The transmitted signals in non-orthogonal multiple access (NOMA) schemes can have substantial envelope fluctuations, not to mention the inherent high interference levels. This means that a high price in terms of power efficiency can be payed to achieve the substantial capacity gains of NOMA systems. In this paper we consider the use single-carrier signals combined with NOMA schemes in the downlink transmission. We present a multi-antenna transmission technique that is compatible with the use of high-efficiency power amplifiers and does not require any pre-processing and allows the use of power-efficient amplifiers. Moreover, an efficient detection is achieved using iterative receivers with joint multi-user detection and equalization. Our performance results show that the proposed technique allows high power efficiency, with bit-error-rate (BER) performance close to the matched filter bound (MFB).