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Sidelobes

Sidelobes are the secondary lobes or peaks in the far-field radiation pattern of an antenna or in the frequency response of a signal processing system, distinct from the primary main lobe, and typically represent undesired directions of energy radiation or spectral leakage.^[1]^[2] In antenna theory, they manifest as smaller beams emanating at angles away from the main beam's direction, often resulting from diffraction effects at discontinuities in the antenna structure, such as abrupt ends of arrays or imperfections like feed horn supports.^[3] These sidelobes cannot be entirely eliminated but can be minimized through design techniques like amplitude tapering, which trades off main lobe beamwidth and gain for reduced sidelobe levels, typically measured in decibels relative to the main lobe peak (e.g., -13 dB for uniform linear arrays).^[1]^[3] The significance of sidelobes in antennas lies in their potential to cause interference, such as spurious echoes in radar systems or increased susceptibility to jamming in military applications, where levels below -40 dB are often required for optimal performance.^[3] High sidelobe levels can degrade system efficiency by directing energy toward unintended targets or sources, impacting directivity and overall pattern control.^[1] In practical designs, such as phased array antennas, sidelobe suppression is achieved via windowing functions or nonuniform element excitation, balancing cost, complexity, and beam broadening.^[4]^[3] In digital signal processing (DSP), sidelobes appear as secondary maxima in the Discrete-Time Fourier Transform (DTFT) of windowed signals, primarily due to the abrupt transitions in time-domain windows like the rectangular window, leading to the Gibbs phenomenon and spectral leakage.^[2] For instance, the first sidelobe of a rectangular window is approximately 13 dB below the main lobe, with a roll-off rate of about 6 dB per octave, which can mask weak nearby frequency components in applications like spectral analysis or FFT-based measurements.^[2] Mitigation strategies include using smoother windows (e.g., Hamming or Blackman) to lower sidelobe levels at the expense of main lobe widening, enhancing resolution in fields such as audio processing, ultrasound imaging, and radar signal filtering.^[3]^[2]

Definition and Fundamentals

Definition of Sidelobes

Sidelobes refer to the secondary maxima, or peaks, in the far-field radiation pattern of an antenna or radiating aperture, distinct from the primary main lobe, and arise primarily from diffraction and interference effects among the radiated waves. These unintended lobes represent regions of elevated radiation intensity in directions away from the desired main beam, often resulting in energy leakage that can interfere with signal reception or transmission in those off-axis directions.^[3]^[1] The phenomenon of sidelobes traces its origins to optical diffraction experiments conducted by Joseph von Fraunhofer in the early 19th century, during which secondary maxima were observed in the far-field patterns produced by light diffracting through finite apertures, such as slits. Fraunhofer's work on diffraction gratings and single-slit patterns revealed these secondary peaks as inherent consequences of wave propagation through limited openings, laying the groundwork for understanding similar behaviors in electromagnetic radiation. This optical insight was later extended to radio-frequency antennas in the early 20th century, as engineers applied diffraction principles to design directional antennas for wireless communication and early radar systems, recognizing sidelobes as a natural outcome of finite antenna structures.^[5] In general, sidelobes occur due to the finite size of the radiating aperture or array, which causes diffraction at the edges, spreading electromagnetic energy beyond the main beam and creating these auxiliary peaks through constructive and destructive interference. This energy redistribution is unavoidable in practical antennas, as the abrupt termination of the aperture introduces phase variations that prevent all power from concentrating solely in the intended direction. Visually, a typical radiation pattern plot—often represented in polar coordinates—depicts the main lobe as a prominent central peak, with progressively smaller sidelobes extending outward, interspersed by nulls where radiation intensity drops to near zero, illustrating the oscillatory nature of the diffracted field.^[3]^[1]

Distinction from Main Lobe and Back Lobe

The main lobe constitutes the primary beam in an antenna's radiation pattern, exhibiting the maximum gain and directed toward the intended path of signal transmission or reception. This lobe focuses the majority of the antenna's radiated power in directive systems.^[6]^[7] The back lobe, by comparison, describes radiation propagating in the direction opposite to the main lobe, generally at an angular separation of 180 degrees. It arises from design imperfections, such as energy spillover beyond the edges of a reflector or scattering effects, resulting in unintended rearward emission.^[8]^[9] Sidelobes encompass all secondary lobes positioned off the main axis, appearing at various angular offsets around the primary beam rather than in direct opposition. These lobes differ in amplitude and quantity depending on the antenna's aperture and illumination, often stemming from diffraction phenomena similar to those affecting the main pattern. Unlike the back lobe's fixed oppositional orientation, sidelobes can occur in multiple directions and pose risks of interference through off-axis signal pickup or emission.^[8]^[10]^[9] In terms of functionality, the main lobe enables efficient energy transfer for the targeted application, whereas sidelobes introduce spillover that can degrade system performance by capturing or radiating extraneous signals. Back lobes, meanwhile, represent efficiency losses via radiation in the undesired rear hemisphere, often minimized in directional designs to preserve overall gain.^[8]

