Ergodic Sum Capacity of Spectrum-Sharing Multiple Access with Collision Metric

This paper investigates the ergodic sum capacity of a spectrum-shared Multiple Access Channel (MAC). We assume that the secondary service (SS) only knows the channel distribution information (CDI) between its transmitters and the primary receivers. Availability of CDI results in collision incidences at the primary receivers because of conflicting levels of intolerable interference. We introduce the concept of collision probability constraint to manage the unexpected QoS degradation of primary service in the secondary resource allocation (RA). This RA problem is inherently difficult to solve and its objective function is not necessarily convex. Two well-known approaches, called Iterative Approach (IA) and Analytical Approach (AA), each with several cases/categories, are then used to find solutions. IA solves the problem iteratively by reconstructing convex optimization problems from the original (non-convex) one in a number of iterative loops until the collision probability constraints are satisfied. IA is shown to converge quickly to a suitable solution. Furthermore, by using a control parameter, the system designer can make a tradeoff between the speed of convergence and the ergodic sum capacity. AA, on the other hand, solves the RA problem by suggesting tractable versions of collision probability constraints. Unlike IA, AA does not require extra signaling between transmitters and the base station to tune parameters, thus facilitating the implementation of SS. Our in-depth simulations have shown the proposed approach to yield lower spectral efficiency than IA.