Enhancing Secure C-RAN Communications via Fronthaul Quantization as Artificial Noise

Abstract

—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