A software-defined receiver (SDR) for navigation using cellular code-division multiple access (CDMA) signals is presented. The cellular forward link signal structure is described, and models for the transmitted and received signals are developed. Particular attention is paid to relevant information that could be extracted and subsequently exploited for positioning and timing purposes. The pseudorange from the proposed receiver is modeled and the pseudorange error is studied in an additive white Gaussian channel. Experimental results with aerial and ground vehicles utilizing the proposed SDR are presented demonstrating a close match between the variation in pseudoranges and the variation in true ranges between the receiver and two cellular CDMA base transceiver stations (BTSs). Moreover, the dynamics of the discrepancy between the observed clock biases of different sectors of the same BTS cell is modeled and validated experimentally. The consistency of the obtained model is analyzed through experimental tests in different locations, at different times, and for different cellular providers.