**2.1. An historical overview**

The main historical events which make the MIMO systems [2][3] are summarized as follows:

• In 1984, Jack Winters at Bell Laboratories wrote a patent on wireless communications using multiple antennas. Jack Winters in [4] presented a study of the fundamental limits on the data rate of multiple antenna systems in a Rayleigh fading environment.

Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Maha and Kosai; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

©2012 Ben Zid, Raoof, licensee InTech. This is an open access chapter distributed under the terms of the

• In 1993, Arogyaswami Paulraj and Thomas Kailath proposed the concept of spatial multiplexing using MIMO.

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Antennas *Tx*1,..., *TxNT* respectively send signals *x*1,..., *xNT* to receive antennas *Rx*1,..., *RxNR* . Each receive antenna combines the incoming signals which coherently add up. The received signals at antennas *Rx*1,,..., *RxNR* are respectively denoted by *y*1,..., *yNR* .

The flat fading MIMO channel model is described by the input-output relationship as:

*h*<sup>11</sup> *h*<sup>12</sup> ... *h*1*NT h*<sup>21</sup> *h*<sup>22</sup> ... *h*2*NT*

*hNR*<sup>1</sup> *hNR*<sup>2</sup> ... *hNRNT*

*hqp*; *p* = 1, . . . , *NT*; *q* = 1, . . . , *NR* is the complex channel gain which links transmit

*<sup>T</sup>* is the (*NT* × <sup>1</sup>) complex transmitted signal vector.

*<sup>T</sup>* is the (*NR* × <sup>1</sup>) complex additive noise signal vector.

The continuous time delay MIMO channel model of the (*NR* × *NT*) MIMO channel *<sup>H</sup>*

Several MIMO channel models [7] have been proposed in literature. These models mainly

*<sup>T</sup>* is the (*NR* × <sup>1</sup>) complex received signal vector.

*hqp* · *xp* + *bq* ; *<sup>q</sup>* = 1, . . . , *NR* (1)

Multi User MIMO Communication: Basic Aspects, Benefits and Challenges

*y* = *H* · *x* + *b* (2)

*H* (*t*, *τ*) *x* (*t* − *τ*) *dτ* + *b*(*t*) (3)

We express the received signal at antenna *Txq*; *q* = 1, . . . , *NR* as:

*NT* ∑ *p*=1

*H* =

associated with time delay *τ* and noise signal *b*(*t*) is expressed as:

� *τ*

*y* (*t*) =

. . . . . . ... . . .

*yq* =

• *<sup>H</sup>* is the (*NR* × *NT*) complex channel matrix given by:

antenna *Txp* to receive antenna *Rxq*.

• *y*(*t*) is the spatio-temporel output signal. • *x*(*t*) is the spatio-temporel input signal. • *b*(*t*) is the spatio-temporel noise signal.

fall into two categories as depicted in Figure 2.

(·)*<sup>T</sup>* denotes the transpose operator.

**2.3. MIMO channel modeling**

• *x* = [*x*1,..., *xNT* ]

• *y* = [*y*1,..., *yNR* ]

• *b* = [*b*1,..., *bNR* ]


Nowadays, MIMO systems are implemented in many advanced technologies such as various standard proposals for the Fourth Generation (4G) of wireless communication systems and LTE. MIMO technology was shown to boost the communication system capacity and to enhance the reliability of the communication link since it uses several diversity schemes beyond the spatial diversity.

#### **2.2. Fundamentals of MIMO system**

MIMO system model is depicted in Figure 1. We present a communication system with *NT* transmit antennas and *NR* receive antennas.

**Figure 1.** MIMO system model

Antennas *Tx*1,..., *TxNT* respectively send signals *x*1,..., *xNT* to receive antennas *Rx*1,..., *RxNR* . Each receive antenna combines the incoming signals which coherently add up. The received signals at antennas *Rx*1,,..., *RxNR* are respectively denoted by *y*1,..., *yNR* . We express the received signal at antenna *Txq*; *q* = 1, . . . , *NR* as:

$$y\_q = \sum\_{p=1}^{N\_T} h\_{qp} \cdot x\_p + b\_q \quad ; \ q = 1, \dots, N\_R \tag{1}$$

The flat fading MIMO channel model is described by the input-output relationship as:

$$y = H \cdot \mathfrak{x} + b \tag{2}$$

• *<sup>H</sup>* is the (*NR* × *NT*) complex channel matrix given by:

2 Recent Trends in Multiuser MIMO Communications

multiplexing using MIMO.

information theory aspects.

systems is named IEEE 802.11n.

**2.2. Fundamentals of MIMO system**

transmit antennas and *NR* receive antennas.

*x*2

✎

☞

. . . . .

*xNT*

✌

✍

**Figure 1.** MIMO system model

beyond the spatial diversity.

