Unit II�Antenna Arrays

Pattern Multiplication

Binomial Array

• It is a system of similar antennas oriented similarly to get greater directivity in a desired direction.

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• Total field produced by an antenna system is the vector sum of the fields produced by the individual antennas of the array system.

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• Uniform linear array – equal magnitude and uniform phase shift

Various forms of antenna array

• Broadside array
• End Fire array
• Co-linear array
• Parasitic array

Broadside array

• Individual elements are equally spaced along a line.
• Each element is fed with a current of equal magnitude, all in the same phase.

• Radiates in broadside direction (i.e perpendicular to the line of array axis)

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• The radiation pattern is bidirectional.

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• Bidirectional pattern can be converted into unidirectional by installing an identical array behind this array at a distance quarter wavelength and exciting it by a current leading in phase by 90 degree.

End fire array

• Equal magnitude and phase varies progressively along the line.

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Co-linear array

• Antennas are mounted end to end in single line.

Parasitic array

• Multi element arrays having number of parasitic elements are called parasitic arrays ‘whether driven element is one or more’.

Array of two point sources

• An antenna is considered as a point source or volumeless radiator.

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• Array of two point sources is the simplest situation in the arrays of isotropic point sources.

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• Assume that two point sources are separated by a distance (say d) and have the same polarization.

Case I) Array of two point sources with equal amplitude and phase.

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• Determine fields at a distant point P at distance R from origin O
• Taking origin O as reference point for phase calculation.
• The waves from source 1 reaches the point P at a latter time than the waves from source 2 because of path difference (1’2’).
• The fields due to source 1 lags while that due to source 2 leads.

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Maxima direction

Minima direction

Half power point direction

Radiation Pattern

Case ii) Arrays of two point sources with equal amplitude and opposite phase

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• Here the point source 1 is out of phase to source 2 by 180 degree.

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• The total field at point P is,

Maxima direction

Minima directions

Radiation pattern

Case iii) Arrays of two point sources with unequal amplitude and any phase

• Amplitudes of two sources are not equal and any phase difference say α.
• Assume the source 1 is taken as reference for phase.
• The amplitude of E1 is greater than E2.
• Total phase difference between the radiations of two sources at point P is given by,

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Fig. Two point source with unequal amplitude and any phase difference α

Array of n Isotropic sources of equal amplitude and spacing : Broadside case

• An array is said to be broadside if the maximum radiation is perpendicular to the axis of the array
• For that α = 0 and ψ = 0 for maximum must be satisfied
• The phase angle is

ψ = βd cosθ + α

• Substituting, α = 0 and ψ = 0, we get
• Principal maxima occurs at θ = 90ᵒ and 270ᵒ
• Other pattern maxima, pattern minima and beamwidth of major lobe can be calculated

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• The total field by ULA is 🡪

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• Direction of Pattern Maxima

Direction of Pattern Minima

• To obtain pattern minima

• The above equation is general equation, for broadside array

Beam Width of the Major Lobe

Example : 4 element Uniform Linear array with radiation in Broadside direction

To get the pattern Maxima of minor lobes

• To get pattern minima or nulls

Radiation pattern of 4 element broadside uniform linear array

Uniform linear array

• An array is said to be linear,
• if the individual elements of the array are spaced equally along a line and uniform

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• An array is said to be uniform
• If the same are fed with currents of equal amplitude and having an uniform progressive phase shift along the line.

• Considering a linear array of n isotropic point sources in which
• point sources are spaced equally (say d)
• Fed with in-phase currents of equal amplitude (say Eo)

=‘/

For ψ = 0, becomes indeterminant and hence L’ hospital rule must be applied to evaluate the function

Pattern Multiplication

• Radiation pattern of an array can be obtained by pattern multiplication principle as follows
• Pattern Multiplication Theorem: the total field pattern of an array of non-isotropic but similar source is the multiplication of the individual source patterns and the pattern of an array of isotropic point sources each located at the phase center of individual source and having the relative amplitude and phase.

