The information-theoretic concept of identification describes a sender-receiver architecture in which the receiver only checks whether a particular message was sent or not, thereby promising a low-energy receiver design. In low received-energy regimes, quantum receivers are a promising tool for studying the system limits. However, the known information-theoretically optimal identification codes typically assume perfect synchronization. In this work, we study deterministic identification in a satellite setting under explicit synchronization constraints, where a satellite broadcasts the signature of a specific User Equipment (UE) which it assumes to be attached to one out of several possible Ground Station (GS), with the goal of establishing communication with the target UE. Within the proposed design, and assuming a specific phase-encoded coherent-state clock scheme in which the discrete time index is represented by equidistant phase rotations on the unit circle, our results reveal a fundamental asymmetry: At any transmission power, identification performance improves with blocklength, whereas synchronization accuracy degrades. In particular, the energy needed for transmitting the satellite clock to the GS can be several orders of magnitude higher than the one needed for the identification signal. This indicates that synchronization strongly impacts identification performance and motivates the investigation of the error-correcting capabilities of bosonic codes under jitter.
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Accepted for presentation at European Wireless 2026
The information-theoretic concept of identification describes a sender-receiver architecture in which the receiver only checks whether a particular message was sent or not, thereby promising a low-energy receiver design. In low received-energy regimes, quantum receivers are a promising tool for studying the system limits. However, the known information-theoretically optimal identification codes typically assume perfect synchronization. In this work, we study deterministic identification in a satellite setting under explicit synchronization constraints, where a satellite broadcasts the signature of a specific User Equipment (UE) which it assumes to be attached to one out of several possible Ground Station (GS), with the goal of establishing communication with the target UE. Within the proposed design, and assuming a specific phase-encoded coherent-state clock scheme in which the discrete time index is represented by equidistant phase rotations on the unit circle, our results reveal a fundamental asymmetry: At any transmission power, identification performance improves with blocklength, whereas synchronization accuracy degrades. In particular, the energy needed for transmitting the satellite clock to the GS can be several orders of magnitude higher than the one needed for the identification signal. This indicates that synchronization strongly impacts identification performance and motivates the investigation of the error-correcting capabilities of bosonic codes under jitter.
Born about a century ago, Quantum Mechanics has revolutionized the description and the interpretation of Physics at sub-microscopic level. In the last decades, due to the influence of mathematical and engineering research fields, Quantum Mechanics has given birth to related research areas like Quantum Computation, Quantum Information and Quantum Communication. With the discovery of the laser, and later the development of fiber optics and satellite networks, Quantum Communication and Quantum Optics seems to have a natural field of application in Communication Systems. Despite this, the interest in this technology and studies for communication purpose has been overshadowed by the great results in communication networks achieved in the last decades with classical paradigms. However, due to the increasing demand of communication data rate, system designers are now looking at Quantum Mechanics for new and more performanting solutions in communication purposes. Early theoretical studies on Quantum Discrimination Theory and Quantum Information predict better performance for Communication Systems that take advantage of the quantum laws. In addition, Quantum Mechanics provides the deepest description of the physical phenomena, and there are scenarios where a quantum model fits best, as in in deep space communications, where the received signal is really weak, or in a satellite networks, where we are interested in strongly reducing the power of transmitted signals, possibly without sacrificing performance significantly. However, if on one side Quantum Communication Theory promises great gains in the performance of communication systems, on the other hand it fails to describe how to implement physical devices that reach these ultimate limits. So far, only a few architectures achieving these performances are known, and only for simple modulation formats. We are interested in the scenario of optical communications, where the message transmitted is encoded in a sequence of coherent states. Transmitter devices for coherent modulation are well known and consist in laser pulse generators. Instead, receiver implementations working at the quantum limit performance limit are yet to be found. In this Thesis I deal with different topics in the quantum transmission scenario. First, I review existing classical (suboptimal) and quantum (suboptimal and optimal) receiver schemes for the binary coherent modulation. I present a new formulation of the optimal scheme known as Dolinar Receiver with the multiple copies problem, focusing on the information gained during the measurement. Second, I analyze the binary communication in a noisy environment, studying the error probability and the capacity of the binary channel induced. Given the description of the quantum channel, I optimize both the transmitted quantum states and the measurement operators employed in the communication. Third, I consider the Pulse Position Modulation, that is particularly suitable for space and satellite communication due to its simplicity of implementation and high capacity. I review some known suboptimal receivers, and I propose a receiver scheme which approaches the limit performance predicted with quantum theory outperforming the existing schemes. To sum up the results of this Thesis, in order to approach the limit performance predicted by Quantum Mechanics, an optimization is always necessary to exceed the classical effects and trigger the quantum phenomena. In particular, the information gained during the measurement plays an important role, for example in the definition of adaptive receivers. In this Thesis both these aspects have been deeply investigated.
