Orthogonal frequency division multiplexing is one of the efficient and flexible modulation techniques, and which is considered as the central part of many wired and wireless standards. Orthogonal frequency division multiplexing (OFDM) and multiple-input multiple-output (MIMO) achieves maximum spectral efficiency and data rates for wireless mobile communication systems. Though it offers better quality of services, high peak-to-average power ratio (PAPR) is the major issue that needs to be resolved in the MIMO-OFDM system. Earlier studies have addressed the high PAPR of OFDM system using clipping, coding, selected mapping, tone injection, peak windowing, etc. Recently, deep learning (DL) models have exhibited improved performance on channel estimation, signal recognition, channel decoding, modulation identification, and end-to-end wireless system. In this view, this paper presents a new Hyperparameter Tuned Deep Learning based Stacked Sparse Autoencoder (HPT-SSAE) for PAPR Reduction Technique in OFDM system. The proposed model aims to substantially reduce the peaks in the OFDM signal. The presented HPT-SSAE model is utilized to adaptively create a peak-canceling signal based on the features of the input signal. In the HPT-SSAE model, the constellation mapping and demapping of symbols take place on every individual subcarrier adaptively using the SSAE model in such a way that bit error rate (BER) and the PAPR of the OFDM systems are cooperatively diminished. Besides, to enhance the performance of the SSAE model, the hyperparameter tuning process takes place using monarch butterfly optimization (MBO) algorithm. A comprehensive set of simulations were performed to highlight the supremacy of the HPT-SSAE model. The obtained experimental values showcased the betterment of the proposed model over the compared methods interms of bit error rate (BER), complementary cumulative distribution function (CCDF), and execution time.

Advanced development in new wireless communication technologies has resulted in an increasing need for higher data rate owing to the familiarity of multimedia services, like real-time streaming media, games, and other social media services. Since these requirements result in maximum bandwidth technologies [

The integration of OFDM with Multiple-Input Multiple-Output (MIMO) wireless communication system leads to the design of MIMO-OFDM system [

With the recently available commercial wireless system, the PAPR problem is highly important in uplink [

An inclination in 5G allows high frequency bands to attain extra unused spectrum, and several researches have been carried out to accomplish it [

This paper develops a novel Hyperparameter Tuned Deep Learning based Stacked Sparse Autoencoder (HPT-SSAE) for PAPR Reduction Technique in OFDM system. The goal of the proposed HPT-SSAE model is to train the network in such a way as to minimize PAPR with no degradation of the BER. The presented HPT-SSAE model is employed to dynamically generate a peak-canceling signal depending upon the characteristics of the input signal. For further improving the efficiency of the SSAE model, the hyperparameters can be tuned by the use of monarch butterfly optimization (MBO) algorithm. Extensive experimental analysis of the HPT-SSAE model takes place to point out the betterment of the HPT-SSAE model. In short, the contribution of the paper is given as follows.

Propose a new HPT-SSAE based PAPR Reduction Technique for OFDM system

Aims to substantially reduce the peaks in the OFDM signal

Employ SSAE model for the peak cancelling signal generation

Perform hyperparameter tuning of SSAE model using MBO algorithm

Validate the results of the HPT-SSAE model interms of different measures.

Al-Jawhar et al. [

In Wang et al. [

Sohn et al. [

For reducing the high PAPR, a PTS model depending upon the adaptive particle swarm optimization (PSO) algorithm is presented [

In Wang et al. [

A paper for publication should be divided into multiple sections: a Title, Full names of all the authors including their affiliations, a concise Abstract, a list of Keywords, Main text (including figures, equations, and tables), Acknowledgments, Funding Statement, Conflict of Interests, References, and Appendix. The suggested length of a manuscript is 10 pages. Each page in excess of 15 will be charged an extra fee. The transmission of signal using transceiver depending upon OFDM systems is a commonly employed technique. It partitions the efficient spectrum channels as to a set of orthogonal subchannels with equivalent bandwidth, every individual sub-channel autonomously manages the individual data utilizing separate subcarrier. In addition, the OFDM signals are the total of every independent subcarrier. With the multi-carrier signal transmission system, the input data of binary sequence undergo mapping to a set of symbols through a modulation technique. Next, the

where

In

SSAE is a NN comprised of multiple SAEs connected in an end-to-end way. The output of the preceding layer of sparse self encoder is utilized as the input of the subsequent layer of self-encoder, therefore higher-level feature illustrations of an input data are achieved. A greedy layerwise pretraining model is utilized for the sequential training of all layers of SSAE for accessing the optimization connection weights as well as bias values of the whole SSAE network.