• The pattern multiplication is applicable to two and three dimensional patterns
• Let

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• Total field pattern of an array of non-isotropic but similar sources may be written as

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• For two dimensional case

• Principle of pattern multiplication provides speedy methods for sketching the pattern of complicated arrays
• Width of the principle lobe and the width of the array pattern are same
• Secondary lobes are determined from the number of nulls and its angular position

Radiation pattern of 4-isotropic elements fed in phase, spaced λ/2

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• Radiation pattern to be found for

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• Radiation pattern of dipole spaced λ/2 Radiation pattern of dipole spaced λ

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• Four isotropic point sources spaced λ/2 can be replaced as two isotropic sources spaced λ as below
• Elements 1,2 🡪 1’
• Elements 3,4 🡪 2’
• The units 1’ and 2’ have same radiation patterns
• The resultant radiation pattern is obtained by multiplying individual pattern and group pattern

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Unit pattern Group Pattern 4-element array pattern

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Radiation pattern of 8-isotropic elements fed in phase, spaced λ/2 apart

• Group pattern of 8 isotropic elements spaced λ/2 equals to the radiation pattern of two dipoles spaced 2λ as shown below

• Radiation pattern of 8 isotropic element is obtained by multiplying the unit pattern of 4 element and the group pattern of two isotropic radiators spaced 2λ
• The resultant radiation pattern is

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Unit pattern Group pattern Resultant

pattern of 8-isotropic

element

Binomial Arrays

• Coming under the category of arrays with non-uniform excitation amplitude
• Amplitudes of radiating sources are arranged according to the coefficients of binomial series

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• With uniform linear array, as the array length is increased to increase directivity, the minor lobes also appear
• For certain applications it is highly desirable the minor lobes should be totally eliminated or reduced to minimum level compared with main lobes
• It can be accomplished by making the elements at the center of the broadside array radiates more strongly that at the edges

• The secondary (minor) lobes can be eliminated by
• - spacing between the radiators should not exceed λ/2
• - the current amplitudes in radiating sources are proportional to the coefficients of binomial series

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• However, the elimination of secondary lobes takes place at the cost of directivity
• For ex. a five element uniform linear array has the HPBW of 23ᵒ, but for binomial array of 5 element the HPBW is 31

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Derivation of Binomial Array

• Pattern multiplication is used
• Consider the far field pattern of two point sources of broadside spaced by λ/2
• This pattern has no minor lobe

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• Superimposing the identical array of two point sources on the array will take the same shape without minor lobes
• The total field is obtained by pattern multiplication

• The resultant pattern is obtained by

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• Similarly if this three source array is superimposed with another identical array, then the amplitude of current ratio is 1:3:3:1
• The normalized field is

• The far field pattern of binomial array with ‘n’ elements is

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Disadvantages of Binomial arrays:

• HPBW increases and hence directivity decreases
• For large array, large amplitude ratio of sources is required

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Advantages of Binomial arrays:

• Secondary lobes are not appearing in the radiation
• Pattern multiplication principle is used for deriving the pattern

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The Log-Periodic antenna

• It is a frequency independent antenna.
• A frequency independent antenna is one that is physically fixed in size and operates on an instantaneous basis over a wide bandwidth with relatively constant impedance, pattern, polarization, gain etc.
• As per V. H. Rumsey’s principle, an antenna will be frequency independent if the antenna shape is specified only in terms of angles.

Log-Periodic Dipole Array (LPDA)

Kraus: Fig. 11-17

The dipole lengths l and spacing R (or s) are related as

τ: Scale factor or design ratio. τ < 1

So,

Alternatively,

k: Scale factor. k > 1

Analysis and working

1. Inactive (transmission line) region (l < λ/2)
2. Active (radiating) region (l ≈ λ/2)
3. Inactive (stop) region (l > λ/2)

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Analysis can be done by considering 3 regions of antenna, at a wavelength near middle of operating range.

1. Inactive (transmission line) region (l < λ/2):

Antenna elements in this region are less than resonant length i.e. λ/2 long & they present a large capacitive reactance to the line.

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Currents in the elements are small and lead the base voltage supplied by transmission line by 90° approx. The radiation towards left is small.

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2. Active (radiating) region (l ≈ λ/2):

In this region, elements are of resonant length approx. i.e. λ/2 long so impedance offered by dipoles of this region is resistive in nature.

