In the direction of arrival (DoA) estimation, typically sensor arrays are used where the number of required sensors can be large depending on the application. With the help of compressed sensing (CS), hardware complexity of the sensor array system can be reduced since reliable estimations are possible by using the compressed measurements where the compression is done by measurement matrices. After the compression, DoAs are reconstructed by using sparsity promoting algorithms such as alternating direction method of multipliers (ADMM). For the given procedure, both the measurement matrix design and the reconstruction algorithm may include computationally intensive operations, which are addressed in this study. The presented simulation results imply the feasibility of the system in real-time processing with energy efficient implementations. We propose employing parallel programming to satisfy the real-time processing requirements. While the measurement matrix design has been accelerated 16x with CPU based parallel version with respect to the fastest serial implementation, ADMM based DoA estimation has been improved 1.1x with GPU based parallel version compared to the fastest CPU parallel implementation. In addition, we achieved, to the best of our knowledge, the first energy-efficient real-time DoA estimation on embedded Jetson GPGPUs in 15 W power consumption without affecting the DoA accuracy performance.