In general if you have a total power P and N ransmit antennas, the power is divided uniformly, i.e.: each antenna transmits with P/N. For the normalization, it is usually done for simplicity of exposition without any loss of generality.
If the power is not uniformly distributed, then you have P1, P2, ..., PN such that P1+P2+...+PN=P. Then you can find the equivalent SNR and BER expression, based on that try to minimize BER such that P1+P2+...+PN=P. Try this if it leads any where.
Explore the literature if there are some papers done on this.
Regards