So, element currents are large & in-phase with base voltage. Hence, there is strong radiation towards left in backward direction from this region.

3. Inactive (stop) region (l > λ/2):

The element lengths are longer than the resonant length i.e. λ/2 and so they present inductive reactance to the line. Due to this, currents in the elements are small & lag the base voltage.

Small currents in elements mean that the antenna is effectively truncated at the right of active region.

Any small fields from these elements tend to cancel in forward & backward direction so radiation from this region is small.

Thus, when wavelength is increased, radiation region moves to the right & when wavelength is decreased, radiation region moves to the left with maximum radiation towards the apex or feed point of array.

Design of LPDA

In general, the dipole lengths (l), spacing R (or s), diameters (d) and gap spacing at dipole centers (a) are related as,

From the geometry,

Kraus: Fig. 11-18

As,

so,

Using this,

or

n = 1, 2, 3 …..

Taking l_n+1 = λ/2, when active, we have

α: apex angle

k: scale factor

s_λ: spacing in wavelengths shortward of λ/2 element

or,

Also, spacing factor

so,

Hence, we have

and

Applications of Log-Periodic antenna

• In television and FM reception
• EMC and EMI testing
• Radio link testing
• Surveillance and all round monitoring

Practical log-periodic antenna

Advantages

• Wide Band, High Gain, Low VSWR
• Small Size, Light Weight, Easy Assembly
• Low return loss
• Constant gain with frequency

Smart Antennas

Introduction

• New antenna array designs referred to as smart antenna is based on basic technology of 1970s and 1980s.
• Designed mostly for wireless communication
• It is combination of antenna technology and Digital Signal Processing.
• The DSP along with the antenna make the system acts as smart.
• A smart antenna can be viewed as a combination of regular or conventional antenna elements whose transmit or received signals are processed using smart algorithm.

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Implementation of smart antenna system

• The antenna arrays have input or output as RF signals on analog domain.
• RF front end consists of LNA, mixer and analog filters.
• In Rx mode, ADCs are used to convert RF signals into digital domain.
• In Tx mode, DACs are used to convert based band digital signals into RF signals.
• The down conversion from RF to baseband or up conversion from base band to RF can involve the use of IF signals.
• The DSP section is implemented on microprocessor or DSP or FPGA.
• The smart algorithm implementation is normally a software code implement in ASIC or FPGA.

Antenna array processing

Contd…

Contd…

• The error signal produced is adaptively minimized by an adaptive algorithm.
• This adaption process involves the updating of weight vectors to some minimization criteria.
• Mostly the weight vectors are updated during some training sequence when some known or pilot symbols are transmitted.
• At the end of training sequence, the array output is fed to the demodulator and finally to the upper layers of the system.

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Classification of smart antenna

• Smart-antenna systems are basically an extension of cell sectoring in which the sector coverage is composed of multiple beams
• Depending on signal processing technique and at the baseband output of the antenna array, smart antennas are grouped into four basic types:

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• Beamforming
• Diversity combining
• Space time equalization and
• Multiple input multiple output

(MIMO) processing

1. Beamforming

• An DSP algorithm is developed to transmit or receive the signal only in the desired direction.
• This algorithm shape the beam of radiation pattern and adaptively steer beams in the desired direction and put nulls to the interfering signals.
• This permits low co-channel interference and high gain to the desired signals.
• Two ways of beamforming systems:
1. Fixed beamforming system
2. Fully adaptive beam forming systems

Contd…

a. Fixed beamforming system:

• It has a beam forming network followed by RF switches which works in RF/analog domain.
• The switches are controlled by a logic which selects a particular beam
• The control logic has to select one of the predetermined set of weights to choose a beam.

b. Fully adaptive beamforming systems:

• The antenna gain or weights are being chosen adaptively through running array algorithm in digital domain.
• Adaptive array track signals and then fine tune themselves for the best reception.

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2. Diversity Reception or Diversity combining:

• Limiting factor in wireless communication is multipath fading

- The amplitude of the received signal fluctuates over time.

• Due to the availability of a deep fade, the signal strength decreases and

affect the communication links for a conventional single antenna system.

