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In this paper, we propose a novel technique for the inspection of high-density polyethylene (HDPE) pipes using ultrasonic sensors, signal processing, and deep neural networks (DNNs). Specifically, we propose a technique that detects whether there is a diversion on a pipe or not. The proposed model transmits ultrasound signals through a pipe using a custom-designed array of piezoelectric transmitters and receivers. We propose to use the Zadoff–Chu sequence to modulate the input signals, then utilize its correlation properties to estimate the pipe channel response. The processed signal is then fed to a DNN that extracts the features and decides whether there is a diversion or not. The proposed technique demonstrates an average classification accuracy of 90.3 % (when one sensor is used) and 99.6 % (when two sensors are used) on 3 4 inch pipes. The technique can be readily generalized for pipes of different diameters and materials. [ABSTRACT FROM AUTHOR]

Passive technologies, including intelligent reflecting surfaces (IRS), are gaining traction thanks to their ability to enhance communication systems while maintaining minimal cost and low complexity. They can assist a wireless sensor network (WSN) by achieving low power requirements for sensors and aid communication needs in many applications, for instance, environmental monitoring. In this paper, we propose an IRS-equipped WSN which describes sensors equipped with IRSs instead of active radio frequency (RF) electronics. The IRS sensor node (ISN) intercepts a dedicated signal from a power source such as a base station (BS) and modulates the transmission of that signal to an intended recipient. In order to enable multiple sensors to transmit to the receiver, we study opportunistic scheduling (OS) utilizing multi-sensor diversity while considering blind IRS operation, and compare it with round-robin (RR), proportional fairness (PF), and a theoretical upper bound. We study the effect of the choice of the number of IRS elements N and number of ISNs L on the average throughput of the system under OS. Finally, we provide pertinent comparisons for the different scheduling schemes and IRS configurations under relevant system performance metrics, highlighting different scenarios in which each scheme performs better. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surfaces (RISs) have drawn considerable attention due to their ability to direct electromagnetic waves into desirable directions. Although RISs share some similarities with relays, the two have fundamental differences impacting their performance. To harness the benefits of both, we propose a downlink system wherein a relay and an RIS improve performance in terms of energy-efficiency. Using singular value decomposition (SVD), semidefinite programming (SDP), and function approximations, we propose different solutions for optimizing the beamforming matrices at the base-station (BS), the relay, and the phase shifts at the RIS to minimize the total power under quality-of-service (QoS) constraints. The problem is solved when the relay operates in half-duplex and full-duplex modes and when the reflecting elements have continuous and discrete phase shifts. Simulation results compare the performance of the system with and without the RIS or the relay, under different optimization solutions. The results show that the system with full-duplex relay and RIS outperforms the other scenarios, and the contribution of full-duplex relay is higher than that of the RIS. However, an RIS outperforms a half-duplex relay when the required QoS is high. The results also show that increasing the number of reflecting elements improves the performance better in the presence of a relay than in its absence. [ABSTRACT FROM AUTHOR]

This paper studies the capacity of the two-user intensity-modulation/direct-detection (IM/DD) interference channel (IC), which is relevant in the context of multi-user optical wireless communications. Despite some known single-letter capacity characterizations for general discrete-memoryless ICs, a computable capacity expression for the IM/DD IC is missing. In this paper, we provide tight and easily computable inner and outer bounds for a general two-user IM/DD IC under peak and average optical intensity constraints. The bounds enable characterizing the asymptotic sum-rate capacity in the strong and weak interference regimes, as well as the generalized degrees of freedom (GDoF) in the symmetric case. Using the obtained bounds, the GDoF of the IM/DD IC is shown to have a ‘W’ shape similar to the Gaussian IC with power constraints. The obtained bounds are also evaluated numerically in different interference regimes to show their tightness, and used to study the performance of on-chip and indoor OWC systems. [ABSTRACT FROM AUTHOR]

