A Generalized Zero-Forcing Precoder With Successive Dirty-Paper Coding in MISO Broadcast Channels

In this paper, we consider precoder designs for multiuser multiple-input-single-output broadcasting channels. Instead of using a traditional linear zero-forcing (ZF) precoder, we propose a generalized ZF (GZF) precoder in conjunction with successive dirty-paper coding (DPC) for data transmissions, namely, the GZF-DP precoder, where the suffix “DP” stands for “dirty-paper.” The GZF-DP precoder is designed to generate a band-shaped and lower triangular effective channel F, such that only the entries along the main diagonal and the v first lower-diagonals can take non-zero values. Utilizing the successive DPC, the known non-causal inter-user interferences from the other (up to) v users are canceled through successive encoding. We analyze optimal GZF-DP precoder designs both for sumrate and minimum user-rate maximizations. Utilizing Lagrange multipliers, the optimal precoders for both cases are solved in closed-forms in relation to optimal power allocations. For the sum-rate maximization, the optimal power allocation can be found through water filling, but with modified water levels depending on the parameter v, while for the minimum user-rate maximization that measures the quality of the service, the optimal power allocation is directly solved in closed-form, which also depends on v. Moreover, we propose two low-complexity userordering algorithms for the GZF-DP precoder designs for both maximizations, respectively. We show, through numerical results, that the proposed GZF-DP precoder with a small v value (≤ 3) renders significant rate increments compared with the previous precoder designs, such as the linear ZF and the user-groupingbased DPC precoders.