Collinear factorization violation and effective field theory

The factorization of amplitudes into hard, soft and collinear parts is known to be violated in situations where incoming particles are collinear to outgoing ones. This result was first derived by studying limits where non-collinear particles become collinear. We show that through an effective field theory framework with Glauber operators, these factorization-violating effects can be reproduced from an amplitude that is factorized before the splitting occurs. We confirm results at one-loop, through single Glauber exchange, and at two-loops, through double Glauber exchange. To approach the calculation, we begin by reviewing the importance of Glauber scaling for factorization. We show that for any situation where initial state and final state particles are not collinear, the Glauber contribution is entirely contained in the soft contribution. The contributions coming from Glauber operators are necessarily non-analytic functions of external momentum, with the non-analyticity arising from the rapidity regulator. The non-analyticity is critical so that Glauber operators can both preserve factorization when it holds and produce factorization-violating effects when they are present.Comment: 55 Pages, 5 figure

To Harvest and Jam: A Paradigm of Self-Sustaining Friendly Jammers for Secure AF Relaying

This paper studies the use of multi-antenna harvest-and-jam (HJ) helpers in a multi-antenna amplify-and-forward (AF) relay wiretap channel assuming that the direct link between the source and destination is broken. Our objective is to maximize the secrecy rate at the destination subject to the transmit power constraints of the AF relay and the HJ helpers. In the case of perfect channel state information (CSI), the joint optimization of the artificial noise (AN) covariance matrix for cooperative jamming and the AF beamforming matrix is studied using semi-definite relaxation (SDR) which is tight, while suboptimal solutions are also devised with lower complexity. For the imperfect CSI case, we provide the equivalent reformulation of the worst-case robust optimization to maximize the minimum achievable secrecy rate. Inspired by the optimal solution to the case of perfect CSI, a suboptimal robust scheme is proposed striking a good tradeoff between complexity and performance. Finally, numerical results for various settings are provided to evaluate the proposed schemes.Comment: 16 pages (double column), 8 figures, submitted for possible journal publicatio

A New Exposed-terminal-free MAC Protocol for Multi-hop Wireless Networks

AbstractThis article presents a new multichannel medium access control (MAC) protocol to solve the exposed-terminal (ET) problem for efficient channel sharing in multi-hop wireless networks. It uses request-to-send and clear-to-send (RTS/CTS) dialogue on a common channel and flexibly opts for conflict-free traffic channels to carry out the data packet transmission on the basis of a new channel selection scheme. The acknowledgment (ACK) packet for the data packet transmission is sent back to the sender over another common channel thus completely eliminating the exposed-terminal effects. Any adjacent communication pair can take full advantage of multiple traffic channels without collision and the spatial reuse of the same channel is extended to other communication pairs which are even within 2 hops from them. In addition, the hidden-terminal effect is also considerably reduced because most of possible packet collisions on a single channel are avoided due to traffic load balance on multichannels. Finally, a performance comparison is made between the proposed protocol and other typical MAC protocols. Simulation results evidence its obvious superiority to the MAC protocols associated with other channel selection schemes and traditional ACK transmission scheme as well as cooperative asynchronous multichannel MAC (CAM-MAC) protocol in terms of four performance indices: total channel utilization, average channel utilization, average packet delay, and packet dropping rate