Cloud radio-access networks (C-RAN) have been proposed as an enabling technology for keeping up with the requirements of next-generation wireless networks. Most existing works on C-RAN study the uplink or the downlink separately. However, designing the uplink and the downlink jointly may bring additional advantages, especially if message source-destination information is taken into account. In this paper, this idea is demonstrated by considering pairwise message exchange between users in a C-RAN. A multi-pair two-way transmission scheme is proposed which targets maximizing the end-to-end sum rate. In the proposed scheme, a lattice-based computation strategy is used, where the baseband processing unit (BBU) pool decodes integer linear combinations of paired users’ codewords instead of decoding linear combinations of individual codewords. The BBU pool then precodes the computed signals, compresses, and forwards them to the remote radio heads (RRHs), which in turn decompress the signals and send them to the users. Finally, each user decodes its desired message using its own message as side information. The achievable rate of this scheme is derived, optimized, and evaluated numerically. Simulation results reveal that significant end-to-end rate improvement can be achieved using the proposed scheme compared to existing schemes. [ABSTRACT FROM AUTHOR]

We consider an additive white Gaussian noise (AWGN) channel with erasures. This channel behaves as an AWGN channel with probability $1-\alpha $ , and produces an erased output with probability $\alpha $. The capacity of this channel is $1-\alpha $ times the capacity of the underlying AWGN channel without erasures. It is shown in the literature that the capacity of the underlying AWGN channel without erasures is achievable using nested lattice code with Construction A. Here, we extend the proof to show that the same code achieves the capacity of the channel with erasures, with a simplified decoder that drops erasures. Our approach provides a simpler decoder and a simpler proof than related works in the literature. [ABSTRACT FROM AUTHOR]

The current literature on intelligent reflecting surface (IRS) focuses on optimizing the IRS phase shifts to yield coherent beamforming gains, under the assumption of perfect channel state information (CSI) of individual IRS-assisted links, which is highly impractical. This work, instead, considers the random rotations scheme at the IRS in which the reflecting elements only employ random phase rotations without requiring any CSI. The only CSI then needed is at the base station (BS) of the overall channel to implement the beamforming transmission scheme. Under this framework, we derive the sum-rate scaling laws in the large number of users regime for the IRS-assisted multiple-input single-output (MISO) broadcast channel, with optimal dirty paper coding (DPC) scheme and the lower-complexity random beamforming (RBF) and deterministic beamforming (DBF) schemes at the BS. The random rotations scheme increases the sum-rate by exploiting multi-user diversity, but also compromises the gain to some extent due to correlation. Finally, energy efficiency maximization problems in terms of the number of BS antennas, IRS elements and transmit power are solved using the derived scaling laws. Simulation results show the proposed scheme to improve the sum-rate, with performance becoming close to that under coherent beamforming for a large number of users. [ABSTRACT FROM AUTHOR]

In next-generation wireless networks, providing secure transmission and delay guarantees are two critical goals. However, either of them requires a concession on the transmission rate. In this article, we consider a visible light network consisting of multiple access points and multiple users. Our first objective is to mathematically evaluate the achievable rate under constraints on delay and security. The second objective is to provide a cell formation with customized statistical delay and security guarantees for each user. First, we propose a user-centric design called secure cell formation, in which artificial noise is considered, and flexible user scheduling is determined. Then, based on the effective capacity theory, we derive the statistical-delay-constrained secrecy rate and formulate the cell formation problem as a stochastic optimization problem (OP). Further, based on the Lyapunov optimization theory, we transform the stochastic OP into a series of evolutionary per-slot drift-plus-penalty OPs. Finally, a modified particle swarm optimization algorithm and an interference graph-based user-centric scheduling algorithm are proposed to solve the OPs. We obtain a dynamic independent set of scheduled users as well as secure cell formation parameters. Simulation results show that the proposed algorithm can achieve a better delay-constrained secrecy rate than the existing cell formation approaches. [ABSTRACT FROM AUTHOR]

