Degrees of Freedom for Half-Duplex and Full-Duplex Multi-User Cognitive Radios

Abstract

The degrees of freedom (DoF) of multi-user cognitive radios (CR) under half-duplex (HD) and full-duplex (FD) are studied in this work. Due to the fact that FD adopted multiple cognitive users (CUs) suffer not only self-interference (SI) and primary-user interference (PUI) but also multi-user interference (MUI) from the other CUs, the DoF metric is constrained by various interference factors and shows scale invariance properties with respect to the temporal, frequency and spatial dimensions. In this regard, the average DoF is characterized in both spatio and temporal dimensions using limitation calculation (LC) and interference alignment (IA) methods, under interweave, underlay, overlay and hybrid CR patterns. Due to the multi-user specified impacts, the achievable DoF of CU is constrained by the maximum transmit power of the other CUs, and the HD and FD tradeoff for multi-user CR is determined by both MUI and time-antenna splitting. Theoretical analysis indicates that the secondary user power and secondary user number only inflict impacts on LC and IA based average DoF respectively. Moreover, because of distributed CR processing, the average DoF for MU CR is upper-bounded by that of single-user CR. Simulation results validate the effects of MUI, SI, PUI and user number on the average DoF. It shows that IA achieves higher DoF than that of LC for multi-user CR, indicating that the DoF loss due to MUI can be reduced if interference mitigation is available.