The power domain non-orthogonal multiple access (PD-NOMA) performs reasonably well under perfect successive interference cancellation (SIC) conditions. However, under imperfect SIC, the average sum-rate (ASR), outage performance, and $\epsilon -$outage capacity of PD-NOMA diminish drastically. This work introduces a new PD-NOMA system called multidimensional signal space NOMA (MD-NOMA) to mitigate this sudden decrease in performance. Employing multidimensional signal space significantly reduces the number of SICs, leading to less stringent constraints on the power allocation, reducing the detection delay, and decoding complexity. The analytical expressions of ASR, outage-probability (OP), $\epsilon -$outage capacity, and diversity order of MD-NOMA, Quadrature-NOMA (Q-NOMA), and PD-NOMA are evaluated under Nakagami-$m$ fading channel with the help of order statistics for a generalized-$K$ user scenario. It is noticed from the analysis that MD-NOMA, with a higher number of signal spaces, significantly outperforms all other systems under imperfect SIC and exhibits comparable performance with them under perfect SIC. Furthermore, the analytical expression for bit error rate (BER) and average-BER (ABER) is determined for MD-NOMA. It is noticed that MD-NOMA can withstand higher modulation order ($M$), whereas the performance of all other systems degrades drastically as $M$ increases. Furthermore, numerical results demonstrate there is a tradeoff between ABER and spectral efficiency.