Microwave Antennas, Propagation and Link Engineering

Introduction and context

Microwave systems convert guided electromagnetic energy into radiated waves, allow those waves to propagate through space or the atmosphere, and recover useful information at a receiving terminal. Antenna design, propagation analysis, and link engineering are therefore inseparable activities. A high-gain antenna cannot compensate indefinitely for excessive atmospheric attenuation, while an excellent propagation path is of little value if impedance mismatch, polarization loss, or inadequate receiver sensitivity limits the link.

At postgraduate level, microwave link engineering requires simultaneous attention to electromagnetic theory, system budgets, statistical propagation effects, hardware constraints, spectrum regulation, and reliability. This chapter develops that integrated view for terrestrial point-to-point links, satellite links, radar-related systems, and other microwave applications.

Learning objectives

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

1. Explain the radiation mechanism, principal parameters, and practical types of microwave antennas.
2. Relate antenna aperture, gain, beamwidth, efficiency, polarization, and impedance.
3. Analyse free-space and atmospheric propagation at microwave frequencies.
4. Construct a microwave link budget and assess fade margin and availability.
5. Explain multipath fading, rain attenuation, ducting, depolarization, and diversity methods.
6. Select antennas and mitigation techniques for a specified engineering scenario.
7. Evaluate practical, regulatory, environmental, and safety issues in microwave deployment.

1. Electromagnetic basis of microwave radiation

An antenna is a transducer between a guided electromagnetic wave and a radiated wave. In a transmission line or waveguide, electric and magnetic fields are primarily confined to the guiding structure. At an antenna aperture or radiating element, the fields are redistributed so that a portion of the electromagnetic energy propagates outward.

In the far field, the electric and magnetic fields are approximately transverse to the direction of propagation and satisfy

where E is electric-field magnitude in volts per metre, H is magnetic-field magnitude in amperes per metre, and η₀ is the intrinsic impedance of free space. This relation assumes a plane wave in free space.

The time-average power density of a plane wave is

where S is in watts per square metre for sinusoidal peak field amplitudes. If root-mean-square field amplitudes are used, the factor 2 is omitted. Consistent use of peak or rms quantities is essential.

The far-field region begins approximately at

where D is the largest antenna dimension and λ is wavelength. The additional practical condition R_ff ≫ λ is also required. In the far field, the angular radiation pattern is independent of distance apart from the overall 1/R amplitude decrease. The reactive near field and radiating near field have different field structures and should not be used for ordinary link-budget calculations.

2. Principal antenna parameters

2.1 Radiation pattern and beamwidth

The radiation pattern describes field or power variation with direction. The main lobe contains the intended radiation; sidelobes represent radiation in other directions, and the back lobe is radiation approximately opposite the main beam. The half-power beamwidth (HPBW) is the angular separation between directions at which power falls to one-half of its maximum, or −3 dB. The first-null beamwidth is the angular separation between the first nulls surrounding the main lobe.

A narrow beam generally implies high directivity and improved spatial frequency reuse, but it also increases pointing sensitivity. Sidelobe control is important in radar, satellite frequency reuse, and dense microwave networks because sidelobes can produce interference.

2.2 Directivity, gain, and efficiency

Directivity is the ratio of radiation intensity in a specified direction to the average radiation intensity over all directions. If U(θ,φ) is radiation intensity and P_rad is total radiated power,

The maximum directivity is normally quoted for an antenna. Antenna gain includes radiation efficiency:

where G is gain, D is directivity, and η_a is total antenna efficiency, dimensionless. Efficiency includes conductor, dielectric, reflection, and other losses. Gain is commonly expressed in dBi, referenced to an isotropic radiator:

An isotropic radiator is an ideal reference and is not a physically realizable antenna.

2.3 Effective aperture and reciprocity

The receiving effective aperture A_e relates incident power density to available received power:

For a receiving antenna with gain G,

This relation assumes polarization match, conjugate impedance match, and an incident plane wave. More generally, polarization and mismatch factors must be included separately. Reciprocity states that, for a linear passive reciprocal antenna, the transmitting and receiving patterns are identical when the same polarization and reference conditions are used.

