An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> Ensuring the confidentiality of communications is fundamental to securing any network. This requirement becomes particularly important for wireless systems, where eavesdropping is facilitated by the broadcast nature of the wireless medium. Rather than physically guard the communication medium to provide confidentiality, the traditional approach is to employ cryptographic algorithms to ensure that only legitimate users can correctly interpret the messages, while all other entities fail to glean any useful information. <s> BIB001 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> This paper investigates the secrecy capacity of the Gaussian wiretap channel with M-PAM inputs, by capitalizing on the relationship between mutual information and minimum mean squared error (MMSE). In particular, we establish optimality conditions for both the M-PAM input power and the M-PAM input distribution, which we specialize to the asymptotic low-power and high-power regimes. By using the properties of the MMSE to establish sufficient conditions for the uniqueness of the solution of some of the underlying non-convex optimization problems, we also propose efficient algorithms to compute the optimal solutions. Interestingly, we show that with M-PAM inputs it is sub-optimal to use all the available power for some range of parameters — this is in sharp contrast to standard Gaussian channels. We also extend the results to the parallel Gaussian wiretap channel with M-PAM inputs. We put forth a mercury-waterfilling interpretation of the optimal power allocation procedure for parallel Gaussian wiretap channels which generalizes the conventional mercury-waterfilling interpretation for parallel Gaussian channels, with the mercury level amending the base level to account for both the non-Gaussianess of the input and the secrecy constraint. <s> BIB002 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> Previous studies on the cyclostationarity aspect of orthogonal frequency division multiplexing (OFDM) and single carrier linearly digitally modulated (SCLD) signals assumed simplified signal and channel models or considered only second-order cyclostationarity. This paper presents new results concerning the cyclostationarity of these signals under more general conditions, including time dispersive channels, additive Gaussian noise, and carrier phase, frequency, and timing offsets. Analytical closed-form expressions are derived for time- and frequency-domain parameters of the cyclostationarity of OFDM and SCLD signals. In addition, a condition to eliminate aliasing in the cycle and spectral frequency domains is derived. Based on these results, an algorithm is developed for recognizing OFDM versus SCLD signals. This algorithm obviates the need for commonly required signal preprocessing tasks, such as signal and noise power estimation and the recovery of symbol timing and carrier information. <s> BIB003 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> Orthogonal frequency division multiplexing (OFDM) systems have enjoyed widespread adoption as the physical layer standard for high data rate wired and wireless networks, due to their ability to efficiently cope with slowly varying dispersive channels. Therefore in searching for feasible implementations of physical layer security techniques, it is appropriate to analyze how existing information theoretic results can be applied to the OFDM structure This paper considers the information theoretic secrecy rates that are achievable in a wiretap OFDM channel when transmitting quadrature amplitude modulation (QAM) constellation symbols. The loss with respect to the secrecy rates obtained with Gaussian distributed inputs is evaluated for both finite constellation cardinalities and in the asymptotic approximation of arbitrarily high cardinality. Moving from the insight gained with this analysis, we propose bit-loading strategies to efficiently allocate the appropriate number of bits in each subchannel, by considering the twofold objective of minimizing the loss with respect to the Gaussian input secrecy capacity and minimizing the total bit load. <s> BIB004 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> This paper considers the information theoretic secrecy rates that are achievable by an orthogonal frequency-division multiplexing (OFDM) transmitter/receiver pair in the presence of an eavesdropper that might either use an OFDM structure or choose a more complex receiver architecture. The analysis is made possible by modeling the system as a particular instance of a high dimensional multiple-input multiple-output wiretap channel. The secrecy capacity is formulated as a maximization problem under a trace constraint, and simple expressions are given for its high signal-to-noise (SNR) limit. The low rate limit of the secrecy outage probability is also evaluated under a fading channel model. As for the finite SNR case, the secrecy rates that can be achieved with particular inputs are considered. Numerical results are provided under a Rayleigh fading channel model and under dependence of the main and eavesdropper channels. The secrecy loss due to the OFDM structure constraints, and the information gain for an eavesdropper that uses a more complex receiver, are also considered. <s> BIB005 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> In this paper, resource allocation for energy-efficient