Precoding

Precoding is generalized beamforming to support multi-layer transmission in MIMO radio systems. Conventional beamforming considers linear single-layer precoding so that the same signal is emitted from each of the transmit antennas with appropriate weighting such that the signal power is maximized at the receiver output. When the receiver has multiple antennas, the single-layer beamforming cannot simultaneously maximize the signal level at all of the receive antenna and so precoding is used for multi-layer beamforming. In precoding, the mutiple streams of the signals are emitted from the transmit antennas with independent and appropriate weighting such that the link throughtput is maximized at the receiver output.

Precoding for Single-user MIMO

In Single-user MIMO, identity matrix precoding and SVD precoding can be used to achieve the open-loop and closed-loop MIMO capacities, respectively.

Random unitary precoding

Random unitary precoding including identity transformation matrix can achieve the open-loop MIMO capacity where no signalling burden in the reverse link is required.

Optimal unitary precoding (SVD precoding)

SVD precoding has been proven to achieve the (real) channel capacity of MIMO systems at the cost of closed-loop signalling burden.

Precoding for Multi-user MIMO

In the implementation prospective, precoding algorithms for multi-user MIMO can be sub-divided into linear and nonlinear precoding algorithms. Linear precoding can achieve reasonable performance while the complexity is lower than nonlinear approaches. Linear precoding includes unitary precoding and zero-forcing (ZF) precoding. Nonlinear precoding can achieve near optimal capacity at the expense of complexity. Nonlinear precoding is designed based on the concept of Dirty paper coding (DPC) which shows that any known interefence at the transmitter can be subtracted without the penalty of radio resources when the optimal precoding scheme is applied on the trasmit signal.

Unitary based precoding

This category includes unitary and semi-unitary precoding both of which are simple extension of (matched filter) SVD precoding in single-user MIMO with the addition of the SDMA-based user scheduling technique. The SDMA-based opportunistic user scheduling technique pairs near orthogonal users to avoid intra-group interferences at the minimal cost of the feedback signalling burden.

ZF based precoding

This category includes zero-forcing and regularized zero-forcing precoding. ZF-based precoding can achieve close to the system capacity at the cost of large feedback overhead. It is especially true when the number of users is large. ZF-precoding has an important fact that the feeback overhead should be increased with resepct to operating signal-to-noise-ratio (SNR) to achieve the full multiplexing gain.

DPC concept based precoding

This category includes Costa precoding , Tomlinson-Harashima precoding and the vector perturbation technique.