Afterward, the error backpropagation (BP) technique is utilized for fine-tuning the SSAE till the outcome of error function among the input as well as output data fulfills the predictable necessities, in order to get the better parameter model. The error function

So, the upgraded model of the weight as well as bias are given as follows:

where

Assume that there are sparse restraints from the SSAE model, it requires utilizing several rates of learning for various parameters like decreasing the frequency of upgrade to infrequent features.

In the SSAE, the encoding of the input data takes place at the constellation plane by the use of the encoder of SSAE, comprised of

The recreated symbol at the receiving end

where

In order to tune the parameters of the SSAE model, MBO technique is used. The MBO technique is a population based technique which belongs to the classification of SI techniques that are stimulated by the nature of specific species with swarm tendencies like bees, butterflies, etc. As above mentioned, the MBO was currently proposed by Wang et al. [

Each butterfly from the population is either existing in land1 (the home beforehand migration) or in land2 (the home afterward migration).

All children of every butterfly is made by the migration operator, nevertheless either the parent is existing in land1 or 2.

The population shouldn’t alter and must be continuous forever, thus between 2 (novel child or parent) would be detached by a fitness function.

The butterfly is chosen depending upon fitness function are moved to the succeeding round and hasn’t been altered by the migration operator.

The butterfly starts migration initially in April if they exit land1 and head to land2, and the inverse migration starts in September. The overall monarch butterflies in the lands denote the entire population that is termed as NP.

The migration procedure of the butterfly is demonstrated as:

where

where peri denotes migration period time. Alternatively, when

where

With these techniques, the tradeoff among the way of migration from land1 to land2 is attained by adapting the ratio of

where

where BAR denotes the adaptation rate of butterfly and

where

Alternatively, when the rand is larger than BAR, the novel position is upgraded as:

The HPT-SSAE model undergoes effective training process to decrease PAPR and avoid the degradation of BER. Initially, the HPT-SSAE is required for reconstructing the broadcast signal from the received signal ensured that the BER remains same. Next, the HPT-SSAE produces a transmission signal which exhibits minimum PAPR [

where

Here, the training process takes place on two levels. During the initial level of training, the correct corruption level,

where

In this section, a detailed set of simulations were performed to highlight the better performance of the HPT-SSAE model with other existing methods such as original OFDM, with GA, and with FSO algorithms. The results are examined under different subcarriers such as 128, 256, and 512.

^{–0.73} whereas the OFDM, with-GA, and with-FSO algorithms have demonstrated an increased BER of 10^{–0.44}, 10^{–0.56}, and 10^{–0.62} respectively.

Moreover, on determining the results with respect to SER, the experimental result represented that the OFDM technique has shown insignificant performance over all the other models by attaining higher SER. Simultaneously, the with-GA method has accomplished slightly decreased SER over the OFDM approach whereas even increased SER has been achieved by the with-FSO model. But the proposed HPT-SSAE model has resulted in effective performance and achieved a minimum SER. The HPT-SSAE model has reached the least SER of 10^{–0.61} whereas the OFDM, with-GA, and with-FSO techniques have outperformed an improved SER of 10^{–0.11}, 10^{–0.45}, and 10^{–0.53} correspondingly. Lastly, on determining the outcomes interms of CCDF, the experimental result indicated that the OFDM model has depicted insignificant performance over all the other techniques by obtaining superior CCDF. Likewise, the with-GA algorithm has accomplished somewhat reduced CCDF over the OFDM model whereas even higher CCDF has been reached by the with-FSO algorithm. But the proposed HPT-SSAE model has resulted in effective performance and achieved a lesser CCDF. The HPT-SSAE approach has achieved a minimum CCDF of 5.8 dB whereas the OFDM, with-GA, and with-FSO methods have outperformed an increased CCDF of 11 dB, 6.2 dB, and 7 dB correspondingly.

