los and nlos channel capacities for mimo polarization...

Los and Nlos Channel Capacities for MIMO Polarization Diversity

Nuttapol PRAYONGPUN , Kosai RAOOF Laboratoire des Images et Signaux (LIS) CNRS-UMR 5083

961, Rue de la Houille Blanche - BP 46 - 38402 Saint Martin d'Hères, France

Abstract: - As a result of the desired high-data transmission rate in the outdoor and indoor environment, an exploitation of multiple-input multiple output (MIMO) systems appears recently under the condition of rich scattering environments. The MIMO channel, correponding really to transmission capacity, is obviously characterized by antenna configuration and propagation environment. In this paper, we assume that all scatterers are uncorrelated, independent and identically distributed (i.i.d). In addition, we investigate the channel capacity of single, dual and triple polarized dipole antennas compared to omni-vertical and omni-horizontal antennas based on 2×2 and 3×3 MIMO systems for narrow transmission bandwidth. Moreover, the results of simulations illustrate that while the antenna correlation is eliminated by polarization diversity technique, the problems of cross-polar discrimination (XPD) and line of sight (LOS) can be also resolved. Key-Words: - Capacity, channel correlation, multiple input multiple output (MIMO), multipolarized antenna arrays, narrow band systems 1 Introduction

Recently multiple antennas at both transmitter and receiver have chosed to increase the capacity and reliability of wireless communication channels. These systems are normally called multiple-input multiple-output (MIMO) systems. The efficiency of MIMO system has been improved on a limited bandwidth and transmission power. The initial research based on an uncorrelated channel model demonstrate that the channel capacity [8], [13] can be proportionally increased according to the number of antennas. In fact, the antenna configurations produce the local correlations that reduce unexpectedly the channel performances. Especially, in a high spatial correlation transmission, the channel capacity is significantly degraded [4-6]. There are other effects that can degrade the MIMO channel capacity such as “pinhole” effects, insufficient number of scatterers and distance between transmitter and receiver. But these problems are not concerned in this paper. Therefore, in order to keep high transmission performance, angular and polarization diversity [3], [9], [10], [12] have been explored to decrease the correlation effect.

In this paper, we examine different oriented

dipole antennas on our geometric scattering model based on a three-dimensional double bouncing model. Since MIMO channel capacity depends on the fading and correlation properties of the radio channel at both transmit and receive antenna arrays, the design of antenna configurations is effectively

equivalent to the design of correlation diversity channel. However it is possible to reduce this effect, traditionally by increasing antenna array spacing or, recently by using multi-polarized antenna arrays. With polarization diversity techniques, the capacity can be kept high even if the cross-polar discrimina-tion (XPD) has lower or higher values.

We present a simulation study to investigate the

antenna correlation and the channel capacities for single- dual- and triple-polarized antenna arrays on 2×2 and 3×3 MIMO systems with a finite number of scatterers. The antenna correlations and the capacities depend on the antenna configurations such as antenna type, antenna spacing, solid angle diffusion, and radio propagation pattern. The effects of different propagation environment such as that of LOS, that of NLOS and that of XPD are demonstrated by simulation. This paper starts with the description of MIMO channel model employing multi-polarized antennas. Then different MIMO channel capacities are inspected in terms of signal to noise ratio and antenna spacing. Finally the results are summarized with a discussion. 2 Antennas

The propagation environment has in practical an important role in determining the transmission performances. However, for the multiple antenna systems, the proper implementation of the antennas plays also another dominant role, for example uniform linear arrays and uniform circular arrays.

