Radar Antennas, Arrays and Beamforming

Introduction and Context

A radar antenna is the electromagnetic interface between the radar hardware and the propagation medium. It transmits energy toward a region of interest, receives echoes from targets, and determines, either directly or through signal processing, the angular location of those targets. Antenna design therefore influences detection range, angular resolution, clutter suppression, measurement accuracy, electronic protection, and the number of targets that can be handled simultaneously.

Modern radar antennas range from mechanically rotated reflectors to electronically steered phased arrays and digitally controlled multiple-input multiple-output (MIMO) apertures. The central engineering problem is to control the spatial distribution of electromagnetic energy while satisfying constraints on frequency, bandwidth, power, size, cost, reliability, scan rate, and regulatory emissions.

This chapter develops the principles of radar antenna parameters, linear and planar arrays, beam steering, phased-array architectures, digital beamforming, monopulse angle estimation, adaptive arrays, calibration, sidelobe control, and MIMO radar. Emphasis is placed on assumptions, design trade-offs, implementation limitations, and the interpretation of antenna performance in operational radar systems.

Learning Objectives

After studying this chapter, the reader should be able to:

1. Define and interpret gain, directivity, beamwidth, efficiency, polarization, aperture, and sidelobe level.

2. Derive and use the array factor for uniformly spaced linear arrays.

3. Explain mechanical scanning, frequency scanning, phased-array steering, and hybrid architectures.

4. Distinguish analog, hybrid, and fully digital beamforming.

5. Explain monopulse angle estimation and identify its practical error sources.

6. Describe adaptive arrays, calibration procedures, and sidelobe-control methods.

7. Analyze the benefits and limitations of MIMO radar.

8. Select an antenna and beamforming architecture for a representative radar mission.

1. Fundamental Radar Antenna Parameters

1.1 Radiation pattern

The radiation pattern describes the variation of radiated power or field strength with direction. A three-dimensional pattern is usually represented using azimuth and elevation cuts. Important regions are the main beam, sidelobes, backlobe, and nulls. The main beam contains the intended high-gain radiation. Sidelobes are secondary maxima and are important because strong interference or clutter entering through them can mask weak targets.

The half-power beamwidth (HPBW) is the angular separation between directions at which the power is one-half of its peak value, or −3 dB. The first-null beamwidth is the separation between the first nulls surrounding the main beam. HPBW is commonly used as a practical measure of angular resolution, although actual resolution also depends on signal-to-noise ratio, target extent, waveform processing, and estimation algorithms.

1.2 Directivity, gain, and efficiency

Directivity is the ratio of radiation intensity in a specified direction to the average radiation intensity over all directions. It characterizes concentration of radiated power and excludes losses. Antenna gain includes radiation efficiency:

G(θ,φ) = ηD(θ,φ),

where G is gain, D is directivity, and η is the dimensionless total efficiency, including conductor, dielectric, mismatch, and related losses. Values may be expressed linearly or in decibels using 10 log10 for power ratios.

For an aperture antenna with effective aperture A_e, the receive relationship is

A_e = (λ²G)/(4π),

where λ is wavelength. This equation assumes the gain is specified in the direction of arrival and that polarization mismatch is excluded from G or treated separately. It demonstrates why a larger physical aperture or a shorter wavelength generally permits higher gain, although efficiency and scan performance may limit the practical result.

For a uniformly illuminated aperture of physical area A, a useful approximation is

D ≈ 4πA/λ².

The approximation is most reliable for an aperture with a well-defined broadside radiation pattern. Tapering, element spacing, blockage, edge diffraction, and scan loss reduce the realized gain.