2.4 Polarization

Polarization is the trajectory followed by the electric-field vector at a fixed location. Linear, circular, and elliptical polarizations are common. A polarization mismatch produces a loss factor. If the transmitting and receiving unit polarization vectors are p_t and p_r, the polarization coupling factor is

where the asterisk denotes complex conjugation. For two linearly polarized antennas misaligned by angle ψ, L_p = cos²ψ. In decibels, polarization loss is −10 log₁₀(L_p). Circular polarization is useful where orientation changes, but the handedness of circular polarization must be matched; opposite senses ideally produce zero coupling.

2.5 Input impedance and voltage standing-wave ratio

The antenna input impedance is

where R_rad is radiation resistance, R_loss represents dissipative resistance, and X_A is reactance. If an antenna is connected to a line with characteristic impedance Z₀, the reflection coefficient is

and the voltage standing-wave ratio is

These expressions assume a single-port impedance interface. Mismatch loss for available power transfer is

2.6 Antenna temperature and noise

A receiving antenna collects thermal radiation from the environment. Its noise contribution can be represented by antenna temperature T_A. For a matched receiver of noise temperature T_sys, thermal noise power over bandwidth B is

where k = 1.380649 × 10⁻²³ J/K is Boltzmann’s constant. The system noise temperature includes antenna, feed, receiver, and external contributions referred to a common reference plane. At microwave frequencies, sky noise, atmospheric emission, rain, and losses in the feed can be significant.

3. Microwave antenna types and selection

3.1 Aperture antennas

Horn antennas are flared waveguides. They provide moderate gain, broad bandwidth, low loss, and relatively predictable patterns. They are used as standard-gain measurement antennas, feeds, and compact communication antennas.

Parabolic reflector antennas use a feed to illuminate a reflecting paraboloid. A ray emerging from the focus reflects approximately parallel to the axis, producing a narrow beam. Their approximate gain is

where D is reflector diameter and η_ap is aperture efficiency, often between about 0.5 and 0.7 in practical systems, though the actual value depends on illumination, spillover, blockage, surface accuracy, and losses. The formula assumes a well-designed reflector operating in its intended frequency range.

The approximate half-power beamwidth of a circular reflector is often estimated as

The coefficient depends on aperture illumination and pattern definition; it is an engineering approximation, not a universal constant.

Cassegrain and Gregorian reflectors use subreflectors to place the feed near the main reflector vertex. They simplify feed access and can improve mechanical packaging, but subreflector blockage and alignment must be considered.

3.2 Microstrip patch antennas

A rectangular microstrip patch consists of a conducting patch over a dielectric substrate with a ground plane. It is low profile and suitable for arrays and integrated microwave equipment. Its disadvantages include relatively narrow impedance bandwidth, dielectric loss, surface-wave excitation, and sensitivity to substrate properties.

For a first design estimate, the effective patch length is close to one-half guided wavelength, not one-half free-space wavelength. Fringing fields increase the effective electrical length, so accurate design requires effective dielectric constant and fringing corrections, followed by electromagnetic simulation and measurement.

3.3 Arrays

An array combines elements with controlled positions and excitations. For identical elements, the total pattern can be written conceptually as

where F_e is the element pattern and AF is the array factor. Beam steering is obtained by progressive phase excitation. For a uniform linear array with element spacing d and phase difference β, the array-factor phase variable is

where k = 2π/λ. If d exceeds approximately λ/2, grating lobes may occur when the beam is scanned, producing unwanted main-beam replicas. Phased arrays provide electronic steering and multiple beams but require accurate phase, amplitude, thermal, and calibration control.