Mathematical Foundations

Radiation Pattern Formulation

The far-field radiation pattern of an aperture antenna is fundamentally described by the Fourier transform of the aperture field distribution. For a one-dimensional aperture along the x-axis, the electric field in the far field is given by

E(\theta) = \int_{-\infty}^{\infty} e^{j k x \sin\theta} f(x) \, dx,

where f(x) represents the complex aperture illumination function, k = 2\pi / \lambda is the wavenumber, \lambda is the wavelength, and \theta is the observation angle from the broadside direction.^[11] This integral formulation arises from the Huygens-Fresnel principle applied in the far zone, where the phase contributions from aperture elements combine to produce the directional pattern.^[12] In the case of a continuous uniformly illuminated rectangular aperture of width L, the radiation pattern simplifies to a sinc function, defined as \text{sinc}(u) = \frac{\sin(\pi u)}{\pi u}, where u = \frac{L}{\lambda} \sin\theta. This results in an oscillatory pattern characterized by a central main lobe flanked by sidelobes of decreasing amplitude, with the first sidelobe occurring at approximately u \approx 1.5.^[13] The oscillatory nature of the sinc function inherently produces these sidelobes due to the finite extent of the aperture, which introduces diffraction effects that prevent perfect concentration of energy in the main lobe.^[14] For discrete array antennas, the radiation pattern incorporates an array factor that accounts for the spacing and excitation of individual elements. For a linear array of N elements with currents I_n spaced by distance d, the array factor is expressed as

AF(\psi) = \sum_{n=1}^{N} I_n e^{j (n-1) \psi},

where \psi = k d \sin\theta + \beta, \beta is the progressive phase shift between elements, and the total pattern is the product of this factor and the single-element pattern.^[15] This summation leads to interference patterns where constructive and destructive phases define the lobes. Nulls in the radiation pattern occur at angles where the integral or sum evaluates to zero, marking the boundaries between the main lobe and sidelobes as well as between adjacent sidelobes. These null locations, such as at u = m for integer m \neq 0 in the continuous sinc case, delineate the regions of local maxima that constitute sidelobes.

Sidelobe Level Metrics

The sidelobe level (SLL) quantifies the intensity of sidelobes relative to the main lobe in an antenna's radiation pattern, defined as the ratio of the peak power of the strongest sidelobe to the peak power of the main lobe, expressed in decibels (dB).^[1] This metric is crucial for assessing unwanted radiation that can interfere with signal reception or detection in applications such as radar and communications. For a uniformly illuminated rectangular aperture antenna, the first sidelobe level is approximately -13.26 dB relative to the main lobe peak.^[16] Two primary variants of SLL are used: peak sidelobe level (PSL) and integrated (or average) sidelobe level (ISL). The PSL measures the maximum height of any individual sidelobe, providing a worst-case indicator of potential interference from the highest sidelobe, which is particularly relevant for performance degradation in radar systems where isolated high sidelobes can mask targets.^[17] In contrast, the ISL integrates the total power across all sidelobes, offering an average measure that accounts for overall spillover or energy loss, useful for evaluating total radiated inefficiency.^[18] The PSL is computed as \text{PSL} = 10 \log_{10} \left( \max \frac{|Y_s|^2}{\max |Y_m|^2} \right), where Y_s and Y_m represent sidelobe and main lobe data, respectively, while the ISL uses \text{ISL} = 10 \log_{10} \left( \frac{\int |Y_s|^2 d\theta}{\int |Y_m|^2 d\theta} \right) for angular integration.^[18] Military standards often specify low SLL thresholds to minimize electromagnetic interference and enhance stealth in radar antennas. For instance, typical requirements include first major sidelobes below -20 dB and all other sidelobes below -30 dB. In radar applications, requirements frequently demand sidelobe suppression below -20 dB for major sidelobes to reduce vulnerability to jamming and improve signal-to-noise ratios.^[19] Sidelobe levels are measured by normalizing the radiation pattern to the main lobe peak, typically as \frac{|E(\theta)|^2}{|E(0)|^2}, where E(\theta) is the far-field electric field at angle \theta from boresight and E(0) is the on-boresight value.^[1] This normalization identifies local maxima beyond the main lobe, distinguishing the first sidelobe (nearest to the main lobe) from subsequent ones, with levels reported in dB relative to the normalized main lobe unity gain.^[15]

