Optimal Beamforming for Physical Layer Security in MISO Wireless Networks

A wireless network of multiple transmitter-user pairs overheard by an eavesdropper, where the transmitters are equipped with multiple antennas while the users and eavesdropper are equipped with a single antenna, is considered. At different levels of wireless channel knowledge, the problem of interest is beamforming to optimize the users' quality-of-service (QoS) in terms of their secrecy throughputs or maximize the network's energy efficiency under users' QoS. All these problems are seen as very difficult optimization problems with many nonconvex constraints and nonlinear equality constraints in beamforming vectors. The paper develops path-following computational procedures of low-complexity and rapid convergence for the optimal beamforming solution. Their practicability is demonstrated through numerical examples

Two-loop vacuum energy for Calabi-Yau orbifold models

A precise evaluation of the two-loop vacuum energy is provided for certain Z_2 x Z_2 Calabi-Yau orbifold models in the Heterotic string. The evaluation is based on the recent general prescription for superstring perturbation theory in terms of integration over cycles in supermoduli space, implemented at two-loops with the gauge-fixing methods based on the natural projection of supermoduli space onto moduli space using the super-period matrix. It is shown that the contribution from the interior of supermoduli space (computed with the procedure that has been used in previous two-loop computations) vanishes identically for both the E_8 x E_8 and Spin (32)/Z_2 Heterotic strings. The contribution from the boundary of supermoduli space is also evaluated, and shown to vanish for the E_8 x E_8 string but not for the Spin (32)/Z_2 string, thus breaking supersymmetry in this last model. As a byproduct, the vacuum energy in Type II superstrings is shown to vanish as well for these orbifolds.Comment: 70 pages, 2 figure

Higher Order Deformations of Complex Structures

Deformations of complex structures by finite Beltrami differentials are considered on general Riemann surfaces. Exact formulas to any fixed order are derived for the corresponding deformations of the period matrix, Green's functions, and correlation functions in conformal field theories with vanishing total central charge. The stress tensor is shown to give a simple representation of these deformations valid to all orders. Such deformation formulas naturally enter into the evaluation of superstring amplitudes at two-loop order with Ramond punctures, and at higher loop order, in the supergravity formulation of the RNS superstring