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We focus on the design of vector perturbation (VP) precoding for multiuser multiple-input-single-output (MU-MISO) broadcast channel systems where the centralized transmitter equipped with multiple antennas and communicates simultaneously to multiple single-antenna receivers. While conventional VP requires the feedback of the channel matrix at the transmitter for precoding and the power scaling factor at the receivers for detection, VP precoding has so far been developed and analyzed under assumptions that the transmitter has perfect channel state information (CSI) or the receivers have perfect knowledge of the channel- and data-dependent power scaling factors. In practical limited feedback scenarios, wireless communication systems suffer from limited time and frequency resource for pilots to feed-forward information and only a quantized version of power scaling factors is available at the receivers; under such limitations, the performance of VP precoding will degrade significantly compared with ideal scenarios and would always encounter an error floor at mid-to-high signal-to-noise ratio (SNR) regions. Motivated by such observations, we propose a robust VP precoder design, which takes the imperfectness of CSI and power scaling factor jointly into account under the criterion of minimum mean-square error (MMSE). The closed-form expressions of the proposed precoder are then derived. As illustrated by the simulation results, the proposed VP precoder is less sensitive to CSI and power scaling factor imperfections compared with the classic VP precoder and other existing MMSE-based VP precoders, as it has a lower error floor when imperfectness is assumed to be fixed, and power scaling factor accuracy is shown to offer a non-linear performance gain compared with that of the linear gain CSI accuracy could offer.

Vector Perturbation Precoding Under Imperfect CSI and Inaccurate Power Scaling Factors