Sidelobes in Aperture Antennas

Uniformly Illuminated Aperture

In aperture antennas, uniform illumination refers to a constant amplitude excitation across the entire aperture surface, typically modeled as a rectangular distribution for simplicity. This configuration produces a far-field radiation pattern given by the squared sinc function, expressed as \left( \frac{\sin(\pi U)}{\pi U} \right)^2, where U = \frac{a}{\lambda} \sin \theta and a is the aperture width, \lambda is the wavelength, and \theta is the observation angle from broadside.^[20] The resulting pattern features a narrow main beam with the first nulls occurring at angles where \pi U = \pm \pi, or \theta \approx \pm \lambda / a.^[20] This uniform excitation maximizes directivity and aperture efficiency but inherently generates sidelobes due to the abrupt truncation at the aperture edges. For rectangular apertures, the first sidelobe is at -13.2 dB; for circular apertures, it is -17.6 dB.^[20]^[21] The sidelobes in this pattern form an infinite sequence of local maxima, with subsequent sidelobes decreasing gradually, their envelope following an asymptotic decay proportional to $1/\theta (or equivalently $1/U for small angles), which results in relatively high levels even at large angular separations from the main beam.^[20] The positions of these sidelobes occur at angles roughly corresponding to multiples of the fundamental beamwidth, specifically near \theta \approx (n + 0.5) \lambda / a for integer n \geq 1, scaling inversely with aperture size and thus widening as a decreases.^[20] These elevated sidelobe levels arise primarily from the Gibbs phenomenon, a well-known oscillatory overshoot in the Fourier transform of a discontinuous function, here induced by the sharp edge discontinuities in the uniform aperture field.^[20] The abrupt transition from illuminated to non-illuminated regions causes ringing artifacts that manifest as persistent sidelobes, limiting the pattern's isolation and making uniform illumination unsuitable for applications requiring low secondary radiation.^[20] Despite these drawbacks, the configuration serves as a baseline for understanding aperture behavior, as referenced in the general radiation pattern formulation.^[20]

Effects of Non-Uniform Illumination

Non-uniform illumination of an aperture antenna involves varying the amplitude distribution across the aperture to mitigate the high sidelobe levels inherent in uniform illumination, where abrupt field discontinuities at the edges cause significant diffraction effects leading to sidelobes around -13 dB.^[21] By gradually tapering the amplitude toward the aperture edges, the radiation pattern experiences smoother transitions that reduce these diffraction ripples, typically lowering the first sidelobe level by 10-20 dB depending on the taper severity.^[21] Common tapering functions include linear (triangular), cosine, and Gaussian distributions, which progressively reduce edge amplitudes to suppress sidelobes while preserving a directive main beam. For instance, a linear taper decreases amplitude linearly from the center to zero at the edges, achieving sidelobe levels around -26.5 dB but at the expense of increased main beam width and aperture efficiency of about 81%.^[21] A cosine taper yields sidelobe suppression to -23 dB with an efficiency of about 84%, broadening the half-power beamwidth multiplier to approximately 69° (λ/a). A cosine-squared taper provides even smoother profiles, yielding sidelobe suppression to -31 dB with an efficiency of 66.7%, though it further broadens the half-power beamwidth to approximately 84° (λ/a).^[21] Gaussian tapers, characterized by their exponential decay, offer the most gradual edge reduction, minimizing sidelobes effectively but resulting in the widest beams and lowest gains among these options.^[4] A representative example is the parabolic taper for a linear aperture of width a, defined by the distribution

f(x) = 1 - \left( \frac{2x}{a} \right)^2, \quad -a/2 \leq x \leq a/2,

which is a full quadratic amplitude profile to zero at edges and produces a radiation pattern with sidelobes lowered to around -30 dB, compared to the uniform case.^[21] This taper exemplifies how non-uniformity trades off directivity—reducing gain by up to 30% relative to uniform illumination—for improved sidelobe performance, with the main beam half-power beamwidth expanding by 20-50% depending on the taper parameter.^[21] Overall, these effects highlight the fundamental compromise in aperture antenna design: enhanced sidelobe control through edge tapering inevitably widens the beam and diminishes peak gain, optimizing for applications where interference rejection outweighs maximum directivity.^[4]

Sidelobes in Array Antennas

Origin of Grating Lobes

Grating lobes represent a specific class of sidelobes inherent to periodic structures in array antennas, manifesting as additional peaks in the radiation pattern that closely resemble the main lobe in shape and intensity. These lobes emerge due to the periodic nature of the array, where the constructive interference of waves from elements spaced too far apart creates unintended secondary beams. Specifically, grating lobes appear when the inter-element spacing d exceeds \lambda/2, where \lambda is the operating wavelength, leading to spatial aliasing analogous to undersampling in signal processing.^[22]^[23] The locations of these grating lobes are determined by the grating lobe equation, derived from the array factor:

\sin \theta_m = \sin \theta_0 + m \frac{\lambda}{d}

where \theta_0 is the desired beam direction (scan angle), \theta_m is the angle of the m-th order grating lobe, and m is a non-zero integer (typically m = \pm 1, \pm 2, \ldots). This formula highlights the geometric origin: the lobes occur at angles where the phase progression aligns constructively, shifted by multiples of the spatial period \lambda/d in the sine space. For broadside arrays (\theta_0 = 0^\circ), grating lobes are avoided in the visible region (|\theta| < 90^\circ) if d \leq \lambda, as the first-order lobes then fall outside |\sin \theta| \leq 1. However, for arrays with scanned beams to large angles, the condition tightens to d \leq \lambda/2 to ensure no grating lobes enter the visible space across the full scan range.^[22]^[24] Grating lobes become visible and prominent when the scan angle \theta_0 positions a secondary peak within the visible region, often exhibiting gain comparable to the main lobe due to the uniform replication of the array factor pattern. This visibility degrades performance by distributing energy away from the intended direction, mimicking the main beam's characteristics but at undesired angles.^[22]^[24]

Array Factor Contributions

In array antennas, the array factor (AF) describes the interference pattern produced by the collective contributions of multiple radiating elements, which inherently generates sidelobes in addition to the main beam. For a uniform linear array of N isotropic elements spaced by distance d along the z-axis, the array factor is given by

AF(\psi) = \frac{\sin\left(N \psi / 2\right)}{\sin\left(\psi / 2\right)},

where \psi = kd \cos\theta + \beta, with k = 2\pi / \lambda the wavenumber, \theta the observation angle from the array axis, and \beta the progressive phase shift between elements.^[25] This expression, a quantized approximation of the continuous sinc function, results in a main lobe surrounded by sidelobes whose levels decrease gradually, with the first sidelobe typically at approximately -13 dB relative to the main lobe for large N and spacing d = \lambda/2.^[25] The discrete nature of the array causes these sidelobes to exhibit periodic ripples, distinct from grating lobes that arise under specific spacing conditions. The total radiation pattern of the array is the product of the array factor and the individual element pattern: G(\theta, \phi) = g_e(\theta, \phi) \cdot AF(\psi), where g_e is the embedded element pattern. The element pattern modulates the array factor, potentially amplifying or suppressing certain sidelobes depending on the element type (e.g., dipoles or patches), thus influencing the overall sidelobe structure beyond the pure AF contribution.^[25] In broadside configurations (\beta = 0), the main beam points perpendicular to the array axis, yielding symmetric sidelobes with levels around -13 dB for uniform excitation. In contrast, end-fire arrays (\beta = -kd) direct the beam along the array axis, with sidelobe levels around -13 dB but the first sidelobe closer to the main beam due to the progressive phase shift compressing the pattern, resulting in increased interference in the forward direction.^[26] For planar arrays, the array factor extends to two dimensions, typically as the product of two orthogonal linear array factors for a rectangular grid: AF(\psi_x, \psi_y) = AF_x(\psi_x) \cdot AF_y(\psi_y), where \psi_x = k d_x \sin\theta \cos\phi + \beta_x and \psi_y = k d_y \sin\theta \sin\phi + \beta_y. This separable form produces a grid-like sidelobe structure in the elevation and azimuth planes, creating more complex interference patterns with multiple sidelobe peaks that can exceed linear array levels in certain directions.^[27]

Suppression and Mitigation Techniques

Amplitude Tapering Methods

Amplitude tapering methods involve applying non-uniform amplitude distributions to antenna elements or apertures to suppress sidelobes while maintaining a specified main beam performance. These techniques reduce the excitation levels toward the array edges or aperture periphery, which lowers the contributions from outer elements that generate higher-order sidelobes.^[4] Dolph-Chebyshev tapering achieves the optimal trade-off between beamwidth and peak sidelobe level by deriving element weights from Chebyshev polynomials, ensuring equal-ripple sidelobes at a user-specified level, such as -25 dB relative to the main lobe. This method maximizes directivity for a given sidelobe constraint, making it widely adopted for broadside arrays where the lowest possible peak sidelobe is prioritized.^[28] Taylor line source tapering provides a family of distributions parameterized by the desired average sidelobe level and number of controlled near-in sidelobes, producing a smooth envelope decay beyond the inner region, for example, maintaining an average of -25 dB for outer sidelobes while preserving narrow beamwidth. Unlike Dolph-Chebyshev, it avoids equal ripples in the far-out sidelobes, offering flexibility for applications requiring controlled envelope shape without excessive near-sidelobe variation.^[29] Implementation of these tapers occurs through feed networks that introduce attenuation or via variable amplifier gains to set element amplitudes, with the binomial distribution serving as a simple example where weights follow binomial coefficients, progressively tapering from center to edges and eliminating the first few sidelobes at the cost of beam broadening.^[27]^[30] Such tapering typically reduces aperture efficiency by 1-3 dB due to the uneven power distribution, which lowers overall gain, but it can suppress sidelobe-induced interference by more than 10 dB compared to uniform illumination, enhancing signal-to-interference ratios in practical systems.^[31]^[32]

