In this treatise, we consider a power non-orthogonal multiple access (NOMA) design based on the minimum bit error ratio (MBER) criterion. Existing literatures have shown that the MBER based works show a considerable performance improvement in terms of bit error ratio (BER) for a communication system. We have proposed to design the power coefficients for multiple users with the aid of optimized BER, which is adopted as the cost function. In this work, we have considered a transceiver system having a single-input single-output (SISO) antenna configuration with the M-quadrature amplitude modulation (M-QAM) signal constellation. The optimization ensures that each user maintains a minimum rate requirement. In this work, we have extensively analyzed the BER performance due to estimated channel for any link. The numerical results demonstrate an overall BER improvement compared to the existing schemes, albeit, the scheme attracts large computational complexity. We have also proposed a variation of the MBER based optimization algorithm, which improves the BER performance. This variation is based on the splitting of the search space for the algorithm and it results in a better performance benefit. Traditionally, NOMA increases the spectral efficiency compared to its orthogonal counterpart. Nevertheless, our proposed solution will still hold this feature along with a better BER performance, though its spectral efficiency will be slightly less compared to the traditional sum-rate based power NOMA.