This letter proposes and optimizes a cooperative non-orthogonal multiple-access (Co-NOMA) scheme in the context of multicell visible light communications (VLC) networks to mitigate inter-cell interference. Consider a network where each access-point (AP) serves two users. In each cell, the weak user (cell-edge user) can be served either directly by the VLC AP, or through the strong user that decodes the weak user message and forwards it through the radio-frequency (RF) link. The paper then considers the problem of maximizing the sum-rate under quality-of-service constraints by allocating the powers of the messages and APs, and determining the links serving each weak user. The paper solves this non-convex problem by first finding closed-form solutions of the users’ powers and link selection for fixed APs powers. The APs powers are then iteratively solved in an outer loop. Simulation results show that the proposed scheme improves the sum-rate and fairness as compared to non-orthogonal multiple-access (NOMA) scheme. [ABSTRACT FROM AUTHOR]

The classical approach of avoiding or ignoring interference in wireless networks cannot accommodate the ambitious quality-of-service (QoS) demands of ultradense cellular networks (CNs). However, recent ground-breaking information-theoretic advances have changed our perception of interference from that of a foe to a friend. This article aims to shed light on harnessing the benefits of integrating modern interference management (IM) schemes into future CNs. To this end, we envision a hybrid multiple-access (HMA) scheme that decomposes the network into subtopologies of potential IM schemes for more efficient utilization of network resources. Preliminary results show that an HMA scheme can multiply nonorthogonal multiple-access (NOMA) performance, especially under dense user deployment. [ABSTRACT FROM AUTHOR]

This work focuses on the downlink of a single-cell multi-user system in which a base station (BS) equipped with $M$ antennas communicates with $K$ single-antenna users through a reconfigurable intelligent surface (RIS) installed in the line-of-sight (LoS) of the BS. RIS is envisioned to offer unprecedented spectral efficiency gains by utilizing $N$ passive reflecting elements that induce phase shifts on the impinging electromagnetic waves to smartly reconfigure the signal propagation environment. We study the minimum signal-to-interference-plus-noise ratio (SINR) achieved by the optimal linear precoder (OLP), that maximizes the minimum SINR subject to a given power constraint for any given RIS phase matrix, for the cases where the LoS channel matrix between the BS and the RIS is of rank-one and of full-rank. In the former scenario, the minimum SINR achieved by the RIS-assisted link is bounded by a quantity that goes to zero with $K$. For the high-rank scenario, we develop accurate deterministic approximations for the parameters of the asymptotically OLP, which are then utilized to optimize the RIS phase matrix. Simulation results show that RISs can outperform half-duplex relays with a small number of passive reflecting elements while large RISs are needed to outperform full-duplex relays. [ABSTRACT FROM AUTHOR]

Optical orthogonal frequency division multiplexing (O-OFDM) schemes are variations of OFDM schemes that produce non-negative signals. Asymmetrically-clipped O-OFDM (ACO-OFDM) is a single-layer O-OFDM scheme, whose spectral efficiency can be enhanced by adopting multiple ACO-OFDM layers or a combination of ACO-OFDM and other O-OFDM schemes. However, since symbol detection in such enhanced ACO-OFDM (eACO-OFDM) is done iteratively, erroneous detection leads to residual clipping noise (RCN) which can degrade performance in practice. Thus, it is necessary to develop an accurate model for RCN in designing RCN-aware eACO-OFDM schemes. To this end, this paper provides a mathematical analysis of RCN leading to an accurate model of RCN power. The obtained model is used to analyse the performance of various eACO-OFDM schemes. It is shown that the model provides an accurate evaluation of symbol error rate (SER), which would be underestimated if RCN is ignored. Moreover, the model is shown to be useful for designing an RCN-aware resource allocation that increases the robustness of the system in terms of meeting a target SER, compared to an RCN-unaware design. [ABSTRACT FROM AUTHOR]

