Instances of dirty paper coding include Costa precoding (1983).

The sender does precoding of the data so as to cancel the effect of the interference.

In wireless communications, spatial precoding has been developing for high reliability, high rate and lower interference as shown in the following table.

Note that precoding requires knowledge of channel state information (CSI) at the transmitter and the receiver.

Spatial precoding of intelligent antenna includes spatial beamforming and spatial coding.

In spatially correlated environments, the long-term channel statistics can be combined with low-rate feedback to perform multi-user precoding.

Note that the optimal linear precoding can be computed using monotonic optimization algorithms, but the computational complexity scales exponentially fast with the number of users.

Finding the optimal weighted MMSE precoding is difficult, leading to approximate approaches where the weights are selected heuristically.

Zero-forcing precoding may even achieve the full multiplexing gain, but only provided that the accuracy of the channel feedback increases linearly with signal-to-noise ratio (in dB).

Suboptimal approximations of dirty paper coding include Tomlinson-Harashima precoding (1971) and the vector perturbation technique of Hochwald et al. (2005).

This suboptimal approach cannot achieve the weighted sum rate, but it can still maximize the weighted sum performance (or some other metric of achievable rates under linear precoding).

Spatial processing includes spatial precoding at the transmitter and spatial postcoding at the receiver, which are dual each other from information signal processing theoretic point of view.

Examples of advanced transmit processing for MIMO BC are interference aware precoding and SDMA-based downlink user scheduling.

The optimal linear precoding does not have any closed-form expression, but it takes the form of a weighted MMSE precoding for single-antenna receivers.

ZF precoding can achieve performance close to the sum capacity when the number of users is large or the system is interference-limited (i.e., the noise is weak compared to the interference).

The future Gigabit POF standard is based on multilevel PAM modulation a Frame structure, Tomlinson-Harashima Precoding and Multilevel coset coding modulation.

Differently from conventional approaches, an advanced IA based terminal will perform spatial precoding (spatial beamforming and/or spatial coding) not only to enhance the signal power at the destination terminal but also to diminish the interferening power at interference terminals.

Regularized zero-forcing precoding is enhanced processing to consider the impact on a background noise and unknown user interference, where the background noise and the unknown user interference can be emphasized in the result of (known) interference signal nulling.

Meng Ma, Xiaojing Huang, Bingli Jiao, and Y. Jay Guo,"Optimal Orthogonal Precoding for Power Leakage Suppression in DFT-Based Systems," IEEE Trans.

Nonlinear precoding is designed based on the concept of dirty paper coding (DPC), which shows that any known interference at the transmitter can be subtracted without the penalty of radio resources if the optimal precoding scheme can be applied on the transmit signal.