Phase and Spatial Techniques

Phase tapering involves applying progressive phase shifts across antenna elements or the aperture to shape the radiation pattern and suppress sidelobes, often without altering amplitudes to maintain efficiency. This technique modifies the array factor by introducing controlled phase variations that destructively interfere in unwanted directions, enabling low-sidelobe patterns in uniformly excited arrays. For instance, phase-only synthesis methods, such as iterative Fourier techniques, can achieve sidelobe reductions of up to 10 dB in linear arrays by optimizing element phases while keeping uniform spacing and excitation.^[33] A specific application of phase tapering uses quadratic phase distributions to defocus the edges of the aperture, effectively tapering the illumination and lowering sidelobe levels at the expense of beam broadening. In reflector antennas, feed defocusing introduces a quadratic phase error across the aperture, which reduces peak sidelobes by 3-5 dB for edge errors up to π/2 radians, as the phase variation diminishes contributions from the aperture periphery. This approach is particularly useful in scanned arrays where maintaining gain during defocus is critical. Subarraying groups array elements into contiguous or overlapped subarrays, each fed with independent phase control, to average out grating lobes and reduce overall sidelobe levels through constructive pattern synthesis. By phasing subarrays differently, the technique creates a composite array factor that fills in nulls and suppresses secondary peaks, achieving sidelobe improvements of 6-8 dB in large planar arrays without increasing the number of control channels proportionally. This method is widely adopted in phased arrays for radar, where subarray overlap randomizes periodicity effects.^[34] Random spacing disrupts the periodic structure of uniform arrays by positioning elements at irregular intervals, which scatters potential grating lobes and lowers their peak levels by randomizing constructive interference. In sparse arrays with interelement spacings up to several wavelengths, aperiodic distributions based on deterministic or stochastic methods can suppress grating lobes by 5-10 dB compared to periodic designs, while maintaining main beam integrity. Poisson disk sampling further enhances this by ensuring minimum spacing to avoid clustering, resulting in integrated sidelobe reductions suitable for wide-angle scanning.^[35] Polarization filtering exploits orthogonal polarizations to null sidelobe responses in targeted directions, particularly for interference suppression in dual-polarized arrays. By processing signals in the space-polarization domain, adaptive beamforming forms deep nulls (up to 30 dB) in sidelobe regions where jammers or multipath exhibit specific polarization states, without affecting the main beam. This technique integrates with array phasing to enhance angular resolution in cluttered environments.

Recent Developments

As of 2025, recent advances in sidelobe suppression include hybrid synthesis approaches combining genetic algorithms with the method of moments for optimized array patterns, achieving enhanced suppression in wideband applications. Additionally, metasurface-based transmitarrays and full-range amplitude-phase metacells have enabled low-profile antennas with sidelobe levels below -20 dB and improved gain flatness. Machine learning techniques for taper optimization have also emerged, offering automated designs for complex environments like 5G and radar systems.^[36]^[37]^[38]

