In this paper, a frequency domain adaptive antenna array (FDAAA) algorithm is proposed for broadband single-carrier uplink transmissions in a cellular system. By employing AAA weight control in the frequency domain, the FDAAA receiver is able to suppress the multi-user interference (MUI) and the co-channel interference (CCI). In addition, the channel frequency selectivity can be exploited to suppress the inter-symbol interference (ISI) and to obtain frequency diversity (or the multi-path diversity). Another advantage of the FDAAA algorithm is that its performance is not affected by the spread of angles of arrival (AOA) of the received multi-path signal. In this study the structure of FDAAA receiver is discussed and the frequency domain signal-to-interference-plus-noise-ratio (SINR) after weight control is investigated. The performance of the FDAAA algorithm is confirmed by simulation results. It is shown that, the optimal FDAAA weight to obtain the best BER performance is that which fully cancels the interference when single-cell system is considered; On the other hand, when multi-cell cellular system is considered, the optimal FDAAA weight depends on both the cellular structure and the target signal to noise ratio (SNR) of transmit power control (TPC).