channel capacity enhancement using mimo

IEEE-International Conference On Advances In Engineering, Science And Management (ICAESM -2012) March 30, 31, 2012 10

Channel capacity enhancement using MIMO

Technology

Akhilesh Kumar Department of Electronics Design &Technology National Institute of Electronics and Information

Technology Gorakhpur India 273010

[email protected]

KamtaNath Mishra Department of Electronics Design &Technology National Institute of Electronics and Information


[email protected]

Abstract-This paper will describe the signal processing and

channel enhancement using MIMO technology In order to have

flexibility in transmission system, wireless systems are always

considered better as compared to wired channel. Having known

the drawbacks of the Single Input Single Output system, and

having computed the advantages of Multiple Input Multiple Out,

several techniques have been developed to implement space

multiplexed codes. In wireless MIMO the transmitting end as

well as the receiving end is equipped with multiple antenna

elements, as such MIMO can be viewed as an extension of the

very popular 'smart antennas'. In MIMO though the transmit

antennas and receive antennas are jointly combined in such a

way that the quality (Bit Error Rate) or the rate (Bit/Sec) of the

communication is improved. At the system level, careful design of

MIMO signal processing and coding algorithms can help increase

dramatically capacity and coverage.

Keywords-Wireless, MlMO, Channel, Transmitter, Receiver. I. Introduction

The paper will present a continuous higher data rate for wireless system under limited power, bandwidth and complexity. Another domain can be exploited to significantly increase channel capacity: the use of multiple transmit and receive antennas.MIMO channel capacity depends heavily on the statistical properties and antenna element correlations of the channel [1].Antenna correlation varies drastically as a function of the scattering environment, the distance between transmitter and receiver, the antenna configurations, and the Doppler spread [3]." The channel gain matrix is very small, leading to limited capacity gains.We focus on MIMO channel capacity in the Shannon theoretic sense.

For single-user MIMO channels with perfect transmitter and receiver CSI the ergodic and outage capacity calculations are straightforward since the capacity is known for every channel state. In multiuser channels, capacity becomes a -dimensional region defming the set of all rate vectors (RJ, .. ,Rk)

Abhay Mukherjee Department of Electronics Design &Technology National Institute of Electronics and Information


[email protected]

Ani! KumarChaudhary Department of Electronics Design &Technology National Institute of Electronics and Information


ani I. [email protected]

simultaneously achievable by all K users. The multiple capacity defmitions for time-varying channels under different transmitter and receiver CSI and CDI assumptions extend to the capacity region of the multiple-access channel (MAC) and broadcast channel (BC) in the obvious way. However, these MIMO multiuser capacity regions, even for time-invariant channels, are difficult to find. Few capacity results exist for time varying multiuser MIMO channels, especially under the realistic assumption that the transmitter(s) and/or receiver(s) have cm only. Many practical MIMO techniques have been developed to capitalize on the theoretical capacity gains predicted by Shannon theory. A major focus of such work is space-time coding: recent work in this area is summarized in. Other techniques for MIMO systems include space-time modulation, adaptive modulation and coding, space-time equalization, space-time signal processing, space-time CDMA and space-time OFDM.

II.MIMO CHANNEL MODELING

It is common to model a wireless channel as a sum of two components, a LOS component and a NLOS component

1. LOS Component Model

The Rician factor is the ratio between the power of the LOS component and the mean power of the NLOS component [6]. For MIMO systems, however, the higher the Rician factor K, the more dominant NLOS becomes. Since NLOS is a timeinvariant, it allows high antenna correlation, low spatial degree of freedom, hence, a lower MIMO capacity for the same SNR.In fixed wireless network (macro cell) MIMO improve the quality of service in areas that are far away from the base station, or are physically limited to using low antennas. In an indoor environment, many simulations and measurements have shown that typically the multipath scattering is rich enough that the LOS component rarely dominates. This plays in favor of in-building MIMO deployments (e.g., WLAN).

ISBN: 978-81-909042-2-3 ©2012 IEEE

IEEE-International Conference On Advances In Engineering, Science And Management (ICAESM -2012) March 30, 31, 2012 II

2 Correlation Model for NLOS Component:

In the absence of a LOS component, the channel matrix modeled with Gaussian random variables (i.e., Rayleigh fading). The antenna elements can be correlated, often due to insufficient antenna spacing and existence of few dominant scatters. Antenna correlation is considered the leading cause of rank deficiency in the channel matrix, to obtain the highest diversity.

