4.3 Antenna arrays

Antenna arrays are a powerful tool in electromagnetic engineering, combining multiple antenna elements to enhance performance. They offer improved gain, directivity, and beam steering capabilities compared to single antennas, making them crucial in various applications.

This topic explores the fundamentals of antenna arrays, including their types, design principles, and analysis methods. We'll examine linear and planar arrays, phased arrays, and smart antenna systems, as well as synthesis techniques and measurement methods for optimizing array performance.

Fundamentals of antenna arrays

• Antenna arrays consist of multiple antenna elements arranged in a specific geometry to achieve desired radiation characteristics
• Antenna arrays enable enhanced performance compared to single antennas, including higher gain, directivity, and the ability to steer the beam electronically
• Antenna arrays find applications in various fields, such as wireless communications, radar systems, and radio astronomy

Antenna array definition

• An antenna array is a configuration of multiple antenna elements arranged in a specific pattern to achieve desired radiation characteristics
• The elements in an antenna array can be identical or different, depending on the desired performance and application
• The spacing between the elements, their excitation amplitudes, and phases determine the overall radiation pattern of the array

Advantages vs single antennas

• Antenna arrays offer several advantages over single antennas:
  • Higher gain and directivity, leading to increased range and improved signal-to-noise ratio
  • Ability to steer the beam electronically without physically moving the antenna
  • Capability to form nulls in the direction of interfering signals, enhancing signal quality
• Arrays also provide flexibility in shaping the radiation pattern to meet specific requirements (sectorized antennas)

Types of antenna arrays

• Linear arrays: Elements arranged along a straight line (dipole arrays, patch arrays)
• Planar arrays: Elements arranged in a two-dimensional plane (microstrip patch arrays)
• Conformal arrays: Elements conforming to a non-planar surface (cylindrical arrays, spherical arrays)
• Phased arrays: Elements with adjustable phase shifters for electronic beam steering

Linear antenna arrays

• Linear antenna arrays consist of elements arranged along a straight line, with uniform or non-uniform spacing and excitation
• The radiation pattern of a linear array is determined by the array factor, which depends on the number of elements, their spacing, and excitation

Uniform linear arrays

• In a uniform linear array (ULA), the elements are equally spaced and have identical excitation amplitudes
• The array factor for a ULA is given by: $AF = \frac{\sin(N\psi/2)}{N\sin(\psi/2)}$, where $\psi = kd\cos\theta + \beta$
• ULAs are simple to analyze and implement but have limited control over sidelobe levels and null positions

Non-uniform linear arrays

• Non-uniform linear arrays have unequal spacing between elements and/or non-identical excitation amplitudes
• Non-uniform arrays offer more degrees of freedom in controlling the radiation pattern, including sidelobe levels and null positions
• Examples of non-uniform arrays include binomial arrays, Dolph-Chebyshev arrays, and Taylor arrays

Array factor for linear arrays

• The array factor (AF) is a mathematical expression that describes the radiation pattern of an array, independent of the individual element pattern
• For a linear array with N elements, the AF is given by: $AF = \sum_{n=1}^{N} I_n e^{j(n-1)\psi}$, where $I_n$ is the excitation of the nth element and $\psi = kd\cos\theta + \beta$
• The AF determines the main lobe width, sidelobe levels, and null positions in the radiation pattern

Directivity and gain

• Directivity is a measure of an antenna's ability to concentrate radiation in a specific direction compared to an isotropic radiator
• The directivity of a linear array is proportional to the number of elements and their spacing
• Gain is the product of directivity and efficiency, taking into account losses in the antenna system
• The gain of an array can be increased by using more elements or optimizing the element spacing and excitation

Planar antenna arrays

• Planar antenna arrays have elements arranged in a two-dimensional plane, providing control over the radiation pattern in both elevation and azimuth planes
• Planar arrays offer higher gain and directivity compared to linear arrays and allow for more advanced beamforming techniques

Uniform planar arrays

• In a uniform planar array, the elements are arranged in a rectangular grid with equal spacing in both dimensions
• The array factor for a uniform planar array is the product of the array factors for the two linear arrays along the principal axes
• Uniform planar arrays have a pencil-shaped main beam and sidelobes in both planes

Non-uniform planar arrays

• Non-uniform planar arrays have unequal spacing and/or non-identical excitation amplitudes in one or both dimensions
• Non-uniform planar arrays provide more flexibility in shaping the radiation pattern and controlling sidelobe levels and null positions
• Examples include circular arrays, concentric ring arrays, and aperiodic arrays

