*2.3.2. Analytical models*

The second class of MIMO channel models includes analytical models which are based on the statistical properties obtained through measurement (Distribution of Direction of Departure (DOD), distribution of Direction of Arrival (DOA),. . .). Analytical channel models can be 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 propagation-based models (such as Müller model and Finite scatterer model).

We provide in [8] a detailed description of MIMO systems with geometric wide MIMO channel models where advanced polarization techniques [9][10] are exploited.

#### **2.4. MIMO system performances**

4 Recent Trends in Multiuser MIMO Communications

**Physical models**

**Figure 2.** MIMO channel propagation models

stochastic channel models (GSCMs).

antennas or receive antennas.

*2.3.2. Analytical models*

propagation signal.

*2.3.1. Physical models*

✬

✩

✪

Propagation-based models

**Analytical models**

✫

**MIMO channel models**

Deterministic models Correlation-based models

Geometry-based models Statiscal-based 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

• Deterministic models define a channel model according to the prediction of the

• Geometry-based Stochastic Channel Models (GSCMs) have an immediate relation with the physical characteristics of the propagation channel. These models suppose that clusters of scatterers are distributed around the transmitter and the receiver. The scatterers locations are defined according to a random fashion that follows a particular probability distribution. Scatterers result in discrete channel paths and can involve statistical characterizations of several propagation parameters such as delay spread, angular spread, spatial correlation and cross polarization discrimination. We distinguish two possible schemes which are the Double Bounce Geometry-based Stochastic Channel Models (DB-GSCMs) and the Single Bounce Geometry-based Stochastic Channel Models (SB-GSCMs). That is when a single bounce of scatterers is placed around the transmit

The second class of MIMO channel models includes analytical models which are based on the statistical properties obtained through measurement (Distribution of Direction of Departure (DOD), distribution of Direction of Arrival (DOA),. . .). Analytical channel models can be

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

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 evaluated according to the following scenarios:

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 then given by:

$$\mathcal{C}(H) = \log\_2\left[ \det\left( I\_{\mathcal{N}\_\mathbb{R}} + \frac{\gamma}{N\_T} \cdot HH^\* \right) \right] \quad \text{bits/s/Hz} \tag{4}$$

*γ* denotes the Signal to Noise Ratio (SNR).

(·)<sup>∗</sup> stands for the conjugate transpose operator.

2. When CSI is available at the receiver, Singular Value Decomposition (SVD) is used to derive the MIMO channel capacity which is given by:

$$\mathcal{C}\_{SVD}(H) = R \cdot \log\_2 \left[ \det \left( 1 + \frac{\gamma}{N\_T} HH^\* \right) \right] \quad \text{bits/s/Hz} \tag{5}$$

#### 6 Recent Trends in Multiuser MIMO Communications <sup>8</sup> Recent Trends in Multi-user MIMO Communications Multi User MIMO Communication: Basic Aspects, Benefits and Challenges 7

*R* = *min*(*NR*, *NT*) is the rank of the channel matrix *H*

3. When CSI is available at both the transmitter and the receiver, the channel capacity is computed by performing the water-filling algorithm. The instantaneous channel capacity is then:

$$\mathcal{C}\_{WF}(H) = \sum\_{p=1}^{R} \log\_2 \left[ \left( \frac{\lambda\_{H,p} \cdot \mu}{\sigma\_b^2} \right)^{+} \right] \quad \text{bits/s/Hz} \tag{6}$$

10.5772/57133

9

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

Multi User MIMO Communication: Basic Aspects, Benefits and Challenges

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

established between base stations [2]. Basic configurations of downlink multi-user MIMO systems are depicted in Figure 5. Figure 5(a) represents the SU-MIMO system where a Base Station (BS) equipped with antennas *Tx*1,..., *TxN* communicates with user *U* which is equipped with *M* antennas *Rx*1,..., *RxM*. In Figure 5(b), the presented MU-MIMO system consists of two base stations *BS*<sup>1</sup> and *BS*<sup>2</sup> each one is equipped with *N* antennas. Generalized MU-MIMO systems may consist of more base stations where the number of antennas could be different. At the receive side, *K* users *U*1,..., *UK* with respectively *M*1,..., *MK* antennas communicate with the transmit base stations. The same communication model is performed for the MU-MIMO with cooperation (Figure 5(c)) where cooperation is established between

Once multi-user communication systems are introduced, we explain in the following section

Table 1 summarizes the main features of both SU-MIMO and MU-MIMO systems [13]. In contrast to MU-MIMO systems where one base station could communicate with multiple users, base station only communicate with a single user in the case of SU-MIMO systems. In addition, MU-MIMO systems are intended to employ multiple receivers so that to improve the rate of communication while keeping the same level of reliability. These systems are able to achieve the overall multiplexing gain obtained as the minimum value between the number of antennas at base stations and the number of antennas at users. The fact that multiple users could simultaneously communicate over the same spectrum improves the system performance. Nevertheless, MU-MIMO networks are exposed to strong co-channel interference which is not the case for SU-MIMO ones. In order to solve the problem of interference in MU-MIMO systems, several approaches have been proposed for interference management [14][15]. Some of these approaches are based on beamforming technique [31]. Moreover, in contrast to SU-MIMO systems, MU-MIMO systems require perfect CSI in

**Figure 4.** Improvement of the BER for MIMO (*NR* × <sup>2</sup>) as a function of receive antennas number

SNR (dB)

10−5

10−4

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

the difference between SU-MIMO and MU-MIMO configurations.

10−3

BER

*BS*<sup>1</sup> and *BS*2.

**4. MU-MIMO vs SU-MIMO**

10−2

10−1

100


We consider the case where CSI is available at the receiver, the simulated ergodic MIMO capacity is depicted in Figure 3. For a MIMO system with two transmit antennas, numerical results show that ergodic capacity linearly increases with the number of antennas. Plotted curves are presented for different levels of the SNR. The use of additional antennas improves the performances of the communication system. Moreover, MIMO system takes advantage of multipath propagation. The performances of MIMO system are observed in the following in terms of the Bit Error Rate (BER). We consider a MIMO system with various receive antennas, the BER is evaluated for communication systems with Rayleigh fading MIMO channel and additive gaussian noise. At the receive side, the Maximum Ratio Combining (MRC) technique is performed. According to Figure 4, it is obvious that MIMO technology allows for a significant improvement of the BER.

Once the MIMO technology is presented, we introduce in the following multi-user MIMO systems.
