Receiver design for practical implementation is an issue worthy of study. Among various noise models, Middleton Class A noise is one of the most widely investigated one which well matches the physical channel of wireless communications. The optimal receiver has a complex and non-reducible structure which makes the optimal receiver unimplementable, due to the weighted infinite sum of Gaussian distributions with different parameters in the probability density function (pdf) of the noise. Although several receivers based on Locally Optimal Detector (LOD) have been proposed and they can achieve a good performance under small signal assumption, the Bit Error Rate (BER) performance will drastically degrade with the signal power getting high. In this paper, we propose a Fractional Lower Order Moments (FLOM) based detector under Middleton Class A noise as an implementable detector. For evaluating the performance, the analytical expressions of the BER are derived. The theoretical analysis and simulation results show that our proposed detector achieves a satisfactory performance.