Full-duplex communication allows a terminal to transmit and receive signals simultaneously, and hence, it is helpful in general to adapt transmissions to received signals. However, this often requires unaffordable complexity. This work focuses on simple non-adaptive transmission, and provides two classes of channels for which Shannon’s information capacity regions are achieved without adaptation. The first is the injective semi-deterministic two-way channel that includes additive channels with various types of noises modeling wireless, coaxial cable, and other settings. The other is the Poisson two-way channel, for which we show that non-adaptive transmission is asymptotically optimal in the high dark current regime. [ABSTRACT FROM AUTHOR]

The continuous improvement in optical energy harvesting devices motivates the development of visible light communication systems that utilize such available free energy. In this paper, an outdoor visible light communications (VLC) system is considered where a VLC base station sends data to multiple users that are capable of harvesting optical energy. The proposed VLC system serves multiple users using time division multiple access (TDMA) with unequal time and power allocation, which are allocated to achieve the system communications and illumination objectives. In an outdoor setup, the system lighting objective is to maximize the average illumination flux, while the communication design objective is to maximize the spectral efficiency (SE). A multiobjective optimization problem is formulated to obtain the Pareto front of the SE-illumination region. To this end, the marginal optimization problems are solved first using low complexity algorithms. Then, based on the proposed algorithms, a Karush-Kuhn-Tucker-based algorithm is developed to obtain an inner bound of the Pareto front for the SE-illumination tradeoff. The inner bound for the Pareto-front is shown to be close to the optimal Pareto-frontier via several simulation scenarios for different system parameters. [ABSTRACT FROM AUTHOR]

In this work, we consider a sparse code multiple access uplink system, where $J$ users simultaneously transmit data over $K$ subcarriers, such that $J > K$ , with a constraint on the power transmitted by each user. To jointly optimize the subcarrier assignment and the transmitted power per subcarrier, two new iterative algorithms are proposed, the first one aims to maximize the sum-rate (Max-SR) of the network, while the second aims to maximize the fairness (Max-Min). In both cases, the optimization problem is of the mixed-integer nonlinear programming (MINLP) type, with non-convex objective functions, which are generally not tractable. We prove that both joint allocation problems are NP-hard. To address these issues, we employ a variant of the block successive upper-bound minimization (BSUM) framework, obtaining polynomial-time approximation algorithms to the original problem. Moreover, we evaluate the algorithms’ robustness against outdated channel state information (CSI), present an analysis of the convergence of the algorithms, and a comparison of the sum-rate and Jain’s fairness index of the novel algorithms with three other algorithms proposed in the literature. The Max-SR algorithm outperforms the others in the sum-rate sense, while the Max-Min outperforms them in the fairness sense. [ABSTRACT FROM AUTHOR]

The characterization of fundamental performance bounds of many-to-many communication systems in which participating nodes are active in an intermittent way is one of the major challenges in communication theory. In order to address this issue, we introduce the multiple-input multiple-output (MIMO) three-way channel (3WC) with an intermittent node and study its degrees-of-freedom (DoF) region and sum-DoF. We devise a non-adaptive encoding scheme based on zero-forcing, interference alignment, and erasure coding, and show its DoF region (and thus sum-DoF) optimality for non-intermittent 3WCs and its sum-DoF optimality for (node-) intermittent 3WCs. However, we show by example that in general some DoF tuples in the intermittent 3WC can only be achieved by adaptive schemes such as decode-forward relaying. This shows that non-adaptive encoding is sufficient for the non-intermittent 3WC and for the sum-DoF of intermittent 3WCs but adaptive encoding is necessary for the DoF region of intermittent 3WCs. This paper contributes to a better understanding of the fundamental limits of multi-way communication systems with intermittency and the impact of adaptation therein. [ABSTRACT FROM AUTHOR]

