**6. Fields of application**

10 Recent Trends in Multiuser MIMO Communications

User selection

**5.2. DL-MU-MIMO**

of signals intended to users *U*1,..., *UK*:

✲ Users data

• Each user should have as many transmit antennas as the number of data streams.

*U*<sup>1</sup>

*X*1

✲

*XK*

*F*1,..., *FK*. The received signal vector at the BS is then expressed as :

*y* = *K* ∑ *k*=1

using the linear decoders *G*1,..., *GK*. The decoding process is such that :

✲

In Figure 7, the block diagram for the UL-MU-MIMO includes a joint linear precoder and decoder. Linear precoders associated to users *U*1,..., *UK* will be respectively denoted by *Tx*<sup>1</sup>

*Tx*<sup>1</sup>

*UK*

. .

. .

*FK*

*F*1

✲

✲

. . .

*TxMK*

An estimate of the transmitted signal vectors denoted by *Yk*; *k* = 1, . . . , *K* are obtained by

*Yk* = *Gk* · *<sup>y</sup>*

DL-MU-MIMO communication model assumes that *K* users are simultaneously receiving signals from the base station. The transmitted signal vector *x*(*N* × 1) is expressed as the sum

The channel matrix between user *Uk*; *<sup>k</sup>* = 1, . . . , *<sup>K</sup>* and the base station is denoted by *Hk*(*Mk* × *<sup>N</sup>*). At each user, received signal vector of dimension (*Mk* × <sup>1</sup>); *<sup>k</sup>* = 1, . . . , *<sup>K</sup>* is given by:

*x* = *K* ∑ *k*=1

**Figure 7.** Block diagram for the UL-MU-MIMO with coding techniques: *N* antenna BS and *K* multiple antenna users

. . .

*TxM*<sup>1</sup>

. . .

*Rx*<sup>1</sup>

BS

✇

Precoding Decoding

✣

*H*<sup>1</sup>

. .

*HK*

*RxN*

. . . ✲<sup>+</sup> ❄ ❥

*b*

*Hk* · *Fk* · *Xk* + *<sup>b</sup>* (9)

*Xk* (10)

*Yk* = *Hk* · *<sup>x</sup>* + *Bk* ; *<sup>k</sup>* = 1, . . . , *<sup>K</sup>* (11)

✲ *y*

. . .

*GK*

*G*1

*Y*1

✲

*YK*

✲

✲

✲

MU-MIMO technology finds its applications in many areas and is nowadays exploited in many evolving technologies wich are described in the following.

	- Coordinated cells
	- Central cell
	- Interfering cells

The coordination between cells is performed by the Central Station (CS). The aim of this coordination is to mitigate the effect of inter-cells interference. Coding techniques should be employed in order to mitigate the effect of interfering cells.

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

(15)

(16)

**7.1. Capacity region of UL-MU-MIMO with single antenna users**

for the presented communication model is given by:

as the set of rates (*R*1, *R*2) associated to users *U*<sup>1</sup> and *U*2.

*Rx*<sup>1</sup>

✾

⑥

✰

❨

*<sup>R</sup>*<sup>1</sup> <sup>≤</sup> log2

Similarly, an upper bound for the maximum achievable rate for user *U*<sup>2</sup> is:

*<sup>R</sup>*<sup>2</sup> <sup>≤</sup> log2

BS

**Figure 9.** UL-MU-MIMO with *N* multiple antenna BS and *K* single antenna users

*RxN* . .

• *P*1: average power constraint on user *U*<sup>1</sup> • *P*2: average power constraint on user *U*<sup>2</sup>

We consider the notations:

• *N*0: noise signal power

achievable rate is given by :

� · � indicates the Frobenius norm.

We consider the UL-MU-MIMO with *N* multiple antenna BS and *K* single antenna users. The performed communication scheme is depicted in Figure 9. The equivalent MIMO channel

*Hk*(*<sup>N</sup>* <sup>×</sup>1); *<sup>k</sup>* <sup>=</sup> 1, . . . , *<sup>K</sup>* represents the Single Input Multiple Output (SIMO) channel between user *Uk*; *k* = 1, . . . , *K* and the BS. Case of two users (i.e. *K*=2), the capacity region is defined

. .

The capacity region [25] is evaluated by determining the individual rate constraint for each user. Assuming that user *U*<sup>1</sup> has the entire channel, an upper bound of the maximum

> <sup>1</sup> <sup>+</sup> �*H*1�<sup>2</sup> · *<sup>P</sup>*<sup>1</sup> *N*<sup>0</sup>

> <sup>1</sup> <sup>+</sup> �*H*2�<sup>2</sup> · *<sup>P</sup>*<sup>2</sup> *N*<sup>0</sup>

*H* = [*H*1,..., *HK*] (14)

Multi User MIMO Communication: Basic Aspects, Benefits and Challenges

*Tx*<sup>1</sup>

*U*<sup>1</sup>

*Tx*<sup>1</sup>

*UK*

. .

**Figure 8.** MU-MIMO coordinated network in cellular network [20]

**Digital Subscriber Line (DSL):** MU-MIMO systems are not only performed by multi-cell systems but also find their applications in other systems such as the downlink of a Digital Subscriber Line (DSL)[22][13].

The performance of MU-MIMO could be improved via the use of Orthogonal Frequency Division Multiplexing (OFDM) or Orthogonal Frequency Division Multiplexing Access (OFDMA) for multiple access scenarios in frequency selective channels. MU-MIMO systems could also improve multi-user diversity by performing High Data Rate (HDR) or Code Division Multiple Access (CDMA) techniques.