3.4 Lens, dielectric, and slotted antennas

Lens antennas transform spherical or cylindrical wavefronts into approximately planar wavefronts and are useful at millimetre-wave frequencies. Dielectric antennas can be compact and low loss when carefully designed. Slotted waveguide arrays offer high efficiency and robust power handling, especially in radar and communication systems.

Selection depends on gain, bandwidth, polarization, scan requirement, mass, wind loading, radome effects, cost, manufacturing tolerance, and regulatory emission limits—not merely on nominal gain.

4. Propagation mechanisms

4.1 Free-space propagation

For a line-of-sight link in free space, the Friis transmission equation is

where P_t and P_r are received and transmitted powers in watts, G_t and G_r are dimensionless antenna gains in the link direction, λ is wavelength in metres, and R is separation in metres. The assumptions are far-field operation, line of sight, matched polarizations, matched impedances, no additional losses, and a free-space environment.

The free-space path loss is

or, in decibels with R in kilometres and f in gigahertz,

The received power in dBm is consequently

where L_add includes feeder, radome, polarization, mismatch, atmospheric, and implementation losses.

4.2 Earth curvature and radio horizon

A line-of-sight path is influenced by Earth curvature and atmospheric refraction. Under a standard effective-Earth-radius approximation, the radio horizon distance in kilometres is approximately

where h₁ and h₂ are antenna heights in metres. This expression is an engineering approximation based on a commonly used effective Earth radius; terrain obstruction, local refractivity, and Fresnel clearance must also be checked.

The first Fresnel-zone radius at a point along a path is

where d₁ and d₂ are distances from that point to the two terminals. A common planning rule is to keep at least 60% of the first Fresnel zone clear of obstacles. This is not a law; it is a practical criterion balancing diffraction loss and construction constraints.

4.3 Atmospheric absorption and scattering

Oxygen and water vapour absorb microwave energy through molecular resonance. Specific attenuation γ in dB/km depends strongly on frequency, pressure, temperature, and water-vapour density. Strong oxygen absorption occurs near 60 GHz, while water-vapour absorption is prominent near 22 GHz and other higher-frequency lines. These bands may be used deliberately for short-range frequency reuse or sensing, but they are unsuitable for long links unless the loss is acceptable.

Rain attenuation is especially important above roughly 10 GHz. A widely used engineering model expresses specific rain attenuation as

where R is rain rate in millimetres per hour and k and α are frequency-, polarization-, and elevation-dependent empirical coefficients. Total attenuation is not simply γ_R times the full path length because rain is spatially variable; effective path-length models are therefore used. Design should employ the relevant regional propagation recommendation or measured climatic data.

Cloud, fog, and wet antenna surfaces also contribute loss at sufficiently high frequencies. Wet radomes may cause reflection, depolarization, and pattern distortion.

4.4 Multipath and fading

Reflections from terrain, buildings, water, and atmospheric layers create multiple delayed components. Their vector addition can produce rapid amplitude and phase variation. Flat fading affects the whole signal bandwidth approximately equally; frequency-selective fading produces amplitude and phase distortion across the channel.

A simplified two-ray model illustrates interference between direct and reflected paths:

where Γ is the reflection coefficient and Δφ is the phase difference. The model is useful for insight but does not replace site-specific propagation prediction.

Multipath fading is often statistically described using Rayleigh or Rician distributions. Rayleigh fading is appropriate when no dominant direct component exists; Rician fading includes a dominant component and scattered components. These models are approximations whose validity must be checked against measurements and terrain conditions.

4.5 Atmospheric ducting and anomalous propagation

Strong vertical refractivity gradients can trap microwave energy in atmospheric ducts. Ducting may extend radio range but can also produce severe fading, interference, or unexpected signals from distant transmitters. Super-refraction and sub-refraction alter the effective radio horizon. Coastal regions and large bodies of water can be especially susceptible to evaporation ducts.

