It is well known that a cognitive radio network (CRN) may further enhance the sum spectral efficiency using temporarily idle spectrum. However, we usually ignore the spatial domain behaviors to fully utilize the radio resource to approach available system capacity. When a signal is transmitted, we usually treat its occupancy of spectrum along all propagation directions. However, up to certain range (distance), the signal strength is weak and possibly allow another co-existing transmission happening with a satisfactory signal to interference-and-noise ratio (SINR) at both transmit-receive (T-R) pairs. In this paper, we realize this concept for a CRN consisting of a primary (PR) T-R pair and a cognitive radio (CR) T-R pair; furthermore, we consider to what condition concurrent transmission can happen.We use the Lagrange multiplier method to determine the optimal power allocation scheme for such a CRN and then determine to what extent can the sum spectral efficiency be enhanced. It is found that the CR transmitter (CR-TX) may either transmit at its maximum allowable power or just turn off with no transmission power. Concurrent transmission of the PR T-R and CR T-R pairs with distance as a new dimension of multiplexing can be considered as a new version of CRN.