The problem of synchronous multiuser receiver design in the case of direct-sequence single-antenna code division multiple access (DS-CDMA) uplink networks is studied over frequency selective fading channels. An exact expression for the bit error rate (BER) is derived in the case of BPSK signaling. Moreover, an algorithm is proposed for finding the finite impulse response (FIR) receiver filters with block memory such that the exact BER of the active users is minimized. Several properties of the minimum BER FIR filters with block memory are identified. The algorithm performance is found for scenarios with different channel qualities, spreading code lengths, receiver block memory size, near-far effects, and channel mismatch. For the BPSK constellation, the proposed FIR receiver structure with block memory has significant better BER with respect to Eb/N0 and near-far resistance than the corresponding minimum mean square error (MMSE) filters with block memory.