NARROW BAND AND WIDE BAND BEAMFORMING · BEAMFORMING ADAPTIVE ANTENNAS. ADAPTIVE ANTENNAS. PROF....

ADAPTIVE ANTENNAS. PROF. A.M.ALLAM

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NARROW BAND AND WIDE BAND

BEAMFORMING

ADAPTIVE

ANTENNAS


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


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


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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


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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


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


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Number of array elements is 8oriented on y axis, d/λ=0.5 Example:


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


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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


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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


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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


-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


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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


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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


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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

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