Optimum Linear Block Precoding for Multi-Point Cooperative Transmission with Per-Antenna Power Constraints

Using cyclic prefix (CP), the transmission schemes, orthogonal frequency-division multiplexing (OFDM), single carrier block transmission, and time reversal, can be unified as linear block precoding. Considering frequency-selective channels, this paper studies linear block precoding for CP-based multi-point transmission with per-antenna power constraints (PAPCs) under capacity maximization and mean-square-error (MSE) minimization criteria. We show that, the optimal precoders for both criteria could be, but not necessarily, in the form of OFDM transmission (i.e., an inverse discrete fourier transformation (IDFT) matrix multiplying a complex diagonal matrix). Based on the optimal precoder structure, the two problems are simplified to two matrix-free optimization problems for which we prove strong duality holds. Moreover, it is shown that the dual problems can be equivalent to two unconstrained convex optimization problems. Efficient optimum precoding algorithms are proposed for both problems. Simulation results show that the maximum capacity (or minimum MSE) in the PAPC case almost coincides with that in the sum power constraint (SPC) case when the power budgets for each antenna are equal, but a capacity (or MSE) gap exists between the two power constraint cases when the power budgets for each antenna are different.