In the Rician channel case, the channel matrix can be represented as a sum of the line-of-sight (LOS) and non-Iineof-sight (NLOS) components

H = HLOS + HNLOS Where, HLOS E{H} and HNLOS H - HLOS' According to this model

HNLOS = (R r) II2H",(RR)'h ... (1)

Where, RR is the M xMcorrelation matrix of the receive antennas, Rr is the N x N correlation matrix of the transmit antennas, and H",is a complex N xMmatrix whose elements are zero-mean independent and identically distributed (i.i.d)complex Gaussian random variables

For a MIMO system the channel matrix is written as [ hll h1 nT 1 .

hn�l .

hn�nT .

• • •

Where, hI} = a + j f3

Fig .. l Model For Gaussian Channel Matrix According to Fig.l, The M-element receive array then

samples this field and generates the Mx 1 signal vector YA(t) at the array terminals. Noise in the system is typically generated in the physical propagation channel (interference) and the receiver front-end electronics (thermal noise). To simplify the

discussion, we will lump all additive noise into a single contribution represented by the Mx 1 vector 11(t) that is injected at the receive antenna terminals. The resulting signal plus noise vector YA(t) is then down converted to produce the Mx 1 baseband output vector y(t). Finally, y(t) is passed through a matched filter whose output is sampled once per symbol to produce y(k), after which the space-time decoder produces estimatesof the originally transmitted symbols.

III.SP ACE DIVERSITY

Diversity techniques can be used to improve system performance in fading channels. Instead of transmitting and receiving the desired signal through one channel, we obtain L copies of the desired signal through M different channels [7]. The idea is that while some copies may undergo deep fades, others may not. We might still be able to obtain enough energy to make the correct decision on the transmitted symbol.

Another approach to achieve diversity is to use M antennas to receive M copies of the transmitted signal shown in fig.2. The antennae should be spaced far enough apart so that different received copies of the signal undergo independent fading. Different from frequency diversity and temporal diversity, no additional work is required on the transmission end, and no additional bandwidth or transmission time is required.

~ :/ ~

Transmitt er

Fig. 2. Space diversity However, physical constraints may limit its applications.

Sometimes, several transmission antennae are also employed to send out several copies of the transmitted signal. Spatial diversity can be employed to combat both frequency selective fading and time selective fading.

IV. INTRODUCTION TO V ARIOUS SYSTEMS

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--03 LD--SISO --03 U-SIMO tl LD-MISO ---[Y U-M1MO FIg 3.: Antenna configuratIOns In dIfferent systems

Presently four different types (Input and output refers to number of antennas) of systems can be categorized as far as diversity is concerned (as shown in figure 3.). l.Single Input Single Output (SISO)-No diversity

This system has single antenna both side. Due to single transmitter and receiver antenna, it is less complex than mUltiple input and multiple output (MIMO).SISO is the simplest antenna technology.

---------�}J

Lo SISO Tx

Fig.4. A SISO System

Capacity [10] of a SISO is given by:

C = [092(1 + plhI2)b/s/Hz······(2)

Where h is the normalized complex gain of a fixed wireless channel and is the SNRthe plot between the C and SNR will be

4.5 r-----,--�-__._-�-�-r-�---,

___ 3.5 ...... .... ...... .. , . .!OJ

� 3

<..> 2.G : . : : : : : : ........... ....... : ...

10

: : .... = ......... : . ....... : .. ;

'2 14 16 SMR(rlR)

18 20

Fig 4.1 Graph Between C And SNR(SISO) In some environments, SISO systems are vulnerable to

problems caused by multipath effects.!n a digital communications system, it can cause a reduction in data speed and an increase in the number of errors.

2. Multiple Inputs Single Output (MISO)-Transmit diversity

It's a system with Multiple-antenna arrays are known to perform better than their single-antenna counterparts, because they can more effectively counter the effects of mUltipath fading and interference. However, the enhanced performance depends on the amount of channel information at the transmitter and on whether the transmitter is able to take advantage of this information. [3]

We have a multiple input- single-output (MISO) system with N Tx antennas and the capacity is given by [3]

Where the normalization by N ensures a fixed total transmitter power and show the absence of array gain in that case

MIMO Tx

Fig. 5. A MISO System

MIMO Rx

Graph between C and SNR is given by for 2 transmitting antennas

7r--.--.--.---'---.-�-.--__._-.---.

