Search

This paper presents an exact statistical analysis for the best relay location in a random two‐way relay network whose channels are subject to multi‐slope path loss and Rayleigh fading. In this network, relays are distributed randomly as a two‐dimensional Poisson point process, and the best relay is selected according to a max–min criterion. The midpoint between the two sources is adopted as a reference point and the relays are indexed such that the closer to the reference point, the smaller is the index. An exact analytical expression is derived for the probability that the kth nearest relay to the reference point is the best relay. Then, a detailed statistical analysis for the location of the best relay with respect to the reference point is presented. In each case, a low‐complexity approximation is also derived and its accuracy is verified by numerical simulation. The proposed analysis demonstrates the counter‐intuitive fact that the best relay in a random two‐way relay network is quite unlikely to be located on, or very close to the reference point. Numerical results also suggest that the proposed analysis can be used to restrict the search region for finding the best relay. [ABSTRACT FROM AUTHOR]

This work considers a two-user multiple access channel in which both users have Age of Information (AoI)-oriented traffic with different characteristics. More specifically, the first user has external traffic and cannot control the generation of status updates, and the second user monitors a sensor and transmits status updates to the receiver according to a generate-at-will policy. The receiver is equipped with multiple antennas and the transmitters have single antennas; the channels are subject to Rayleigh fading and path loss. We analyze the average AoI of the first user for a discrete-time first-come-first-served (FCFS) queue, last-come-first-served (LCFS) queue, and queue with packet replacement. We derive the AoI distribution and the average AoI of the second user for a threshold policy. Then, we formulate an optimization problem to minimize the average AoI of the first user for the FCFS and LCFS with preemption queue discipline to maintain the average AoI of the second user below a given level. The constraints of the optimization problem are shown to be convex. It is also shown that the objective function of the problem for the first-come-first-served queue policy is non-convex, and a suboptimal technique is introduced to effectively solve the problem using the algorithms developed for solving a convex optimization problem. Numerical results illustrate the performance of the considered optimization algorithm versus the different parameters of the system. Finally, we discuss how the analytical results of this work can be extended to capture larger setups with more than two users.