secure communication in an orthogonal frequency-division multiple-access (OFDMA) downlink network is studied. The considered problem is modeled as a nonconvex optimization problem that takes into account the sum-rate-dependent circuit power consumption, multiple-antenna eavesdropper, artificial noise generation, and different quality-of-service (QoS) requirements, including a minimum required secrecy sum rate and a maximum tolerable secrecy outage probability. The power, secrecy data rate, and subcarrier allocation policies are optimized for maximization of the energy efficiency of secure data transmission (bit/joule securely delivered to the users). The considered nonconvex optimization problem is transformed into a convex optimization problem by exploiting the properties of fractional programming, which results in an efficient iterative resource allocation algorithm. In each iteration, the transformed problem is solved by using dual decomposition. Simulation results illustrate that the proposed iterative resource allocation algorithm not only converges in a small number of iterations but maximizes the system energy efficiency and guarantees a nonzero secrecy data rate for the desired users as well. In addition, the obtained results unveil a tradeoff between energy efficiency and secure communication. <s> BIB006 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> Optimal power allocation for orthogonal frequency division multiplexing (OFDM) wiretap channels with Gaussian channel inputs has already been studied in some previous works from an information theoretical viewpoint. However, these results are not sufficient for practical system design. One reason is that discrete channel inputs, such as quadrature amplitude modulation (QAM) signals, instead of Gaussian channel inputs, are deployed in current practical wireless systems to maintain moderate peak transmission power and receiver complexity. In this paper, we investigate the power allocation and artificial noise design for OFDM wiretap channels with discrete channel inputs. We first prove that the secrecy rate function for discrete channel inputs is nonconcave with respect to the transmission power. To resolve the corresponding nonconvex secrecy rate maximization problem, we develop a low-complexity power allocation algorithm, which yields a duality gap diminishing in the order of O(1/\sqrt{N}), where N is the number of subcarriers of OFDM. We then show that independent frequency-domain artificial noise cannot improve the secrecy rate of single-antenna wiretap channels. Towards this end, we propose a novel time-domain artificial noise design which exploits temporal degrees of freedom provided by the cyclic prefix of OFDM systems {to jam the eavesdropper and boost the secrecy rate even with a single antenna at the transmitter}. Numerical results are provided to illustrate the performance of the proposed design schemes. <s> BIB007 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> In order to improve the confidentiality and security of orthogonal frequency division multiplexing (OFDM) systems, a physical layer security enhancement scheme by using time domain scrambling techniques is proposed in this paper. The approach is based on secretly scrambling the sample sequence within each time domain OFDM symbol, which is equivalent to constellation transformation over each subcarrier in the frequency domain. Consequently, the unique signal characteristics of the standardized OFDM transmission can be removed. The efficacy of the security enhancement is analyzed by means of the secrecy capacity. Moreover, related simulation results under the AWGN and the Rayleigh channel models indicate that our proposed scheme can improve the system secrecy significantly and the corresponding system performance will not be degraded. <s> BIB008 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> Artificial noise (AN) is one of physical layer security techniques, which can realize secure communication. AN is a noise signal which is intentionally transmitted from transmitter along with data signals. Since AN is generated to be canceled out at legitimate receivers, it can prevent eavesdroppers from eavesdropping even if transmitters do not know the existence of eavesdroppers. In spite of its usefulness, most of the AN generation techniques cannot be applied to multiple-input multiple-output (MIMO) systems when the number of antennas at the transmitter is less than that at the legitimate receiver. In this paper, we consider time-domain AN generation techniques for MIMO orthogonal frequency division multiplexing (OFDM) systems. A time-domain AN generation technique is originally proposed for single-input single-output (SISO) OFDM systems. Thus, we first consider to apply the conventional time-domain AN generation technique to MIMO-OFDM systems, and show that this technique requires a large number of antennas at the transmitter and/or a longer cyclic prefix (CP). Next, to solve this problem, we propose another time-domain AN generation technique. Our proposed time-domain AN is generated to be canceled out at the legitimate receiver in the frequency domain, while the conventional time-domain AN is canceled out in the time domain. As a result, the proposed time-domain AN generation technique can be applied to MIMO-OFDM systems, irrespective of the number of antennas and the length of CP. Simulation results can show that the proposed AN