6 .. '

2

I ' " , . " ... "''" ""' . , . " "

1 0L-�10�� 20�-3�O--4�O-�5�O-�6�O -�70��80�-9�O��100 S�0� 8

g5.1 Graph Between C and SNR

3.Multiple Inputs Multiple Outputs (MIMO)-Transmit

receive diversity

ISBN: 978-81-909042-2-3 ©2012 IEEE


Multiple antennas can be used either at the transmitter or receiver or at both.

Compared to

Transmit Receive Data Single Type

Antenna Antenna Rate Antenna

Technologies

SIMO Single Multiple Same Greater range

Same range

MISO Multiple Single Same but More

reliable

MIMO Multiple Multiple Greater Greater range

TABLE I. COMPARISON OF DIFFERENT ANTENNA SYSTEMS

These various configurations are referred to as multiple input single output MISO, Single Input Multiple Output SIMO, or Multiple Input Multiple Output MIMO.

The SIMO and MISO architectures are a form of receive and transmit diversity schemes respectively. On the other hand, MIMO architectures can be used for combined transmit and receive diversity, as well as for the parallel transmission of data or spatial mUltiplexing. When used for spatial multiplexing MIMO technology promises high bit rates in a narrow band-width and as such it is of high significance to spectrum users [9].

V.MATHEMA TICAL MODEL OF MIMO

Consider a wireless communication system with Nt transmit (T x) and Nr receive (Rx) antennas. The idea is to transmit different streams of data on the different transmit antennas, but at the same carrier frequency. The stream on the p-th transmit antenna, as function of the time t, will be denoted by sp(t). When a transmission occurs, the transmitted signal from the p-th T x antenna might find different paths to arrive at the q-th Rx antenna, namely, a direct path and indirect paths through a number of reflections[ 4].

For such a system, all the multi-path components between the p-th T x and q-th Rx antenna can be summed up to one term, say hqp(t). Since the signals from all transmit antennas are sent at the same frequency, the q-th receive antenna will not only receive signals from the p-th, but from all Nt transmitters. This can be denoted by the following equation (the additive noise at the receiver IS omitted for clarity).

Xq(t) = L��l hqp (t)sp(t), .... (4)

To capture all Nt received signals into one equation, the matrix notation can be used:

x(t) = H(t)s(t) ................. (5)

s, -cjf Y:l B x ,

s, -cjf <�, B >, ·5 .�

�>�� Figure 6: Schematic Representation Of A MIMO

Communication System where, set) is an Ncdirnensional column vector with sp(t)

being its p-th element, x(t) is Nr-dimensional with xq(t) on its q-th position and the matrix H(t) is Nr x Nt with hqp(t) as its (q,p)-th element, with p = 1, ... , Nt and q = I, ... , N" A schematic representation of a MIMO communication scheme can be found in Figure 6.

Mathematically, a MIMO transmission can be seen as a set of equations (the recordings on each Rx antenna) with a number of unknowns (the transmitted signals). If every equation represents a unique combination of the unknown variables and the number of equations is equal to the number of unknowns, then their exists a unique solution to the problem. If the number of equations is larger than the number of unknowns, a solution can be found by perfonning a projection using the least squares method , also known as the Zero Forcing (ZF) method. For the symmetric case, the ZF solution results in the unique solution.

VI.CAPACITY ENHANCEMENT USING MIMO

MIMO technologies overcome the deficiencies of these traditional methods through the use of spatial diversity. Data in a MIMO system is transmitted over T transmit antennas through what is referred to as a "MIMO channel" to R receive antennas supported by the receiver tenninal.

For a memory less Jxl (SISO) system the capacity is given by:

C = [09z(1 + plhlZ)bjsjHz ... (6)

Where h is the normalizes complex gain of a fixed wireless channel or that of a particular realization of a random channel.

ISBN: 978-81-909042-2-3 ©2012 IEEE


As we deploy more Rx antennas the statIstics of capacity will improve and with M Rx antennas, we have a SIMO system with capacity given by

Where is the gain of Rxantenna.

Now, we consider the use of diversity at both transmitter and receiver giving rise to a MIMO system. For N T x and M Rx antennas, we have the now famous capacity equation [3], [4], [5]

Where ( * ) means transpose-conjugate and H is the MxN channel matrix.

For the i.i.d. Rayleigh fading case we have the impressive linear capacity growth discussed above. For a wider range of channel models including, for example, correlated fading and specular components, we must ask whether this behavior still holds. Below we report a variety of work on the effects of feedback and different channel models. It is important to note that (8) can be rewritten as [4].

