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This paper studies the fundamental relations between key design parameters of millimeter wave (mmWave) multiple input multiple output (MIMO) communication systems and subarray structures deployed at both the transmitter and the receiver with each radio frequency (RF) chain connected to only a specific subset of the antennas. The concept of effective degrees of freedom (EDoF) is introduced to measure the maximum spatial multiplexing gain available for the MIMO system. An analytical expression for the EDoF with respect to the parameters of antenna configuration and transmission distance is obtained for the line of sight (LoS) scenario. In addition, the upper and lower bounds of the EDoF are further obtained for some special cases. A fast beam training algorithm based on the codebook is developed to reduce the number of training for the designed mmWave system. Extensive simulation results indicate that the proposed scheme reduces the computational load of the exhaustive approach with only minimal loss in performance. Moreover, the proposed design is robust to the geometrical change and misplacement.