**Author details**

18 Recent Trends in Multiuser MIMO Communications

The resulting signal at user *Uk* is:

of the MU-MIMO system expressed as:

interference such as [32]:

**9. Conclusion**

*C*(*k*) is the covariance matrix of *Hk*. �·�<sup>2</sup> stands for the 2-norm operator.

matrix is :

• *VtBF*(*k*)(*<sup>N</sup>* × <sup>1</sup>) is the transmit beamforming vector of index *<sup>k</sup>*. The transmit beamforming

*BF* ,..., *Vt*(*k*)

*BF* ,..., *vr*(*Mk* )

log2(<sup>1</sup> <sup>+</sup> *SINR*(*k*)

*BF* ] *T*

*BF* ] (27)

) (30)

(28)

(31)

(32)

*BF* (*Mk* <sup>×</sup> <sup>1</sup>).

*BF* ; *k* = 1, . . . , *K* (29)

*VtBF* = [*Vt*(1)

*BF* = [*vr*(1)

<sup>∗</sup> · *Vr*(*k*)

*K* ∑ *k*=1

strength of undesired signal obtained as the sum of noise and interference signal.

� *Vr* (*k*) *BF* · *<sup>H</sup>*<sup>∗</sup>

Beamforming weights at the receiver are determined so that to suppress inter-user

�[*C*(*k*)]<sup>−</sup><sup>1</sup> · *Hk* · *Vt*

This chapter presents a basic introduction to the fundamentals of multi-user MIMO communication. MU-MIMO is considered as an enhanced form of MIMO technology. Such technology has been a topic of extensive research since the last three decades. The attractive features of MIMO systems have shown that the use of multiple antennas at both the ends of

The conjoint receive-transmit beamforming weights are obtained by maximizing the sum rate

*SINR*(*k*); *k* = 1, . . . , *K* is the Single Interference Noise Ratio (SINR) [31] associated to user *Uk*. The SINR is determined as the ratio of the received strength for the desired signal to the

*BF* · *<sup>H</sup>*<sup>∗</sup>

*<sup>k</sup>* · *Vt*(*k*) *BF* �<sup>2</sup>

*<sup>k</sup>* · *Vt*(*k*) *BF* �<sup>2</sup> + 1

<sup>−</sup><sup>1</sup> · *Hk* · *Vr*(*k*)

*BF*

(*k*) *BF* �<sup>2</sup>

At the receive side, beamforming vectors are denoted by *Vr*(*k*)

*Vr*(*k*)

*zk* = *Yk*

*Rsum* =

For unit signal noise variance, the SINR for user *Uk* is given by :

*SINR*(*k*) <sup>=</sup> � *Vr*(*k*)

*Vr*(*k*)

 *K* ∑ *k*=1

*BF* <sup>=</sup> [*C*(*k*)]

Ben Zid Maha1,<sup>⋆</sup> and Raoof Kosai1,2

<sup>⋆</sup> Address all correspondence to: maha.ben-zid@gipsa-lab.grenoble-inp.fr

1 École Nationale Supérieure d'Ingénieurs du Mans (ENSIM), Le Mans, France 2 Laboratoire d'Acoustique de l'Université du Maine, (LAUM), UMR CNRS 6613, Le Mans, France
