Deep Learning-Based Index Modulation for Underground Communications

The world population is rapidly increasing, which in turn increases food needs. On the other hand, food production is the main cause of water withdrawal. Precision agriculture, based on the Internet of Underground Things (IoUT), has recently been proposed to reduce water withdrawals. IoUT comprises sensors and communication devices that are partially or fully submerged beneath the ground surface. However, the current technology used in IoUT is challenged by inefficient spectral and energy efficiency. This paper proposes a deep learning (DL)-based index modulation technique to increase spectral efficiency without raising the system’s bit error rate. The article decreases the peak-to-average power ratio (PAPR) and enhances energy efficiency by employing the X-transform time-domain synchronous index modulation (TDS-IM) orthogonal frequency division multiplexing (OFDM) in underground communication. Unlike the radio frequency channel, the underground channel is environment-dependent. Therefore, in this paper, we propose a DL receiver detector to eliminate such environmental dependency and simplify the system’s complexity. This proposal can establish new identification parameters, achieving accurate estimation of the modulated symbols even in harsh communication channels. The results of the simulation indicate the superior performance of the proposed scheme in terms of both spectral and energy efficiency compared to the benchmarks, as well as its ability to improve the system’s bit error rate.


I. INTRODUCTION
T HE INTERNET of Underground Things (IoUT)   operates through underground sensors, networking protocols, and communication technology to facilitate the seamless incorporation of sensing and communication in subterranean settings.This innovative concept empowers diverse applications such as agriculture, gas, seismic mapping, and border monitoring, necessitating the retrieval of critical data from deployed underground sensors.However, the demanding natural conditions below the surface, marked by sand, rock, and water, impose limitations on employing a singular communication technology for transmitting data between the surface and underground devices.As a result, various communication technologies are utilized for underground communications.Underground wireless communication primarily relies on acoustic, electromagnetic (EM), magnetic induction (MI), and optical waves.Conversely, wired technologies make use of coaxial cables and optical fibers [1].
Researchers predict a 31% increase in the world population by 2050 [1], which will consequently require additional physical supplies and food.With such population growth over the next three decades, an additional 71% of funds will also be needed [1].Food production alone accounts for 70% of water withdrawals [2].This escalating demand for resources necessitates the development of new technologies to facilitate the exploration of underground natural resources and increase crop production.The underground environment and agricultural lands possess a range of valuable natural resources, including fuels, fossils, minerals, groundwater, metal ores, and food.In order to effectively harness and utilize these resources, the IoUT emerges as a facilitating technology.It enables the creation of intelligent gas and oil fields, agricultural fields, and quality control systems for seismic activities.However, implementing IoUT presents significant challenges due to the demanding underground conditions.Consequently, the need arises for employing underground sensors that are low-power and compact, networking solutions, and long-range communication technology that are efficient, and precise techniques for localization.The aforementioned challenges and applications of IoUT drive intensive research efforts in the area of underground communication.IoUT differs from the terrestrial Internet of Things due to its reliance on soil as the communication medium.However, it should be noted that IoUT is not limited only to soil-based communication, as underground devices are sometimes deployed in open underground spaces like tunnels and mines.In such cases, the network configuration is still classified as underground while the air is used as the communication medium where conventional terrestrial communication technologies such as VCL and radio frequency (RF).
The underground environment presents heightened difficulties due to its diverse composition, including sand, rock, and water reservoirs.In the past, different approaches have been adopted to address underground communication requirements.For instance, mud pulse telemetry (MPT) communication techniques have been employed to observe the gas and oil industry [3].These MPT systems operate by leveraging mud circulation in pipes for communication [4].Unfortunately, MPT systems are limited to down-hole observation, and low-rate data transmission, which is usually measured in bits per second.Researchers are striving to enhance such limited data transmissions by employing wired options, including fiber optic and coaxial cables.These wired communication techniques are considered a successful alternative for achieving effective data rates, reliability, and precise solutions, especially when it comes to deep underground monitoring.As a result, connected technologies incorporating coaxial cables and optical fiber have been employed in numerous studies, such as [5], [6], [7] for down-hole monitoring.However, wired solutions are complex and not always accessible.Consequently, researchers have turned to wireless solutions to explore and provide high-data-rate, low-complexity, and scalable alternatives.
