Precoding

Precoding is a signal processing technique used in multiple-input multiple-output (MIMO) wireless communications to pre-process transmitted signals using knowledge of the propagation channel so that the received signals can be separated more easily or energy is directed toward intended receivers. In downlink transmission, precoding acts as transmit beamforming to mitigate interference among users sharing the same time-frequency resources.

Common linear precoders include zero-forcing (ZF), minimum mean square error (MMSE), and maximum ratio transmission (MRT, also called matched filter). These choose a precoding matrix W to minimize interference or maximize signal power; for example, ZF uses W to invert the channel, while MMSE balances interference cancellation against noise amplification. Nonlinear precoding includes dirty paper coding (DPC), which is theoretically capacity-achieving for the broadcast channel, and practical approximations such as Tomlinson-Harashima precoding (THP) or vector perturbation, which try to pre-cancel known interference without excessive complexity.

Precoding requires channel state information at the transmitter (CSIT). Imperfect CSI degrades performance; CSI can be obtained via feedback from receivers in frequency-division duplex (FDD) systems or via channel reciprocity in time-division duplex (TDD) systems. Precoding is often applied on a per-subcarrier basis in OFDM or over blocks.

In modern wireless systems, such as LTE and 5G NR, downlink multi-user MIMO uses precoding to serve multiple users on the same resources. Performance depends on the accuracy of CSIT and the number of transmit antennas. Complexity and feedback overhead are practical considerations; robust and adaptive precoding schemes address CSI uncertainty. Research into precoding also includes machine learning-based approaches and advanced nonlinear precoding techniques. Precoding remains a central technique for improving spectral efficiency in wireless networks.