This paper investigates the secrecy performance of the multiple-input single-output visible light communication (VLC) wiretap channel. The considered system model comprises three nodes: a transmitter (Alice) equipped with multiple fixtures of LEDs, a legitimate receiver (Bob), and an eavesdropper (Eve), each equipped with one photo-diode. The VLC channel is modeled as a real-valued amplitude-constrained Gaussian channel. Eve is assumed to be randomly located in the same area as Bob. Due to this, artificial noise-based beamforming is adopted as a transmission strategy in order to degrade Eve’s signal-to-noise ratio. Assuming discrete input signaling, we derive an achievable secrecy rate in a closed-form expression as a function of the beamforming vectors and the input distribution. We investigate the average secrecy performance of the system using stochastic geometry to account for the location randomness of Eve. We also adopt the truncated discrete generalized normal (TDGN) as a discrete input distribution. We present several examples through which we confirm the accuracy of the analytical results via Monte Carlo simulations. The results also demonstrate that the TDGN distribution, albeit being not optimal, yields performance close to the secrecy capacity. [ABSTRACT FROM AUTHOR]

In this paper, we comprehensively investigate the achievable rates of selected band-limited intensity modulation schemes, which are important for optical wireless communication applications, while accounting for the specific nature of their signal construction (non-negative, real, and baseband), and imposing identical bandwidth and average optical power constraints. Furthermore, we identify/devise methods to effectively trade between these parameters. Three variants of orthogonal frequency division multiplexing (OFDM), namely, asymmetrically clipped optical OFDM (ACO-OFDM), spectrally and energy efficient OFDM (SEE-OFDM), and dc-biased optical OFDM (DCO-OFDM), and single-carrier pulse amplitude modulation are studied. The clipping noise in ACO-OFDM and SEE-OFDM is found to consume a large excess bandwidth. The detrimental effects of this excess bandwidth on the achievable rate are evaluated. For SEE-OFDM, the problem of optimal power allocation among its components is formulated and solved using the Karush–Kuhn–Tucker method. For DCO-OFDM, the clipping noise is modeled and incorporated in the analysis. Among the existing schemes, DCO-OFDM yields the best overall performance, due to its compact spectrum. In order to improve the achievable rate, we propose and analyze two improved distortionless variants, filtered ACO-OFDM and filtered SEE-OFDM (FSEE-OFDM), which yield better spectral efficiency than ACO-OFDM and SEE-OFDM, respectively. FSEE-OFDM, being the most spectrally efficient, outperforms all schemes. [ABSTRACT FROM AUTHOR]

A network model is considered, where Poisson distributed base stations transmit to $N$ power-domain non-orthogonal multiple access (NOMA) users (UEs) each that employ successive interference cancellation (SIC) for decoding. We propose three models for the clustering of NOMA UEs and consider two different ordering techniques for the NOMA UEs: mean signal power-based and instantaneous signal-to-intercell-interference-and-noise-ratio-based. For each technique, we present a signal-to-interference-and-noise ratio analysis for the coverage of the typical UE. We plot the rate region for the two-user case and show that neither ordering technique is consistently superior to the other. We propose two efficient algorithms for finding a feasible resource allocation that maximize the cell sum rate $\mathcal {R}_{\mathrm{ tot}}$ , for general $N$ , constrained to: 1) a minimum throughput $\mathcal {T}$ for each UE, 2) identical throughput for all UEs. We show the existence of: 1) an optimum $N$ that maximizes the constrained $\mathcal {R}_{\mathrm{ tot}}$ given a set of network parameters and 2) a critical SIC level necessary for NOMA to outperform orthogonal multiple access. The results highlight the importance in choosing the network parameters $N$ , the constraints, and the ordering technique to balance the $\mathcal {R}_{\mathrm{ tot}}$ and fairness requirements. We also show that interference-aware UE clustering can significantly improve performance. [ABSTRACT FROM AUTHOR]

