Dual-functional radar-communication (DFRC) is a promising new solution to simultaneously probe the radar target and transmit information in wireless networks. In this paper, we study the joint optimization of transmit and receive beamforming for the DFRC system. Specifically, the signal to interference plus noise ratio (SINR) of the radar is maximized under the SINR constraints of the communication user (CU), which characterizes the optimal tradeoff between radar and communication. In addition to simply using the communication signal for target probing, we further consider to exploit dedicated probing signals to enhance the radar sensing performance. We commence by studying the single-CU scenario, where a closed-form solution to the beamforming design problem is provided. It is then proved that a dedicated radar probing signal is not needed. As a further step, we consider a more complicated multi-CU scenario, where the beamforming design is formulated as a non-convex quadratically constrained quadratic programming. The optimal solutions are obtained by applying semidefinite relaxation with guaranteed rank-1 property. It is shown that under the multi-CU scenario, the dedicated probing signal should be employed to improve the radar performance at the cost of implementing an additional interference cancellation at the CU. Finally, the numerical simulations are provided to verify the effectiveness of the proposed algorithm.