This paper investigates the average throughput of a wireless powered communications system, where an energy constrained source, powered by a dedicated power beacon (PB), communicates with a destination. It is assumed that the PB is capable of performing channel estimation, digital beamforming, and spectrum sensing as a communication device. Considering a time splitting approach, the source first harvests energy from the PB equipped with multiple antennas, and then transmits information to the destination. Assuming Nakagami-m fading channels, analytical expressions for the average throughput are derived for two different transmission modes, namely, delay tolerant and delay intolerant. In addition, closed-form solutions for the optimal time split, which maximize the average throughput are obtained in some special cases, i.e., high transmit power regime and large number of antennas. Finally, the impact of co-channel interference is studied. Numerical and simulation results have shown that increasing the number of transmit antennas at the PB is an effective tool to improve the average throughput and the interference can be potentially exploited to enhance the average throughput, since it can be utilized as an extra source of energy. Also, the impact of fading severity level of the energy transfer link on the average throughput is not significant, especially if the number of PB antennas is large. Finally, it is observed that the source position has a great impact on the average throughput.