1.3 Radar equation and antenna relevance

For a monostatic radar, the received power from a target at range R is commonly written as

P_r = (P_t G_t G_r λ² σ)/[(4π)³R⁴ L],

where P_t is transmitted power, G_t and G_r are transmit and receive gains toward the target, σ is radar cross section, and L represents aggregate losses. The equation assumes free-space spreading, a point target, a stationary or appropriately integrated return, and gains evaluated in the target direction. For a reciprocal antenna used in both functions, G_t = G_r = G. The R⁻⁴ dependence reflects two-way propagation loss and is a major reason for using high-gain antennas and coherent integration.

Antenna gain cannot be considered independently of beamwidth. Increasing aperture normally increases gain and narrows the beam, improving angular discrimination but reducing instantaneous angular coverage. A surveillance radar may therefore use rapid electronic scanning, multiple simultaneous beams, or waveform scheduling to compensate for narrow beams.

1.4 Polarization

Polarization describes the time-varying orientation of the electric-field vector. Linear, circular, and elliptical polarizations are used in radar. Polarization mismatch introduces a loss that depends on the transmitted and received polarization states. Polarization diversity can help distinguish objects, mitigate rain or surface effects, and improve classification, but it requires additional hardware and signal processing.

1.5 Aperture and scan performance

An antenna can have high broadside gain yet suffer substantial scan loss away from broadside. Scan loss results from projected aperture reduction, element-pattern reduction, impedance changes, mutual coupling, and beamformer limitations. A simplified projected-aperture argument suggests a factor proportional to cos θ for scan angle θ, but this is not a universal scan-loss formula; real arrays require electromagnetic and measured characterization.

2. Array Theory

2.1 Array factor

The pattern of an array is determined by the individual element pattern and the array factor. For identical, similarly oriented elements without significant mutual coupling, the total field can be approximated as

E_total(θ,φ) = E_element(θ,φ) AF(θ,φ).

For a uniform linear array of N elements spaced d along an axis, with progressive excitation phase β, the array factor is

AF(ψ) = Σ from n=0 to N−1 exp(jnψ),

where

ψ = kd cos θ + β, k = 2π/λ.

Here θ is measured from the array axis, and the sign convention for β depends on the assumed time and spatial phase conventions. The principal beam is directed toward θ_0 when

β = −kd cos θ_0.

The closed form is

AF(ψ) = exp[j(N−1)ψ/2] sin(Nψ/2)/sin(ψ/2).

The exponential factor affects phase but not magnitude. This result assumes identical elements, uniform amplitude, fixed spacing, and negligible mutual coupling.

2.2 Grating lobes

A grating lobe is an unwanted beam of approximately main-beam strength caused by spatial undersampling. For a broadside array scanned to θ_0, a common design condition for avoiding visible grating lobes over a specified scan sector is approximately

d ≤ λ/[1 + |sin θ_max|]

when θ is measured from broadside and θ_max is the maximum scan angle. The exact condition depends on coordinate definitions and element pattern. In many wide-scan planar arrays, spacing near λ/2 or less is selected, but this increases the number of elements, feed complexity, and cost.

2.3 Beamwidth and sidelobes

For a uniformly illuminated broadside linear array, the HPBW is approximately

HPBW ≈ 0.886 λ/(Nd)

radians when the array length is approximately Nd and the array is sufficiently large. A more precise expression uses the physical length (N−1)d and depends on the chosen angular coordinate. Therefore, the formula is a design estimate rather than an exact result for small arrays.

Uniform excitation gives maximum directivity for a fixed aperture but has relatively high sidelobes; the first sidelobe of a large uniform array is approximately −13.2 dB relative to the main beam. Amplitude tapering, such as Taylor, Dolph–Chebyshev, or cosine tapering, reduces sidelobes at the cost of increased beamwidth and reduced gain. A taper should be specified by its sidelobe objective, beamwidth penalty, and robustness to errors.

2.4 Planar arrays

A planar array uses elements positioned in two dimensions. Its pattern can often be treated as the product of two one-dimensional array factors for a rectangular separable array with separable excitation. Planar arrays provide independent azimuth and elevation control and are suitable for multifunction radar. Nonseparable tapers, irregular arrays, sparse arrays, and conformal arrays require more general two-dimensional analysis.