Visible light communications (VLCs), in general, and resource allocation for VLC networks in particular, have gained lots of attention recently. In this paper, we consider the resource allocation problem of a VLC downlink transmission system employing dynamic time division multiple access, where time and power variables are tuned to maximize the downlink spectral efficiency (SE). As for the operational conditions, we impose constraints on the average optical intensity, the energy budget, and the quality-of-service. To solve this non-convex problem, we transform the objective function into a difference of concave functions by solving a second-order differential inequality. Then, we propose a low-complexity algorithm to solve the resource allocation problem. Finally, we show by simulations the SE performance gains achieved by optimizing time and power allocation over the initial total power minimization solution for the considered system. [ABSTRACT FROM AUTHOR]

An optical wireless intensity-modulation direct-detection multiple-input multiple-output communication system is considered. The performance of $M$ -PAM rate-1 direct current offset space-time block codes is studied in terms of average worst-case pairwise error probability (WC-PEP) in quasi-static channels. It is shown that within this code class, the average WC-PEP is minimized by repetition coding (RC) under both electrical and optical individual power constraints, irrespective of channel statistics. This agrees with previously published results related to ON–OFF keying RC. This is further extended to sum power constraints, where it is shown that spatial beamforming minimizes the average WC-PEP within this code class, which simplifies to RC if the channel matrix has independent and indentically distributed columns and a sum electrical power constraint. Under a sum optical power constraint, this also holds true at high signal-to-noise ratio (SNR), but not at low SNR. Generally, the time dimension of this code class is redundant from an average WC-PEP perspective. Numerical results are provided to support the theoretical findings and to show that the average WC-PEP leads to a good approximation of the actual error probability at high SNR. [ABSTRACT FROM AUTHOR]

The low-SNR asymptotic capacity of the multiple-input multiple-output (MIMO) optical intensity channel is studied under both average and peak intensity constraints. We focus on low SNR, which can be modeled as the scenario where both constraints proportionally vanish, or where the peak constraint is held constant while the average constraint vanishes. A capacity upper bound is derived and is shown to be tight at low SNR under both scenarios. The capacity achieving input distribution at low SNR is shown to be a maximally correlated vector-binary input distribution. Consequently, the low-SNR capacity of the channel is characterized. As a byproduct, it is shown that for a channel with peak intensity constraints only, or with peak intensity constraints and individual (per aperture) average intensity constraints, a simple scheme composed of coded ON–OFF keying, spatial repetition, and maximum-ratio combining is optimal at low SNR. [ABSTRACT FROM AUTHOR]

The capacity of the intensity modulation direct detection multiple-input-multiple-output channel is studied. Therein, the nonnegativity constraint of the transmit signal limits the applicability of classical schemes, including precoding. Thus, new ways are required for deriving capacity bounds for this channel. To this end, capacity lower bounds are developed in this paper by deriving the achievable rates of two precoding-free schemes: channel inversion and orthogonal-upper triangular matrix product decomposition. The achievable rate of a dc-offset singular-value decomposition-based scheme is also derived as a benchmark. Then, capacity upper bounds are derived and compared against the lower bounds. As a result, the capacity at high signal-to-noise ratio (SNR) is characterized for the case where the number of transmit apertures is not larger than the number of receive apertures, and is shown to be achievable by the QR decomposition scheme. This is shown for a channel with average intensity or peak intensity constraints. Under both constraints, the high-SNR capacity is approximated within a small gap. Extensions to a channel with more transmit apertures than receive apertures are discussed, and capacity bounds for this case are derived. [ABSTRACT FROM PUBLISHER]

Antenna selection for full-duplex communication between two nodes, each equipped with a predefined number of antennae and transmit/receive chains, is studied. Selection algorithms are proposed based on magnitude, orthogonality, and determinant criteria. The algorithms are compared to optimal selection obtained by exhaustive search as well as random selection, and are shown to yield performance fairly close to optimal at a much lower complexity. Performance comparison for a Rayleigh fading symmetric channel reveals that selecting a single transmit antenna is best at low signal-to-noise ratio (SNR), while selecting an equal number of transmit and receive antennae is best at high SNR. [ABSTRACT FROM PUBLISHER]

