Secrecy Capacity Analysis Over κ–μ Fading Channels: Theory and Applications

In this paper, we consider the transmission of confidential information over a κ-μ fading channel in the presence of an eavesdropper who also experiences κ-μ fading. In particular, we obtain novel analytical solutions for the probability of strictly positive secrecy capacity (SPSC) and a lower bound of secure outage probability (SOPL) for independent and non-identically distributed channel coefficients without parameter constraints. We also provide a closed-form expression for the probability of SPSC when the μ parameter is assumed to take positive integer values. Monte-Carlo simulations are performed to verify the derived results. The versatility of the κ-μ fading model means that the results presented in this paper can be used to determine the probability of SPSC and SOPL for a large number of other fading scenarios, such as Rayleigh, Rice (Nakagamin), Nakagami-m, One-Sided Gaussian, and mixtures of these common fading models. In addition, due to the duality of the analysis of secrecy capacity and co-channel interference (CCI), the results presented here will have immediate applicability in the analysis of outage probability in wireless systems affected by CCI and background noise (BN). To demonstrate the efficacy of the novel formulations proposed here, we use the derived equations to provide a useful insight into the probability of SPSC and SOPL for a range of emerging wireless applications, such as cellular device-to-device, peer-to-peer, vehicle-to-vehicle, and body centric communications using data obtained from real channel measurements.

Secrecy Performance of Wirelessly Powered Wiretap Channels

This paper considers a wirelessly powered wiretap channel, where an energy constrained multi-antenna information source, powered by a dedicated power beacon, communicates with a legitimate user in the presence of a passive eavesdropper. Based on a simple time-switching protocol where power transfer and information transmission are separated in time, we investigate two popular multi-antenna transmission schemes at the information source, namely maximum ratio transmission (MRT) and transmit antenna selection (TAS). Closed-form expressions are derived for the achievable secrecy outage probability and average secrecy rate for both schemes. In addition, simple approximations are obtained at the high signal-to-noise ratio (SNR) regime. Our results demonstrate that by exploiting the full knowledge of channel state information (CSI), we can achieve a better secrecy performance, e.g., with full CSI of the main channel, the system can achieve substantial secrecy diversity gain. On the other hand, without the CSI of the main channel, no diversity gain can be attained. Moreover, we show that the additional level of randomness induced by wireless power transfer does not affect the secrecy performance in the high SNR regime. Finally, our theoretical claims are validated by the numerical results.

Secure Transmission in Spectrum Sharing MIMO Networks with Generalized Antenna Selection over Nakagami-m Channels

In this paper, we investigate the secrecy outage performance of spectrum sharing multiple-input multiple-output networks using generalized transmit antenna selection with maximal ratio combining over Nakagami-m channels. In particular, the outdated channel state information is considered at the process of antenna selection due to feedback delay. Considering a practical passive eavesdropper scenario, we derive the exact and asymptotic closed-form expressions of secrecy outage probability, which enable us to evaluate the secrecy performance with high efficiency and present a new design insight into the impact of key parameters on the secrecy performance. In addition, the analytical results demonstrate that the achievable secrecy diversity order is only determined by the parameters of the secondary network, while other parameters related to primary or eavesdropper’s channels have a significantly impact on the secrecy coding gain. 

Performance of downlink massive MIMO in Ricean fading channels with ZF precoder

We investigate the achievable sum rate and energy efficiency of zero-forcing precoded downlink massive multiple-input multiple-output systems in Ricean fading channels. A simple and accurate approximation of the average sum rate is presented, which is valid for a system with arbitrary rank channel means. Based on this expression, the optimal power allocation strategy maximizing the average sum rate is derived. Moreover, considering a general power consumption model, the energy efficiency of the system with rank-1 channel means is characterized. Specifically, the impact of key system parameters, such as the number of users N, the number of BS antennas M, Ricean factor K and the signal-to-noise ratio (SNR) ρ are studied, and closed-form expressions for the optimal ρ and M maximizing the energy efficiency are derived. Our findings show that the optimal power allocation scheme follows the water filling principle, and it can substantially enhance the average sum rate in the presence of strong line-of-sight effect in the low SNR regime. In addition, we demonstrate that the Ricean factor K has significant impact on the optimal values of M, N and ρ.

