In this paper, full-duplex radios are used to continuously update the channel state information at the transmitter, which is required to compute the downlink precoding matrix in MIMO broadcast channels. The full-duplex operation allows leveraging channel reciprocity for open-loop uplink training to estimate the downlink channels. However, the uplink transmission of training creates interference at the downlink receiving mobile nodes. We characterize the optimal training resource allocation and its associated spectral efficiency, in the proposed open-loop training based full-duplex system. We also evaluate the performance of the half-duplex counterpart to derive the relative gains of full-duplex training. Despite the existence of the inter-node interference due to full-duplex, significant spectral efficiency improvement is attained over half-duplex operation.