5. Microwave link engineering

5.1 Link-budget structure

A link budget accounts for all gains and losses between a defined transmitter and receiver reference plane. A robust budget includes:

• transmitter output power and feeder loss;
• transmit antenna gain;
• free-space path loss;
• atmospheric, rain, and scintillation losses;
• polarization and impedance mismatch losses;
• receive antenna gain and feeder loss;
• receiver noise figure or noise temperature;
• required signal-to-noise ratio or carrier-to-noise ratio;
• implementation and interference margins.

The receiver thermal noise in dBm is

for a room-temperature reference of approximately 290 K, where B_Hz is noise bandwidth in hertz and NF is receiver noise figure in decibels. The −174 dBm/Hz value is an approximation to 10log₁₀(kT/1 mW) at 290 K.

If receiver sensitivity is specified as the minimum required input power P_min, the fade margin is

where P_r,clear is clear-sky received power in dBm. A positive margin indicates tolerance to additional attenuation.

Worked example: terrestrial microwave link

A 12 GHz point-to-point link has a path length of 25 km. The transmitter output is 20 dBm, transmit and receive antenna gains are 35 dBi each, and total feeder loss is 4 dB. Allow 2 dB for atmospheric and miscellaneous clear-sky losses. The receiver requires −72 dBm.

First, calculate free-space loss:

Since 20log₁₀(12) ≈ 21.58 dB and 20log₁₀(25) ≈ 27.96 dB,

The clear-sky received power is

Therefore,

The link has approximately 14 dB clear-sky fade margin. Whether this is adequate depends on rain climate, path geometry, modulation, required availability, and the applicable outage model. The calculation does not by itself guarantee 99.99% availability.

5.2 Availability and fade-countermeasure design

Availability is the fraction of time a service meets its specified performance. A target of 99.99% permits approximately 52.6 minutes of unavailability per year, while 99.999% permits approximately 5.26 minutes, assuming a 365-day year. These totals may be allocated among equipment failure, planned maintenance, propagation outage, and power interruption.

Countermeasures include increased antenna diameter, adaptive modulation and coding, power control, space diversity, frequency diversity, route diversity, site diversity, forward-error correction, and automatic retransmission. Each has cost and engineering trade-offs. Increasing transmit power can raise interference and regulatory concerns; increasing antenna gain narrows beamwidth and increases pointing sensitivity; adaptive modulation improves availability but reduces throughput during fades.

Space diversity uses vertically separated antennas so that the fading experienced on the two paths is not perfectly correlated. The required separation is environment-dependent and should be designed using propagation models or measurements. Frequency diversity uses sufficiently separated frequencies so that multipath fades are less correlated, while route diversity avoids common obstructions and rain cells.

5.3 Interference and frequency coordination

The received wanted signal must be evaluated against co-channel, adjacent-channel, cross-polarization, and intermodulation interference. Antenna sidelobes, polarization discrimination, frequency stability, transmitter spectral regrowth, and receiver selectivity all affect system performance.

Regulators generally specify frequency bands, maximum equivalent isotropically radiated power, channel bandwidth, out-of-band emissions, antenna discrimination, coordination distances, and exposure limits. A design that satisfies a link budget but violates spectrum rules is not an acceptable engineering solution.

6. Practical design workflow

A defensible microwave design normally follows these steps:

1. Define service requirements: data rate, latency, availability, coverage, and acceptable outage.
2. Select frequency band after considering propagation, licensing, equipment availability, and atmospheric attenuation.
3. Perform path-profile analysis using accurate terrain and clutter data.
4. Check line of sight, Fresnel-zone clearance, Earth curvature, and diffraction.
5. Select antenna diameter, gain, polarization, mounting, and radome configuration.
6. Build a complete nominal and degraded link budget.
7. Estimate rain, multipath, and equipment-failure outage using regional models.
8. Evaluate interference, electromagnetic exposure, lightning protection, grounding, and structural loading.
9. Verify installation tolerances, alignment, cable losses, and commissioning measurements.
10. Monitor performance and revise the model using field data.

