In the context of recent research on relay-assisted mm-Wave MIMO systems with hybrid beamforming architecture, one of the major design goals is to enhance the reliability of transmitted data, even under the worst channel impairments. This objective can be achieved by deploying multiple relays in the communication path between source and end-user. Moreover, this paradigm enables having several channels for data transmission from the source to the destination. It is highly unlikely that all the available links are suffering due to severe channel impairments. To enhance the spectral efficiency and overall system performance, some suitable mechanism is required for relay selection along with the hybrid beamforming design at all communicating nodes. Therefore, the proposed algorithm is an attempt to address hybrid transceiver design and relay selection while considering relay-based mm-Wave MIMO system. In contrast to an iterative approach and codebook-based method for hybrid precoding design, the proposed methodology is free from the iterative procedure and searching algorithm associated with codebook in finding the best possible solution. Furthermore, an analytic solution is provided for deriving the analog RF beamformers and digital baseband processing components at all communicating nodes. While relay selection is made by considering the highest SNR from the source to the destination. The contributions of the proposed scheme are summarized as follows:  
* The proposed research work introduces the hybrid beamforming and relay selection mechanism in a single-user multi-relay mm-Wave MIMO system. In order to avoid performance degradation in a multi-hop transmission network due to poor channel characteristics, the proposed algorithm selects the relay node which gives maximum SNR from the source to the destination. This selection criterion enables maximizing the spectral efficiency even in the presence of unfavorable conditions on several transmission paths. * The proposed hybrid beamforming scheme derives the common analog RF precoder at source by finding the orthonormal basis for column space spanned by all the channels from source to relay nodes. The common analog RF combiner at the destination is obtained by minimizing the error over all optimal combiners corresponding to the channels from relay nodes to the destination. Finally, the analog precoder/combiner at relay nodes are derived by solving the respective SNR maximization problems. * By considering the equivalence of spectral efficiency maximization and MSE minimization, digital baseband processing components at communicating nodes are obtained under MMSE criterion. This design procedure leads to the condition for minimizing interference and hence, maximizing the spectral efficiency. * Computer simulations were conducted to evaluate the performance of the proposed hybrid beamforming algorithm by varying system configuration parameters. It is obvious from the obtained results that the proposed approach has a great potential to show good performance in sparse and rich scattering environments such as mm-Wave and Rayleigh fading channels, respectively. * The existing works (e.g., [34; 35; 36; 37; 38]) only focus on the hybrid beamforming design for relay-assisted mm-Wave MIMO systems under different scenarios. With this perspective, there is a need to address relay-assisted MIMO communication in conjunction with a relay selection mechanism to enhance spectral efficiency of the system. Therefore, the proposed methodology may be considered as an important application area in the scope of hybrid relaying, which is capable of avoiding performance degradation. The rest of the paper is organized as follows. System model and problem formulation are given in Section 2. Analog RF beamforming design at different communicating nodes and relay selection scheme are presented in Section 3. Derivation of digital baseband processing units and complexity analysis are included in Section 4. Computer simulations to evaluate the performance of the proposed algorithm are provided in Section 5.