In this study, the performance of the proposed receiver with the neural network Multiple Access Interference (MAI) detector is compared with the matched filter bank (classical receiver), neural network that detects user's signal and single user bound for Additive White Gaussian Noise (AWGN) and Rayleigh fading asynchronous channels by computer simulations. There are a lot of study in the literature that compare the neural network receiver and other methods. These neural network receivers detect the user bits after the matched filter. In this study, MAI is detected after the matched filter with the proposed neural network receiver and then user bits are obtained by subtracting MAI from the matched filter output. The proposed receiver with the neural network MAI detector has got better Bit Error Rate (BER) performance than the neural network that detects user's signal in AWGN and Rayleigh fading asynchronous channels for Signal Noise Ratio (SNR) simulations, and in AWGN asynchronous channels for the number of users simulations, although both have the same complexity. However, both have almost same BER performance in AWGN and Rayleigh fading asynchronous channels for Near Far Ratio (NFR) simulations, and in Rayleigh fading asynchronous channels for the number of users simulations.