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.

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

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

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

described as

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

Quantify the feedback amount

Quantify the amount of the feedback resource required to maintain at least a given throughput performance gapbetween zero-forcing with perfect feedback and with limited feedback, i.e.,

.

Jindal showed that the required feedback bits of a spatially uncorrelated channel should be scaled according to SNR

of the downlink channel, which is given by:

where M is the number of transmit antennas and is the SNR of the downlink channel.

To feed back B bits though the uplink channel, the throughput performance of the uplink channel should be larger

than or equal to 'B'

where

resource to satisfy is the feedback resource consisted by multiplying the feedback frequency resource and theis SNR of the feedback channel. Then, the required feedbackis

.frequency temporal resource subsequently and

Note that differently from the feedback bits case, the required feedback resource is a function of both downlink anduplink channel conditions. It is reasonable to include the uplink channel status in the calculation of the feedbackresource since the uplink channel status determines the capacity, i.e., bits/second per unit frequency band (Hz), of thefeedback link. Consided a case when SNR of the downlink and uplink are proportion such that

is constant and both SNRs are sufficiently high. Then, the feedback resource will be onlyproportional to the number of transmit antennas.

It follows from the above equation that the feedback resource ( ) is not necessary to scale according to SNR ofthe downlink channel, which is almost contradict to the case of the feedback bits. One, hence, sees that the wholesystematic analysis can reverse the facts resulted from each reductioned situation.

References

External links

Schelkunoff Polynomial Method (Null-Steering) (http://doc.guandang.net/arrays/weights/zeros.php)http://doc.guandang.net

Article Sources and Contributors

Zero-forcing precoding  Source: http://doc.guandang.net/w/index.php?oldid=605524718  Contributors: Agrawalmayur, Elkman, Jamessungjin.kim, John of Reading, Mayalld, Mild Bill Hiccup,10 anonymous editsLicense

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