A method includes, in a receiver, receiving a signal carrying data using multiple antennas, so as to produce multiple respective input signals. The input signals are divided into two or more subsets. The input signals within each of the subsets are combined in a first diversity-combining stage, to produce respective intermediate signals. In a second diversity-combining stage, the intermediate signals are combined to produce an output signal. The output signal is decoded so as to reconstruct the data carried by the received signal.