achieves the same secrecy rate as the conventional time-domain AN. Moreover, the proposed technique achieves a higher secrecy rate when a MIMO-OFDM system is employed with the antenna configuration to which the conventional time-domain AN generation technique is hard to be applied. <s> BIB009 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> In this paper, we present a novel eavesdropping-resilient OFDM system through sorted subcarrier interleaving. The transmitter interleaves subcarriers in each OFDM signal according to its dynamic channel state information (CSI) to the legitimate receiver. More specifically, subcarriers are interleaved according to the sorted order of their instantaneous channel gains that are observed at the transmitter. Based on channel reciprocity, the legitimate receiver can derive the interleaving pattern initiated by the transmitter through its local channel estimate, and then de-interleave the received signals. In contrast, since spatially separated wireless channels in rich multipath environments are independent of each other, an eavesdropper at a third location cannot follow the dynamic subcarrier interleaving permutation, and thus fails to eavesdrop this transmission. Considering the imperfect reciprocity of noisy channel estimates at the legitimate terminals, only a subset of subcarriers in each OFDM signal is involved in the interleaving. A subcarrier selection algorithm is investigated to realize a trade-off between the eavesdropping resilience and transmission reliability. Theoretical analysis and Monte Carlo simulations have been provided to validate the proposed system. Compared with prior security enhancement schemes, the proposed approach requires only minor modifications to off-the-shelf systems and avoids additional resource consumption. <s> BIB010 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> Performance of OFDM is known to be very sensitive to frequency synchronization errors. By exploiting this feature, a novel technique is proposed to provide secure communication against eavesdropping. The technique is based on introducing self inter-carrier interference to pre-compensate the carrier offset only for the legitimate user. This pre-compensation process depends on both the channel and the local carrier offset of the legitimate user, hence provides another degree of freedom for secrecy. Since an eavesdropper experiences an uncorrelated channel, his performance is expected to be degraded. Also our approach converts the simple one-tap frequency domain channel equalization to a very complex receiver operation for the eavesdropper. Moreover, the power aspects of this technique are discussed. By setting a threshold in the pre-compensation stage, we provide an acceptable trade-off between the transmitted power and the error performance. <s> BIB011 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> An effective and hardware-friendly physical layer security design, composed of a channel-based frequency pre-coder and a post-coder for OFDM-based systems, is proposed. The design is achieved by decomposing the diagonal matrix of the channel frequency amplitude of the legitimate receiver in order to obtain two unitary orthonormal matrices. The first matrix is used as a pre-coder just before the IFFT process at the transmitter, while the second matrix is used as a post-coder just after the FFT process at the receiver. Besides security, the presented design is interestingly found out to work as a shuffler or inter-leaver, which does not only provide secrecy, but also enhances the performance against burst errors. Moreover, a new channel calibration technique is developed to overcome the effect of channel reciprocity mismatch on the proposed scheme. The provided simulations and USRP hardware testbed implementation results validate the effectiveness of the proposed design in achieving practical and reliable secrecy with just minor modifications on the OFDM structure. <s> BIB012 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> Abstract Signal space diversity is a powerful technique that increases reliability of detection over fading channels. In this paper, we explore the ability of this technique to provide secure communication. We enhance the security of OFDM systems in frequency selective fading channels by providing more diversity gain to the legitimate user compared to an eavesdropper. This is done by adapting the interleaving pattern to the channel of the legitimate user in rich multipath environments, where spatially separated channels are typically independent to each other. This ensures secrecy in a time division duplex system, where the eavesdropper has no information regarding the channel of the legitimate user. The scheme can also be used in the conventional frequency division duplex system, which is more challenging in terms of security aspects because of the channel state information leakage. A theoretical analysis is presented on the bit-error probability in Rayleigh fading environment. The numerical results support the conclusion that adapting the interleaving pattern to the CSI of the legitimate user provides a gain in the bit-error rate performance over the eavesdropper. <s> BIB013 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> An efficient physical layer security technique, referred to as OFDM with subcarrier index selection (OFDM-SIS), is proposed for safeguarding the transmission of OFDM-based