The capacity of parallel intensity-modulation and direct-detection optical wireless channels with total average intensity and per-channel peak intensity constraints is studied. The optimal intensity allocation at low signal-to-noise ratio (SNR) is derived, leading to the capacity-achieving ON–OFF keying distribution. Interestingly, while activating the strongest channel is optimal if 1) the peak intensity is fixed, this is not the case if 2) the peak intensity is proportional to the average intensity. The minimum average optical intensity per bit is also studied, and is characterized for case 1) where it is achievable at low SNR. However, in case 2), the average optical intensity per bit grows indefinitely as SNR decreases, indicating that lower optical intensity per bit can be achieved at moderate SNR than low SNR. [ABSTRACT FROM PUBLISHER]

Multi-channel (MC) optical wireless communication (OWC) systems employing wave-division multiplexing for outdoors free-space optical communications, or multi-user time-division multiple access for indoors visible-light communications, e.g., can be modeled as parallel channels. Multi-input multi-output OWC systems can also be transformed, possibly with some performance loss, to parallel channels using pre-/post-coding. Studying the performance of such MC-OWC systems requires characterizing the capacity of the underlying parallel channels. In this paper, upper and lower bounds on the capacity of constant parallel OWC channels with a total average intensity constraint are derived. Then, this paper focuses on finding intensity allocations that maximize the lower bounds given channel-state information at the transmitter (CSIT). Due to its nonconvexity, the Karush–Kuhn–Tucker conditions are used to describe a list of candidate allocations. Instead searching exhaustively for the best solution, low-complexity near-optimal algorithms are proposed. The resulting optimized lower bound nearly coincides with capacity at high signal-to-noise ratio (SNR). Under a quasi-static channel model and in the absence of CSIT, outage probability upper and lower bounds are derived. Those bounds also meet at high SNR, thus characterizing the outage capacity in this regime. Finally, the results are extended to a system with both average and peak intensity constraints. [ABSTRACT FROM PUBLISHER]

Treating interference as noise (TIN) as the most appropriate approach in dealing with interference and the conditions on its optimality has attracted the interest of researchers recently. However, our knowledge on necessary and sufficient conditions of TIN is restricted to a few setups with limited number of users. In this paper, we study the optimality of TIN in terms of the generalized degrees of freedom (GDoF) for a fundamental network, namely, the $M\times 2$ X-channel. To this end, the achievable GDoF of TIN with power allocations at the transmitters is studied. It turns out that the transmit power allocation maximizing the achievable GDOF is given by on–off signaling as long as the receivers use TIN. This leads to two variants of TIN, namely, P2P-TIN and 2-IC-TIN. While in the first variant the $M\times 2$ X-channel is reduced to a point-to-point (P2P) channel, in the second variant, the setup is reduced to a two-user interference channel in which the receivers use TIN. The optimality of these two variants is studied separately. To this end, novel genie-aided upper bounds on the capacity of the X-channel are established. The conditions on the optimality of P2P-TIN can be summarized as follows. P2P-TIN is GDoF-optimal if there exists a dominant multiple access channel or a dominant broadcast channel embedded in the X channel. Furthermore, the necessary and sufficient conditions on the GDoF-optimality of 2-IC-TIN are presented. Interestingly, it turns out that operating the $M\times 2$ X-channel in the 2-IC-TIN mode might be still GDOF optimal, although the conditions given by Geng et al. are violated. However, 2-IC-TIN is sub-optimal if there exists a single interferer which causes sufficiently strong interference at both receivers. The comparison of the results with the state of the art shows that the GDOF optimality of TIN is expanded significantldy. [ABSTRACT FROM PUBLISHER]