Accurate timekeeping is essential for scientific and technological advancements, particularly in areas of communication, networking, navigation, and high precision measurements. While many methods of time resolution are already established using classical resources, they fail to combine high precision outcomes with large-scale implementations. Additionally, numerous quantum networking architectures using satellite-assisted methods have demonstrated quantum communication on scales exceeding ground-based methods. For these reasons, we propose the use of a time synchronization method by which pairs of highly time-correlated photons are exchanged between clocks on satellites and clocks on Earth, al- lowing users to reconstruct the time offsets between their clocks. This is known as Quantum Clock Synchronization (QCS). We analyze global time synchronization, via numerical simulation, using a network of satellites equipped with quantum resources, such as entangled photon sources (SPDC) and single photon detectors. We find that for satellites in low-earth orbits, a configuration of 50 evenly-space satellites provides constant visibility and sub-nanosecond time synchronization to any location on Earth. Due to practical constraints, clocks available for use on satellites are often of lesser quality than those available for ground use. However, by allowing the satellites in our network to synchronize among themselves, we overcome this limitation, forming a highly precise “master clock” capable of global, high precision time synchronization. We then examine the amount of quantum security provided by polarization-entangled photon sources as a potential way to protect an experimental implementation of QCS from attacks such as signal spoofing. To do this, we identify regions on Earth where Bell violations between exchanged entangled photons can ensure quantum security at various confidence vii levels. Combined with similar insights gained from determining the network scale of our QCS protocol at the single-link level, we demonstrate the potential for highly precise, global, and potentially quantum-secure clock synchronization. Finally, we modify our QCS protocol to support frequency, or tick-rate, offsets in addition to constant time offsets. We motivate this by presenting some relativistic effects that can introduce frequency differences between clocks in space and on Earth. Provided that relative velocities between clocks are corrected for, we identify constant and variable clock defects through numerical simulations.
We study the quantum limits of the ELROI beacon concept introduced by Holmes, Weaver, and Palmer. In this concept, a satellite continuously emits a weak optical signal to broadcast its identity. Via analysis of the fundamental limits on communication introduced by Shannon, Gordon, and Holevo, we demonstrate that in such scenarios, incorporating quantum technology into the design of a ground station significantly enhances performance. Specifically, the Time-To-Read the beacon signal and thereby identify the satellite is greatly reduced in situations where weather conditions obstruct the signal, allowing the Active Time Window, during which the satellite can be utilized for subsequent network operations, to be extended by nearly a factor of 20. In this particular case, the quantum technology concept that is employed is the so-called Joint Detector Receiver, which is a system aiming to operate at the Gordon-Holevo limit by performing joint quantum operations on sequences of incoming signals.