Unfortunately, the unique characteristics of the underground propagation medium pose significant challenges for efficient wireless communication at the physical (PHY) layer in underground scenarios.Apart from acoustic waves, three other primary PHY technologies are utilized in IoUT [8]: EM, MI, and VLC.Acoustic waves are employed for object discovery underground, soil humidity detection, and down-hole communications.However, acoustic-based IoUT encounters limitations such as low data rates, typically in the range of tens of bits per second for down-hole monitoring, and susceptibility to underground noise and attenuation.EM-IoUT employs frequency-based communication, relying on EM frequencies.The transmission range of EM signals can vary from a few meters at frequencies in the range of a few hundred kHz to centimeters in the terahertz (THz) frequency range.As a result, EM-IoUT is primarily applicable to agriculture applications [2].Nonetheless, EM-IoUT waves face significant path loss when propagating through the soil, resulting in a limited transmission range.Recently magnetic induction has emerged as a proposed solution for IoUT [9].Although the MI channel is a suitable option for underground environments, it faces limitations such as a restricted transmission range and the need for precise alignment between the transmitter and receiver coils.This alignment requirement poses a significant challenge in the underground environment [8].Consequently, MI-based IoUT is currently under research and encounters numerous challenges.The acoustic is the widest technology used in underground technology.In this paper, our focus will be on enhancing the drawbacks of acoustic-based IoUT, particularly in terms of spectral and energy efficiency.
One direct method to enhance the spectrum and energy efficiency of any communication system is through the utilization of higher-order modulations.However, increasing the modulation order used in transmission/receiving processing is a two-dimensional consideration problem.As the modulation order is made to be small, the frequency spacing for each symbol will be large and the system will be more resilient in bit error rate (BER); however, as the modulation order increases the spectral efficiency improves.To address the BER problem that arises from increasing the modulation order, this paper proposes two research directions.Firstly, DL-based semiperfect channel estimation techniques are suggested for equalization.Secondly, the paper explores the utilization of index modulation with time-domain synchronous orthogonal frequency division multiplexing (TDS-OFDM) based on the X-transform [10], [11].These two directions will improve the system throughput and provide the capabilities for acoustic-based IoUT data transmission.
On one hand, OFDM with Index Modulation (OFDM-IM) is an innovative communication technique that combines the principles of OFDM with the concept of index modulation [12], [13], [14].OFDM-IM takes advantage of the available subcarriers and their indices to convey additional information.Instead of transmitting data symbols directly on all subcarriers, some subcarriers are selectively activated while others remain idle, thereby introducing an index modulation scheme.This process allows OFDM-IM to achieve higher spectral efficiency and enhanced robustness in challenging communication scenarios.The receiver can exploit the presence or absence of subcarrier activations to decode the transmitted information accurately.OFDM-IM has received significant attention in recent years due to its potential to improve the performance of wireless communication systems, making it a popular paradigm for future wireless networks.
On the other hand, X-transform-based OFDM is a technique that improves the efficiency and performance of OFDM systems.It achieves this by replacing the discrete Fourier transform (DFT) used at the transmitting end with a low-complexity matrix known as the X-transform [15], [16], [17].The X-transform matrix is created by combining the DFT matrix and the Hartley transform matrix, resulting in a unified low-complexity unitary matrix.This replacement of the DFT with the X-transform matrix contributes to reducing computational complexity and removing the multipath effects while maintaining the unitary properties necessary for efficient signal processing in OFDM systems.However, it is still restricted by the need to perform the DFT and discrete Hartley transform (DHT) separately to enable frequency-domain channel estimation and equalization at the receiving end.Moreover, its sensitivity to the CFO effect increases because of the use of multiple transforms.
In this paper, we design acoustic-based IOUT nodes including a robust underground low-power index modulation technique [18], [19], [20], [21], [22] using X-transform [11], [15], [16] at the transmitter end and based DL [23], [24] at the receiving end.DL is used on the data collected from proposed underground nodes to an accurate prediction model for the underground soil environment.The use of X-transform at the transmitting end eases the DL to predict the time-domain received data leading to improving the limited data transmission of the acoustic-based IoUTs and enhancing the spectral and energy efficiency limitations of current technologies.This reliable communication system can help in fully monitoring the environment of soils and exploiting their natural resources.
The remaining sections of this paper are organized as follows: Section II provides an explanation of the system model for the proposed underground IoUT based on acoustic technology.Section III presents the theoretical analyses of the proposed DL IM-based detector.Section IV discusses and evaluates the proposed system performance via the underground channel.Finally, the conclusion is discussed in Section V.

