narrow band and wide band beamformingeee.guc.edu.eg/courses/communications/comm1002...ultrawide band...
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ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
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NARROW BAND AND WIDE BAND
BEAMFORMING
ADAPTIVE
ANTENNAS
ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
2 2 2/27/2017 LECTURES 2
Narrowband beamforming array -1
An array operating with signals having a fractional bandwidth (FB)
of less than 1%
where fh and fl are the highest and lowest components of the
signal respectively
As the bandwidth of the signal is increased the phase weighting
computed to steer the beam at a particular angle is no longer
correct, therefore a more complex weighting arrangement is
required (Wideband beamforming)
%1002/)(x
ff
ffFB
lh
lh
The bandwidth of the impinging signal should be narrow enough to
make sure that the signals received by the opposite ends of the array
are still correlated with each other
ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
3 2/27/2017 LECTURES 3
Let us demonstrate that the bandwidth of the impinging signal should
be narrow enough to make sure that the signals received by the
opposite ends of the array are still correlated with each other
Let the maximum delay between the first and last element in an array is
τmax , this delay should be less than the time period in time domain then:
1/τmax.>>Bandwidth of the signal
Example: GSM, f=900MHz, BW=200KHz, 10 elements broad side array
oriented along y-axis with half wave spacing
τmax = (M-1)dsinθ/C
=(M-1)(λ/2)/C =(M-1)/2f
1/τmax = 2x900x106/9=200x106>>200KHz
The narrowband is valid in GSM system
ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
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When it is connected to an array antenna, it will act such that,
the array will have a uniform amplitude and constant phase
shift between the element of the array. This will result in
radiation at one of M different discrete directions covering a
180o angular sector of space
Butler matrix is a microwave network, employed in beamforming
(switched beam networks) and scanning networks for linear and
circular antenna arrays at narrowband
Butler matrix for narrowband switching (fixed) beamforming
ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
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The actual direction of the beams depends on which
one of the input the signal is introduced
i.e., when one of the input ports is excited by an RF
signal, all the output ports feeding the array elements
are equally excited but with a progressive phase
between them. This results in the radiation of the
beam at a certain angle
If multiple beams are required, two or more input ports
need to be excited simultaneously. In that case the
beams should be orthogonal ( the angles of minima of
one beam pattern are corresponding to the angles of
the main beams of the other beams)
The phase difference between the array radiating
elements due to the path difference and also the
beam location are given by
ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
The Butler matrix is consisting of hybrid junctions couplers and phase shifters
which can be implemented by MW technology such as WG or microstrip technology
It requires an (M/2)log2(M) 90° hybrids interconnected by rows of (M/2)(log₂ M-1)
fixed phase shifters to form the beam pattern
p=1,2,...
± tends for the right and left beams
Number of array elements is 4 oriented on y axis, d/λ=0.5 Example:
-Number of couplers= (M/2)log2(M)=4
-Number of phase shifters= (M/2)(log2M-1) =2
- p=1,2 ± tends for the right and left beams
-Phase shift between elements due to phase shifts are
p =1 ∆φ=180/4=45o θo=sin-1(45/180)= 14.47o 1R,
p= -1 ∆φ=-180/4=-45o θo=sin-1(-45/180)= -14.47o 1L,
p=2 ∆φ=3x180/4=135o θo=sin-1(135/180)= 48.6o 2R ,
p=-2 ∆φ=-3x180/4=-135o θo=sin-1(-135/180)= -48.6o 2L ,
oxM
pd180
12cos
2
ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
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Number of array elements is 8oriented on y axis, d/λ=0.5 Example:
ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
Because of the dependence of the phase shift on the frequency the beam angle will vary with
the frequency, i.e., the Butler matrix forms phase steered beams which squint with frequency
Also the beam cluster is narrow for high frequency and vise versa
p=1,2,3,4.
± tends for the right and left beams ox
M
pd180
12cos
2
ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
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-It is easy to implement and requires few components to build compared to other
networks
-The loss involved is very small, which comes from the insertion loss in hybrids,
phase shifters, crossover and transmission lines
•Butler matrix advantages
-Beamwidth and beam angles tend to vary with frequency causing the beam squint
with frequency
- Also, as the matrices get bigger, more and more crossovers make interconnections
complex
•Butler matrix disadvantages
ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
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Wideband beamforming array -2
An array operating with signals having a fractional bandwidth (FB)
up to 25%
Ultrawide band array is an array operating with signals having a
fractional bandwidth (FB) from 25% up to 200%
As the signal bandwidth increases the performance of the
narrowband beamformer starts to deteriorate , a tapped delay line
(TDL) is used on each branch (element) of the array
For wideband signals, since each signal consists of infinite number of
different frequency components, the value of the weights should be
different for different frequencies and we can write the weight vector in
the following form:
T
M fwfwfwfW )](.....)()([)( 21
ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
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The TDL allows each element to have a phase response that varies
with frequency, compensating for the fact that lower frequency signal
components has less phase shift for a given propagation distance,
whereas higher frequency signal components has greater phase shift
as they travel the same length
This structure can be considered to be an equalizer which makes the
response of the array the same across different frequencies by using
temporal signal processing (temporal filter; time delay)
The inter-element distance, d, is determined by the highest frequency of
the input wave and for a uniform one-dimensional linear array, is given by
d = c / 2fh
ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
-The TDL network permits adjustment of gain and phase as desired at a number of frequencies
over the band of interest
-The far-field signal is received by M antenna elements. Each element is connected to J delay lines
with the time delay of T seconds -If the input signals are denoted by x1(t), x2(t),. .. , xM(t),
])1([)(1
0
1
0
Tjtxwty m
M
m
J
j
mj
-the output signal is the sum of all
ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
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Blass matrix for wideband switching (fixed) beamforming
The Blass matrix network uses directional couplers and transmission
lines to provide adjustable TDL phase shift for the arrays in order to
compensate the phase frequency dependence and generates multiple
beams Construction
•M array elements (columns), each
connected to M transmission lines
•M beam ports (rows), each
connected to M transmission lines
•The rows and columns are intersected
on nodes, each has a coupler
•Phase shifters between two consecutive
couplers of the same column may be
needed
Beam forming
•Beam port 1; top feed line provide zero progressive time delays between elements that couples
out a broadside beam and is relatively unaffected by the other feed
•Any other feed line provide progressive time delays between elements that couples out a beam at
different angles off broadside and is affected by the other feed lines
M
ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
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Therefore, when you feed signal into the different inputs, you will get different beams
at steering angles ( M beams )
a11
a21
aM1
•There are M beam ports 1,2,…,M
provides M excitation vectors S1,S2,..,SM
•For each beam there are M
signal amplitudes associated to
the array elements grouped as
excitation vector of length M
•For M simultaneous beams
there is a superposition M
excitation vectors of length M
•The design is to calculate coupling and phase shifting values of the couplers and the phase
shifters to obtain the linear superposition of the M desired excitation vectors on the M outputs
ADAPTIVE ANTENNAS. PROF. A.M.ALLAM
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Blass matrix advantages
-It has a low performance because its loss is attributed to the resistive terminations
Blass matrix disadvantages
-There is no beam squinting with frequency
-The Blass matrix is simple in the sense that it has simpler interconnection layout of
the circuit since it does not involve any crossovers as in Butler matrix
-It requires more components compared to the Butler matrix, which makes it
costlier and heavier
References
B. Allen and M. Ghavami, “ Adaptive array systems”, John Wiley& Sons,
2005