—This work considers the downlink of a cloud radio access network (C-RAN), in which a control unit (CU) encodes confidential messages, each of which is intended for a user equipment (UE) and is to be kept secret from all the other UEs. As per the C-RAN architecture, the encoded baseband signals are quantized and compressed prior to the transfer to distributed radio units (RUs) that are connected to the CU via finite-capacity fronthaul links. This work argues that the quantization noise introduced by fronthaul quantization can be leveraged to act as "artificial" noise in order to enhance the rates achievable under secrecy constraints. To this end, it is proposed to control the statistics of the quantization noise by applying multivariate, or joint, fronthaul quantization/compression at the CU across all outgoing fronthaul links. Assuming wiretap coding, the problem of jointly optimizing the precoding and multivariate compression strategies, along with the covariance matrices of artificial noise signals generated by RUs, is formulated with the goal of maximizing the weighted sum of achievable secrecy rates while satisfying per-RU fronthaul capacity and power constraints. After showing that the artificial noise covariance matrices can be set to zero without loss of optimaliy, an iterative optimization algorithm is derived based on the concave convex procedure (CCCP), and some numerical results are provided to highlight the advantages of leveraging quantization noise as artificial noise. Index Terms—C-RAN, physical-layer security, fronthaul quantization, beamforming I. INTRODUCTION Motivated by the original works on the wiretap channel [1][2], physical-layer security techniques have been extensively studied as effective means of protecting data secrecy for communications over wireless channels in a variety of scenarios [3][4]. One of the key techniques that have been devised for enhancing the rates at which information can be transmitted securely is the addition of artificial noise at the transmitter [5]-[10]. This strategy finds its theoretical justification in the prefix channel approach that was shown in [2] to achieve the secrecy capacity of a general wiretap channel. In this work, we study physical-layer secure communication in the context of the downlink of cloud radio access networks Figure 1. Illustration of the downlink of a C-RAN system with confidential messages for NR = 2 RUs, NU = 2 UEs, nR,i = 2 RU antennas and nU,k =2 UE antennas. (C-RANs). In a C-RAN, a control unit (CU) performs joint encoding of the messages intended for all the user equipments (UEs) located in the geographical area covered by the radio units (RUs) connected to the CU. The encoded baseband signals are then transferred to the RUs on the fronthaul link in analog or digital format. For digital fronthauling, the CU quantizes and compresses the encoded baseband signals prior to the transfer to the RUs due to the limited bit rate of the fronthaul links [11][12]. In this work, we argue that the quantization noise introduced by fronthaul quantization can be leveraged to act as artificial noise in order to enhance the rates achievable under secrecy constraints. To this end, as an extension of the work [11], we propose to apply multivariate, or joint, fronthaul quantization/compression [13] at the CU for all outgoing fronthaul links in order to control the statistics of the quantization noise. Multivariate quantization/compression was recently shown in [11] to improve the performance of C-RANs without secrecy constraints with respect to standard per-fronthaul link pointto-point quantization/compression. In the rest of this paper, we first formulate the problem of jointly optimizing precoding, multivariate compression and the covariance matrices of artificial noise signals generated by RUs, with the goal of maximizing the weighted sum of achievable secrecy rates of the intended UEs subject to perRU fronthaul capacity and power constraints (Sec. III). We show that the artificial noise covariance matrices can be set to zero with no loss of optimality and hence focus on the joint optimization of precoding and multivariate compression. An iterative optimization algorithm is then derived based on the concave convex procedure (CCCP) (Sec. III), and numerical evidence is provided to highlight the advantages of the proposed schemes (Sec. IV). II. SYSTEM MODEL We consider the downlink of a C-RAN in which a single CU controls NR RUs. The CU communicates with the ith RU through a fronthaul link of capacity Ci bits/s/Hz where the normalization is with respect to the downlink bandwidth. The NR RUs transmit signals to NU UEs located in the union of the coverage areas of the RUs. We define the sets NR of the RUs and the UEs, and denote the numbers of antennas of RU i and UE k as nR,i and nU,k, respectively. An illustration is shown in Fig. 1. The signal yk ∈ CnU,k×1 received by UE k is given by y, (1) i∈NR where Hk,i ∈ CnU,k×nR,i represents the channel responseR,i matrix from RU i to UE k; xi ∈ CU,kn ×1 indicates the signal transmitted by RU i; and zk ∈ Cn ×1 is the additive noise at UE k distributed as zk ∼ CN(0,Σzk). Each RU i is subject to the power constraint. The information messages Mk ∈ {1,...,2nRk}, each of rate Rk bits/s/Hz, are encoded within a block of n channel uses, where n is large enough to justify the use of informationtheoretic limits. The message Mk is intended for UE k ∈ NU and is required to be kept