**8.2. Beamforming for linear precoding**

Beamforming paradigms represent another class of linear precoding for MU-MIMO systems. For the communication model with beamforming (Figure 12), we consider a MU-MIMO system with *K* multiple antenna users *U*1,..., *UK* at the receive side which are respectively equipped with *M*1,..., *MK* antennas. At the transmit side, a multiple antenna base station with *N* antennas transmits data signals *x*1,..., *xK* to users *U*1,..., *UK*.

**Figure 12.** MU-MIMO with beamforming

The received signal vector at user *Uk*; *k* = 1, . . . , *K* is expressed as :

$$Y\_k = H\_k \cdot Vt\_{\rm BF}^{(k)} \cdot \mathbf{x}\_k + \sum\_{\substack{j=1,\ k \neq j}}^K H\_k \cdot Vt\_{\rm BF}^{(j)} \cdot \mathbf{x}\_j + B\_k \quad ; \ k = 1, \dots, K \tag{26}$$

where:


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

$$Vt\_{BF} = [Vt\_{BF'}^{(1)} \dots \iota \lrcorner Vt\_{BF}^{(k)}] \tag{27}$$

10.5772/57133

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http://dx.doi.org/10.5772/57133

the communication link significantly improves the spectral efficiency of the communication

Multi User MIMO Communication: Basic Aspects, Benefits and Challenges

In multiuser channels and cellular systems, MIMO is offered for MU-MIMO communication

Nowadays, it has been a great deal with MU-MIMO systems. Several approaches are adopted and different scenarios may be considered. Throughout this chapter, we have presented possible configurations associated with MU-MIMO with particular emphasis on

Some scenarios have been considered for performance evaluation of MU-MIMO

MU-MIMO scenarios follow into UL-MU-MIMO for Multiple Access Channel (MAC) and the DL-MU-MIMO for Broadcast Channel (BC). The DL-MU-MIMO is the more challenging

Througout this chapter, we have presented precoding techniques used within MU-MIMO systems for efficient transmission and interference cancelation. Among the existing techniques, we have introduced ZF and BD methods. Of particular interest, we have

The design of multi-user MIMO systems is attractive for the research field as well for the

2 Laboratoire d'Acoustique de l'Université du Maine, (LAUM), UMR CNRS 6613, Le Mans,

[1] Ben Zid, M., Raoof, K. and Bouallègue, A. (2012). MIMO spectral efficiency over energy consumption requirements: Application to WSNs, *Int'l J. of Communications, Network and*

[2] Ben Zid, M., Raoof, K. and Bouallègue, A. (2012). MIMO Systems and Cooperative Networks Performances, *in: Advanced Cognitive Radio Network*, Scientific Research

[3] Raoof, K. and Zhou, H. (2009). *Advanced MIMO systems*, Scientific Research Publishing,

[4] Winters, J.H. (1987). On the capacity of radio communication systems with diversity in a Rayleigh fading environment, *IEEE Journal on Selected Areas in Communications* Vol.

system as well as the reliability of the communication link.

to allow for spatial sharing of the channel by several users.

communication in terms of the capacity region metric.

described the linear beamforming algorithms.

*System Sciences* Vol. 5(No. 2): 121–129.

Publishing, ISBN: 193–506–874–1.

ISBN:978–1–935068–02–0.

5(No. 5): 871–878.

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

**Author details**

France

**References**

the fundamental differences between SU-MIMO and MU-MIMO.

industrial one and the field of application is extensively growing.

<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

scenario since optimum strategies for interference cancelation are required.

At the receive side, beamforming vectors are denoted by *Vr*(*k*) *BF* (*Mk* <sup>×</sup> <sup>1</sup>).

$$\left[\boldsymbol{V}\boldsymbol{r}\_{\rm BF}^{(k)} = \left[\boldsymbol{\upsilon}\boldsymbol{r}\_{\rm BF}^{(1)}, \dots, \boldsymbol{\upsilon}\boldsymbol{r}\_{\rm BF}^{(M\_k)}\right]^T \tag{28}$$

The resulting signal at user *Uk* is:

$$z\_k = Y\_k^\* \cdot \operatorname{Wr}\_{\mathrm{BF}}^{(k)} \; ; \; k = 1, \dots, K \tag{29}$$

The conjoint receive-transmit beamforming weights are obtained by maximizing the sum rate of the MU-MIMO system expressed as:

$$R\_{sum} = \sum\_{k=1}^{K} \log\_2(1 + SINR^{(k)}) \tag{30}$$

*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 strength of undesired signal obtained as the sum of noise and interference signal. For unit signal noise variance, the SINR for user *Uk* is given by :

$$SINR^{(k)} = \frac{\|\left.\left\|\left.\left.\boldsymbol{V}\_{\mathrm{BF}}^{(k)}\cdot\boldsymbol{H}\_{k}^{\*}\cdot\boldsymbol{V} t\_{\mathrm{BF}}^{(k)}\right\|\right|^{2}}{\left(\sum\_{k=1}^{K} \|\left.\boldsymbol{V} r\_{\mathrm{BF}}^{(k)}\cdot\boldsymbol{H}\_{k}^{\*}\cdot\boldsymbol{V} t\_{\mathrm{BF}}^{(k)}\right\|\right) + 1}\right)}\tag{31}$$

Beamforming weights at the receiver are determined so that to suppress inter-user interference such as [32]:

$$\mathcal{V}r\_{\mathcal{B}F}^{(k)} = \frac{[\mathbb{C}^{(k)}]^{-1} \cdot H\_k \cdot \mathcal{V}r\_{\mathcal{B}F}^{(k)}}{|| [\mathbb{C}^{(k)}]^{-1} \cdot H\_k \cdot \mathcal{V}t\_{\mathcal{B}F}^{(k)}||\_2} \tag{32}$$

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