A non‐coherent serial acquisition scheme for direct sequence spread spectrum communication systems is analyzed and discussed in this paper. The adaptive thresholding based on constant false alarm rate and multilayer perceptron neural network (MLP‐NN) techniques are combined to improve the performance of code division multiple access systems. One of the most important problems in code acquisition of pseudo‐noise sequences for multiuser detection is the presence of interferences caused by the multiple access technique and multipath replicas. To solve this problem, an MLP‐NN is trained and adapted to work as a constant false alarm rate detector using the error back propagation gradient descendent algorithm. It is named MLP‐NN adaptive processor. The performance of this proposed algorithm is presented using the serial search acquisition system, which is chosen because of its simple hardware implementation. The performance of the MLP‐NN adaptive processor algorithm in homogeneous and non‐homogenous environments for additive white Gaussian noise and Rayleigh fading channels is evaluated via computer simulations. The obtained results are compared to other serial acquisition schemes using the cell‐averaging adaptive processor, the order statistics adaptive processor, and the automatic censoring adaptive processor algorithms.