Zero-forcing (or Nullnull-Steeringsteering) precoding is a method of spatial signal processing by which the multiple antenna transmitter can null multiuser interference signals in [[wireless|wireless communications]]. Regularized '''zero-forcing precoding''' is enhanced processing to consider the impact on a background [[noise]] and unknown user [[Interference (communication)|interference]],<ref>{{cite journal|author1=B. C. B. Peel |author2=B. M. Hochwald |author3=A. L. Swindlehurst |last-author-amp=yes |title=A vector-perturbation technique for near-capacity multiantenna multiuser communication - Part I: channel inversion and regularization|journal=IEEE Trans. Commun.|pages=195–202|volume=53|date=Jan 2005|doi=10.1109/TCOMM.2004.840638}}</ref> where the background noise and the unknown user interference can be emphasized in the result of (known) interference signal nulling.
In particular, '''Nullnull-Steeringsteering''' is a method of [[beamforming]] for [[narrowband]] [[signal processing|signals]] where we want to have a simple way of compensating delays of receiving signals from a specific source at different elements of the antenna array. In general to make better use of the antenna arrays, we sum and average the signals coming to different elements, but this is only possible when delays are equal. Otherwise, we first need to compensate the delays and then sum them up. To reach this goal, we may only add the weighted version of the signals with appropriate weight values. We do this in such a way that the frequency ___domain output of this weighted sum produces a zero result. This method is called null steering. The generated weights are of course related to each other and this relation is a function of delay and central working frequency of the source.
==Performance of Zero-forcing Precoding==
If the transmitter knows the downlink [[channel state information]] (CSI) perfectly, ZF-precoding can achieve almost the system capacity when the number of users is large. On the other hand, with limited [[channel state information]] at the transmitter (CSIT) the performance of ZF-precoding decreases depending on the accuracy of CSIT. ZF-precoding requires the significant feedback overhead with respect to signal-to-noise-ratio (SNR) so as to achieve the full multiplexing gain.<ref name="Jindal_ZF">{{cite journal|author=N. Jindal|title=MIMO Broadcast Channels with Finite Rate Feedback|journal=IEEE Transactions on Information Theory.|pages=5045–5059|volume=52|issue=11|date=Nov 2006|doi=10.1109/TIT.2006.883550}}</ref> Inaccurate CSIT results in the significant throughput loss because of residual multiuser interferences. Multiuser interferences remain since they can not be nulled with beams generated by imperfect CSIT.