Applications and Implications

Impact in Radar Systems

In radar systems, high sidelobe levels can lead to the detection of off-boresight clutter or jammers as false targets, introducing significant range and angular errors that degrade overall detection accuracy.^[39] For instance, in airborne radars, surface clutter returns entering through far sidelobes cause false alarms by distorting velocity measurements (e.g., reporting -80 m/s for stationary clutter) and angular positions (up to 70° offsets), complicating target discrimination in cluttered environments.^[40] These false detections reduce the probability of true target identification, as the radar processes sidelobe returns similarly to mainlobe echoes, leading to erroneous tracking.^[39] Sidelobe jamming exploits the gain in a radar's sidelobes to inject noise, overwhelming the receiver and masking legitimate returns, which heightens vulnerability to electronic countermeasures (ECM).^[41] Noise jammers positioned off-boresight can achieve effective signal-to-jammer ratios as high as 18.9 dB when sidelobes are only 23 dB down, but this vulnerability diminishes with ultra-low sidelobe levels (SLL) below -40 dB, requiring jammers to output substantially more power for comparable interference.^[41] Achieving SLL of -50 dB or lower is thus essential for ECM resistance, as it makes barrage jamming ineffective without extreme power levels, preserving radar sensitivity against standoff threats.^[41] In search radars, sidelobe blanking (SLB) techniques employ auxiliary antennas to suppress interference by comparing signals between the main and auxiliary channels, blanking outputs when sidelobe-entered signals exceed thresholds.^[42] These auxiliary systems, often omnidirectional or patterned to cover sidelobe regions, detect jammers or clutter in off-axis directions and inhibit main channel processing, reducing false alarms from deception jamming in dense electronic warfare scenarios.^[42] Multiple auxiliary antennas enhance coverage, minimizing blanking of true mainlobe targets while effectively countering multipath or noise jamming.^[42] Active electronically scanned array (AESA) radars mitigate sidelobe impacts through digital beamforming, routinely achieving first sidelobe levels around -30 dB by applying amplitude tapering and adaptive nulling across elements.^[43] This digital control enables dynamic suppression of interference in specific directions, improving resistance to jamming and clutter compared to traditional mechanically scanned systems.^[43]

Considerations in Wireless Communications

In wireless communications, sidelobes from base station antennas contribute to co-channel interference by radiating energy toward adjacent cells using the same frequency, potentially degrading signal quality and capacity. This unwanted radiation can violate FCC emission masks, which mandate attenuation of at least 43 + 10 log_{10}(P) dB for digital base stations, where P is the maximum output power in watts, to limit out-of-band emissions and protect neighboring channels. Typical first sidelobe levels in cellular antennas are approximately -20 dB relative to the main beam peak, providing a benchmark for interference potential in dense deployments.^[44]^[45] Sidelobes also exacerbate multipath propagation, where signals reflected from obstacles arrive via secondary paths created by lobe radiation patterns, leading to inter-symbol interference, fading, and reduced bit error rates in urban environments. In reconfigurable intelligent surface (RIS)-assisted systems, sidelobes act as diffuse scatterers, introducing unintended multipath components that complicate channel estimation and equalization.^[46] In 5G massive MIMO systems, high sidelobe levels in beamformed patterns limit spatial user isolation, as leaked energy interferes with co-scheduled users, necessitating advanced mitigation to achieve the required signal-to-interference-plus-noise ratios. Hybrid analog-digital beamforming addresses this by combining phase shifters for coarse analog control with digital precoding for fine amplitude tapering, effectively suppressing sidelobes while optimizing power efficiency in large antenna arrays.^[47]^[48] Coverage spillover occurs when sidelobe radiation extends beyond intended cell boundaries, delivering interfering signals to neighboring areas and elevating the overall noise floor, which can degrade receiver sensitivity by several decibels in frequency-reuse scenarios. 3GPP standards enforce sidelobe suppression through unwanted emission limits in TS 36.104 for LTE eNodeB (e.g., operating band emissions below -15 dBm/MHz in adjacent channels) and TS 38.104 for 5G gNodeB (e.g., similar spectral masks scaled for wider bandwidths), ensuring minimal inter-cell interference in multi-operator deployments.^[49]^[50]