waveforms against eavesdropping in 5G and beyond wireless networks. This is achieved by developing a joint optimal subcarrier index selection (SIS) and adaptive interleaving (AI) design, which enables providing two levels (sources) of security in time division duplexing (TDD) mode: one is generated by the optimal selection of the subcarrier indices that can maximize the signal-to-noise ratio at only the legitimate receiver, while the other is produced by the AI performed based on the legitimate user’s channel that is different from that of the eavesdropper. The proposed scheme not only provides a remarkable secrecy gap, but also enhances the reliability performance of the legitimate user compared with the standard OFDM scheme. Particularly, a gain of 5–10 dB is observed at a bit error rate value of 10−3 compared with standard OFDM as a result of using the adaptive channel-based subcarrier selection mechanism. Moreover, the proposed technique saves power, considers no knowledge of the eavesdropper’s channel, and provides secrecy even in the worst security scenario, where the eavesdropper can know the channel of the legitimate link when an explicit channel feedback is used as is the case in frequency division duplexing systems. This is achieved while maintaining low complexity and high reliability at the legitimate user, making the proposed scheme a harmonious candidate technique for secure 5G ultra reliable and low latency communications (URLLC) services. <s> BIB014 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> This work presents a simple, spectral and power efficient scheme for providing secure OFDM communication system using channel shortening. The basic concept is to utilize a channel shortening technique, whose design is based on the channel of the legitimate user (Bob), in such a way that the length of the effective channel is made equal to or less than the cyclic prefix (CP) at Bob only, while the length of the effective channel at the illegitimate receiver (Eve) is greater than CP. Thus, this causes inter-symbol-interference (ISI), loss of orthogonality, and overall performance degradation at Eve. The simulation results show that the presented technique can provide a significant BER performance gap between Bob and Eve, and can provide Quality of Service (QoS) based security. The design is shown to be robust against channel imperfections and can provide spectral and power efficiency beside enhancing security. <s> BIB015 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> We propose a chaotic discrete Hartley transform (DHT) to enhance the physical-layer security and simultaneously improve the transmission performance of optical orthogonal frequency division multiplexing (OFDM) in passive optical network. The theoretical analysis and numerical simulation show that the chaotic DHT precoding matrix after independent row/column permutations can also effectively reduce the peak-to-average power ratio (PAPR) of OFDM signals, which can be generated for OFDM data encryption using digital chaos. The multifold data encryption provides a huge key space of ∼10178 to ensure the physical-layer confidentiality. An encrypted data transmission of 8.9 Gb/s 16-QAM optical OFDM signals is successfully demonstrated over 20 km standard single-mode fiber. Due to the effective reduction in PAPR by the chaotic DHT precoding matrix, the receiver sensitivity is improved by ∼1.4 dB ${(\text{BER}@ 10}^{- 3})$ . Moreover, the proposed scheme has low computational complexity, which also provides high spectral efficiency since no additional sideband information is required. <s> BIB016 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> A. OFDM Wiretap Channel <s> In this paper, robustness of non-contiguous orthogonal frequency division multiplexing (NC-OFDM) transmissions is investigated and contrasted to OFDM transmissions for fending off signal exploitation attacks. In contrast to ODFM transmissions, NC-OFDM transmissions take place over a subset of active subcarriers to either avoid incumbent transmissions or for strategic considerations. A point-to-point communication system is considered in this paper in the presence of an adversary (exploiter) that aims to infer transmission parameters (e.g., the subset of active subcarriers and duration of the signal) using a deep neural network (DNN). This method has been proposed since the existing methods for exploitation, which are based on cyclostationary analysis, have been shown to have limited success in NC-OFDM systems. A good estimation of the transmission parameters allows the adversary to transmit spurious data and attack the legitimate receiver. Simulation results show that the DNN can infer the transmit parameters of OFDM signals with very good accuracy. However, NC-OFDM with fully random selection of active subcarriers makes it difficult for the adversary to exploit the waveform and thus for the receiver to be affected by the spurious data. Moreover, the more structured the set of active subcarriers selected by the transmitter is, the easier it is for the adversary to infer the transmission parameters and attack the receiver using a DNN. <s> BIB017