• This is overcome by using multiple antenna system.
• The diversity in the received signal, for the same transmitted information is exploited by smart antenna processing schemes.

Contd…

• Many algorithms like maximum ratio combining, equal gain combining and selection diversity have developed to have diversity reception in wireless communication.
• Here multiple antennas are used for Tx and Rx of signals.
• A diversity system use multiple Tx’s and Rx’s to mitigate the problems caused by multi path signals.
• The two common types of diversity receptions are:
• Frequency
• Spatial

Contd…

• Two separate sets of Txs, Rxs operating at different frequencies, with frequency diversity are being used to transmit the same information simultaneously.
• The system is more effective since it operates at different frequencies.
• These systems are more costly because of using more Txs and Rxs.
• Next type is where two Rx antennas are spaced as far as possible to receive the signals.
• This type of spatial diversity is used in base stations rather than handheld devices.
• The antenna at different locations receives different signals with one being better than other.

Contd….

• Diversity reception is specially difficult at shortwave frequencies because spacing will be many hundreds or even thousands of feet.
• Thus only horizontal.
• At UHF and microwaves frequencies, antenna spacing is comparatively simple since the wavelength or short.
• Typically 10λ to 20λ spacing is practicable at these frequencies.

3. Space time equalization

• In the above two methods it is assumed that the signal of interest is narrow band signals as compared to the coherence bandwidth of the channel.
• It has flat fading across the bandwidth of the signals.
• Multipath fading in wireless communication may also introduce frequency distortion to the received signal.
• Introducing temporal processing in each antenna to remove the effect of frequency distortion.
• And performing a spatial combining results in mitigating channel induced frequency selective fading and providing antenna gain.
• This scheme is known as space time adaptive processing (STAP) or equalization.

4. Multiple Input Multiple Output (MIMO):

• It uses two or more antennas for Tx and Rx.
• Two types of MIMO schemes:
1. Spatial multiplexing – to increase data rate for a given bandwidth (i.e spectral efficiency)
2. Space time coding – using diversity combining techniques to mitigate fading.

Contd..

• Data is serial to parallel converted and transmitted over multiple antenna elements.
• At Rx end the signals are applied to the maximum likelihood to obtained the transmitted symbols.
• At the Tx end the information are separated into two data streams and fed to the different antennas.
• The Tx antennas are separated physically by a wavelength.
• Most preferable type of modulation is OFDM.
• OFDM – the data is transmitted by simultaneously modulating segments of the high speed bit stream onto multiple carriers.

Contd..

• The four receiver antennas are separated by a wavelength and provide multipath for the two transmitted signals.
• The output of the four antennas are digitized with ADC.
• The ADC outputs are combined in DSP section.
• A special DSP algorithm is used to minimize the multipath effect.
• MIMO gives an amazing enhancement in signal gain and reliability.
• In space time coding time duration, symbols to be transmitted are coded over multiple antennas and symbol time durations.
• Hence the receiver can easily regenerate the transmitted signals by linear processing on received signals.
• The space time codes rely on the orthogonality present in the coded symbols for proper detection.

Advantages

1. Used at base station in a cellular network to improve user capacity.

• User capacity refers to number of subscribers
• Beams are focus to the desired subscribers
• Reducing interference to other subscribers, using same frequency band
• Use capacity can be improved using Spatial Division Multiple Access(SDMA)

2. Other advantages

• Robustness against multipath fading and noise, which improves reliability of received signal
• Reduced power consumption for handsets
• Low probability of interception and detection
• Enhanced range of reception

Disadvantages

• Multiple RF chains can increase the cost and make the transreceiver bulkier.
• Most of the baseband processing needs coherent signals.
• Implies that all the LO and ADC clocks require to be derived from the same sources. It is the present design challenges.
• The phase characteristics of RF components may change over time.
• Need calibration procedures for accounting phase differences.
• Non linear devices like mixers, amplifiers and ADC are used to develop smart antenna system. This might affect the performance of array, hence it is periodically checked.
• More than one sources are used, this increases the data bandwidth required for digital processing.
• This limit the data rate for different applications.