References

[1]
Beamwidths and Sidelobe Levels - Antenna Theory
The sidelobes are smaller beams that are away from the main beam. These sidelobes are usually radiation in undesired directions which can never be completely ...
[2]
Side Lobes - Stanford CCRMA
The Discrete Time Fourier Transform (DTFT) is the appropriate Fourier transform for discrete-time signals of arbitrary length.
[3]
Sidelobes - an overview | ScienceDirect Topics
Sidelobes are defined as undesired radiation patterns produced by directional antennas due to diffraction effects, which occur at sharp discontinuities in ...
[4]
Phased Array Antenna Patterns—Part 3: Sidelobes and Tapering
Tapering provides a method to reduce antenna sidelobes at some expense to the antenna gain and main lobe beamwidth.
[5]
[PDF] Chapter 3 Diffraction - Home | EE293, Winter 18, Section 02
3.2 Fraunhofer diffraction. Fraunhofer diffraction, named after Joseph von Fraunhofer (1787-1826), a German op- tician, is actually Fresnel diffraction in ...
[6]
[PDF] Models of antennas, including center-fed antenna - Physics Courses
90% of the power is radiated into the main lobe, which has angular width. X/I, implying that the radiation from the antenna is highly directional, a fea-.
[7]
[PDF] Sparse Phased Array Antennas on Planar and ... - CDC Stacks
the main beam or main lobe of the antenna, which is the direction of maximum radiation, given by (θ0,φ0). Antennas will also have a side lobe region, which are ...
[8]
[PDF] CHAPTER 3: ANTENNAS
The sidelobes illustrated in Figure 3.3-5 originate primarily from the diffraction pattern of the circular aperture, whereas the back lobes generally originate ...
[9]
[PDF] C. Antenna Pattern
Nov 8, 2007 · * There frequently are also very small lobes that appear in the pattern, usually in the opposite direction of the main lobe. We call these tiny ...
[10]
[PDF] Earth Station Antenna Sidelobe Characteristics
These reference radiation diagram expressions define envelopes that should not be exceeded by more than 10% of the side- lobe peaks in an actual radiation ...
[11]
Chapter 3 Radio Telescopes and Radiometers
An antenna is a passive device that converts electromagnetic radiation in space into electrical currents in conductors or vice versa, depending on whether ...
[12]
[PDF] Chapter 11: Common Antennas and Applications
Jan 11, 2011 · 10) showed how the angular dependence of the far-fields of an aperture was proportional to the Fourier transform of the aperture excitation ...
[13]
[PDF] Aperture Antennas - ECEn 665
Feb 3, 2015 · For a rectangular aperture, the radiation pattern is given by a squared sinc function over angle, and for a circular aperture, it is a squared ...
[14]
Computing Antenna Patterns
This is called a 1D sinc function. The 1st null is at $\mu =\lambda/l$ , the 1st sidelobe is at $\mu = 3/2 (\lambda/l)$ and is of strength $2/(3 \pi)$ . The ...
[15]
[PDF] 1 LECTURE 13: LINEAR ARRAY THEORY
The total field of the array is equal to the product of the field created by a single element if located at the origin (element factor) and the array factor (AF):.
[16]
The first-level of the side lobe occurs at ______ dB for a uniform ...
Feb 18, 2022 · The first-level of the side lobe occurs at ______ dB for a uniform rectangular aperture antenna. (a) -13.26 (b) -6.63 (c) 3 (d) 8.5.
[17]
[PDF] Predicting Antenna Sidelobe Performance - DTIC
Aug 15, 1986 · Since the peak and not the average sidelobes degrade performance, the probability associated with peaks is a better indicator.
[18]
sidelobelevel - Peak and integrated side-lobe levels - MATLAB
When the sidelobes and mainlobes are identified, the peak and integrated sidelobe levels can be calculated from the formulas below. The peak sidelobe level (PSL) ...Missing: average | Show results with:average
[19]
[PDF] 7 8 17 18 27 2S 30 March 1967 1 December1967 30 Ma - EverySpec
- The ffrst major antenna side lobes shall be down at least 20 db from the main bcam, and all oZher lobes shall be at least SOdb down from the main beam. 6.6 ...
[20]
[PDF] Millimeter-Wave System EMC Study - DTIC
their side lobes suppressed to meet MIL-STD-469 requirements. Most milli- meter wave antennas investigated in this study had their major side lobes down. 20 ...
[21]
None
Below is a merged summary of the information on **Uniformly Illuminated Aperture Antennas (Sidelobes)**, consolidating all details from the provided segments into a comprehensive response. To maximize density and clarity, I will use a table in CSV format to capture the recurring and detailed information across the summaries, followed by a narrative summary that includes additional context and unique details not suited for the table. The table will focus on key attributes (Radiation Pattern, First Sidelobe Level, Number and Decay of Sidelobes, Positions of Sidelobes, and Gibbs Phenomenon) with page references and any mathematical or specific details. The narrative will address variations, additional insights, and useful URLs.
[22]
[PDF] Introduction to Radar Systems and Signal Processing
Nov 22, 2013 · For the uniform illumination pattern, the peak sidelobe is. 13.2 dB below the mainlobe peak. This is often considered too high in radar systems.
[23]
None
Below is a merged summary of non-uniform aperture illumination and tapering functions in antenna theory, based on the provided segments from *Antenna Theory: Analysis and Design* (3rd Ed. by Constantine A. Balanis). The response consolidates all relevant information into a comprehensive narrative, supplemented with detailed tables in CSV format where applicable to retain quantitative data and specifics efficiently. The content is organized by key topics (non-uniform illumination, tapering functions, effects, formulas, and examples), drawing from the most detailed and relevant segments (e.g., Chapters 6, 7, 12, 13, 14, 15, 16, and 17).
