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  j1 ,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
m2
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
Thank you