In this paper, we consider a single group massive MIMO system, which consists of one receiver (base station) deployed with a large number of antennas and multiple users with each having single antenna. In the uplink transmissions from users to base station, we focus on an efficient signal reconstruction of all the users' transmitted symbols. We build a statistic decision matrix based on the received signals, whose eigenvectors and eigenvalues constitute the key components of our signal reconstruction algorithm. Then, an optimization problem is formulated and we convert this problem to two sub-problems: obtaining the optimal weights by solving Semidefinite Relaxation (SDR) optimization and obtaining the optimal rotation phases. Finally, an iterative algorithm framework is proposed for multi-user signal reconstruction. Numerical results are also carried out to verify the bit-error-ratio (BER) performance compared with the several coherent detection schemes and the noncoherent transmission schemes.