An adaptive technique for underwater acoustic communication using passive phase conjugation (PPC) is developed. Multipath channel parameter identification is accomplished by decision-directed model building and finite-window, block-updated least-squares computed by LSQR (an iterative linear systems solver). The resulting channel estimates are then used by the PPC processor to generate decisions for use in the next processing block. This architecture effectively accomplishes array equalization with low computation cost in shallow water environments that exhibit rapidly fluctuating multipath scattering. Performance on shallow-water acoustic communications channels is demonstrated at ranges of 0.9 to 4.6 \km\ under windy surface conditions and shipping noise, using measured wideband telemetry data with BPSK signaling. The algorithm is evaluated with sparse receiver apertures using subsets of a 14-element array.