We consider a system that integrates positioning and single-user millimeter wave (mmWave) communication, where the communication part adopts wavelength division multiplexing (WDM) and orbital angular momentum (OAM). This paper addresses the multi-dimensional constellation design in shortrange line-of-sight (LOS) environment, with stable communication links. We propose a map-assisted method to quantify the system parameters based on positions and reduce real-time computing overhead. We explore the possibility of using a few patterns in the maps, and investigate its performance loss. We first investigate the features of OAM beams, and find that the link gain ratio between any two sub-channels remains unchanged at some postions. Then, we prove that a fixed constellation can be adopted for the positions where the link gain matrices are sufficiently close to be proportional. Moreover, we prove that the system can adopt a fixed power vector to generate a multidimensional constellation if the difference between fixed power vector and optimal power vector is small. Finally, we figure out that the constellation design for all receiver locations can be represented by a few constellation sets.