  This paper investigates radar-assisted user acquisition for downlink
multi-user multiple-input multiple-output (MIMO) transmission using Orthogonal
Frequency Division Multiplexing (OFDM) signals. Specifically, we formulate a
concise mathematical model for the user acquisition problem, where each user is
characterized by its delay and beamspace response. Therefore, we propose a
two-stage method for user acquisition, where the Multiple Signal Classification
(MUSIC) algorithm is adopted for delay estimation, and then a least absolute
shrinkage and selection operator (LASSO) is applied for estimating the user
response in the beamspace. Furthermore, we also provide a comprehensive
performance analysis of the considered problem based on the pair-wise error
probability (PEP). Particularly, we show that the rank and the geometric mean
of non-zero eigenvalues of the squared beamspace difference matrix determines
the user acquisition performance. More importantly, we reveal that
simultaneously probing multiple beams outperforms concentrating power on a
specific beam direction in each time slot under the power constraint, when only
limited OFDM symbols are transmitted. Our numerical results confirm our
conclusions and also demonstrate a promising acquisition performance of the
proposed two-stage method.
