Wireless powered communications allow sustainable operations of low‐power applications by supplying wireless power remotely. In this study, the performance of wireless powered communications is evaluated in terms of achievable rate and bit error rate (BER), for applications where the downlink and the uplink are correlated, in contrast to previous works that assume independent uplink and downlink. Semi‐closed expressions for the achievable rate and series expressions for the BER are derived in Nakagami m fading channels, based on which the effect of link correlation is examined. Numerical results show that the link correlation has a significant impact on the achievable rate. Consequently, the optimum system parameter for correlated links is very different from that for independent links, showing the usefulness of the authors' results. Also, the link correlation has a noticeable effect on the BER, depending on the system parameters considered.