presented system, one of the two mappers for mapping active subcarriers uses the same signal constellation as the one used in the previous work, and the other exploits a constellation larger than the one used in [

As a result of simulation in ideal AWGN and frequency-selective Rayleigh fading channel environments, the ZTM-OFDM-IM system with the proposed constellation pairs has much lower BER than the typical OFDM system with IM scheme such as OFDM-IM and DM-OFDM-IM. In addition, the new ZTM-OFDM-IM system shows slightly better performance than the same system with the conventional constellation pairs. The new constellation pairs proposed in this paper increase the MED between subblocks, demonstrating the possibility of improving error performance of the ZTM-OFDM-IM system. Hence, it is considered that a further study on generalized design of the constellation pairs for the mappers of the ZTM-OFDM-IM system is necessary in the future. In addition, another investigation on the IM-based OFDM system is necessary to further improve spectral and energy efficiencies while suppressing system complexity.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.