Array factor for planar arrays

• The array factor for a planar array is the product of the array factors for the two linear arrays along the principal axes
• For an M×N planar array, the AF is given by: $AF = \sum_{m=1}^{M} \sum_{n=1}^{N} I_{mn} e^{j(m-1)\psi_x} e^{j(n-1)\psi_y}$, where $\psi_x = kdx\sin\theta\cos\phi + \beta_x$ and $\psi_y = kdy\sin\theta\sin\phi + \beta_y$
• The AF determines the main beam shape, sidelobe levels, and null positions in both elevation and azimuth planes

Grating lobes in planar arrays

• Grating lobes are undesired high-intensity lobes that appear in the radiation pattern when the element spacing exceeds a certain threshold
• Grating lobes occur when the phase difference between adjacent elements is an integer multiple of 2π
• To avoid grating lobes, the element spacing should be less than λ/2 in both dimensions, where λ is the wavelength

Phased antenna arrays

• Phased antenna arrays consist of elements with adjustable phase shifters, allowing for electronic beam steering without physically moving the antenna
• Phased arrays find applications in radar systems, satellite communications, and 5G wireless networks

Principles of phased arrays

• In a phased array, the phase of each element is controlled independently to steer the main beam in a desired direction
• The phase shifts introduce a progressive phase delay across the array, resulting in constructive interference in the desired direction
• The beam steering angle depends on the phase gradient across the array and the element spacing

Phase shifters in antenna arrays

• Phase shifters are devices that introduce a controllable phase delay in the signal path of each antenna element
• Common types of phase shifters include analog phase shifters (ferrite, PIN diode) and digital phase shifters (switched delay lines, vector modulators)
• The resolution and accuracy of the phase shifters determine the beam steering precision and sidelobe levels

Beam steering and scanning

• Beam steering refers to the ability to point the main beam of the array in a specific direction by adjusting the phase shifts
• Scanning is the process of continuously steering the beam over a range of angles to cover a desired region
• Phased arrays can perform electronic scanning in one plane (1D scanning) or both planes (2D scanning)

Applications of phased arrays

• Radar systems: Phased arrays enable rapid scanning and tracking of targets
• Satellite communications: Phased arrays allow for dynamic beam pointing and interference mitigation
• 5G wireless networks: Massive MIMO systems employ phased arrays for beamforming and spatial multiplexing
• Radio astronomy: Phased arrays are used in large-scale interferometric arrays for high-resolution imaging

Array synthesis techniques

• Array synthesis techniques involve determining the element excitations and positions to achieve a desired radiation pattern
• These techniques aim to optimize the array performance in terms of main beam shape, sidelobe levels, and null positions

Schelkunoff polynomial method

• The Schelkunoff polynomial method represents the array factor as a polynomial in the complex plane
• The zeros of the polynomial correspond to the nulls in the radiation pattern
• By placing the zeros appropriately, the desired sidelobe levels and null positions can be achieved

Fourier transform method

• The Fourier transform method exploits the relationship between the array factor and the element excitations
• The desired radiation pattern is specified in the angular domain, and the inverse Fourier transform is used to determine the element excitations
• This method is suitable for synthesizing arrays with a specified main beam shape and sidelobe envelope

Woodward-Lawson method

• The Woodward-Lawson method is an iterative technique that synthesizes the array pattern as a sum of basis functions
• The basis functions are chosen to approximate the desired pattern, and their coefficients are determined through a least-squares fit
• This method allows for the synthesis of arrays with arbitrary radiation patterns

Optimization methods for array synthesis

• Optimization methods formulate the array synthesis problem as an optimization problem, where the objective is to minimize the difference between the desired and actual patterns
• Common optimization techniques include genetic algorithms, particle swarm optimization, and convex optimization
• These methods can handle complex constraints and non-linear effects, such as mutual coupling and element pattern variations

Mutual coupling in antenna arrays

• Mutual coupling refers to the electromagnetic interaction between antenna elements in an array
• Mutual coupling affects the radiation pattern, input impedance, and overall performance of the array

Effects of mutual coupling

• Mutual coupling can cause distortion in the radiation pattern, leading to increased sidelobe levels and pointing errors
• It also affects the input impedance of the elements, resulting in mismatch losses and reduced efficiency
• The severity of mutual coupling depends on the element spacing, type, and polarization

Compensation techniques for mutual coupling

• Compensation techniques aim to mitigate the effects of mutual coupling and restore the desired array performance
• Element pattern compensation involves modifying the excitation of each element based on the measured or simulated active element pattern
• Impedance matching networks can be designed to compensate for the changes in input impedance due to mutual coupling

Active element pattern

• The active element pattern (AEP) is the radiation pattern of an individual element in the presence of other elements in the array
• The AEP takes into account the mutual coupling effects and differs from the isolated element pattern
• Measuring or simulating the AEPs is essential for accurate array analysis and synthesis

Scanning impedance and matching

• Scanning impedance refers to the input impedance of an array element as a function of the scan angle
• Mutual coupling causes the scanning impedance to vary with the scan angle, leading to mismatch losses and scan blindness
• Wideband matching networks and adaptive impedance tuning can be used to maintain good matching over a wide scan range