Proceedings of the 10th WSEAS International Conference on COMMUNICATIONS, Vouliagmeni, Athens, Greece, July 10-12, 2006 (pp350-354)

φ

θ

θ∆

φ∆

θ∆

φ∆

Fig. 1: Geometries of MIMO channel The different array configurations produce actually different correlation effects. For this reason, in this paper, we are interesting in two dipole linear antenna arrays with two different kind of polarization.

xE yE zE

( ),Eθ θ φ cos cos θ φ− cos sinθ φ− sin θ

( ),Eφ θ φ sinφ cosφ− 0

Table 1. Patterns for different electric dipoles

Different radiating patterns of the antennas are in the far field case simplified by neglecting pathloss and distance phase. Specifically these radiating patterns depend on the azimuth and elevation angle directions as shown in table 1 where a general expression of radiation patterns are given by [1]

( ) ( ),E E Eθ φ ,θ φ θ θ φ φ= +

r r (1)

where ( ),Eθ θ φ and ( ),Eφ θ φ are the amplitudes of

polarization vector at θr

- and φr

-direction and x,y and z are the antenna orientation. In this paper, we also employ the omni-directional antennas that can be expressed as ( ),Eθ θ φ =1 or ( ),Eφ θ φ =1. So it is necessary to normalize the radiation pattern for comparing all channel performances. The normalized radiation patterns of the antennas are written as following

( ) ( )

( ) ( )2

22

0 0

(2), ,

1 , , sin

4

E EG

E E d d

θ φ

π π

θ φ

θ φ θ θ φ φ

θ φ θ φ θ θ φπ

+=

⎡ ⎤+⎢ ⎥⎣ ⎦∫ ∫

r r

where G is the antenna gain that is used to calculate channel transmission matrix. 3 Geometric scattering modeling

Radio propagation is always at the heart of wireless communication. In order to understand the radio channel mechanisms, a lot of researches have recently focused on the field of propagation measurements for multiple element antenna arrays to explore its phenomena. Various channel models have also been proposed to provide estimated MIMO performances which match closely measured observations.

Our channel model is one of the general

geometric scattering model [5], [7] which is based on an assumption that scatterers around the transmitter and receiver organize the AOD and AOA respectively. In particular, for polarized channel case, scatterers are also used to depolarize the propagated wave. Consequently there are two scattering areas with centers at the transmitter and receiver in Fig.1. All scatterers are randomly distributed on these areas. Thus after placing randomly all scatterers, transmit and receive scatterers are randomly linked. For determining one propagation path, each transmit and receive scatterer is connected together to reduce the computation time. Due to this simple generation of transmission channels for modeling different environments, the statistical distribution of delay spread, angular spread, spatial correlations and cross-polarization discrimination can be easily integrated.

By using our simulated double bounce

geometric scattering model as seen in Fig.1, we employ a uniform linear array at both transmitter


and receiver. Moreover, transmit and receive scatterers are uniformly distributed within an angular region characterized by 2 2φ π φ− ≤ ∆ in

elevation and 2 2θ π θ− ≤ ∆ in azimuth. Subsequently transmit and receive scatterers are randomly paired. From one transmit scatterer to one receive scatterer for one propagation path, there is a double depolari-zation mechanism which can be replaced by one scattering matrix. We also assume that the channel coherence bandwidth is larger than the transmitted bandwidth of the signal. This channel is usually called frequency non-selective or flat fading channel.

In case of far field transmission without line of sight, the downlink transmission channel in function of time [9], [10] between the antenna p at the transmitter and the antenna m at the receiver can be expressed as

( ) { }

( ) ( )( )( )

( ) ( ) ( ) ( )

1

( )

1, exp

, , , (3)

,

NSi i i i

mp m p Rx Tx mpiS

pi im m i

i i i i mp pi i

h t f a a jk v t jk v tN

GG G S

Gθ

θ φφ

ϕ

θ φθ φ θ φ

θ φ

=

′= − ⋅ − ⋅

⎡ ⎤⎡ ⎤ ⎢ ⎥⎣ ⎦ ⎢ ⎥⎣ ⎦

∑r rr r

+

where is the number of scatterers at the receiver and the transmitter; and are the velocity vector of the

transmitter and the receiver;

SN

Txvr Rxvr

( )ik ′r

and are the vectors of wave number in the direction of the ith transmit scatterer and the ith receive scatterer where

( )ikr

( ) ( ) 2i ik k π λ′= =v v

; ( ,pi iGθ )θ φ and ( ),p

i iGφ θ φ are the

gain in the direction of θr

and φr

of the pth transmit antenna in the direction of the ith transmit scatterer.

