The FMCW(Frequency Modulation Continuous Wave) radar possesses range-velocity ambiguity to identify the correct combination of beat frequencies for each target in the multi-target situation. It can lead to ghost targets and missing targets, and it can reduce the detection probability. In this paper, we propose an effective identification algorithm for the correct pairs of beat frequencies and the signal processing hardware architecture to effectively support the algorithm. First, using the correlation of the detected up- and down-beat frequencies and Doppler frequencies, the possible combinations are determined. Then, final pairing algorithm is completed with the power spectrum density of the correlated up- and down-beat frequencies. The proposed hardware processor has the basic architecture consisting of beat-frequency registers, pairing table memory, and decision unit. This method will be useful to improve the radar detection probability and reduce the false alarm rate.