3. Scanning Architectures

3.1 Mechanical scanning

A mechanically rotated antenna changes pointing direction by physically moving the aperture. It can provide high efficiency and relatively low RF channel count, but scan rate is limited by inertia, drive power, vibration, and maintenance. Mechanical systems remain attractive for long-range surveillance and cost-sensitive applications.

3.2 Frequency scanning

In a frequency-scanned array, frequency-dependent phase progression in a feed network changes the beam angle. It can scan rapidly without phase shifters, but beam direction becomes coupled to operating frequency. This coupling complicates waveform design, range measurement, wideband operation, and simultaneous beams.

3.3 Phased-array scanning

A phased array steers the beam by controlling the relative phase of element excitations. For narrowband signals, a phase shift approximates the required time delay. For a signal with bandwidth B centered at f_c, the narrowband approximation is generally acceptable when the differential delay across the aperture produces negligible beam squint over B. True-time-delay beamforming is preferred when wide bandwidth or large scan angles make phase-only steering inadequate.

In a transmit array, element excitations are selected to form one or more beams. In a receive array, the received channels are phase-shifted and summed. A monostatic phased array may use separate transmit and receive beamformers or a common reciprocal aperture.

3.4 Architectures

A passive electronically scanned array often uses one high-power transmitter and a corporate feed with phase shifters. An active electronically scanned array uses transmit/receive modules distributed across the aperture. Active arrays offer graceful degradation, flexible waveform and beam control, and improved reliability, but require thermal management, calibration, power conversion, and many RF channels.

Hybrid beamforming divides control between analog RF networks and a smaller number of digital channels. It reduces converter count and data movement while retaining some digital flexibility. Fully digital arrays digitize signals at or near each element or subarray. They support multiple simultaneous beams, adaptive nulling, and waveform diversity, but impose demanding requirements on analog bandwidth, dynamic range, clock synchronization, data transport, and computation.

4. Digital Beamforming

For M received channels represented by complex baseband samples x, a beamformer output is

y = wᴴx,

where w is the complex weight vector and ᴴ denotes conjugate transpose. The weight phase aligns signals from the desired direction; amplitude weights control taper and sidelobes. For a steering vector a(θ), an ideal conventional beamformer may use w proportional to a(θ_0), with normalization selected according to gain or noise criteria.

Digital beamforming enables beam formation after digitization. A radar can create several beams from the same data, change beam shapes adaptively, and form difference channels for angle estimation. Its limitations include quantization noise, receiver gain mismatch, phase drift, latency, finite word length, and high data rates. A practical architecture must also address electromagnetic compatibility and cyber security of software-controlled beamforming functions.

For wideband signals, frequency-domain beamforming or true-delay methods prevent beam squint more effectively than a single phase-shift vector. Subband processing divides the signal into frequency bins and applies frequency-dependent steering weights.

5. Monopulse Angle Estimation

Monopulse radar estimates angular error from a single pulse or coherent processing interval, rather than comparing target amplitudes from successive scans. A common amplitude-comparison monopulse system forms a sum channel Σ and a difference channel Δ. Near boresight, the normalized monopulse ratio is approximately

m = Re{Δ/Σ},

where Re denotes the real part for an appropriate in-phase implementation. Over a limited angular region,

m ≈ Kθ θ_e,

where θ_e is angular error and Kθ is a calibration slope. The exact slope depends on aperture, beamformer normalization, frequency, and channel definitions; it must normally be obtained from analysis, simulation, or calibration.

A phase-comparison monopulse system compares phase between subapertures and is especially useful when amplitude stability is difficult. Monopulse processing is resistant to target amplitude fluctuations because sum and difference signals are formed from the same echo. Nevertheless, glint, multipath, extended targets, sidelobe responses, channel imbalance, radome distortion, and low signal-to-noise ratio can produce angle bias.