( ),mi iGθ θ φ and ( ),m

i iGφ θ φ are the gain in the direction

θr

and φr

of the mth receive antenna in the direction of

the ith receive scatterer; t is time; is the mth element of the local vector of the receive antenna, so that the local receive vector can be expressed as

( )ima

( ) ( )( ) 1 1Rx [1 ]

i ii jk r jk rMe e− ⋅ − ⋅ −=ar rr r

L ( )ipa; is the pth

element of the local vector of the transmit antenna, where a local transmit vector is expressed as

; are the scattering matrix for the ith transmit scatterer and the ith receive scatterer. We consider that is a 2×2 matrix

containing the random coefficients of the i = 1,..,

( )( )( ) 11Tx [1 ]

ii jk ri jk r Ne e ′ ′′ ′ − ⋅− ⋅ −=arr rr

L ( )impS

( )impS

SN wave components given by

( ) ( )1

1( )

( ) ( )2

2 2

xpd 11 xpd 1 xpd

xpd11 xpd 1 xpd

i i

imp

i i

S S

S S

1θθ θφ

φθ φφ

⎡ ⎤⎢ ⎥

+ +⎢ ⎥= ⎢ ⎥⎢ ⎥⎢ ⎥+ +⎣ ⎦

S

(4) where the S terms are defined as independent

identically distributed (i.i.d) complex Gaussian for two co-polarized and two cross-polarized channels.

and are the power ratio of waves of θ-θ and θ-φ and the power ratio of waves of φ-φ and φ-θ. In the literature, and are equal to one for maximum channel capacity.

1xpd 2xpd

1xpd 2xpd

The whole transmission channel matrix can be

composed of a constant matrix (a channel matrix of line of sight) and a variable matrix (a channel matrix of non-line of sight of which the antenna element is ) as follows

losH

nlosH

mph

11 1los nlos

KK K

= ++ +

H H H (5)

K is the Ricean K factor. A higher K factor means experimentally a higher correlation. Then, in this paper, the lower and upper bound capacity is of particular interest by assuming that in case of the identically polarized antenna, all elements and

of transmit and receive local vectors are approximately equal to one and in case of orthogonally polarized antenna apart from y-oriented dipole as seen in Fig.1, and are equal to one when m=p. In that case, the MIMO channel of a line of sight can be defined by

ma

pa

ma pa

( ) ( ) ( )( )( )

{ }

,, , ,

,

exp (6)

plos losm m

mp los los los los plos los

los losRx Tx mp

Gh t f G G

G

jk v t jk v t

θθ φ

φ

θ φθ φ θ φ

θ φ

ϕ

⎡ ⎤⎡ ⎤ ⎢ ⎥= ⋅⎣ ⎦ ⎢ ⎥⎣ ⎦

′⋅ − ⋅ − ⋅ +r rr r

where loskr

and losk ′r

are the receive and transmit vectors of wave number in the LOS direction and

( ),mlos losGθ θ φ are the mth receive antenna gain in

the θr

-LOS direction. 4 MIMO Capacities

In this paper, mean or ergodic capacity is employed to demonstrate the MIMO channel


performances with N transmit and M receive antennas. The channel is perfectly known to the receiver but unknown to the transmitter. At each transmit antenna, the transmitted signals have the same power. To investigate the potential of using the polarized antennas, the MIMO systems are employing differently oriented dipole antennas. The advantages of antenna polarization diversity are valuable such as reducing the antenna array size and the spatial correlation in order to obtain better capacity. that is why the polarized antennas become more and more interesting in MIMO transmission. However, multi-polarized antenna arrays can occasionally produce some mutual coupling effects. This effect can significantly degrade the communication performance. The ergodic channel capacity taken over the probability distribution of transmission channel matrix H is given by [13]

[ ] 2log det HErg MC E C E

Nρ⎡ ⎤⎛ ⎞= = +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

I HH (7)

where M and N denote the number of antennas at receivers and transmitters. H is the transmission channel matrix and ρ is signal-to-noise ratio. The transmission channel matrix H is naturally correlated by transmit and receive antenna arrays. Additionally, the channel capacity is generally degraded by the high signal correlation of LOS path.

