8/10/2019 Indoor Millimeter Wave Mimo
1/28
INDOOR MILLIMETER WAVE MIMO
FEASIBILITY &
PERFORMANCE
SAIDEEP
MTECH-CESP
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
2/28
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.
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
3/28
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.
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
4/28
INTRODUCTION:
This motivates our proposed mm-wave MIMO architectur
utilizes array of sub arrays to provide both directivity and s
multiplexing gains.
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
5/28
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
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
6/28
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
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
7/28
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 .
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
8/28
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
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
9/28
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
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
10/28
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.
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
11/28
OPTIMALLY SPACED ARRAYS
11/29/2014 AMRITA SCHOOL OF ENGINEERING
Denoting the ith column of H by ,the inner product betwkth and ith column is given by
8/10/2019 Indoor Millimeter Wave Mimo
12/28
OPTIMALLY SPACED ARRAYS
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.
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
13/28
OPTIMALLY SPACED ARRAYS
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.
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
14/28
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
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
15/28
SPATIAL DEGREES OF FREEDOM
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).
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
16/28
SPATIAL DEGREES OF FREEDOM
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
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
17/28
LOS MM-WAVE MIMO ARCHITECTURE
Proposed architecture is based on optimal spacing conditio
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
18/28
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.
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
19/28
WATERFILLING BENCHMARK
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
20/28
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
11/29/2014 AMRITA SCHOOL OF ENGINEERING
LOS
componentFirst order
reflections path
Second
reflection
8/10/2019 Indoor Millimeter Wave Mimo
21/28
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 oreflection to the mth RX antenna
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
22/28
INDOOR PROPAGATION MODEL
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
23/28
INDOOR PROPAGATION MODEL
Similarly the (m,n)th entry of 2,
is given by
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
24/28
RESULT
We evaluate the spectral efficiency achieved by mm-wave Marchitecture proposed using indoor propagation model.
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
25/28
RESULT
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
26/28
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.
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
27/28
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
11/29/2014 AMRITA SCHOOL OF ENGINEERING
8/10/2019 Indoor Millimeter Wave Mimo
28/28
THANK YOU
11/29/2014 AMRITA SCHOOL OF ENGINEERING