The rapid growth of Internet-of-Things (IoT) devices demands communication systems that are both spectrally efficient and energy frugal. Backscatter communication (BackCom) is an attractive low-power paradigm, but its spectral efficiency declines in dense deployments. This paper presents an uplink BackCom design that integrates non-orthogonal multiple access (NOMA) and maximizes system energy efficiency (EE). In a bistatic network where multiple backscatter nodes (BNs) harvest RF energy and alternate between sleep and active modes, we formulate a fractional program with coupled time, power, and reflection variables and develop a Dinkelbach-based alternating optimization (AO) algorithm with closed-form updates. Analysis reveals two operating modes depending on power availability, circuit demands and propagation conditions. Simulations show the proposed design adapts the time allocation, achieving up to 8% higher EE than fixed-power and 68% than no-sleep baselines, and delivering up to 127% EE gains over orthogonal multiple access (OMA). These results establish NOMA-enabled BackCom as a scalable, energy efficient solution for large-scale IoT deployments.

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