This paper proposes signal detection schemes for massive multiple-input multiple-output (MIMO) systems, where the number of receive antennas is less than that of transmitted streams. Assuming practical baseband digital modulation and taking advantage of the discreteness of transmitted symbols, we formulate the signal detection problem as a convex optimization problem, called sum-of-absolute-value (SOAV) optimization. Moreover, we extend the SOAV optimization into the weighted-SOAV (W-SOAV) optimization and propose an iterative approach to solve the W-SOAV optimization with updating the weights in the objective function. Furthermore, for coded MIMO systems, we also propose a joint detection and decoding scheme, where log likelihood ratios of transmitted symbols are iteratively updated between the MIMO detector and the channel decoder. In addition, a theoretical performance analysis is provided in terms of the upper bound of the size of the estimation error obtained with the W-SOAV optimization. Simulation results show that the bit error rate performance of the proposed scheme is better than that of conventional schemes, especially in large-scale overloaded MIMO systems.