Zero-forcing precoding

Zero-forcing 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 other user interference^[1], where the noise and interference can be emphasized in the result of desired signal beamforming.

Performance of Zero-forcing Precoding

If the transmitter knows the downlink channel status information almost perfectly, ZF-based precoding can achieve close to the system capacity when the number of users is large. With limited channel status information at the transmitter, ZF-precoding requires the feedback overhead increasement with respect to signal-to-noise-ratio (SNR) to achieve the full multiplexing gain^[2]. Hence, inaccurate channel state information at the transmitter may result in the significant loss of the system throughput because of the residual interference among transmit streams.

Mathematical Description

In a Precoded MIMO BC system with ${\displaystyle N_{t}}$  transmitter antennas at AP and a receiver antenna for each user ${\displaystyle k}$ , the input-output relationship can be described as

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

where ${\displaystyle \mathbf {x} =\sum _{i=1}^{K}s_{i}P_{i}\mathbf {w} _{i}}$  is the ${\displaystyle N_{t}\times 1}$  vector of transmitted symbols, ${\displaystyle y_{k}}$  and ${\displaystyle n_{k}}$  are the received symbol and noise respectively, ${\displaystyle \mathbf {h} _{k}}$  is the ${\displaystyle N_{t}\times 1}$  vector of channel coefficients and ${\displaystyle \mathbf {w} _{i}}$  is the ${\displaystyle N_{t}\times 1}$  linear precoding vector.

For the comparison purpose, we describe the mathematical description of MIMO MAC. In a MIMO MAC system with ${\displaystyle N_{r}}$  receiver antennas at AP and a transmit antenna for each user ${\displaystyle k}$  where ${\displaystyle k=1,2,\ldots ,K}$ , the input-output relationship can be described as

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

where ${\displaystyle s_{i}}$  is the transmitted symbol for user ${\displaystyle i}$ , ${\displaystyle \mathbf {y} }$  and ${\displaystyle \mathbf {n} }$  are the ${\displaystyle N_{r}\times 1}$  vector of received symbols and noise respectively, ${\displaystyle \mathbf {h} _{k}}$  is the ${\displaystyle N_{r}\times 1}$  vector of channel coefficients.

See Also

• Precoding
• MIMO

References

1. B. C. B. Peel, B. M. Hochwald, and A. L. Swindlehurst (Jan. 2005). "A vector-perturbation technique for near-capacity multiantenna multiuser communication - Part I: channel inversion and regularization". IEEE Trans. Commun. 53: 195–202. doi:10.1109/TCOMM.2004.840638. {{cite journal}}: Check date values in: |date= (help)
2. N. Jindal (Nov. 2006). "MIMO Broadcast Channels with Finite Rate Feedback". IEEE Trans. Information Theory. 52 (11): 5045–5059. doi:10.1109/TIT.2006.883550. {{cite journal}}: Check date values in: |date= (help)