In this paper, we propose a novel adaptive reducedrank strategy for very large multiuser multi-input multi-output (MIMO) systems. The proposed reduced-rank scheme is based on the concept of joint iterative optimization (JIO) of filters according to the minimization of the bit error rate (BER) cost function. The proposed optimization technique adjusts the weights of a projection matrix and a reduced-rank filter jointly. We develop stochastic gradient (SG) algorithms for their adaptive implementation and introduce a novel automatic rank selection method based on the BER criterion. Simulation results for multiuser MIMO systems show that the proposed adaptive algorithms significantly outperform existing schemes. (5 pages)