We propose a secure transmission scheme for a relay wiretap channel, where a source communicates with a destination via a decode-and-forward relay in the presence of spatially random-distributed eavesdroppers. We assume that the source is equipped with multiple antennas, whereas the relay, the destination, and the eavesdroppers are equipped with a single antenna each. In the proposed scheme, in addition to information signals, the source transmits artificial noise signals in order to confuse the eavesdroppers. With the target of maximizing the secrecy throughput of the relay wiretap channel, we derive a closed-form expression for the transmission outage probability and an easy-to-compute expression for the secrecy outage probability. Using these expressions, we determine the optimal power allocation factor and wiretap code rates that guarantee the maximum secrecy throughput, while satisfying a secrecy outage probability constraint. Furthermore, we examine the impact of source antenna number on the secrecy throughput, showing that adding extra transmit antennas at the source brings about a significant increase in the secrecy throughput.