Zero-forcing precoding

Zero-forcing precoding (or ZF-precoding) is a spatial signal processing that nulls multiuser interference at the multiple antenna transmitter in wireless communications. Regularized zero-forcing precoding is enhanced processing to consider the impact on a background noise and unknown user interference, where the background noise and the unknown user interference can be emphasized in the result of (known) interference signal nulling.

Performance of Zero-forcing Precoding

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, wth limited channel state information at the transmitter (CSIT) the performance of ZF-precoding decrease 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. Inaccurate CSIT results in the significant throughput loss because of residual multiuser interferences. Multiuser interferences are remained since those can not be nulled with beams generated by imperfect CSIT.

Mathematical Description

In multiple antenna downlink systems which comprises a $N_{t}$ transmit antenna access point (AP) and $K$ single receive antenna users, the received signal of user $k$ is described as

$y_{k}=\mathbf {h} _{k}^{T}\mathbf {x} +n_{k},\quad k=1,2,\ldots ,K$

where $\mathbf {x} =\sum _{i=1}^{K}s_{i}P_{i}\mathbf {w} _{i}$ is the $N_{t}\times 1$ vector of transmitted symbols, $n_{k}$ is the noise signal, $\mathbf {h} _{k}$ is the $N_{t}\times 1$ channel vector and $\mathbf {w} _{i}$ is the $N_{t}\times 1$ linear precoding vector. From the fact that each Beam generated by ZF-precoding is orthogonal to all the other user channel vectors, we can rewrite the received signal as

$y_{k}=\mathbf {h} _{k}^{T}\sum _{i=1}^{K}s_{i}P_{i}\mathbf {w} _{i}+n_{k}=\mathbf {h} _{k}^{T}s_{k}P_{k}\mathbf {w} _{k}+n_{k},\quad k=1,2,\ldots ,K$

For comparison purpose, we describe the received signal model for multiple antenna uplink systems. In the uplink system with a $N_{r}$ receiver antenna AP and $K$ K single transmit antenna user, the received signal at the AP is described as

$\mathbf {y} =\sum _{i=1}^{K}s_{i}\mathbf {h} _{i}+\mathbf {n}$

where $s_{i}$ is the transmitted signal of user $i$, $\mathbf {n}$ is the $N_{r}\times 1$ noise vector, $\mathbf {h} _{k}$ is the $N_{r}\times 1$ channel vector.

See Also

• Precoding
• MIMO