secret from the other UEs. Specifically, we impose that the UEs l ∈ NU\{k} be unable to decode the message Mk even in the worst-case scenario where they cooperate since the CU cannot control the activities of the UEs (see [1]). The messages {Mk}k∈NU are processed by the CU in the two steps described in the following subsections before being transferred to the RUs. A. Linear Precoding The CU first encodes each message Mk using a wiretap code [1] and obtaining an encoded signal sk ∈ Cdk×1, which is distributed as sk ∼ CN(0,I). We assume that the number dk of data streams satisfies the condition dk ≤ min{nR,nU,k} with the notation . In order to enable the management of the inter-UE interference and to enhance secrecy, the CU performs linear precoding, or beamforming, with a precoding matrix A ∈ CRnR×d, yielding the precoded signal x˜ = [x˜1;...;x˜NR] ∈ Cn ×1 with x˜ = As, (2) where x˜i ∈ CnR,i×1 is the signal to be communicated to RU i; s [s1;...;sNU] is the vector of the signals encoded for the UEs; and we have defined the notation . We note that the discussion can be easily extended to systems, in which the CU performs non-linear secrecy dirty-paper coding (S-DPC) precoding proposed in [10]. B. Fronthaul Compression The precoded baseband signal x˜i needs to be compressed prior to transmission to the RU, since the CU communicates to RU i through a fronthaul link of capacity Ci bits/s/Hz. Using standard rate-distortion considerations, we model the impact of compression by adding a quantization noise qi to the compression input signal x˜i so that the compression output signal xˆi is given as xˆi = x˜i + qi, (3) where the quantization noise qi is independent of the signal x˜i and is distributed as qi ∼ CN(0,Ωi,i). Each RU i decompresses the baseband signal xˆi based on the bit stream received on the fronthaul link. We emphasize that, as done in, e.g., [11], quantization is not designed so as to minimize the (e.g., quadratic) distortion between the precoded signals x˜i and the compressed signals xˆi, but rather with the aim of maximizing the weighted sum of achievable secrecy rates, which will be defined in Sec. II-D. In the standard point-to-point compression approach [14], in which the precoded signals x˜i and x˜j for different RUs are separately compressed, the quantization noises qi and qj are independent, i.e., . Instead, multivariate, or joint, compression [13, Ch. 9] allows the CU to correlate the quantization noises q1,...,qNR by jointly compressing the signals x˜1,...,x˜NR. This adds a further degree of freedom to the system design, which will be leveraged here to enhance physical-layer security. It was shown in [11, Sec. IV-D] that multivariate compression can be implemented with no loss of optimality using a low-complexity sequential processing architecture. Specifically, in this work, we propose to shape the quantization noise signals in order to enhance the secrecy performance by controlling the correlation matrix Ω of the quantization noise vector q [q1;...;qNR], where the covariance matrix is given as a block matrix whose (i,j)th block is . As mentioned, this control can be realized by means of multivariate compression, which was recently demonstrated in [11] to achieve performance gains in terms of non-secrecy information rates. It is a classic result in network information theory that the quantized signals (3) with the given quantization noise covariance Ω can be recovered by the RUs if the conditions (4) are satisfied for all subsets S ⊆ NR, where we have defined the set xˆ and the matrix ES obtained by stacking the matrices Ei for i ∈ S horizontally with the matrices Ei ∈ CnR×nR,i having all-zero elements except for the rows from being the identity matrix of size nR,i [13, Ch. 9]. C. Artificial Noise Based on the decompressed baseband signal xˆi, each RU i creates the signal xi to be transmitted in the downlink as xi = xˆi + ni, (5) where ni represents the artificial noise signal generated by RU i and is distributed as ni ∼ CN(0,Φi). The artificial noise signals ni are independent across the index i since each signal ni is locally produced by the corresponding RU. As for the quantization noise signal qi, we need to carefully design the covariance matrix Φi based on the channel matrices in order to enhance secrecy. D. Achievable Secrecy Rates The signal yk in (1) received by UE k can be written as y l∈NU\{k} where we defined the channel matrix H from all the RUs to UE k, the aggregate vector n [n1;...;nNR] of the artificial
Abstract Time synchronization is one of the most crucial issues that must be addressed in developing quantum key distribution (QKD) systems. It not only lets the transmitter and the receiver to assign a sequence number to each event and then do correct basis reconciliation, but also allows to increase signal-to-noise ratio. Time synchronization in satellite communications is especially complicated due to such factors as high loss, signal fading and Doppler effect. In this work, a simple, efficient and robust algorithm for time synchronization is proposed. It was tested during experiments on QKD between Micius, the world’s first quantum communications satellite, and an optical ground station located in Russia. The obtained synchronization precision lies in the range from 467 to 497 ps. The authors compare their algorithm for time synchronization with the previously used methods. The proposed approach can also be applied to terrestrial QKD systems.
