In orthogonal frequency division multiple access (OFDMA) systems, the cyclic prefix (CP) length needs to be no less than the longest delay spread of the channels of many users, reducing bandwidth efficiency more significantly than in single user OFDM systems. In this paper, we address OFDMA downlink data transmission when a short CP is used to mitigate the inefficient bandwidth usage. Previous time domain equalizers (TEQs) can be used to shorten the channel, however, they tend to increase noise by introducing spectral nulls. A previous work per tone equalization (PTEQ) structure involves a multitap frequency domain equalizer (FEQ) for each tone, and shows better performance than TEQ-based receiver structure. We propose a novel receiver structure with only one-tap FEQ for OFDMA systems with reduced CP, exploiting the unused subchannels for a user. We formulate an optimization problem to set the FEQ coefficients at the unused subchannels such that the channel is shortened (approximation is involved) and noise is not enhanced at the used subchannels. With the aid of computer simulations, it is demonstrated that the proposed equalization method is superior to the conventional TEQ-based receivers, and is comparable to the previous PTEQ-based receiver in terms of the achievable SNR, error performance, and bandwidth efficiency. Although the throughput curve versus synchronization delay of the PTEQ is smoother than that of the proposed receiver, the proposed method shows proper throughput over a wider range of the delay values than PTEQ receiver when the system parameters are set so that the complexities are comparable.