[24]
Phased Array Antenna Patterns—Part 2: Grating Lobes and Beam ...
In Part 1, we introduced beam pointing and the array factor. In Part 2, we introduced imperfections of grating lobes and beam squint.
[25]
Grating Lobes in Antenna Arrays
They occur in uniformly spaced arrays (arrays with an equal distance between adjacent elements) when the antenna element separation is too large. As an example, ...
[26]
Microwaves101 | Grating Lobes - Microwave Encyclopedia
A grating lobe occurs when you steer too far with a phased array and the main beam reappears on the wrong side. Elements must be spaced properly in order to ...
[27]
Phased Array Antenna Basics | PDF | Radar - Scribd
A major advance in phased array technology was made in the early 1950s with the replacement of ... grating lobes, and they are identical, or nearly identical to ...Phased Array Antenna Basics · The Vswr Is A Measure Of The... · Applications Of The Array In...
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Phased Array Antenna Patterns—Part 1 - Analog Devices
The array factor is calculated based on array geometry (d for our uniform linear array) and beam weights (amplitude and phase). Deriving the array factor for a ...
[29]
[PDF] Introduction to Antennas & Arrays
Sep 20, 2021 · C.A. Balanis, Antenna Theory: Analysis and Design, John Wiley & Sons ... Uniform linear array. Array pattern, beamwidth, sidelobe level.
[30]
[PDF] Antenna Arrays
To plot the radiation pattern pattern as a function of θ, we plot |f(ψ)| and a circle of radius ψ = kd = 2π λ λ. 2. = π below the plot, as shown in the ...
[31]
A Current Distribution for Broadside Arrays Which Optimizes the ...
A Current Distribution for Broadside Arrays Which Optimizes the Relationship between Beam Width and Side-Lobe Level.Missing: CL | Show results with:CL
[32]
https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/iet-map.2016.0883
[33]
[PDF] TAPERING OF ANTENNA ARRAY FOR EFFICIENT RADIATION ...
The amplitude distribution is often referred to as the amplitude weighting. The following section will present a review of techniques for synthesizing amplitude.
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Antenna Array Performance with Number of Elements for Aperture ...
Feb 18, 2016 · The amplitude tapering for side lobe reduction decreases the spatial efficiency (or aperture efficiency) of the antenna [13]. Along with the ...
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Sidelobe‐level reduction of a linear array using two amplitude ...
Jul 18, 2017 · The amplitude tapering for sidelobe reduction, however, reduces the spatial efficiency (or aperture efficiency) of the antenna.
[36]
https://www.sciencedirect.com/science/article/abs/pii/S1051200425003951
[37]
https://ieeexplore.ieee.org/document/11006946
[38]
https://ieeeaps.org/ieee-tap/for-readers/ieee-tap-videos
[39]
[PDF] Effects of RF Interference on Radar Receivers
Once the interference causes a high increase of false targets and strobing, the radar cannot recover the targets even when the target power increases to its ...
[40]
[PDF] Rejection of Surface Clutter in Far Sidelobes for Airborne Radars
In airborne radar, false alarms caused by surface clutter returns through antenna sidelobes need to be suppressed to detect the target of interest. Sidelobe ...
[41]
None
### Summary on Sidelobe Jamming and Low Sidelobe Levels (SLL) for ECM Resistance
[42]
Using Multiple Auxiliary Antennas for Sidelobe Blanking to Counter ...
Sidelobe blanking (SLB) is a technique employed in radar signal processing to inhibit detection when an unwanted signal enters the radar receiver through ...
[43]
[PDF] Frequently Asked Questions on AESAs and Highly-Integrated ...
... side lobe levels, which may be unacceptable for some applications due to regulatory, interference or stealth reasons. So gain control allows the AESA system ...
[44]
47 CFR 27.53 -- Emission limits. - eCFR
(2) For digital base stations, the attenuation shall be not less than 43 + 10 log (P) dB, unless a documented interference complaint is received from an ...<|control11|><|separator|>
[45]
Sidelobe Level (SLL) of an antenna radiation pattern - Elboxrf
Sidelobe Level is information how large (or small) are side lobes in the radiation pattern of an antenna. Usually they are compared to the maximum level of the ...
[46]
https://ieeexplore.ieee.org/document/10685980
[47]
Beamforming techniques for massive MIMO systems in 5G
Jun 30, 2017 · The main objective of this review paper is to discuss the state-of-the-art research on the most favourable types of beamforming techniques that can be deployed ...Missing: sidelobes isolation
[48]
Hybrid beamforming for massive MIMO in 5G wireless networks
Apr 11, 2024 · To accomplish the high sign strength in the principal curve, Chebyshev tapering has been utilized to stifle the side lobes signals. As such, the ...
[49]
[PDF] ETSI TS 136 104 V17.6.0 (2022-07)
This Technical Specification (TS) has been produced by ETSI 3rd Generation Partnership Project (3GPP). The present document may refer to technical ...Missing: sidelobe | Show results with:sidelobe
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[PDF] ETSI TS 138 104 V18.9.0 (2025-04)
The present document may refer to technical specifications or reports using their 3GPP identities. These shall be interpreted as being references to the ...