Virtual Sectorization (ViSn) aims at covering a confined area such as a traffic hot-spot using a narrow beam. The beam is generated by a remote antenna array located at-or close to the Base Station (BS). This paper develops the ViSn model and provides the guidelines for designing the Virtual Sector (ViS) antenna. In order to mitigate interference between the ViS and the traditional macro sector covering the rest of the area, a Dynamic Spectrum Allocation (DSA) algorithm that self-optimizes the frequency bandwidth split between the macro cell and the ViS is also proposed. The Self-Organizing Network (SON) algorithm is constructed to maximize the proportional fair utility of all the users throughputs. Numerical simulations show the interest in deploying ViSn, and the significant capacity gain brought about by the self-optimized bandwidth sharing with respect to a full reuse of the bandwidth by the ViS.