Our objective is to detect and localize potential targets using stepped-frequency measurements consisting of both wall and target return from multiple antenna elements. We investigate the wall and target return subspaces both (i) for each antenna element separately and (ii) jointly for all antenna elements. Both the individual wall return subspace and the joint wall return subspace can capture most of the energy of the wall return, but the latter has much smaller dimensionality and thus captures less energy from the target return. Then, in each step of an iterative algorithm for detecting the target positions, we cancel the return from previously selected targets using a joint target return subspace model. The joint target return subspace offers improved target detection since this is better able to capture the return from a given target without capturing the energy of other targets.