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In this work, we consider the front-end receivers for flat fading MIMO transmission, whose essential feature is the calculation of the log-likelihood ratios (LLRs) for the transmitted bits. When the number of transmit antennas and the modulation size grow, the exact calculation of the LLRs becomes unfeasible due to the necessity to enumerate the symbols affecting the output. In this work, to avoid the burden of explicit enumeration, instead of calculating the likelihoods exactly, we explore the possibilities offered by the saddlepoint approximation of the likelihood functions. The resulting fixed-complexity approach significantly outperforms the well known linear-filter based minimum mean square error detection. A complexity analysis identifies the main computational bottleneck of the proposed detection algorithm.