Zero-forcing beamforming for physical layer security of energy harvesting wireless communications

Zhu et al. EURASIP Journal on Wireless Communications and Networking Zero-forcing beamforming for physical layer security of energy harvesting wireless communications Fengchao Zhu 0 Feifei Gao 0 Minli Yao 1 0 Department of Automation, Tsinghua University, State Key Lab of Intelligent Technologies and Systems, Tsinghua National Laboratory for Information Science and Technology (TNList) , No. 30 Shuang Qing Road, 100084 Beijing , P. R. China 1 High-Tech Institute of Xi'an , No. 2 Tong Xin Road, 710025 Xi'an, Shaanxi , P. R. China In this paper, we consider the physical layer security for simultaneous wireless information and power transfer (SWIPT) in a multiple-input single-output (MISO) system that is consisted of three nodes: one transmitter with multiple antennas, one information decoding (ID) receiver with single antenna, and one energy harvesting (EH) receiver with single antenna. We propose a new zero-forcing based strategy that contains both the information beamforming and the energy beamforming, pointing to different receivers. To prevent the energy receiver from possibly eavesdropping the information, our target is to maximize the secrecy-rate of the ID receiver while at the same time maintaining a minimum required energy for the EH receiver. For the case that artificial noise is not used, the original non-convex problem can be directly converted into convex subproblems, where the closed-form optimal solutions are derived. For the case that artificial noise is used, the initial non-convex problem can be decomposed into two quasi-convex subproblems where closed-form solutions are derived, and the global optimal solutions are obtained with the aid of one-dimensional search. Simulations results demonstrate the trade-off between the maximum secret information rate and the transferred energy, which is characterized by the boundary of secret rate-energy (R-E) region. Physical layer security; Simultaneous wireless information and power transfer; Beamforming; Energy harvesting - Introduction Since radio-frequency (RF) signals that carry information can, at the same time, be used for transporting energy, simultaneous wireless information and power transfer (SWIPT) is made possible in energy-constrained wireless networks and has become an interesting research area recently [1-5]. In [1], Varshney proposed a capacity-energy function for SWIPT, where a fundamental trade-off between the energy and the reliable information transmitted over a single noisy line is studied. In [2], Grover and Sahai extended the results of [1] to frequency-selective singleantenna additive white Gaussian noise (AWGN) channels, where a similar trade-off in frequency-domain is demonstrated. In [3], the robust case for SWIPT was studied using beamforming. In [4], Zhang revealed some fundamental issues in designing wireless multiple-input multiple-output (MIMO) systems to maximize the efficiency of SWIPT. Both information decoding (ID) receiver and energy harvesting (EH) receiver that are separated or co-located were investigated in [4], and the optimal transmission strategy was derived to achieve different tradeoffs between maximal information rate and transferred energy. Most recently, in [5], the authors studied MIMO beamforming with partial channel state information (CSI) under energy harvesting constraints. On the other hand, information-theoretic approach to guarantee secrecy was initiated by Wyner [6], where the concept of secrecy capacity was, for the first time, defined in degraded discrete memoryless wiretap channels. In [7], the results of [6] was generalized to a broadcast channel. Moreover, information secrecy in multiple access channels (MAC) was studied in [8-10], and information secrecy in single-input single-output (SISO) fading channels was also studied in [11-13]. To guarantee information secrecy using Wyners model, the channel condition of the legitimate user is required to be better than that of the eavesdropper. In practice, however, this requirement may not be satisfied. Recently, an interesting way to achieve the secrecy using the aided noise was proposed in [14], where the information secrecy could be guaranteed even when the channel condition of the legitimate user is worse than that of the eavesdropper. Then the idea of aided noise were used in lots of works [15-22] where the physical layer security were studied. For example, [18-20] assume that transmitters cooperate to generate the aided noise, while [15-17,21,22] require the aided noise spread in the null-space of the legitimate receivers channel. Moreover, [23] studied the case where the noise covariance could take any spatial pattern. In addition, some other secure transmitting designs with the aided noise were also proposed aiming to provide the legitimate receiver with different quality-of-service (QoS), e.g., the SINR-based design [24] and the mean squared error (MSE)-based design [25]. The physical layer security for SWIPT system was first studied in [26], where secret information beamforming vector and artificial noise transmit covariance were designed. However, in [26], the closed-form solutions for information beamforming vector and energy beamforming vector cannot be derived. In this paper, we study information secrecy of SWIPT using zero-forcing beamforming which has lower computational complexity than the algorithm proposed in [26]. Remarkably, closed-form solutions are derived for both information beamforming vector and artificial noise (also used as energy) beamforming vector. The main contributions of this paper are summarized as follows: 1. For the feasibility problem, we obtain the closed-form solutions for energy beamforming vector, which can be derived with maximal-ratio-combining (MRC) principle. 2. For the conventional physical layer security problem without artificial noise, we first prove that the initial non-convex problem can be divided into two subproblems, based on different values of energy harvest requirements. Then, the closed-form solutions for the subproblems are derived. 3. For SWIPT with joint energy beamforming and information beamforming, we design zero-forcing beamforming for physical layer security. The optimal solutions for the non-convex problem is obtained using one-dimensional search. Remarkably, at each search step, closed-form solutions can be derived for all subproblems. Notation: Vectors and matrices are boldface small and capital letters, respectively; the transpose, complex conjugate, Hermitian, inverse, and the pseudo-inverse of A are denoted by AT, A, AH, A1, and A, respectively; Tr(A) and A1/2 denote the trace and the square-root, respectively; I and 0 denote an identity matrix and an all-zero matrix, respectively, with appropriate dimensions; A 0 and A 0 mean that A is positive semi-definite and positive definite, respectively; E[ ] denotes the statistical expectation; The distribution of a CSCG random variable with zero mean and variance 2 is denoted a (...truncated)