The sum channel usually supports detection, while the difference channel supplies signed angular error. For two-dimensional tracking, separate azimuth and elevation difference channels are required. Monopulse does not eliminate the need for accurate calibration: an incorrect difference-channel phase or amplitude changes the slope and may reverse or bias the estimated error.

6. Adaptive Arrays and Sidelobe Control

Adaptive beamforming uses received data to modify weights in response to interference and clutter. A widely used criterion minimizes output power subject to a distortionless response in the desired direction. If R is the interference-plus-noise covariance matrix and a is the desired steering vector, the minimum-variance distortionless-response (MVDR) weights are

w_MVDR = R⁻¹a/(aᴴR⁻¹a).

This expression assumes R is nonsingular, the steering vector is accurately known, and the desired signal is not incorrectly included as interference. In practice, diagonal loading replaces R by R + μI, where μ is a nonnegative loading factor and I is the identity matrix. Loading improves robustness when the covariance estimate is poor or the steering vector is mismatched, but excessive loading reduces adaptive suppression.

Adaptive processing may place nulls toward jammers or clutter while preserving the main beam. It is limited by the number of independent channels, sample support, stationarity of the environment, covariance estimation error, target self-nulling, mutual coupling, and hardware dynamic range. A radar should not rely exclusively on adaptive nulling; deterministic sidelobe control, frequency agility, waveform design, and scheduling remain important.

Sidelobe-control methods include amplitude tapering, phase-only optimization, element placement, subarraying, auxiliary antennas, adaptive nulling, and transmit waveform diversity. Lower sidelobes usually require reduced aperture efficiency or increased processing complexity. The appropriate objective is mission-dependent: a weather radar, air-surveillance radar, and electronic-support-resistant radar may have different sidelobe priorities.

7. Calibration and Error Management

Array performance depends on the accuracy of channel amplitude, phase, delay, frequency, and position. Errors arise from manufacturing tolerances, temperature, aging, mutual coupling, cable variation, oscillator phase noise, power-amplifier drift, receiver compression, and radome effects.

Calibration commonly includes:

• factory calibration using conducted or near-field measurements;
• built-in calibration using couplers, reference receivers, or calibration loops;
• over-the-air calibration using a known source or transponder;
• periodic monitoring over temperature, frequency, power, and scan angle.

A practical calibration chain measures complex channel response, estimates correction coefficients, validates beam pointing and sidelobe levels, and records uncertainty. Calibration must be traceable to defined reference conditions. A single boresight measurement is insufficient for a wideband, wide-scan array because mutual coupling and element patterns vary with frequency and direction.

Calibration data should be version-controlled and protected because unauthorized modification can redirect beams, degrade detection, or create unsafe emissions. Built-in tests should identify failed modules and permit graceful degradation rather than masking faults.

8. MIMO Radar

MIMO radar uses multiple transmit waveforms, multiple receive channels, or both to create spatial diversity. If transmitted waveforms are sufficiently separable by correlation, the receiver can estimate responses for different transmit–receive paths. The resulting virtual array may provide more spatial samples than the number of physical elements.

There are two broad forms. In statistical MIMO radar, widely separated antennas illuminate a target from different aspects, producing diversity in target scattering. In colocated MIMO radar, antennas are close relative to the target range and jointly synthesize transmit and receive spatial channels. Colocated systems can improve parameter estimation and waveform flexibility, but their benefit depends on waveform orthogonality, signal-to-interference ratio, calibration, and target scattering.

MIMO is not automatically superior to a coherent phased array. Orthogonal waveforms may reduce coherent transmit gain, increase receiver complexity, and create cross-correlation leakage. The comparison must consider detection probability, angular resolution, ambiguity, data rate, power-aperture product, waveform design, and computational burden. Hybrid systems can combine coherent beam steering for energy concentration with selected waveform diversity for estimation or interference management.