II. UNDERGROUND ACOUSTIC-BASED IOUT TIME-DOMAIN SYNCHRONOUS IM-OFDM-SS
Fig. 1 illustrates the transmitter configuration of the proposed scheme.Notably, this paper introduces the concept of underground TDS-OFDM using the IM technique for the first time.The main target of the proposed scheme is to enhance the spectral and energy efficiency and, at the same time, to overcome the main impact of inter-block interference (IBI) that existed in conventional TDS-OFDM.Different from the index modulation OFDM spread spectrum (IM-OFDM-SS) systems presented in [25] the proposed system is specifically designed for underground communications, which presents unique challenges that require compensating for the PAPR, channel effects tracking, and synchronization.Consequently, our proposed modulation scheme incorporates several advancements and modifications that differentiate it from the scheme presented in [25].We have introduced novel algorithms and techniques to optimize various aspects of the system, including synchronization mechanisms, resource allocation, and equalization strategies.These enhancements enable our scheme to achieve enhanced performance in underground communication scenarios.Moreover, our work extends beyond the mere combination of the X-transform and TDS-OFDM as we address the issues of PAPR, channel estimation, and synchronization specifically in the harsh underground channel.We have conducted thorough research and analysis to tailor our scheme to the unique characteristics of underground environments, accounting for significant channel variations and impairments.Let's have B data bits to be transmitted in one OFDM symbol.To enable performing the IM, B is first divided using a bit splitter into G groups with g ∈ {1, . . ., G} has b bits; b = B/G and the IM are performed within b bits.Each group has further two sub-groups which are K (g) 1 is transmitted via the index of spreading code c i (g) ∈ C n×1 selected out of available predefined codes C = {c 1 , . . ., c n } following the incoming information bits, where i (g) ∈ {1, . . .n} indicates the index of the spreading codes for the g-th group.On the other hand, K (g) 2 are transmitted physically using modulation to yield a symbol s (g) ∈ χ , and χ represent any M-ary digital modulation having unit average power; so K (g) 2 = log 2 (M).Walsh or Zadoff-Chu (ZC) codes [15] can be chosen to produce c i (g) .Without loss of generality, this paper considers the Walsh code generated by n × n Walsh-Hadamard matrix given for n = 4 as follows: In equation ( 1), the k-th column represents the spreading code c k with a range of 1 ≤ k ≤ n.Thus, when spreading the modulated constellation symbols s (g) using the specific spreading code c i (g) selected based on the K (g) 1 , the resulting signal for the g-th group is given by [26], [27]: The N × 1 OFDM data block is generated by obtaining x g for all values of g, and subsequently interleaving them in the following manner: (1)  n , . . ., x (g) n T . ( Unlike conventional OFDM, the data symbols y is first multiplied by the DHT matrix D who's its (n, m)-entry can be given by a n,m = cos 2π nm N + sin 2π nm N .Then, the resultant N × 1 signal is modulated by the inverse DFT matrix F whose (k,n)-entry is given by f That process of -th symbol is expressed as follows: In ( 4), (.) H indicates the Hermitian operator, and X H = F H D is called the X-transform matrix [15], [16], [17], [28], [29].
Irrespective of the dimension of the X-transform matrix, each column contains a maximum of 2 non-zero values with identical amplitudes.Due to interleaved data symbols interleaving in (3), such interleaving can offer an attractive advantage represented by the independence of each group x (g) of the X-transform.Particularly, each couple of elements in x (g) will be multiplied by a small unitary 2 × 2 matrix which is 0.5 + j0.5 0.5 − j0.5 0.5 − j0.5 0.5 + j0.5 or 1 0 0 1 for the first pair of first x (g) .To achieve that goal, it's only required to interleave the elements of each x (g) group to the location's correspondent into the non-zero's values in the X-transform matrix.Therefore, that will lead to an efficient receiver based on DL to separately detect the carried information bits of each x (g)  [23], [24] as will be explained in Section III.Moreover, the X-transform is no longer necessary at the receiving end as the DL model only needs to estimate the small unitary matrix multiplied by each x (g) .This crucially eliminates the effects of IBI since the data will be processed in the time domain.
