Zero-forcing-precoding

Zero-forcing precoding

Zero-forcing (or Null-Steering) precoding is a spatial signal processing by which the multiple antenna transmittercan null multiuser interference signals in wireless communications. Regularized zero-forcing precoding is enhancedprocessing to consider the impact on a background noise and unknown user interference, where the backgroundnoise and the unknown user interference can be emphasized in the result of (known) interference signal nulling.

In particular, Null-Steering is a method of beamforming for narrowband signals where we want to have a simpleway of compensating delays of receiving signals from a specific source at different elements of the antenna array. Ingeneral to make use of the antenna arrays, we better to sum and average the signals coming to different elements, butthis is only possible when delays are equal. Otherwise we first need to compensate the delays and then to sum themup. To reach this goal, we may only add the weighted version of the signals with appropriate weight values. We dothis in such a way that the frequency domain output of this weighted sum produces a zero result. This method iscalled null steering. The generated weights are of course related to each other and this relation is a function of delayand 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 almostthe system capacity when the number of users is large. On the other hand, with limited channel state information atthe 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 achievethe full multiplexing gain. Inaccurate CSIT results in the significant throughput loss because of residual multiuserinterferences. Multiuser interferences remain since they can not be nulled with beams generated by imperfect CSIT.

Zero-forcing-precoding

Zero-forcing-precoding

Zero-forcing-precoding

Mathematical description

In a multiple antenna downlink system which comprises a transmit antenna access point (AP) and singlereceive antenna users, the received signal of user

Zero-forcing-precoding

Zero-forcing-precoding

Zero-forcing-precoding

Zero-forcing-precoding

Zero-forcing-precoding

is described as

where

channel vector and is the is the vector of transmitted symbols, is the noise signal, is the linear precoding vector. From the fact that each beam generated by

Zero-forcing-precoding

Zero-forcing-precoding

ZF-precoding is orthogonal to all the other user channel vectors, one can rewrite the received signal as

For comparison purpose, we describe the received signal model for multiple antenna uplink systems. In the uplinksystem with a receiver antenna AP and K single transmit antenna user, the received signal at the AP is

Zero-forcing-precoding

Zero-forcing-precoding

described as

where is the transmitted signal of user , is the noise vector, is the channel vector.

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