Backscatter communication (BackCom) has been emerging as a prospective candidate in tackling lifetime management problems for massively deployed Internet-of-Things devices, which suffer from battery-related issues, i.e., replacements, charging, and recycling. This passive sensing approach allows a backscatter sensor node (BSN) to transmit information by reflecting the incident signal from a carrier emitter without initiating its transmission. To multiplex multiple BSNs, power-domain non-orthogonal multiple access (NOMA), which is a prime candidate for multiple access in beyond 5G systems, is fully exploited in this work. Recently, considerable attention has been devoted to the NOMA-aided BackCom networks in the context of outage probabilities and system throughput. However, the closed-form expressions of bit error rate (BER) for such a system have not been studied. In this paper, we present the design and analysis of a NOMA enhanced bistatic BackCom system for a battery-less smart communication paradigm. Specifically, we derive the closed-form BER expressions for a cluster of two devices in a bistatic BackCom system employing NOMA with imperfect successive interference cancellation under Nakagami-$m$ fading channel. The obtained expressions are utilized to evaluate the reflection coefficients of devices needed for the most favorable system performance. Our results also show that NOMA-BackCom achieves better data throughput compared to the orthogonal multiple access-time domain multiple access schemes (OMA-TDMA).