—This work considers the downlink of a cloud radio access network (C-RAN), in which a control unit (CU) encodes confidential messages, each of which is intended for a user equipment (UE) and is to be kept secret from all the other UEs. As per the C-RAN architecture, the encoded baseband signals are quantized and compressed prior to the transfer to distributed radio units (RUs) that are connected to the CU via finite-capacity fronthaul links. This work argues that the quantization noise introduced by fronthaul quantization can be leveraged to act as "artificial" noise in order to enhance the rates achievable under secrecy constraints. To this end, it is proposed to control the statistics of the quantization noise by applying multivariate, or joint, fronthaul quantization/compression at the CU across all outgoing fronthaul links. Assuming wiretap coding, the problem of jointly optimizing the precoding and multivariate compression strategies, along with the covariance matrices of artificial noise signals generated by RUs, is formulated with the goal of maximizing the weighted sum of achievable secrecy rates while satisfying per-RU fronthaul capacity and power constraints. After showing that the artificial noise covariance matrices can be set to zero without loss of optimaliy, an iterative optimization algorithm is derived based on the concave convex procedure (CCCP), and some numerical results are provided to highlight the advantages of leveraging quantization noise as artificial noise. Index Terms—C-RAN, physical-layer security, fronthaul quantization, beamforming I. INTRODUCTION Motivated by the original works on the wiretap channel [1][2], physical-layer security techniques have been extensively studied as effective means of protecting data secrecy for communications over wireless channels in a variety of scenarios [3][4]. One of the key techniques that have been devised for enhancing the rates at which information can be transmitted securely is the addition of artificial noise at the transmitter [5]-[10]. This strategy finds its theoretical justification in the prefix channel approach that was shown in [2] to achieve the secrecy capacity of a general wiretap channel. In this work, we study physical-layer secure communication in the context of the downlink of cloud radio access networks Figure 1. Illustration of the downlink of a C-RAN system with confidential messages for NR = 2 RUs, NU = 2 UEs, nR,i = 2 RU antennas and nU,k =2 UE antennas. (C-RANs). In a C-RAN, a control unit (CU) performs joint encoding of the messages intended for all the user equipments (UEs) located in the geographical area covered by the radio units (RUs) connected to the CU. The encoded baseband signals are then transferred to the RUs on the fronthaul link in analog or digital format. For digital fronthauling, the CU quantizes and compresses the encoded baseband signals prior to the transfer to the RUs due to the limited bit rate of the fronthaul links [11][12]. In this work, we argue that the quantization noise introduced by fronthaul quantization can be leveraged to act as artificial noise in order to enhance the rates achievable under secrecy constraints. To this end, as an extension of the work [11], we propose to apply multivariate, or joint, fronthaul quantization/compression [13] at the CU for all outgoing fronthaul links in order to control the statistics of the quantization noise. Multivariate quantization/compression was recently shown in [11] to improve the performance of C-RANs without secrecy constraints with respect to standard per-fronthaul link pointto-point quantization/compression. In the rest of this paper, we first formulate the problem of jointly optimizing precoding, multivariate compression and the covariance matrices of artificial noise signals generated by RUs, with the goal of maximizing the weighted sum of achievable secrecy rates of the intended UEs subject to perRU fronthaul capacity and power constraints (Sec. III). We show that the artificial noise covariance matrices can be set to zero with no loss of optimality and hence focus on the joint optimization of precoding and multivariate compression. An iterative optimization algorithm is then derived based on the concave convex procedure (CCCP) (Sec. III), and numerical evidence is provided to highlight the advantages of the proposed schemes (Sec. IV). II. SYSTEM MODEL We consider the downlink of a C-RAN in which a single CU controls NR RUs. The CU communicates with the ith RU through a fronthaul link of capacity Ci bits/s/Hz where the normalization is with respect to the downlink bandwidth. The NR RUs transmit signals to NU UEs located in the union of the coverage areas of the RUs. We define the sets NR of the RUs and the UEs, and denote the numbers of antennas of RU i and UE k as nR,i and nU,k, respectively. An illustration is shown in Fig. 1. The signal yk ∈ CnU,k×1 received by UE k is given by y, (1) i∈NR where Hk,i ∈ CnU,k×nR,i represents the channel