9. Worked Design Example: A Linear Receive Array

Consider a 16-element uniform linear receive array operating at 10 GHz with element spacing d = λ/2. The wavelength is

λ = c/f ≈ (3 × 10⁸)/(10 × 10⁹) = 0.03 m.

Thus d = 0.015 m, and the approximate physical span from the first to the last element is (N−1)d = 15(0.015) = 0.225 m. Using the large-array broadside estimate with length Nd = 0.24 m,

HPBW ≈ 0.886λ/(Nd) = 0.886(0.03)/(0.24) ≈ 0.111 rad ≈ 6.4°.

This is an approximate half-power beamwidth; electromagnetic simulation and measurement are required for a final design. If the array is uniformly weighted, the first sidelobe is approximately −13.2 dB. Applying a taper could reduce sidelobes, but the beamwidth would increase and the peak gain would decrease.

For steering the beam to 30° from broadside, the progressive phase under the convention ψ = kd sin θ + β is

β = −kd sin 30° = −(2π/λ)(λ/2)(0.5) = −π/2 rad,

or −90° between adjacent elements. The sign changes if the opposite time or coordinate convention is used; the physical requirement is that adjacent-element phase differences compensate propagation phase from the desired direction.

The example illustrates three design facts: beamwidth is primarily controlled by aperture, steering requires a phase progression, and sidelobe reduction trades against gain and resolution.

10. Illustrative Case: Multifunction Coastal Surveillance Radar

Background

Consider an illustrative coastal radar required to detect small vessels, track aircraft, and operate in the presence of sea clutter and occasional communication interference. The system must scan rapidly in azimuth, measure elevation, and maintain operation if some RF modules fail.

Problem

A mechanically rotated high-gain antenna provides adequate detection range but cannot revisit rapidly enough for maneuvering aircraft. A fully digital element-level array would provide flexibility but exceeds the initial power, cooling, and data-processing budget.

Analysis and approach

A hybrid active array is selected. Subarrays contain active transmit/receive modules, with digital receivers assigned to subarray outputs. Analog phase control provides rapid coarse steering, while digital beamforming forms simultaneous surveillance and tracking beams. Taylor-type amplitude tapering is applied in the surveillance beam to reduce sea-clutter sidelobes. A separate adaptive receive processor uses covariance estimates to suppress localized interference, with diagonal loading to reduce sensitivity to steering mismatch.

Monopulse sum, azimuth-difference, and elevation-difference channels support precision tracking. Calibration loops monitor module phase and gain, while over-the-air calibration verifies beam pointing through a known reference source. Frequency-dependent weights are used across subbands to limit beam squint.

Outcome

The architecture provides faster revisit than mechanical scanning, more graceful degradation than a single-transmitter passive array, and greater flexibility than a purely analog system. Its costs are increased thermal design effort, calibration complexity, digital data transport, and software assurance requirements.

Learning points

The correct antenna architecture is mission-dependent. Beamforming, waveform scheduling, calibration, clutter processing, and maintenance planning must be designed as one system. A nominally excellent radiation pattern is not sufficient if it cannot be maintained over temperature, scan angle, aging, and failures.

11. Contemporary Developments and Governance

Gallium nitride (GaN) power amplifiers are enabling higher power density and improved efficiency in active arrays, although thermal management remains critical. Photonic beamforming and optical distribution are being investigated for wideband, low-loss signal transport. Compressive and sparse-array methods seek to reduce hardware count, but they can introduce ambiguity, calibration sensitivity, and nonlinear processing requirements. Machine learning is being explored for beam prediction, calibration-error estimation, interference classification, and adaptive resource management. Such methods should be validated against distribution shifts, adversarial interference, explainability requirements, and safety constraints; they should complement, not obscure, physically interpretable controls.

