This paper describes an objective speech quality assessment method developed for the Hungarian NMT-450 mobile telephone system. The method is based on a psychoacoustic front end followed by a cognitive modeling component. Special problems of the NMT system, such as hand-overs, the effects of automatic gain control (AGC) and intrusion of signaling noise are addressed in the cognitive module. Correlation of the subjective and objective quality measures is maximized by finding a transformation that linearizes their relationship. A correlation of 0.94 is achieved on an independent test set between the subjective speech quality and the proposed objective quality measure.