responseR,i matrix from RU i to UE k; xi ∈ CU,kn ×1 indicates the signal transmitted by RU i; and zk ∈ Cn ×1 is the additive noise at UE k distributed as zk ∼ CN(0,Σzk). Each RU i is subject to the power constraint. The information messages Mk ∈ {1,...,2nRk}, each of rate Rk bits/s/Hz, are encoded within a block of n channel uses, where n is large enough to justify the use of informationtheoretic limits. The message Mk is intended for UE k ∈ NU and is required to be kept secret from the other UEs. Specifically, we impose that the UEs l ∈ NU\{k} be unable to decode the message Mk even in the worst-case scenario where they cooperate since the CU cannot control the activities of the UEs (see [1]). The messages {Mk}k∈NU are processed by the CU in the two steps described in the following subsections before being transferred to the RUs. A. Linear Precoding The CU first encodes each message Mk using a wiretap code [1] and obtaining an encoded signal sk ∈ Cdk×1, which is distributed as sk ∼ CN(0,I). We assume that the number dk of data streams satisfies the condition dk ≤ min{nR,nU,k} with the notation . In order to enable the management of the inter-UE interference and to enhance secrecy, the CU performs linear precoding, or beamforming, with a precoding matrix A ∈ CRnR×d, yielding the precoded signal x˜ = [x˜1;...;x˜NR] ∈ Cn ×1 with x˜ = As, (2) where x˜i ∈ CnR,i×1 is the signal to be communicated to RU i; s [s1;...;sNU] is the vector of the signals encoded for the UEs; and we have defined the notation . We note that the discussion can be easily extended to systems, in which the CU performs non-linear secrecy dirty-paper coding (S-DPC) precoding proposed in [10]. B. Fronthaul Compression The precoded baseband signal x˜i needs to be compressed prior to transmission to the RU, since the CU communicates to RU i through a fronthaul link of capacity Ci bits/s/Hz. Using standard rate-distortion considerations, we model the impact of compression by adding a quantization noise qi to the compression input signal x˜i so that the compression output signal xˆi is given as xˆi = x˜i + qi, (3) where the quantization noise qi is independent of the signal x˜i and is distributed as qi ∼ CN(0,Ωi,i). Each RU i decompresses the baseband signal xˆi based on the bit stream received on the fronthaul link. We emphasize that, as done in, e.g., [11], quantization is not designed so as to minimize the (e.g., quadratic) distortion between the precoded signals x˜i and the compressed signals xˆi, but rather with the aim of maximizing the weighted sum of achievable secrecy rates, which will be defined in Sec. II-D. In the standard point-to-point compression approach [14], in which the precoded signals x˜i and x˜j for different RUs are separately compressed, the quantization noises qi and qj are independent, i.e., . Instead, multivariate, or joint, compression [13, Ch. 9] allows the CU to correlate the quantization noises q1,...,qNR by jointly compressing the signals x˜1,...,x˜NR. This adds a further degree of freedom to the system design, which will be leveraged here to enhance physical-layer security. It was shown in [11, Sec. IV-D] that multivariate compression can be implemented with no loss of optimality using a low-complexity sequential processing architecture. Specifically, in this work, we propose to shape the quantization noise signals in order to enhance the secrecy performance by controlling the correlation matrix Ω of the quantization noise vector q [q1;...;qNR], where the covariance matrix is given as a block matrix whose (i,j)th block is . As mentioned, this control can be realized by means of multivariate compression, which was recently demonstrated in [11] to achieve performance gains in terms of non-secrecy information rates. It is a classic result in network information theory that the quantized signals (3) with the given quantization noise covariance Ω can be recovered by the RUs if the conditions (4) are satisfied for all subsets S ⊆ NR, where we have defined the set xˆ and the matrix ES obtained by stacking the matrices Ei for i ∈ S horizontally with the matrices Ei ∈ CnR×nR,i having all-zero elements except for the rows from being the identity matrix of size nR,i [13, Ch. 9]. C. Artificial Noise Based on the decompressed baseband signal xˆi, each RU i creates the signal xi to be transmitted in the downlink as xi = xˆi + ni, (5) where ni represents the artificial noise signal generated by RU i and is distributed as ni ∼ CN(0,Φi). The artificial noise signals ni are independent across the index i since each signal ni is locally produced by the corresponding RU. As for the quantization noise signal qi, we need to carefully design the covariance matrix Φi based on the channel matrices in order to enhance secrecy. D. Achievable Secrecy Rates The signal yk in (1) received by UE k can be written as y l∈NU\{k} where we defined the channel matrix H from all the RUs to UE k, the aggregate vector n [n1;...;nNR] of the artificial