Zero-forcing precoding: Difference between revisions

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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 Trans. 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.

==Mathematical Descriptiondescription==

In a multiple antenna downlink systemssystem 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>

where <math>\mathbf{x} = \sum_{i=1}^K s_i P_i \mathbf{w}_i</math> is the <math>N_t \times 1</math> vector of transmitted symbols, <math>n_k</math> is the noise signal, <math>\mathbf{h}_k</math> is the <math>N_t \times 1</math> channel vector and <math>\mathbf{w}_i</math> is the <math>N_t \times 1</math> linear precoding vector. From the fact that each Beambeam generated by ZF-precoding is orthogonal to all the other user channel vectors, weone can rewrite the received signal as

:<math>y_k = \mathbf{h}_k^T \sum_{i=1}^K s_i P_i \mathbf{w}_i+n_k = \mathbf{h}_k^T s_k P_k \mathbf{w}_k +n_k, \quad k=1,2, \ldots, K</math>