Abstract: This is the fourth paper in a series of articles devoted to modern methods of protection of coherent-pulse radars against the combined interference (i.e., an additive mixture of internal noise, masking noise jamming and clutter). It proposes the structures of an adaptive system of cooperative space-time signal processing (STSP) against the background of masking combined interference based on a two-dimensional adaptive lattice filter with matrix elementary lattice filters. These structures eliminate significant energy losses of adaptive systems of separate STSP caused by the non-classified nature of training samples of noise jamming and clutter in estimating the weight vectors of spatial and inter-period signal processing and the need to store the spatial weight vector during the time of inter-period compensation of clutter. The results of mathematical simulation of the developed parallel-sequential adaptive system of cooperative STSP with reduced number of complex multiplication operations as compared with direct inversion of interference correlation matrix are presented that confirm its high efficiency. © 2022, Allerton Press, Inc.