Transcript Slide 1
Performance of Adaptive Array Antennas
in Mobile Fading Environment
by:
Amin Al-Ka’bi, M. Bialkowski and John Homer
School of Information Technology & Electrical Engineering
The University of Queensland, Australia
Outline
I. Abstract
II. Introduction
III. Problem formulation
IV. Modeling of Mobile Fading Channel
V. Results and Discussion
VI. Conclusions
I. Abstract
The
performance of steered beam
adaptive array antennas in mobile fading
environment is presented, using simulation model of the mobile fading channel.
The
behaviour of the adaptive array
antenna in terms of the output Signal-toInterference-plus-Noise Ratio (SINR) and
pointing accuracy is investigated .
II. Introduction
It
is desirable that the output SINR
exceeds a certain threshold; hence the
adaptive algorithm aimed at SINR
maximization is used to set the
elements weights.
The output SINR is affected by the
signal fading due to multipath propagation. Moreover, the movement of the
mobile unit causes frequency shift
called Doppler Effect.
II. Introduction (cont.)
It is assumed that the array is fixed on a
highly mounted base station or on a
satellite system that communicates with
mobile units surrounded by scatterers.
Modified Loo’s model of the mobile
fading channel was found to be suitable
for this case.
The performance of uniformly spaced
and non-uniformly spaced steered beam
adaptive arrays has been studied under
the same operating conditions.
III. Problem Formulation
Consider the array with N vertical
dipoles separated by non-uniform
distances l1 , l 2 , l 3 ,..., l N 1 along
the y-axis
The output signal from each element x i (t ) , which is assumed to
be a complex random process, is multiplied by a complex weight
w i and summed to produce the array output so (t ) .
III. Problem Formulation (cont.)
The steady state weight vector is given by:1
w [w1, w2 , ......wN ] [ I k] w0
T
I is the identity matrix, k is the feedback loop gain, and
Φ E{X*X T } is the covariance matrix
w 0 [w 01 , w 02 ,....w0N ] is the steering vectorof the array
I is the identity matrix; k is the feedback loop gain
X [x1 (t),x 2 (t),....x N (t)]T is the random signal vector
M
X Sd ( Si ) Sn
i 1
Sd , SI i and Sn are the desired, interference and noise vectors
III. Problem Formulation (cont.)
Assuming that the desired narrowband signal comes from θmax:
w0 [e j N 1 ,....,e j 2 , e j1 ,1]T
i
where i ( l j ) sin( max )
j 1
The SINR is calculated from:
Pd
SINR 10 log
M
Pn PI i
i 1
Pn
N
2
| w |
i 1
2
i
N 1
N
Pd STd [ | wn |
2
n 1
n 1
N
2 Re{w w
m2
n
*
m
d }]
is the norm alized autocorrelation
STd received power per elem ent
T he expression for PIi is similar
nm
IV. Modelling of Mobile Fading
Channel
Loo’s model applies to frequency-non-selective
terrestrial mobile radio channels, where the line-ofsight m(t) component under-goes slow-amplitude
lognormally-distributed fluctuations, caused by
shadowing effects. m(t) is given as:
m(t ) m1 (t ) jm2 (t ) (t ).e
j (2 f t )
where f and denote the Doppler frequency
and phase of the line-of-sight component
(t ) m
respectively, and (t ) e
is the lognormal
process, with m3
and 32 are the mean and
variance, of the white Gaussian process 3 (t ) .
3 3
3
IV. Modelling of Mobile Fading Channel (Cont.)
The short-term fading caused by the multipath
propagation, behaves like the Rice process, and it is
represented by a complex-valued Gaussian random
process
(t ) 1 (t ) j 2 (t )
where,
1 (t ) 1 (t ) 2 (t )
2 (t ) ˆ1 (t ) ˆ2 (t )
Here, 1 (t ) and 2 (t ) represent zero-mean colored
Gaussian random processes, and ˆi (t ) is the Hilbert
transform of i (t ) for (i=1, 2).