Different from the conventional OFDM schemes, TDS-OFDM uses PN as a guard interval as well as for channel and phase offset estimations.The baseband signal s ∈ N × 1 of the -th symbol is given by: where P ∈ M × 1 is the time-domain of the PN sequences P ∈ M ×1, and N = N + M. The pseudo-noise (PN) sequences are carefully chosen with specific auto-correlation characteristics and undergo preprocessing using inverse Fast Fourier Transform (IFFT).This preprocessing step reduces the amplitude of the PN sequence, subsequently minimizing the energy associated with the IBI effect that occurs between the PN sequence and the time-domain OFDM symbol.Mathematically, this process can be expressed as follows: where f is the frequency spacing.Then, s is converted to a passband before transmitting it through an underground channel.The passband signal can be expressed as: In ( 7) f c , g(t), T and Re(.), respectively, represent the carrier frequency, ADC/DAC combination, symbol time duration, and real part of (.).
The underground channel, which relies on acoustic signals, can be effectively represented by a time-varying impulse response.This impulse response, which characterizes the channel's behavior, is described in detail in [30]: where A ρ (t), denote the time-varying amplitudes of the path ρ, u ρ (t) = u ρ − β ρ t is the L multipath delay component, β ρ is the Doppler scalar factor (DSF) and δ(t) is the Dirac delta function.Therefore, the received passband signal through the underground channel when assuming all paths have the same DSF can be given as: where s(t) indicates the additive white Gaussian noise (AWGN).Fig. 2, shows the DL-based receiver structure of the proposed scheme.At the receiving end, synchronization and DSF estimation should be first performed based on r(t).Practically, probe signals are appended at the head and end of every frame for synchronization and DSF estimation.Hence, r(t) is cross correlated with those probe signals to estimate the length of the received signal B .Therefore, the estimated DSF β is found as: where B is the length of the transmitted signal which is well-known at the transmitting and receiving ends.r(t) is resampled at (1 + β )f s , f s is the ideal sampling frequency of the communications system.While this process effectively estimates and compensates for the integer CFO effect, a residual fractional CFO effect may arise due to passband/baseband conversions.To address this, the inserted PN sequences between symbols are utilized to track and compensate for the fractional CFO effect.In our proposed system, that fractional CFO effect can accurately be estimated and compensated using the DL-based receiver as shown shortly later.Therefore, the PN sequences at the receiving end can be expressed at 1+β 1+β = 1 as: where v(t) is the baseband AWGN, E = β−β 1+β f c is the frequency-independent Doppler shift and j is the channel gain at the j-th PN sample, The Ê can be found by exploring the property of z[ ] = z[ + N]e j2π EN for 0 < ≤ M − 1 as: After the compensation of Ê, the received PN equivalent to z[ ] is given by: At the receiving end, we know P ,j , allowing us to estimate the channel using equation (13).To simplify the process, we can make use of the IBI-free region for CS estimation without sacrificing generality [31], where the observation matrix Ψ is given using the last F = M−L + 1 sample of the received PN sequence as follows [31]: Selecting a sufficient length for M is imperative to mitigate the inter-symbol interference (ISI) since obtaining precise values for both L and accurate channel tracking from a region that is only corrupted by noise is not feasible.In order to estimate the time domain channel ĥ of each symbol, and without loss of generality, we employ the orthogonal matching pursuit (OMP) [31] as follows: Therefore, the received baseband signal r ∈ N × 1, after compensating the phase offset and discarding the guard interval, can be written as: In ( 16), H is a N × N Toeplitz matrix that describes the underground channel ĥ with (a, b)-entry is given by: At the receiver side, equalization is carried out to acquire y , and this paper utilizes the MMSE equalizer for this purpose.

