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In this paper, we investigate the possibility of reliable and computationally efficient detection for spectrally efficient non-orthogonal Multiplexing (FDM) system, exhibiting varying levels of intercarrier interference. Optimum detection is based on the Maximum Likelihood (ML) principle. However, ML is impractical due to its computational complexity. On the other hand, linear detection techniques such as Zero Forcing (ZF) and Minimum Mean Square Error (MMSE) exhibit poor performance. Consequently, we explore the combination of MMSE estimation with ML estimation around a neighborhood of the MMSE estimate. We evaluate the performance of the different schemes in Additive White Gaussian Noise (AWGN), with reference to the number of FDM carriers and their frequency separation. The combined MMSE-ML scheme achieves a near optimum error performance with polynomial complexity for a small number of BPSK FDM carriers. For QPSK modulation the performance of the proposed system improves for a large number of ML comparisons. In all cases, the detectability of the FDM signal is bounded by the signal dimension and the carriers frequency distance.