C=Ii'!llogz(l +( p/N)!..j ... (9)

Where (i=l.. .... m) are the nonzero eignvalues of W,m= min(M,N), and

{HH*, M:::; N W= H*H, N < M ... (10)

This formulation can be easily obtained from the direct use of Eigen value properties. Alternatively, we can decompose the MIMO channel into m equivalent parallel SISO channels by performing a singular value decomposition (SVD) of [4], [8].

s so ��ISO,MI�n Capoci1r

-3iso 8 " '''''' ,lise, \T=2,=�1R='

-,- . ,liMO, �IT=�1R=2

N' 6 ' � I

�5 / .' w

� 4 J o

I��----�--��--��--�-" J 10 2J 30 ,)0 :0 60 :0 EO 90 100

�tJ�

Fig.7.Comparison between SISO,MISO and MIMO

MU;10 Capacity 16 ir=��==��--�'--�,--'-� --��

: : . ... � ¥--- 8IS0 14 """"'MI'v10, NT=NR=2

-'-" MI'v10, NT=NR=3 " .' " " " : �; ... ... �< .. " " . " " ' "

:�,':. . 12

2

- - -MI'v10, NT =NR=4 .., ....... ', ,

. �., .. , .,�, ' .' .( : �. ��. '. " ;' " "- :. -- .. / �.� .

""" ',, " , " , / :;,,' : ""� "...

. :"",,,,- ,,,,,, : /: " , , , " ' ' ' ' .I ' "

"

, " ' , "'' ' ' / ,/ "" " .. , : , , ,

,

/- ;-" ' '''''',,'''''' "",

/ j' "" " " , . , . /11 ,<"" " ,

r/ " , /1 . . '

f· ' : ...... : . . . . . . . � . . . . . . . .:

1/ •

OL-� __ -L __ -L __ � __ L-__ L-� __ -L __ -L� o 10 20 30 40 50 60 70 80 90 100

8NR

Fig .8. CapacityEnhancement in MIMO

VII.CONCLUSIONS AND FUTURE TRENDS

This paper reviews the major features of MIMO links for use in future wireless networks. Information theory reveals the great capacity gains which can be realized from MIMO. Whether we achieve this fully or at least partially in practice depends on a sensible design of transmit and receive signal processing algorithms. It is clear that the success of MIMO algorithm integration into commercial standards such as 3G, WLAN, and beyond will rely on a fine compromise between rate maximization (BLAST type) and diversity (space-time coding) solutions, also including the ability to adapt to the time changing nature of the wireless channel using some form of (at least partial) feedback. To this end more progress in modelling, not only the MIMO channel but its specific dynamics, will be required. As new and more specific channel models are being proposed it will useful to see how those can affect the performance tradeoffs between existing transmission algorithms and whether new algorithms, tailored to specific models, can be developed. Finally, upcoming trials and performance measurements in specific deployment conditions will be key to evaluate precisely the overall benefits of MIMO systems in real-world wireless scenarios such as UMTS.

VIII.REFERENCES

[1] A. Goldsmith et aI., "Capacity Limits of MIMO Channels," IEEE JSAC, vol. 21, June 2003, pp. 684-702.

ISBN: 978-81-909042-2-3 ©2012 IEEE


[2] H. Weingarten, Y. Steinberg, and S. Shamai, "The Capacity Region of the Gaussian MIMO Broadcast Channel," Proc. Conf. Info. Sciences and Systems (CISS), Princeton, NJ, Mar. 2004. [3] G. J. Foschini and M. J. Gans, "On limits of wireless

communicationsin a fading environment when using multiple

antennas," Wireless Pers.Commun., vol. 6, pp. 311-335, Mar.

1998.

[4] E. Telatar, "Capacity of multiantenna Gaussian channels,"

AT&T BellLaboratories, Tech. Memo., June 1995

[5] I. E. Telatar, "Capacity of multi antenna Gaussian

channels," Eur. Trans.Commun., vol. 10, no. 6, pp. 585-595,

1999.

[6] Techniques for 3G and beyond. John Wiley and Sons,

January 2003

[7] Wireless Communication by Theodore S.Rappaport.

[81]Royal institute of technology, stockholm, lecture notes, uri: [9] Wikipedia.

ISBN: 978-81-909042-2-3 ©2012 IEEE

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