Zero-forcing precoding: Difference between revisions

Revision as of 15:22, 30 October 2013

Revision as of 23:58, 7 November 2013

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Zero-forcing (or Null-Steering) precoding is a 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|author=B. C. B. Peel, B. M. Hochwald, and A. L. Swindlehurst|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, '''Null-Steering''' 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 use of the antenna arrays, we better to 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 to 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.

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==Mathematical description==

In a multiple antenna downlink system which comprises a <math>N_t</math> transmit antenna access point (AP) and <math>K</math> single receive antenna users, the received signal of user <math>k</math> is described as

:<math>y_k = \mathbf{h}_k^T\mathbf{x}+n_k, \quad k=1,2, \ldots, K</math>

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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"/>:

:<math> B = (M-1) \log_2 \rho_{b,m} - (M-1) \log_2 (g-1) </math>

where ''M'' is the number of transmit antennas and <math>\rho_{b,m}</math> 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'