Radar emissions must comply with national spectrum regulations and applicable electromagnetic-exposure and safety requirements. Beam steering and adaptive nulling should not create unintended interference to other services. Security controls are needed for software-defined beamforming, calibration files, timing references, and networked sensor data. In defense and civil applications alike, operators should retain authority to constrain emissions and verify automated decisions.

12. Best-Practice Design Procedure

A robust antenna and beamforming design should:

1. Define mission measures such as coverage, revisit time, angular accuracy, detection range, and allowable sidelobes.

2. Convert these measures into aperture, gain, beamwidth, scan, bandwidth, and polarization requirements.

3. Select mechanical, phased, hybrid, digital, or MIMO architecture using power, cooling, cost, reliability, and data-rate constraints.

4. Check grating lobes, scan loss, beam squint, mutual coupling, and polarization performance over the full operating region.

5. Design calibration and built-in test before finalizing the hardware.

6. Evaluate sidelobe and adaptive-processing performance using representative clutter and interference, not only ideal noise.

7. Quantify uncertainty, failure modes, cyber risks, and regulatory constraints.

8. Validate with electromagnetic simulation, hardware-in-the-loop testing, near-field or far-field measurement, and operational trials.

Chapter Summary

Radar antennas determine how electromagnetic energy is transmitted, received, and resolved in angle. Gain, directivity, aperture, efficiency, polarization, beamwidth, and sidelobe level are interrelated performance parameters. Array factors explain how element spacing and excitation create beams, sidelobes, and grating lobes. Mechanical, frequency-scanned, phased, hybrid, and fully digital architectures offer different compromises in speed, bandwidth, flexibility, complexity, and cost.

Digital beamforming forms beams through complex channel weights and enables simultaneous beams and adaptive processing. Monopulse systems estimate angular error from sum and difference channels but depend strongly on calibration and are affected by glint, multipath, and mismatch. Adaptive arrays can suppress interference using covariance-based weights, although robustness requires adequate data, accurate steering information, and regularization. Calibration is a system-level activity covering amplitude, phase, delay, temperature, frequency, scan angle, and failure monitoring. MIMO radar introduces spatial and waveform diversity, but its benefits must be assessed against correlation leakage, power distribution, hardware complexity, and processing requirements. Effective radar antenna engineering therefore integrates electromagnetic design, RF hardware, digital signal processing, thermal management, calibration, governance, and operational mission analysis.

Key Terms

Aperture: Physical or effective radiating area that determines spatial concentration of electromagnetic energy.

Array factor: Pattern contribution produced by the relative positions and excitations of array elements.

Beam squint: Frequency-dependent change in beam direction when phase shifts approximate true time delays.

Beamwidth: Angular width of a beam, commonly specified at the half-power points.

Calibration: Measurement and correction of channel, array, and system errors.

Directivity: Ratio of radiation intensity in a direction to average radiation intensity.

Grating lobe: Unwanted high-level beam caused by spatial undersampling, usually excessive element spacing.

Gain: Directivity including antenna efficiency.

HPBW: Half-power beamwidth, the angular separation between −3 dB points.

Monopulse: Angle-estimation technique using simultaneous sum and difference channels.

MIMO radar: Radar using multiple transmit and/or receive channels to obtain spatial or waveform diversity.

MVDR: Minimum-variance distortionless-response adaptive beamforming criterion.

Phased array: Array whose beam is electronically steered by controlling element phase or delay.

Polarization: Orientation and evolution of the electric-field vector.

Radar cross section: A measure of a target’s ability to scatter energy toward the radar.

Scan loss: Reduction in antenna performance as the beam is steered away from boresight.

Sidelobe: Secondary radiation maximum outside the main beam.

Steering vector: Complex response of array channels for a specified direction and frequency.

Taylor taper: Amplitude weighting method used to control sidelobe levels with a specified beamwidth trade-off.

True-time-delay beamforming: Beam steering using physical or equivalent delays to preserve direction over bandwidth.