Orthogonal frequency-division multiplexing (OFDM) provides robustness against multipath channel fading and offers flexibility in resource allocation. These features have made OFDM a widely used technique in recent wireless standards including 4G and 5G wireless systems. If there are no time variations across an OFDM word (i.e., for slow fading), the system can be modeled as a set of independent parallel channels. It is proved in BIB001 that the secrecy capacity of K independent parallel channels (as depicted in Fig. 7) is achieved when each channel achieves its individual secrecy capacity. For parallel Gaussian wiretap channels, the optimal input is Gaussian distributed BIB005 . However, a more practical study of OFDM wiretap channel is possible by assuming that the data symbols belong to finite constellations. An initial study on parallel Gaussian wiretap channels under finite-alphabet inputs is reported in BIB002 where the authors characterize the secrecy capacity with PAM signaling. They also provide a mercury-waterfilling interpretation of the optimal power allocation strategy. It is observed in BIB002 that dissimilar to standard parallel Gaussian channels (with no constraints on the input distribution), it may not be optimal to use all the available power for PAM inputs. In BIB004 , the OFDM wiretap channel is studied with QAM inputs. After quantifying the loss in the secrecy rates with respect to the scenarios with Gaussian inputs, a bit loading strategy is proposed to minimize this loss by assigning an appropriate number of bits to each subchannel. The sensitivity of OFDM based transmissions to frequency synchronization errors can be exploited to achieve secure transmission as well. Yusuf and Arslan BIB011 propose a secure OFDM transmission over reciprocal channels, which relies on inducing carrier frequency offset that is pre-compensated (using the transmitter's knowledge on the MCSI) in such a way that it is received without inter-carrier interference at the legitimate receiver, while the reception at the eavesdropper receiving the signal through an independent channel is considerably degraded. In BIB010 , an eavesdropping resilient OFDM scheme is developed over reciprocal channels where Alice performs a subcarrier interleaving using her knowledge on the instantaneous MCSI. The legitimate receiver who is also capable of acquiring the MCSI can obtain the interleaving pattern and de-interleave the received signals. In contrast, the eavesdropper cannot derive the interleaving pattern initiated by the transmitter, and as a result, fails to acquire the transmitted information. Cyclic prefix is used in OFDM systems to avoid inter carrier interference (ICI) incurred by multi-path channels. However, using cyclic prefix makes the transmission vulnerable to cyclostationarity based attacks BIB003 . This temporal degrees of freedom offered by the cyclic prefix can be used for artificial noise injection so as to improve secrecy over OFDM wiretap channels. In BIB007 , a single-antenna OFDM wiretap channel is considered and an artificial noise signal is inserted into the time-domain signal (over the cyclic prefix samples). A framework for joint optimization of the power allocated to each subcarrier and artificial noise covariance matrix is also proposed. Akitaya et al. BIB009 study the application of timedomain artificial noise injection in MIMOME OFDM systems. The results in BIB007 and BIB009 demonstrate that this approach is efficient for improving the secrecy rates in OFDM wiretap channels. Efficient resource allocation for secure OFDM systems is formulated as a convex optimization problem in BIB006 , and solved assuming that the transmitter uses artificial noise to combat an eavesdropper equipped with multiple antennas. Li et al. BIB008 propose scrambling of data in the time domain after the IFFT operation in order to improve physical layer security for OFDM signals. This, in fact, corresponds to sending modified constellation points (in terms of phase and amplitude) on each sub-carrier. Hamamreh et al. BIB012 introduce channel frequency response based pre-coder and post-coder designs for enhancing security in OFDM systems. Their solution relies on extracting orthonormal matrices via singular value decomposition (SVD) of the legitimate user's channel frequency amplitude and using it for shuffling OFDM sub-channels as well as for designing the frequency-based precoder and post-coder. In BIB016 , physical layer security is studied for passive OFDM-based optical networks where a scrambled precoding technique is utilized to improve the security. Yusuf and Arslan BIB013 propose an efficient approach to enhance secrecy in OFDM systems that relies on employing an adaptive interleaver maximizing the overall diversity gain delivered to the legitimate receiver. Hamamreh et al. BIB014 propose an efficient physical layer security technique for transmission of OFDM-based waveforms by developing an optimal joint subcarrier index selection and adaptive interleaver design to enhance the security and reliability of 5G services. In order to provide QoS based security for OFDM systems, channel shortening (CS) equalizer coefficients are designed in BIB015 based on the legitimate receiver's channel. Specifically, CS is used at the transmitter in such a way that the effective channel ensures no ISI at Bob, while causing ISI and performance degradation at Eve. More recently, application of deep learning for physical layer security in multi carrier systems is studied in BIB017 where an adversary aims at sending spurious data to the legitimate receiver. Table VII summarizes important results on the study of OFDM wiretap channels under the finite-alphabet input assumption.