Two-Way Training for Discriminatory Channel Estimation in Wireless MIMO Systems

This work examines the use of two-way training to efficiently discriminate the channel estimation performances at a legitimate receiver (LR) and an unauthorized receiver (UR) in a multiple-input multiple-output (MIMO) wireless system. This work improves upon the original discriminatory channel estimation (DCE) scheme proposed by Chang et al where multiple stages of feedback and retraining were used. While most studies on physical layer secrecy are under the information-theoretic framework and focus directly on the data transmission phase, studies on DCE focus on the training phase and aim to provide a practical signal processing technique to discriminate between the channel estimation performances at LR and UR. A key feature of DCE designs is the insertion of artificial noise (AN) in the training signal to degrade the channel estimation performance at UR. To do so, AN must be placed in a carefully chosen subspace based on the transmitter's knowledge of LR's channel in order to minimize its effect on LR. In this paper, we adopt the idea of two-way training that allows both the transmitter and LR to send training signals to facilitate channel estimation at both ends. Both reciprocal and non-reciprocal channels are considered and a two-way DCE scheme is proposed for each scenario. {For mathematical tractability, we assume that all terminals employ the linear minimum mean square error criterion for channel estimation. Based on the mean square error (MSE) of the channel estimates at all terminals,} we formulate and solve an optimization problem where the optimal power allocation between the training signal and AN is found by minimizing the MSE of LR's channel estimate subject to a constraint on the MSE achievable at UR. Numerical results show that the proposed DCE schemes can effectively discriminate between the channel estimation and hence the data detection performances at LR and UR.Comment: 1

On the Evolution of Ion Bunch Profile in the Presence of Longitudinal Coherent Electron Cooling

In the presence of longitudinal coherent electron cooling, the evolution of the line-density profile of a circulating ion bunch can be described by the 1-D Fokker-Planck equation. We show that, in the absence of diffusion, the 1-D equation can be solved analytically for certain dependence of cooling force on the synchrotron amplitude. For more general cases with arbitrary diffusion, we solved the 1-D Fokker-Planck equation numerically and the numerical solutions have been compared with results from macro-particle tracking

Pseuduscalar Heavy Quarkonium Decays With Both Relativistic and QCD Radiative Corrections

We estimate the decay rates of $\eta_c\rightarrow 2\gamma$, $\eta_c'\rightarrow 2\gamma$, and $J/\psi\rightarrow e^+ e^-$, $\psi^\prime\rightarrow e^+e^-$, by taking into account both relativistic and QCD radiative corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism. The Bethe-Salpeter equation with a QCD-inspired interquark potential are used to calculate the wave functions and decay widths for these $c\bar{c}$ states. We find that the relativistic correction to the ratio $R\equiv \Gamma (\eta_c \rightarrow 2\gamma)/ \Gamma (J/ \psi \rightarrow e^+ e^-)$ is negative and tends to compensate the positive contribution from the QCD radiative correction. Our estimate gives $\Gamma(\eta_c \rightarrow 2\gamma)=(6-7) ~keV$ and $\Gamma(\eta_c^\prime \rightarrow 2\gamma)=2 ~keV$, which are smaller than their nonrelativistic values. The hadronic widths $\Gamma(\eta_c \rightarrow 2g)=(17-23) ~MeV$ and $\Gamma(\eta_c^\prime \rightarrow 2g)=(5-7)~MeV$ are then indicated accordingly to the first order QCD radiative correction, if $\alpha_s(m_c)=0.26-0.29$. The decay widths for $b\bar b$ states are also estimated. We show that when making the assmption that the quarks are on their mass shells our expressions for the decay widths will become identical with that in the NRQCD theory to the next to leading order of $v^2$ and $\alpha_s$.Comment: 14 pages LaTex (2 figures included

Detecting Extra Dimension by Helium-like Ions

Considering that gravitational force might deviate from Newton's inverse-square law and become much stronger in small scale, we present a method to detect the possible existence of extra dimensions in the ADD model. By making use of an effective variational wave function, we obtain the nonrelativistic ground energy of a helium atom and its isoelectronic sequence. Based on these results, we calculate gravity correction of the ADD model. Our calculation may provide a rough estimation about the magnitude of the corresponding frequencies which could be measured in later experiments.Comment: 8 pages, no figures, accepted by Mod. Phys. Lett.

Phenomenology of xFx_F Dependence of Quarkonium Production in Proton-Nucleus Interactions

We present a phenomenological study of the $x_F$ dependence of quarkonium production in high energy proton-nucleus collisions. The \xf~dependence of comover contributions is introduced to account for the observed quarkonium suppression at low $x_F$. Combining comover contributions, nuclear shadowing effect, energy loss mechanism and nuclear absorption together we reproduce the overall \xf~dependence of E772/E789 data.Comment: 11 pages(Latex), 4 uuencoded figure

Coherent Beam-Beam Tune Shift of Unsymmetrical Beam-Beam Interactions with Large Beam-Beam Parameter

Coherent beam-beam tune shift of unsymmetrical beam-beam interactions was studied experimentally and numerically in HERA where the lepton beam has a very large beam-beam parameter (up to $\xi_y=0.272$). Unlike the symmetrical case of beam-beam interactions, the ratio of the coherent and incoherent beam-beam tune shift in this unsymmetrical case of beam-beam interactions was found to decrease monotonically with increase of the beam-beam parameter. The results of self-consistent beam-beam simulation, the linearized Vlasov equation, and the rigid-beam model were compared with the experimental measurement. It was found that the coherent beam-beam tune shifts measured in the experiment and calculated in the simulation agree remarkably well but they are much smaller than those calculated by the linearized Vlasov equation with the single-mode approximation or the rigid-beam model. The study indicated that the single-mode approximation in the linearization of Vlasov equation is not valid in the case of unsymmetrical beam-beam interactions. The rigid-beam model is valid only with a small beam-beam parameter in the case of unsymmetrical beam-beam interactions.Comment: 32 pages, 13 figure