^{–1.56} whereas the OFDM, with-GA, and with-FSO techniques have demonstrated a maximum BER of 10^{–0.56}, 10^{–0.98}, and 10^{–1.35} respectively. On measuring the outcomes interms of SER, the experimental result represented that the OFDM technique has illustrated insignificant performance over all the other methods by achieving superior SER. Similarly, the with-GA method has accomplished somewhat reduced SER over the OFDM model whereas even improved SER has been reached by the with-FSO algorithm. But the presented HPT-SSAE manner has resulted in effective performance and achieved a minimal SER. The HPT-SSAE technique has reached the least SER of 10^{–0.75} whereas the OFDM, with-GA, and with-FSO algorithms have demonstrated an increased SER of 10^{–0.42}, 10^{–0.57}, and 10^{–0.62} correspondingly. At last, on determining the results with respect to CCDF, the experimental outcome shown that the OFDM model has displayed insignificant performance over all the other methods by attaining higher CCDF. Concurrently, the with-GA method has accomplished slightly decreased CCDF over the OFDM approach whereas even improved CCDF has been attained by the with-FSO model. However, the proposed HPT-SSAE methodology has resulted in effective performance and achieved a minimal CCDF. The HPT-SSAE model has reached the least CCDF of 5.2 dB whereas the OFDM, with-GA, and with-FSO techniques have demonstrated a maximum CCDF of 11 dB, 7.2 dB, and 6 dB respectively.

^{–2.11} whereas the OFDM, with-GA, and with-FSO algorithms have demonstrated an increased BER of 10^{–0.90}, 10^{–1.15}, and 10^{–1.35} respectively. On calculating the outcomes with respect to SER, the experimental result referred that the OFDM model has shown insignificant performance over all the other methods by attaining higher SER. At the same time, the with-GA algorithm has accomplished somewhat reduced SER over the OFDM model whereas even superior SER has been achieved by the with-FSO algorithm. But the projected HPT-SSAE model has resulted in effective performance and achieved a minimal SER. The HPT-SSAE algorithm has reached the least SER of 10^{–0.8} whereas the OFDM, with-GA, and with-FSO algorithms have outperformed a higher SER of 10^{–0.42}, 10^{–0.58}, and 10^{–0.62} correspondingly. Finally, on evaluating the results interms of CCDF, the experimental outcome indicated that the OFDM model has outperformed insignificant performance over all the other techniques by attaining higher CCDF. At the same time, the with-GA algorithm has accomplished slightly reduced CCDF over the OFDM approach whereas even improved CCDF has been obtained by the with-FSO algorithm. However, the proposed HPT-SSAE method has resulted in effective performance and achieved a minimal CCDF. The HPT-SSAE approach has reached the least CCDF of 5.3 dB whereas the OFDM, with-GA, and with-FSO techniques have showcased a higher CCDF of 11 dB, 5.8 dB, and 7 dB correspondingly.

For addressing the PAPR problem in OFDM systems, this paper has introduced a new HPT-SSAE model for PAPR reduction. The HPT-SSAE model is intended for the substantial reduction in the peaks in the OFDM signal with no degradation of the BER. The presented HPT-SSAE model is exploited to create a peak canceling signal dynamically depending upon the features of the input signal. In the HPT-SSAE model, the constellation mapping and demapping of symbol take place on every individual subcarrier dynamically using the SSAE model. In order to further enhancement in the efficiency of the SSAE model, the hyperparameters can be tuned by the use of MBO algorithm. Extensive experimental analysis of the HPT-SSAE model takes place to point out the betterment of the HPT-SSAE model. The obtained experimental outcomes pointed out that the HPT-SSAE model highlighted the superior performance over the other compared methods interms of different measures.