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Achieving high data rate communications and increasing system reliability are the essentials for 5G networks. Massive MIMO and millimeter wave (mmWave) communications along with the ongoing developments in the underlying infrastructure promise to sharply increase the aggregate capacity. The communication system harnessing the odds of the unused spectrum in mmWave bands is vulnerable to the extreme path loss that severely weakens the strength of the information-bearing signal. Nevertheless, exploiting hybrid beamforming and efficient high-speed channel estimation algorithm can help address this problem and create the communication systems required for 5G. Our main contribution in this paper is to propose a very high speed accurate greedy algorithm called Subspace Pursuit (SP) and we also compare the performance of this algorithm with two other greedy algorithms. Simulation results show that SP algorithm achieves a noticeable improvement in comparison with Orthogonal Matching Pursuit (OMP) and Regularized Orthogonal Matching Pursuit (ROMP) algorithms in terms of both the spectral efficiency and runtime.