Achievable sum-rate of multiuser massive MIMO downlink in ricean fading channels

We investigate the achievable ergodic sum-rate of multi-user multiple-input multiple-output systems in Ricean fading channels. We first derive a lower bound on the average signal-to-leakage-and-noise ratio by utilizing the Mullen's inequality, which is then used to analyze the effect of channel mean information on the achievable sum-rate. With these results, a novel statistical-eigenmode space-division multipleaccess downlink transmission scheme is proposed. For this scheme, we derive an exact closed-form expression for the achievable ergodic sum-rate. Our results show that the achievable ergodic sum-rate converges to a saturation value in the high signal-to-noise ratio (SNR) region and reaches to a lower limit value in the lower Ricean K-factor range. In addition, we present tractable upper and lower bounds, which are shown to be tight for any SNR and Ricean K-factor value. Finally, the theoretical analysis is validated via numerical simulations.

Energy efficiency analysis of rank-1 Ricean fading MIMO channels

This paper studies the energy efficiency (EE) of a point-to-point rank-1 Ricean fading multiple-input-multiple-output (MIMO) channel. In particular, a tight lower bound and an asymptotic approximation for the EE of the considered MIMO system are presented, under the assumption that the channel is unknown at the transmitter and perfectly known at the receiver. Moreover, the effects of different system parameters, namely, transmit power, spectral efficiency (SE), and number of transmit and receive antennas, on the EE are analytically investigated. An important observation is that, in the high signal-to-noise ratio regime and with the other system parameters fixed, the optimal transmit power that maximizes the EE increases as the Ricean-K factor increases. On the contrary, the optimal SE and the optimal number of transmit antennas decrease as K increases.

Massive MIMO in sparse channels

Massive multi-user multiple-input multiple-output (MU-MIMO) systems are cellular networks where the base stations (BSs) are equipped with hundreds of antennas, N, and communicate with tens of mobile stations (MSs), K, such that, N ≫ K ≫ 1. Contrary to most prior works, in this paper, we consider the uplink of a single-cell massive MIMO system operating in sparse channels with limited scattering. This case is of particular importance in most propagation scenarios, where the prevalent Rayleigh fading assumption becomes idealistic. We derive analytical approximations for the achievable rates of maximum-ratio combining (MRC) and zero-forcing (ZF) receivers. Furthermore, we study the asymptotic behavior of the achievable rates for both MRC and ZF receivers, when N and K go to infinity under the condition that N/K → c ≥ 1. Our results indicate that the achievable rate of MRC receivers reaches an asymptotic saturation limit, whereas the achievable rate of ZF receivers grows logarithmically with the number of MSs.

Effects of menthol on rat tail artery mediated by TRPM8 and voltage-gated calcium channels

Transient receptor potential melastatin 8 (TRPM8) is the principal cold and menthol receptor channel. Characterized primarily for its cold sensing role in sensory neurons, it is expressed and functional in several non-neuronal tissues, including vasculature. We previously demonstrated that menthol causes vasoconstriction and vasodilatation in isolated arteries, depending on vascular tone. Here we investigated calcium's role in responses mediated by TRPM8 ligands in rat tail artery myocytes using patch-clamp electrophysiology and ratiometric Ca2+ recording. Isometric contraction studies examined actions of TRPM8 ligands in the presence/absence of L-type calcium channel blocker. Menthol (300 μM), a concentration typically used to induce TRPM8 currents, strongly inhibited L-type voltage-dependent Ca2+ current (L-ICa) in myocytes, especially it's sustained component, most relevant for depolarisation-induced vasoconstriction. In contraction studies, with nifedipine present (10 μM) to abolish L-ICa contribution to phenylephrine (PE)-induced vasoconstrictions of vascular rings, a marked increase in tone was observed with menthol. Menthol-induced increases in PE-induced vasoconstrictions were mediated predominantly by Ca2+-release from sarcoplasmic reticulum, since they were significantly inhibited by cyclopiazonic acid. Pre-incubation of vascular rings with a TRPM8 antagonist strongly inhibited menthol-induced increases in PE-induced vasoconstrictions, thus confirming specific role of TRPM8. Finally, two other common TRPM8 agonists, WS-12 and icilin, inhibited L-ICa. Thus, TRPM8 channels are functionally active in rat tail artery myocytes and play a distinct direct stimulatory role in control of vascular tone. However, indirect effects of TRPM8 agonists, which are unrelated to TRPM8, are mediated by inhibition of L-type Ca2+ channels, and largely obscure TRPM8-mediated vasoconstriction.