• In 1993, Arogyaswami Paulraj and Thomas Kailath proposed the concept of spatial

• Several articles which focused on MIMO concept were published in the period from 1986 to 1995 [5]. This was followed by the work of Greg Raleigh and Gerard Joseph Foschini in 1996 which invented new approaches involving space time coding techniques. These

• In 1999, Thomas L. Marzetta and Bertrand M. Hochwald published an article [6] which provides a rigorous study on the MIMO Rayleigh fading link taking into consideration

• Since 2006, several companies such as Broadcom and Intel have introduced a novel communication technique based on the MIMO technology for improving the performance of wireless Local Area Network (LAN) systems. The new standard of wireless LAN

Nowadays, MIMO systems are implemented in many advanced technologies such as various standard proposals for the Fourth Generation (4G) of wireless communication systems and LTE. MIMO technology was shown to boost the communication system capacity and to enhance the reliability of the communication link since it uses several diversity schemes

MIMO system model is depicted in Figure 1. We present a communication system with *NT*

Transmitter Receiver

✩

*Tx*<sup>1</sup> *Rx*<sup>1</sup>

*x y*

✲

✬

✯

✼

❥

✲

❃

�✲ ✇

✫

*y*2

✎

☞

. . . . .

*yNR*

✍

✌

*Tx*<sup>2</sup> *Rx*<sup>2</sup>

*x*<sup>1</sup> *y*<sup>1</sup>

*<sup>H</sup>*(*NR* × *NT*)

✪

*TxNT RxNR*

. .

approaches were proved to increase the spectral efficiency of MIMO systems.

• The first commercial MIMO system was developed in 2001 by Iospan Wireless Inc.

$$H = \begin{pmatrix} h\_{11} & h\_{12} & \dots & h\_{1N\_T} \\ h\_{21} & h\_{22} & \dots & h\_{2N\_T} \\ \vdots & \vdots & \ddots & \vdots \\ h\_{N\_R1} & h\_{N\_R2} & \dots & h\_{N\_RN\_T} \end{pmatrix}.$$

*hqp*; *p* = 1, . . . , *NT*; *q* = 1, . . . , *NR* is the complex channel gain which links transmit antenna *Txp* to receive antenna *Rxq*.


The continuous time delay MIMO channel model of the (*NR* × *NT*) MIMO channel *<sup>H</sup>* associated with time delay *τ* and noise signal *b*(*t*) is expressed as:

$$\log f(t) = \int\_{\tau} H\left(t, \tau\right) \ge \left(t - \tau\right)d\tau + b(t) \tag{3}$$


(·)*<sup>T</sup>* denotes the transpose operator.

#### **2.3. MIMO channel modeling**

Several MIMO channel models [7] have been proposed in literature. These models mainly fall into two categories as depicted in Figure 2.

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classified into correlation-based models (such as i.i.d model, Kronecker model, Keyhole model,. . .), statistical -based models (such as Saleh-Valenzuela model and Zwick model) and

Multi User MIMO Communication: Basic Aspects, Benefits and Challenges

We provide in [8] a detailed description of MIMO systems with geometric wide MIMO

<sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> <sup>10</sup> 0.5

MIMO technology has been shown to improve the capacity of the communication link without the need to increase the transmission power. MIMO system capacity is mainly

1. When no Channel State Information (CSI) is available at the transmitter, the power is equally split between the *NT* transmit antennas, the instantaneous channel capacity is

> *INR* <sup>+</sup> *<sup>γ</sup> NT*

2. When CSI is available at the receiver, Singular Value Decomposition (SVD) is used to

<sup>1</sup> <sup>+</sup> *<sup>γ</sup> NT*

*HH*<sup>∗</sup>

 det · *HH*<sup>∗</sup>

*bits*/*s*/*Hz* (4)

*bits*/*s*/*Hz* (5)

SNR (dB)

propagation-based models (such as Müller model and Finite scatterer model).

channel models where advanced polarization techniques [9][10] are exploited.

**2.4. MIMO system performances**

1

evaluated according to the following scenarios:

*C*(*H*) = log2

derive the MIMO channel capacity which is given by:

*CSVD*(*H*) = *<sup>R</sup>* · log2

*γ* denotes the Signal to Noise Ratio (SNR). (·)<sup>∗</sup> stands for the conjugate transpose operator.

 det

1.5

2

2.5

Ergodic capacity (bits/s/Hz)

**Figure 3.** Ergodic capacity for MIMO systems

then given by:

3

3.5

4

 *NR=1 NR=2 NR=3 NR=4 NR=5*

**Figure 2.** MIMO channel propagation models

## *2.3.1. Physical models*

MIMO channel impulse response is evaluated according to the radio wave which propagates from the transmitter to the receiver. The MIMO channel model is determined based on the experimental measurements made for extracting channel propagation parameters including antenna configuration at both the transmitter and the receiver, antenna polarization, scatterers,. . . Physical models include both deterministic models and Geometry-based stochastic channel models (GSCMs).

