Single-frequency full-duplex wireless communication (SFD) can increase the efficiency of bandwidth utilization by ideally doubling the spectral efficiency. SFD can be achieved by reducing the level of the self-interference between the transmitter (TX) and receiver (RX) to the RX noise floor. This paper describes a novel decoupling structure to increase the isolation for a collinear dipole array which retains the omnidirectional radiation patterns of the dipole antennas. The structure is based on a parasitic element which couples power from the TX antenna and reradiates it with orthogonal polarized elements cancelling the original field around the RX antenna. A novel analysis is presented for the decoupling structure in which the phase and amplitude radiation pattern of the decoupling structure is calculated. The obtained isolation is more than 50 dB according to the simulation and measurement for a bandwidth of 11 %, fulfilling the required electromagnetic isolation for a full-duplex system in indoor device-to-device communications.