The Modified Loo’s process is given as
(t ) | (t ) m(t ) |
IV. Modelling of Mobile Fading Channel (Cont.)
Stochastic Model of Mobile Fading Channel
(Modified Loo’s Model)
IV. Modelling of Mobile Fading Channel (Cont.)
The simulation model for modified Loo process
approximates the behaviour of the stochastic
reference model, where the three stochastic
Gaussian random processes i (t )(i 1, 2,3) by
deterministic Gaussian processes of the form
Ni
i (t ) ci ,n cos(2 fi ,nt i ,n ), i 1, 2,3
n 1
Therefore, i (t )(i 1, 2,3) can be written as:
N1
N1
n 1
N1
n 1
N2
n 1
n 1
1 (t ) c1,n cos(2 f1,nt 1,n ) c2,n cos(2 f 2,nt 2,n )
2 (t ) c1,n sin(2 f1,nt 1,n ) c2,n sin(2 f 2,nt 2,n )
N3
3 (t ) 3 c3,n cos(2 f3,nt 3,n ) m3
n 1
IV. Modelling of Mobile Fading Channel (Cont.)
Simulation Model of Mobile Fading Channel that
approximates the stochastic model.
IV. Modelling of Mobile Fading Channel (Cont.)
The simulation model for modified Loo process
approximates the behaviour of the stochastic
reference model, where the random processes
i (t )(i 1, 2,3) are replaced by
Ni
i (t ) ci ,n cos(2 fi ,nt i ,n ), i 1, 2, 3
n 1
Therefore, i (t )(i 1, 2,3) can be written as:
N1
N1
n 1
N1
n 1
N2
1 (t ) c1,n cos(2 f1,nt 1,n ) c2,n cos(2 f 2,nt 2,n )
2 (t ) c1,n sin(2 f1,nt 1,n ) c2,n sin(2 f 2,nt 2,n )
n 1
N3
n 1
3 (t ) 3 c3,n cos(2 f3,nt 3,n ) m3
n 1
The Doppler coefficients ci ,n and fi ,n for (i=1,2,3) can be
calculated using Mean Square Error method.
V. Results & Discussion
Two arrangements of 12 array elements are used:
•
Arrangement (a): The elements are uniformly
spaced by λ/2.
•
Arrangement (b): Non-Uniform array elements
arrangement with spacings (0.85λ,0.7λ,0.5λ,0.4λ,
0.25λ, 0.1λ ,0.25λ ,0.4λ ,0.5λ ,0.7λ ,0.85λ)
In arrangement (b), the elements are arranged such
that the elements in the middle of the array are closer
to each other than the elements in the edges of the
array.
It is shown that non-uniform array (arrangement (b))
has better performance than the uniformly spaced
array in terms of sensitivity to pointing errors in nonfading and fading environments.
V. Results & Discussion (Cont.)
Performance of 12-element adaptive array vs.
pointing error (without fading).
V. Results & Discussion (Cont.)
Simulation of the received faded signal for light and
heavy shadowing regions, respectively.
V. Results & Discussion (Cont.)
Output SINR vs. SNR for uniformly and nonuniformly spaced array.
V. Results & Discussion (Cont.)
Output SINR vs. time for light shadowing regions,
with and without pointing error (uniform array).
V. Results & Discussion (Cont.)
Variance and mean of output SINR vs. pointing
error for uniformly and non-uniformly spaced-array.
VI. Conclusions
A suitable simulation model for mobile fading channel
has been suggested.
A comparison between uniformly and non-uniformly
spaced array has been conducted.
It is shown that non-uniform array (arrangement (b))
has better performance than the uniformly spaced
array in terms of sensitivity to pointing errors in nonfading and fading environments.
It is shown that mean output SINR of the non-uniform
array is greater than that of the uniform
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