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Zero-forcing (or null-steering) precoding is a method of spatial signal processing by which a multiple antenna transmitter can null the multiuser interference in a multi-user MIMO wireless communication system.<ref>{{Cite conference |author1first1=Taesang |last1=Yoo |author2first2=AAndrea J. |last2=Goldsmith |date=2005 |title=Optimality of zero-forcing beamforming with multiuser diversity |book-title=IEEE International Conference on Communications, 2005 |publisher=IEEE |volume=1 |pages=542–546 |doi=10.1109/ICC.2005.1494410 |isbn=978-0-7803-8938-0 |___location=Seoul, Korea (South)}}</ref> When the channel state information is perfectly known at the transmitter, the zero-forcing precoder is given by the pseudo-inverse of the channel matrix. Zero-forcing has been used in [[LTE (telecommunication)|LTE]] mobile networks.<ref>{{Cite journal |lastlast1=Aslan |firstfirst1=Yanki |last2=Roederer |first2=Antoine |last3=Fonseca |first3=Nelson |last4=Angeletti |first4=Piero |last5=Yarovoy |first5=Alexander |date=Oct 2021 |title=Orthogonal Versus Zero-Forced Beamforming in Multibeam Antenna Systems: Review and Challenges for Future Wireless Networks |journal=IEEE Journal of Microwaves |volume=1 |issue=4 |pages=879–901 |doi=10.1109/JMW.2021.3109244 |doi-access=free |issn=2692-8388}}</ref>
==Mathematical description==
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:<math>\Delta R = R_{ZF} - R_{FB} \leq \log_2 g</math> .
Jindal showed that the required feedback bits of a [[Spatial Correlation|spatially uncorrelated]] channel should be scaled according to SNR of the downlink channel, which is given by:<ref name="Jindal_ZF" />
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 |authorfirst=N.Nihar |last=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 |arxiv=cs/0603065|s2cid=265096041 }}</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.