Wideband antenna arrays

• Wideband antenna arrays are designed to operate over a wide frequency range while maintaining stable radiation characteristics
• Wideband arrays find applications in multi-function radars, electronic warfare systems, and ultra-wideband communications

Challenges in wideband arrays

• Maintaining a consistent radiation pattern and low sidelobe levels over a wide frequency range is challenging
• Element spacing becomes frequency-dependent, leading to grating lobes at higher frequencies
• Mutual coupling effects vary with frequency, affecting the array performance

Frequency-independent antenna arrays

• Frequency-independent antenna arrays employ elements with inherently wideband characteristics, such as log-periodic dipole arrays and spiral antennas
• These arrays maintain a self-similar geometry over a wide frequency range, resulting in a stable radiation pattern
• However, the size and complexity of frequency-independent arrays can be a limitation

Timed arrays and true-time delay

• Timed arrays and true-time delay (TTD) techniques aim to maintain a constant beam pointing direction over a wide frequency range
• Instead of using phase shifters, TTD systems introduce a frequency-dependent time delay in each element path
• TTD arrays can achieve wideband operation without the beam squint problem associated with phase-steered arrays

Wideband array feeding networks

• Wideband array feeding networks are designed to provide a consistent power distribution and phase relationship across the elements over a wide frequency range
• Examples include corporate feeds, series feeds, and traveling-wave feeds
• These feeding networks should have low insertion loss, good impedance matching, and minimal dispersion to maintain array performance

Smart antenna systems

• Smart antenna systems combine antenna arrays with signal processing algorithms to dynamically adapt the radiation pattern based on the signal environment
• Smart antennas can enhance signal quality, mitigate interference, and increase system capacity

Adaptive antenna arrays

• Adaptive antenna arrays continuously adjust the element weights (amplitudes and phases) based on the received signal statistics
• The adaptation algorithms aim to maximize the signal-to-interference-plus-noise ratio (SINR) or minimize the mean squared error (MSE)
• Examples of adaptive algorithms include least mean squares (LMS), recursive least squares (RLS), and direct matrix inversion (DMI)

Beamforming algorithms

• Beamforming algorithms compute the optimal element weights to steer the main beam towards the desired signal while suppressing interferers
• Conventional beamforming methods, such as delay-and-sum and Capon beamforming, rely on the knowledge of the desired signal direction
• Blind beamforming techniques, such as the constant modulus algorithm (CMA) and the eigenspace-based methods, do not require explicit direction information

Direction-of-arrival estimation

• Direction-of-arrival (DOA) estimation is the process of determining the angular direction of incoming signals based on the received array data
• DOA estimation is crucial for beamforming and source localization in smart antenna systems
• Common DOA estimation techniques include MUSIC (Multiple Signal Classification), ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques), and maximum likelihood methods

MIMO antenna arrays

• MIMO (Multiple-Input Multiple-Output) antenna arrays employ multiple antennas at both the transmitter and receiver to exploit spatial diversity and multiplexing
• MIMO arrays can significantly increase the channel capacity and link reliability compared to single-antenna systems
• Beamforming and precoding techniques are used in MIMO arrays to optimize the signal transmission and reception based on the channel state information (CSI)

Measurement techniques for antenna arrays

• Measuring the radiation characteristics of antenna arrays is essential for validating the design and assessing the performance
• Various measurement techniques are used depending on the array size, frequency range, and required accuracy

Far-field measurement methods

• Far-field measurements are conducted in the radiating far-field region of the array, where the field pattern is fully formed
• Conventional far-field ranges use a transmit antenna to illuminate the array under test (AUT) and measure the received signal as a function of angle
• Compact ranges employ reflectors or lenses to create a plane wave illumination in a shorter distance, reducing the range size

Near-field measurement methods

• Near-field measurements are performed in the radiating near-field region of the array, where the field pattern is not yet fully formed
• Planar, cylindrical, and spherical near-field scanning techniques are used to measure the complex field distribution over a surface close to the array
• The measured near-field data is then transformed to the far-field pattern using mathematical algorithms

Array calibration techniques

• Array calibration is the process of compensating for the amplitude, phase, and position errors of the array elements
• Calibration is essential for achieving accurate beamforming and nulling performance
• Methods include element-level calibration using a reference antenna, mutual coupling calibration, and on-array calibration using built-in sensors

Diagnostic techniques for array performance

• Diagnostic techniques are used to identify and localize faults or performance degradation in antenna arrays
• Element failure detection methods, such as power monitoring and VSWR measurements, can identify non-functioning or degraded elements
• Array imaging techniques, such as near-field holography and array diagnosis using the far-field pattern, can provide a visual representation of the array aperture and reveal anomalies