Gilbert Mixer: Secod order order (IM2/HD2) nonlinearities

In one of our tests, we noticed a significant HD2 at the output of a differential passive Gilbert cell mixer (the mixer performance was supposed to be at least 20dB better than what we measured in the lab). I was looking for a systematic methodology to link this problem to load mismatches on P and N paths. In my research, I came across this paper [this webpage includes better quality images] that categorizes second order nonlinearities of a Gilbert cell. My take on this work is Eq. (16), where the IM2 output voltage is extracted by i_im2_diff (differential current IM2) and i_im2_cm (common mode current IM2). The equation express the relation between the overall IM2 and internally+externally generated IM2. In other words, if the output load is matched (load of path N and P are equal in terms of phase and amplitude) then i_im2_cm's impact will be canceled by teh balance between the loads (P&N) , i.e. delta_Rload*i_im2_cm becomes almost 0. On the other hand, i_im2_diff (generated by internal transconductance/timing mismatches) will be signified by sum_Rload (Rload_P+R_load_N). In my case, I guessed that the strong HD2 would have been generated by P&N load mismatched; however, later we found out that the input signal to the mixer was imbalance!!!