Indoor Millimeter Wave Mimo

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INDOOR MILLIMETER WAVE MIMO

FEASIBILITY &

PERFORMANCE

SAIDEEP

MTECH-CESP

11/29/2014 AMRITA SCHOOL OF ENGINEERING


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CONTENTS:

Introduction.

Literature survey.

Fundamental limits of LOS MIMO.

1.LOS MIMO Channel Model.

2.Optimally Spaced Arrays.

3.Spatial Degrees of Freedom.

LOS MM-wave MIMO Architecture.

1.Waterfilling Benchmark.

Indoor Propagation Model.

Results.

Conclusion.



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INTRODUCTION:

Spatial multiplexing at millimeter wave frequencies for shoindoor applications.

For linear arrays with constraint formfactor , an asymptoti

based on the properties on prolate spheroidal wave functio

shows that a sparse array producing a spatially uncorrelate

channel matrix provides maximum number of spatial degre

freedom.



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INTRODUCTION:

This motivates our proposed mm-wave MIMO architectur

utilizes array of sub arrays to provide both directivity and s

multiplexing gains.



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LITERATURE SURVEY

Spatial multiplexing has drawn considerable attention.Number of spatial degrees of freedom given array constraipreviously evaluated in scattering environment.

The capacity of LOS MIMO channel was previously studiedon optimal array geometry that maximizes LOS channel cap



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FUNDAMENTAL LIMITS OF LOS MIMO

In this section ,we derive limits on the number of spatial dfreedom of a LOS MIMO channel given array length constr

Form factors of typical consumer electronics devices are s

to allow multiple degrees of freedom.

1.LOS MIMO CHANNEL MODEL

2.OPTIMALLY SPACED ARRAYS

3.SPATIAL DEGREE OF FREEDOM



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LOS MIMO CHANNEL MODEL:

Consider a flat fading MIMO channel , with received signal vy 1 is give by

y=Hx+w -

where x is transmitted signal vector ,H is a channel matrix and

w is AWGN with covariance .



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Complex channel gain is given by

, =

4,.

(.,

) -------

where is carrier wavelength,is path length from nth transmit antenna to mreceive antenna.

Lets assume arrays are uniformly spaced and aligned broadsid

------where R is Link range

ante



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LOS MIMO CHANNEL MODEL

When R> array length , path length is approximated by

, =+()

2 --------

The channel gain is given by

,

=

4exp(j

2

(R

()

2))--

High rank LOS MIMO channel is produced if spacing betwee

adjacent elements is chosen appropriately



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OPTIMALLY SPACED ARRAYS

The goal in this section is to determine the optimal spacing elements.

In the moderate to high SNR regime , the Shannon capacityNxN MIMO channel is maximized, when N singular values omatrix are equal.

This is achieved when the columns of H are orthogonal.



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Denoting the ith column of H by ,the inner product betwkth and ith column is given by


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The inner product is made zero when the following conditiosatisfied.

=

----------->

This condition is for linear arrays.

Now ,if the lengths of the transmit and receive arrays areconstrained and N is arbitrary , we can determine the maximnumber of antennas preserving orthogonality condition.



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Now, let the length of ULA is given by L=d(N-1), maximum numbantennas is given by

---------->7

maximum transmit array length

maximum receiver array length

[a] largest integer less than or equal to a.



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SPATIAL DEGREES OF FREEDOM

For larger values of N, what will be the effect on spatial degfreedom ?

For example, let us consider two LOS MIMO wireless links.

Fig 1. Squared singular values of H for N=8(optim

and N=32 assuming fc=60Ghz,R=5m and Lt



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As N-->infinity, the add elements drop to zero.On solving a set of equations, we get

---------

where W= 2 ,

Integral equation 8 denotes a set of prolate spheroidal wavfunctions(PSWFs).



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Property of PSWF is that their Eigen values remain approximequal to one until n nears a critical value i.e

S=2W=

We conclude that Spatial degrees of freedom of Continuouslink is limited approx. to

=

+1



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LOS MM-WAVE MIMO ARCHITECTURE

Proposed architecture is based on optimal spacing conditio



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WATERFILLING BENCHMARK

Performance benchmark is a standard waterfilling based eigtransmission.

The SVD of the channel matrix is given by

---------->9

where U & V are unitary matrices

is a diagonal matrix with non zero entries.



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WATERFILLING BENCHMARK



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INDOOR PROPAGATION MODEL

An indoor propagation model that allows to assess the immultipath propagation, link range variations and LOS bloc

Indoor propagation model is based on method of geomet

The channel matrix H is given by


LOS

componentFirst order

reflections path

Second

reflection


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The (m , n)th entry of

is given by

The (m,n)th entry of 1,is given by

where is length of path from nth TX to point oreflection to the mth RX antenna



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Similarly the (m,n)th entry of 2,

is given by



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RESULT

We evaluate the spectral efficiency achieved by mm-wave Marchitecture proposed using indoor propagation model.



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RESULT



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CONCLUSION

Thus spatial multiplexing gains can be achieved mm-wave

The sub array spacing can be adjusted to provide the maximnumber of degrees of freedom for a given form factor.

Our simulation indicate that the architecture provides spatimultiplexing gain through out an indoor environment.



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REFERENCES

1.E. Torkildson,B. Ananthasubramaniam,U. Madhow,and

M.Rodwell,Millimeter-wave MIMO: wireless links at optical speeProc. Of44th Allerton Conference on Communication, Control anComputing, Sep. 2006.

2.E. Torkildson, C. Sheldon, U. Madhow, and M. Rodwell, Nonunarray design for robust millimeter-wave MIMO links, in IEEE GlobCommunications Conference, Dec. 2009.

3. T. S. Rappaport, Wireless Communications: Principles and PracPrentice Hall, 2002



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Indoor Millimeter Wave Mimo

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