Joint Relay Selection and Power Allocation in Large-Scale MIMO Systems with Untrusted Relays and Passive Eavesdroppers

In this paper, a joint relay selection and power allocation (JRP) scheme is proposed to enhance the physical layer security of a cooperative network, where a multiple antennas source communicates with a single-antenna destination in presence of untrusted relays and passive eavesdroppers (Eves). The objective is to protect the data confidentially while concurrently relying on the untrusted relays as potential Eves to improve both the security and reliability of the network. To realize this objective, we consider cooperative jamming performed by the destination while JRP scheme is implemented. With the aim of maximizing the instantaneous secrecy rate, we derive a new closed-form solution for the optimal power allocation and propose a simple relay selection criterion under two scenarios of non-colluding Eves (NCE) and colluding Eves (CE). For the proposed scheme, a new closed-form expression is derived for the ergodic secrecy rate (ESR) and the secrecy outage probability as security metrics, and a new closed-form expression is presented for the average symbol error rate (SER) as a reliability measure over Rayleigh fading channels. We further explicitly characterize the high signal-to-noise ratio slope and power offset of the ESR to highlight the impacts of system parameters on the ESR. In addition, we examine the diversity order of the proposed scheme to reveal the achievable secrecy performance advantage. Finally, the secrecy and reliability diversity-multiplexing tradeoff of the optimized network are provided. Numerical results highlight that the ESR performance of the proposed JRP scheme for NCE and CE cases is increased with respect to the number of untrustworthy relays.Comment: 18 pages, 10 figures, IEEE Transactions on Information Forensics and Security (In press

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<p>Principal component analysis of ATR spectra of hemp native primary fibers (f1) and secondary native fibers (f2) (a) obtained from F17 and S27 with all growing conditions. Score loading corresponding to PC1 (b).</p

Stereomicroscopy imaging of transverse cross section of the hemp stem.

<p>(a) showing wood and bark including primary fibers (f1), secondary fibers (f2); arrows indicate the dimensions measured to determine wood-/bark-thickness (b) in the basal stem region of F17 and S27 grown under different conditions (standard, irrigation, high sowing density: 100 kg.ha^-1).</p

Principal component analysis of ATR spectra of native primary fibers (f1) (a) and of native secondary fibers (f2) (b) showing dispersion with regards to growing conditions.

<p>Principal component analysis of ATR spectra of native primary fibers (f1) (a) and of native secondary fibers (f2) (b) showing dispersion with regards to growing conditions.</p

Chemical composition of primary and secondary fibers isolated from hemp harvested at the end of flowering stage (variety S27).

<p>Lignin and total sugar contents as percent of cell wall residue; monosaccharides as percent of total sugars. Means not sharing a common letter are significantly different (p<0.05).</p

Fiber yields of F17 and S27 hemp varieties harvested at the end of flowering stage (as percent of straw dry matter).

<p>Fiber yields of F17 and S27 hemp varieties harvested at the end of flowering stage (as percent of straw dry matter).</p

Image treatment of UV auto fluorescence of hemp stem cross-sections (a) used to determine areas of primary fibers (b) and secondary fibers (c) in F17 and S27 varieties grown under different conditions (standard, irrigation, high sowing density: 100 kg.ha^-1) (expressed as μm²) with regards to bark thickness (expressed as μm).

<p>Image treatment of UV auto fluorescence of hemp stem cross-sections (a) used to determine areas of primary fibers (b) and secondary fibers (c) in F17 and S27 varieties grown under different conditions (standard, irrigation, high sowing density: 100 kg.ha^-1) (expressed as μm²) with regards to bark thickness (expressed as μm).</p

Principal component analysis of ATR spectra of native secondary and technical hemp fibers.

<p>Principal component analysis of ATR spectra of native secondary and technical hemp fibers.</p

UV autofluorescence of cross-sections from the basal stem region of hemp.

<p>S27 (a,c,e) and F17 (b,d,f) grown under standard (a,b), high sowing density: 100 kg.ha^-1 (c,d) irrigation (e,f). Primary fibers (f1), secondary fibers (f2).</p

Additional file 5: Table S2. of Spatial regulation of monolignol biosynthesis and laccase genes control developmental and stress-related lignin in flax

Description of the gene expression localization in the tissues of flax roots, stems and leaves. (JPEG 391 kb