III. DEEP LEARNING IM-BASED DETECTOR
The data symbol y is subject to mutual interference resulting from the interaction between the inserted PN sequence and the OFDM data blocks, as illustrated in Fig. 3.This mutual interference provides a severe IBI effect in underground communication, primarily due to the long-delayed time-variant nature of the channel.In terrestrial wireless systems, IBI is subtracted from the received data symbols, assuming a perfectly known or accurately estimated channel at the receiver.However, in underground communication, assuming a fully known channel at the receiver end is impractical as the channel cannot be accurately estimated.Consequently, researchers have made efforts to address the IBI issue in TDS-OFDM using PN sequences [31], [32].Unfortunately, the IBI effect persists and affects the transmitted data symbols.In this paper, thanks to the proposed DL-based receiver and IM techniques, the IBI is removed over a long-delay channel; to guarantee the IBI removal, it's assumed (L G), which is practically always correct.Although the direct adaptation for DL in underground communication is not always practical due to the time-variant nature of the acoustic-based underground channel, the proposed scheme starts recovering the effects of the channel before adapting the DL-based receiver.However, the IBI is partially affecting the timedomain signal as shown in Fig. 3 but performing the DFT

A. PROPOSED DL-BASED DETECTOR
The proposed DL model, depicted in Fig. 4, incorporates fully connected (FC) nonlinear layers.These layers of FC are specifically utilized with our DL-based detector.The first input layer consists of 3n nodes and the hidden layer consists of Q nodes which are carefully tuned to strike a balance between complexity and performance.The size of the output layer is set following the number of x (g) bits b.In the hidden layer, the rectifier linear unit (Relu) is employed as f Relu (x) = max(x, 0), while the output layer utilizes the Sigmoid function (Sig) with f Sig (x) = 1 1+ e −x to estimate the transmitted bits of each group d(g) .As the sigmoid function's output ranges between 0 and 1, a threshold is established to determine whether the output corresponds to 0 or 1.In this study, a threshold of 0.5 is set, designating the output as 0 if it is below 0.5, and as 1 otherwise.It is noteworthy that the output of the deep neural network (DNN) can be represented as: In ( 18), the weights and bias of the first and second hidden layers are, respectively, represented by p 1 , f 1 , and is the output of DL corresponding to the data bits carried by each group x (g) including the bits transmitted through the modulation order and bits transmitted via the index of spreading code.Therefore, the input data in the input layer is a concatenation of Re ŷ(g) , Im ŷ(g) and ŷ(g) 2  of each ŷ(g) extracted from the equalized data symbols y , ŷ(g) denotes the x (g) after performing the X-transform at the transmitting end or after multiplying it with the small unitary matrix explained previously.Im(.) is the imaginary part of (.).The output is the estimated information bits carried physically and via the index of the spreading code.This implies that symbols demapper is unnecessary within the presented scheme, thereby reducing the complexity of the estimation process.Moreover, the proposed (DL detector is independent of variations in the acoustic-based underground channel.Its primary function is to recover the M-ary data symbols bits and indices bits., rendering it robust to channel variations.

B. TRAINING PROCEDURE
To utilize the DNN model as a detector, it is necessary to train it offline [23], [24].During the training process, a random data sequence is generated utilizing a statistical underground channel [30], where various data symbols are generated randomly for transmission.The signal is then transmitted through the channel which is pre-processed as detailed in Section II.The collected data is then employed for DNN training, aiming to minimize the discrepancy between the signal that is detected by the DNN and the modulated symbols vector at the transmitter.The loss function is expressed in the following manner: In (19), d (g) denotes the original data bits of x (g) whose length is b (g) .Most importantly, the offline training process is almost independent of the channel due to the pre-processing of the channel shown in Section II.Moreover, the use of Xtransform at the transmitting end enables to deal with each ŷ(g) independently.That doesn't only reduce the complexity required for the DNN, but also the IBI effect will be handled in the time domain, leading to a focus on a small part of x (g) equivalent into x (g) /n.That also enables us to use the DNN model in online deployment without any extra training despite the time-variant underground channel.
For our training process, we employ adaptive moment estimation (Adam), an advanced optimization algorithm based on stochastic gradient descent (SGD).This allows us to effectively update the parameter θ = p, f as follows: where α and ∇ represent the learning rate and gradient operator respectively.The performance of the DL-based receiver is highly dependent on the signal-to-noise ratio (SNR) γ train .Therefore, careful selection of γ train is crucial to ensure optimal performance of the DL-based detector across various SNR conditions.Due to the utilization of spreading Walsh codes in the presented scheme, the DL-based detector exhibits improved performance, particularly when γ train dB is set to.

C. ONLINE DEPLOYMENT
During online deployment, the optimized θ obtained from offline training can be utilized for the DNN test stage.As a result, the arrived signal is pre-processed and fed into the DNN for real-time estimation of the transmitted bits.Our proposed detector which is based on deep learning does not need additional training for updating the θ parameter.Remarkably, our detector outperforms alternative approaches by eliminating IBI effects and achieving superior results without the need for further DNN model training.