5 Simulations and results The propagation environments are simulated to study the effect of surface solid angle in terms of ergodic capacity. The angular distribution of incident wave is assumed to have a uniform elevation distribution 2 2φ π φ− ≤ ∆ and a

uniform azimuth distribution 2 2θ π θ− ≤ ∆ where ASφ θ∆ = ∆ = and xp xp 1 to show the maximum capacity. On the other hand, all scatterers,

1d = d =

Fi Antenna correlatio

=20, are uniformly distributed within an angular region characterized by

2

g 2. n and channel capacity of two vertical omni directional antennas

SN

2 2θ π θ− ≤ ∆ and

2 2φ π φ≤ ∆ . The 2×2 and 3×3 MIMO systems employing omni-directional antennas, only

nted dipoles and different oriented dipoles for λ/2 antenna spacing are considered.

Fig.2 illustrates the correlation effect and the channel capacity of two vertical omni-direct

−

vertically z-orie

ional nte

ng the polarization antenna in presence and

without polarization dipole antennas

Fig. 4: Cap d without polarization dipole antennas

or single polariz o x- and z-riented dipoles for dual polarization configuration,

Fig.

a nnas within different solid angles and antenna spacing. In MIMO systems, employing antennas with the same polarization give rise to the correlation effect as seen in Fig.2. However, antenna correlation decreases as solid angle and antenna spacing increases. The antenna correlation is indeed corresponding to the channel capacity as shown in the right figure. The channel correlation does not have a significant influence on the channel capacity if it is lower than 0.3.

In Fig.3 and Fig.4, we investigate some

advantages of employi absence of line of sight (LOS) path

with different XPD effects for AS=180°.

Fig. 3: Capacities of 2×2 MIMO with and

acities of 3×3 MIMO with an

While employing two z-oriented dipoles f

ation configuration and two

3 shows that LOS channel produces high correlation coefficients and degrades channel capacity. On the other hand, without LOS, the MIMO channel reduces the correlation effect and


improves the channel capacity. Moreover, while XPD coefficient has above 0dB, the co-channel power has higher than the cross-channel power. In this case, the channel capacity at exploiting the same polarization of MIMO co-channel can be increased. But if XPD has below 0dB, it degrades generally channel capacity because the signal power at receiver is reduced by imbalance of scattering power. Obviously, exploiting polarization diversity allows both transmitter and receiver to obtain fully vertical and horizontal transmission channel and then improves channel performance in presence of LOS path as seen in the right figure.

Fig.4 demonstrates that channel capacity creases as number of antenna increases linearly

com

has demonstrated different many antenna configurations

base

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inpared to Fig.3. In LOS case of 3×3 polarization

antennas, the co-channels have only two channels on both x- and z-oriented dipoles. Then the channel capacity cannot efficiently be augmented due to the disappearance of 3rd LOS co-channel (y-oriented dipole). Although the multi-polarized antennas can increase the channel capacity, the polarization diversity techniques have always the limit of orthogonally generating signal.

6 Conclusion

This paper performances with

d on MIMO systems such as two omni-directional antennas and three orthogonally oriented dipole antennas aligned with the cartisian x, y and z. The antenna correlation effect and the MIMO channel capacities have been presented as a function of antenna configurations and propagation environment. Due to the advantages of polarization diversity, the transmission channels can reduce the correlation effect, XPD problem and increase channel capacity with and without line of sight path. However, in presence of line of sight path, MIMO systems exploit signal orthogonally to create a set of parallel channel through the employed transmit and receive antenna arrays. In this case, the capacity cannot be well progressed. However, in order to achieve better transmission performances, a combination of angular and polarization diversities should be employed for generating the uncorrelated transmission channel.

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