Indoor Millimeter Wave Mimo [Autosaved]

8/10/2019 Indoor Millimeter Wave Mimo [Autosaved]

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INDOOR MILLIMETER WAVE MIMOFEASIBILITY &

PERFORMANCE

11/20/2014 AMIRTA 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 short-rangindoor applications.

For linear arrays with constraint formfactor , an asymptotic analys

based on the properties on prolate spheroidal wave functions

shows that a sparse array producing a spatially uncorrelatedchannel matrix provides maximum number of spatial degrees of

freedom.



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INTRODUCTION:

This motivates our proposed mm-wave MIMO architecture , whicutilizes array of sub arrays to provide both directivity and spatial

multiplexing gains.



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LITERATURE SURVEY

Spatial multiplexing has drawn considerable attention.Designing multigigabit wireless link using spatial multiplexing.

In order to increase mm-wave data rates further by employing

MIMO spatial processing techniques.



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FUNDAMENTAL LIMITS OF LOS MIMO

In this section ,we derive limits on the number of spatial degrees freedom of a LOS MIMO channel given array length constraints.Form factors of typical consumer electronics devices are sufficiento allow multiple degrees of freedom.

1.LOS MIMO CHANNEL MODEL

2.OPTIMALLY SPACED ARRAYS3.SPATIAL DEGREE OF FREEDOM



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LOS MIMO CHANNEL MODEL:

Consider a flat fading MIMO channel , with received signal vectory 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 mth

receive antenna. Lets assume arrays are uniformly spaced and aligned broadside

------where R is Link range

anten



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LOS MIMO CHANNEL MODEL

When R> array length , path length is approximated by

, =+( )

2 --------

The channel gain is given by

,

= 4

exp( j 2 (R ( )2

)) -- High rank LOS MIMO channel is produced if spacing between

adjacent elements is chosen appropriately



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OPTIMALLY SPACED ARRAYS

The goal in this section is to determine the optimal spacing betweeelements. In the moderate to high SNR regime , the Shannon capacity of anNxN MIMO channel is maximized, when N singular values of Chamatrix 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 betweenkth and ith column is given by


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The inner product is made zero when the following condition issatisfied.

= ----------->

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 maximumnumber of antennas preserving orthogonality condition.



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Now, let the length of ULA is given by L=d(N-1), maximum number ofantennas 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 of spatial degrees offreedom ? For example, let us consider two LOS MIMO wireless links. Fig 1. Squared singular values of H for N=8(optimally spa and N=32 assuming fc=60Ghz,R=5m and Lt and L



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

---------

where W= 2 , Integral equation 8 denotes a set of prolate spheroidal wavefunctions(PSWFs).



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

S=2W =

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

=

+1



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LOS MM-WAVE MIMO ARCHITECTURE

Proposed architecture is based on optimal spacing condition given.



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WATERFILLING BENCHMARK

Performance benchmark is a standard waterfilling based eigenmodetransmission. 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 impact ofmultipath propagation, link range variations and LOS blockage. Indoor propagation model is based on method of geometric optic The channel matrix H is given by


LOScomponent

First orderreflections path

Second oreflection


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INDOOR PROPAGATION MODEL 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 ofreflection to the mth RX antenna



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INDOOR PROPAGATION MODEL



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INDOOR PROPAGATION MODEL 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 MIMOarchitecture proposed using indoor propagation model.



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RESULT



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CONCLUSION Thus spatial multiplexing gains can be achieved


Indoor Millimeter Wave Mimo [Autosaved]

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