Review Questions

Short Answer Questions

1. Distinguish antenna directivity from antenna gain.

2. What is a grating lobe, and why is element spacing important?

3. Explain the purpose of sum and difference channels in monopulse radar.

4. State two advantages and two limitations of digital beamforming.

5. Why is calibration required in an active phased array?

Long Answer Questions

1. Derive the array factor of a uniformly excited linear array and explain the effects of element number, spacing, and progressive phase.

2. Compare mechanical scanning, frequency scanning, phased-array scanning, and true-time-delay scanning.

3. Explain MVDR beamforming, including its assumptions, limitations, and the purpose of diagonal loading.

4. Discuss the principal architecture, performance, and maintenance trade-offs between passive, active, hybrid, and fully digital arrays.

5. Explain MIMO radar and critically compare colocated MIMO with a conventional coherent phased array.

Analytical / Application Questions

1. A 32-element broadside linear array operates at 6 GHz with half-wavelength spacing. Estimate its HPBW using the large-array approximation and discuss how a sidelobe-reducing taper would change the result.

2. Design a calibration strategy for a wideband active array operating from −40 °C to +60 °C and scanning ±60°. Identify measurements, reference sources, update intervals, and validation tests.

3. Select an antenna and beamforming architecture for a radar that must track fast aircraft, detect low-flying targets in clutter, and continue operating after several module failures. Justify the choice using coverage, reliability, thermal, processing, and calibration considerations.

Multiple Choice Questions with Answers

Question 1

Which parameter includes radiation efficiency as well as directional concentration of radiation?

A. Directivity

B. Gain

C. Beamwidth

D. Polarization

Correct Answer: B. Gain

Question 2

For a uniformly illuminated large linear array, the approximate first sidelobe level is:

A. −3 dB

B. −6 dB

C. −13.2 dB

D. −30 dB

Correct Answer: C. −13.2 dB

Question 3

What is the principal cause of a grating lobe?

A. Insufficient receiver bandwidth

B. Excessive element spacing relative to wavelength

C. Low target radar cross section

D. Polarization rotation only

Correct Answer: B. Excessive element spacing relative to wavelength

Question 4

Which beamforming method is especially associated with simultaneous sum and difference channels for angle estimation?

A. Monopulse processing

B. Frequency scanning

C. Pulse compression

D. Doppler filtering

Correct Answer: A. Monopulse processing

Question 5

In the expression y = wᴴx, what does x represent?

A. The wavelength scalar

B. The array channel data vector

C. The target radar cross section

D. The antenna physical area

Correct Answer: B. The array channel data vector

Question 6

The MVDR beamformer primarily seeks to:

A. Maximize physical aperture size

B. Minimize output interference-plus-noise power while preserving a desired response

C. Eliminate the need for calibration

D. Force all sidelobes to zero

Correct Answer: B. Minimize output interference-plus-noise power while preserving a desired response

Question 7

What is beam squint?

A. A change in beam direction with frequency

B. A reduction in target radar cross section

C. A mechanical antenna vibration

D. A polarization mismatch loss only

Correct Answer: A. A change in beam direction with frequency

Question 8

For a 10 GHz radar, using c = 3 × 10⁸ m/s, the wavelength is approximately:

A. 0.003 m

B. 0.03 m

C. 0.3 m

D. 3 m

Correct Answer: B. 0.03 m

Question 9

A key advantage of MIMO radar is the ability to obtain:

A. Spatial or waveform diversity

B. Infinite transmit power

C. Zero calibration sensitivity

D. Automatic elimination of clutter

Correct Answer: A. Spatial or waveform diversity

Question 10

Why is diagonal loading used in adaptive beamforming?

A. To increase wavelength

B. To improve robustness to covariance and steering-vector errors

C. To create mechanical rotation

D. To convert gain into directivity

Correct Answer: B. To improve robustness to covariance and steering-vector errors