IV. PERFORMANCE EVALUATION
This section evaluates the performance of the proposed scheme compared to its benchmarks ZP-PFDM [33], conventional TDS-OFDM [31], [34], ZPN-OFDM [32], and IM-OFDM-SS [25].The underground channel is adopted based on simulation statistics acoustic-based underground channel [30].The simulation parameters are shown in Table 1.During the training of the DL-based detector, 10 3 epochs were run, with each epoch consisting of 20 batches comprising 10 3 data samples each.A learning rate α of 10 −3 was utilized.The number of nodes of Q was set to 32, although it can be adjusted to achieve a tradeoff between the complexity and BER performance.

A. BER PERFORMANCE
The performance of BER is investigated in this subsection.To ensure a fair comparison, all schemes are configured so that they all have the same spectral efficiency.However, the proposed scheme achieves a higher spectral efficiency due to the utilization of inserted PN sequences for channel estimation, phase shift estimation, and guard interval purposes.As a result, pilot symbols are no longer necessary in the proposed scheme, leading to an additional N/4 spectral efficiency in comparison to the conventional ZP-OFDM.To maintain fairness in the comparison, channel estimation based on orthogonal matching pursuit (OMP) is performed for all schemes [31].TDS-OFDM, ZPN-OFDM, and the proposed scheme use IBI-free regions for channel estimation, while the ZP-OFDM uses pilot symbols.Fig. 5 shows the comparison of BER performance when conventional schemes employ the modulation order of binary phase shift keying (BPSK).The proposed and IM-OFDM-SS schemes employ quadrature phase shift keying (QPSK) with Walsh spreading code c i (g) whose length n = 4.
As shown, despite the higher spectral efficiency offered by the proposed DL-based TDS-IM-OFDM-SS scheme, it can offer up to 6 dB better performance at BER of 10 −3 .That performance superiority is because of the IM and DL techniques employed with X-transform-based OFDM.In particular, the DL detector allows us to detect the information bits based on the time-domain signal, effectively localizing the impact of IBI to a small portion of the time-domain signal.Consequently, only a fraction of each group x (g)  is affected by IBI.The DL-based detector has the capability to detect the information bits carried by each x (g)  based on the well-received portion.It also can estimate IBI effects and the residual CFO, which may not be accurately estimated at the receiver end.Furthermore, the utilization of the X-transform allows for maximum diversity, enabling the recovery of missed data symbols from the well-received symbols that are carried on other subcarriers.Fig. 6 shows the performance of the BER when the conventional schemes use QPSK for modulation and proposed IM-OFDM-SS schemes use QPSK with Walsh spreading code c i (g) whose length n = 2. It's clear that the proposed scheme still offers up to 4 dB better performance at BER of10 −3 .The superiority of the proposed scheme stems from the reduction in IBI, which is equivalent to x (g) /n.This reduction results in smaller individual group x (g) components.However, the practicality of utilizing high modulation order is diminished due to the challenging characteristics of the underground channel.Moreover, it is evident that at high SNR, the performance of the proposed scheme slightly deteriorates, which can be attributed to the channel characteristics.However, despite this effect, the proposed scheme still exhibits better performance compared to the conventional schemes.To investigate the advantage of the proposed scheme with higher modulation order, we also added the BER performance when using 8QPSK.The proposed scheme is still offering better performance compared to the conventional scheme which higher achieved SE.
CFO is one of the main issues encountered in acoustic channels; it leads to severe deterioration in performance.Direct implementation of X-transform into underground communication increases the sensitivity of the CFO.Hence, it's important to examine the performance of the presented DL-based receiver with CFO effects.Fig. 7 shows the performance of the proposed scheme with CFO = 0.5.BPSK data mapping is used for the conventional schemes and QPSK with Walsh spreading code c i (g) whose length n = 4 is used for the proposed and IM-OFDM-SS schemes.The conventional ZP-OFDM scheme estimates the CFO by utilizing null subcarriers [33].In contrast, the proposed schemes estimate and compensate for the CFO before inputting the data into the DL-based detector.The proposed DL-based receiver exhibits improved robustness against CFO effects since the arrived signal is processed in the time domain, allowing the DNN to estimate and compensate for residual CFO that may not have been detected.
The performance of the proposed scheme can also be enhanced by adjusting the size of the hidden layer Q in the DNN model.By default, setting Q = 32 can provide satisfactory results as shown previously.However, increasing the Q size can enhance the performance, but at the expense of complexity.Fig. 8 shows the BER performance at different Q sizes.QPSK with Walsh spreading code c i (g) whose length n = 4 is used, and CFO is set to be 0.04.As shown, a bigger size of Q , a better performance of BER, but the complexity will also be higher.
It's worth mentioning that the proposed scheme has the same computational complexity as conventional schemes, with the additional complexity required to perform DL-based receiver during the testing stage.The training stage is carried out offline, saving significant computational complexity during online deployment.The testing stage necessitates additional real multiplications for DL-based detection, which can be approximately evaluated by 3n * Q + Q * m.

