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This paper studies a multiple-input multiple-output (MIMO) broadcast relay channel (BRC), in which a multiple-antenna base station (BS) communicates with multiple-antenna users through an infrastructure-based multiple-antenna relay station (RS). Applying dirty paper coding (DPC) at the BS and linear processing at the RS, our aim is to find the input covariance matrices and the RS beamforming matrix that maximize the system sum-rate. To solve this non-convex problem, a more tractable dual multiple access relay channel (MARC) is investigated and an alternating-minimization algorithm is proposed. Furthermore, the mapping from the resulting covariance matrices for the MARC to the covariance matrices for the BRC is derived. Unlike other existing single-antenna-user schemes, our solution is applicable to a more general network with any number of antennas at the users. Compared with two such single-antenna-user schemes, simulations show that the proposed scheme outperforms the all-pass relay design and performs similarly to the SVD-relay design. Moreover, the proposed design performs close to the sum-rate upper bound with the performance gap decreasing with increasing number of antennas per user. It is also observed that having more antennas at the RS than at the BS is desirable for better system performance. [ABSTRACT FROM PUBLISHER]