In the helicopter transient electromagnetic system (HTEM), weak-coupling coils reduce the mutual inductance of the transmitting and receiving coils, which can protect the data acquisition circuit and improve the signal-to-noise of the system. The PRBS HTEM system is a newly proposed multi-receiver EM measurement system, which can effectively identify the system impulse response of the unknown geological model based on the high-precision synchronous recording signal of the PRBS emitted current and induced voltage. However, the standard PRBS current signal is turned on/off very quickly, easily resulting in signal saturation. Concerning this problem, this paper proposes a new weak-coupling structure named eccentric dual bucking coils for the multi-receiver EM system by analyzing the on/off characteristics of PRBS current and the magnetic field distribution of the transmitter–receiver system. It also verifies the feasibility of the proposed structure by Maxwell software simulation. Furthermore, considering the influence of the residual primary field and other factors, the data preprocessing results of the PRBS method and the traditional square wave method are compared by theoretical analysis and data simulation, and the results show that the earlier-time response data can be obtained by PRBS method under the same simulation conditions. Finally, the reliability of the proposed method is verified by ground experiment.