B. ENERGY AND SPECTRAL EFFICIENCY
One of the main issues of underground communications is the energy efficiency E and the throughput B since it's not that easy to frequently recharge the underground nodes.Furthermore, the consumption of energy required for underground communications is higher due to the complicated signal processing.In conventional schemes, spectral and energy efficiency can be mathematically expressed as follows [34]: In (22), N data and N pilots are the number of subcarriers that reserved for data symbols and pilot symbols respectively.N frame = N data + N pilots is the total number of subcarriers including the data and pilot symbols, and M is the guard interval that is used to prevent intersymbol interference (ISI).Furthermore, the amplitude factor b is applied to the frequency-domain pilots, while the amplitude factor a is applied to the guard interval in the time domain.
Different from the conventional schemes, the achieved spectral efficiency of the proposed schemes is represented by the whole information bits carried by the index of spreading codes as well as the physical modulated bits.Therefore,   the spectral efficiency of the proposed scheme B DL−IM can mathematically be expressed as follows: The energy efficiency of the proposed scheme is similar to (22).Table 2, and Table 3 show the spectral and energy efficiency comparison.As shown, the proposed scheme can achieve similar performance to the conventional TDS-OFDM with significant performance improvement.

C. PAPR PERFORMANCE
Despite the ability of OFDM to deal with the acoustic wave's nature, PAPR is still one of the major drawbacks restricting the use of OFDM in underground communications.The underground devices exhibit perfect nonlinearity, resulting in non-linear distortion caused by signal clipping in the solid-state power amplifier (SSPA).This significantly impairs the quality of the OFDM signal.PAPR is caused by the superposition of symbols during DFT processing at the transmitting end.
Fig. 9 shows the performance of the complementary cumulative distribution function (CCDF) of the PAPR comparison at a similar achieved data rate.The proposed and conventional IM-OFDM-SS scheme employs QPSK with Walsh spreading code c i (g) whose length n = 4, while the other schemes employ BPSK.It is worth mentioning that the proposed scheme exhibits a significant enhancement, with the PAPR improving by up to 9 dB.This improvement is anticipated due to the X-transform, which lowers the overlapping of entity data symbols that create the orthogonal OFDM samples.In other words, the proposed scheme relies solely on the modulation order, thanks to the utilization of the X-transform, which limits the superimposition to a maximum of two subcarriers per symbol, as elucidated in (4).Conversely, the PAPR effect of conventional OFDM schemes is influenced by both the modulation order and the number of subcarriers, resulting in the superimposition of N subcarriers at the transmitting end.

V. CONCLUSION
We proposed, in this paper, a novel scheme called DLbased TDS-IM-OFDM-SS to enhance the spectral and energy efficiency of underground communications.X-transform IM-OFDM-SS is utilized to reduce the data symbols superposition at the transmitting end, and DL-based receiver at the receiver end to deal with each time-domain group of data symbols separately.Hence, we can avoid the sensitivity of X-transform OFDM to CFO effects as well as eliminate the IBI effects caused by the harsh nature of the underground channel.Moreover, the proposed scheme solves the underground communication PAPR problem by hugely reducing the data symbols superposition at the transmitting end.The proposed scheme doesn't only offer better performance compared with its benchmarks, but it also improves energy and spectral efficiency.The outperformance validation of the proposed scheme is conducted based on an underground measured channel tap to confirm its superiority over the other benchmarks in the literature.

FIGURE 1 .
FIGURE 1. Transmitter structure of the proposed X-transformed time-domain synchronous IM-OFDM-SS.

FIGURE 2 .
FIGURE 2. Structure of the proposed DL-based receiver.

FIGURE 8 .
FIGURE 8. BER performance comparison with different Q size.