Antenna alignment should use both mechanical surveying and received-signal optimization. At narrow beamwidths, small angular errors can produce substantial loss. Radome deformation, tower flexure, thermal expansion, and wind-induced motion must be included in high-reliability systems.

7. Applied case: illustrative mountain telecommunications link

Background

A network operator must connect two mountain communities separated by 38 km. The service requires 1 Gbit/s under normal conditions and 99.99% annual availability. A licensed 18 GHz band is available, but the path crosses a humid valley with frequent seasonal rainfall.

Problem

A preliminary free-space calculation suggests adequate received power, but a survey reveals a ridge close to the first Fresnel zone. The path is also exposed to strong winds, and the selected high-order modulation has a large required signal-to-noise ratio.

Analysis

The engineering team first obtains a digital terrain profile and determines antenna heights that provide line of sight and at least the chosen Fresnel clearance criterion. The 18 GHz wavelength is approximately

where c is the speed of light. The shorter wavelength permits high antenna gain from moderate reflector diameters, but it also increases rain attenuation and pointing sensitivity.

A complete budget is then prepared for clear-sky, heavy-rain, misalignment, and equipment-failure conditions. The operator compares a single high-capacity modulation scheme with adaptive modulation and coding. The adaptive scheme lowers throughput during severe fading but maintains service for a larger fraction of the year.

Approach and solution

The final design uses high-gain dual-polarized antennas, improved ridge clearance, adaptive modulation, space diversity at the more exposed terminal, and an engineered fade margin. Radome selection is based on wet-loss measurements rather than dry specifications. The design includes lightning protection, tower structural analysis, remote performance monitoring, and a backup power system.

Outcome

The link meets the normal throughput requirement while providing a lower but serviceable rate during intense rain. Diversity and adaptive operation reduce outage probability more effectively than merely increasing transmitter power. Commissioning measurements confirm antenna alignment, polarization isolation, return loss, and received power.

Learning points

The case demonstrates that frequency selection, path geometry, antenna engineering, modulation, and availability cannot be optimized independently. A nominal link budget is only the starting point; reliability depends on degraded-mode analysis and field verification.

8. Limitations, safety, and contemporary developments

Propagation models contain empirical uncertainty. Rain-rate statistics may not represent local microclimates, terrain databases may omit buildings or vegetation, and fading distributions may fail during unusual atmospheric conditions. Consequently, high-consequence links should use conservative assumptions, independent model checks, and measurements where feasible.

Microwave exposure is governed by national and international limits based on frequency, power density, duty cycle, and public or occupational access. Sites require controlled access, warning signs, interlocks where appropriate, and procedures for maintenance personnel. High-power transmitters can also create risks through burns, induced currents, and interference with sensitive equipment.

Modern systems increasingly use electronically steered arrays, massive multiple-input multiple-output architectures, integrated antennas, digital beamforming, and machine-learning-assisted channel prediction. AI can help classify propagation events, predict rain fades, optimize modulation, and detect antenna misalignment. It should not replace physical link budgets, regulatory compliance, explainable alarms, or safety review. Training data can be geographically biased, and an adaptive controller must be constrained so that it cannot violate spectral masks or stability requirements.

Best practice is therefore hybrid: use electromagnetic and propagation models for physical constraints, measurements for calibration, and data-driven tools for prediction and optimization within verified limits.

Chapter Summary

Microwave link performance is governed by the interaction of antenna characteristics, propagation conditions, and system engineering. Antenna gain is related to directivity and efficiency, while effective aperture connects receiving power density to available received power. Reflectors, horns, patches, arrays, lenses, and slotted antennas serve different combinations of gain, bandwidth, scan, size, and power requirements.

The Friis equation describes ideal free-space transmission, but practical links require losses for feeders, mismatch, polarization, atmosphere, rain, multipath, and implementation. Fresnel clearance, Earth curvature, refractivity, and terrain determine whether a nominal line-of-sight path is actually reliable. Link budgets establish received power and fade margin; availability analysis determines whether those margins are sufficient under statistical propagation and equipment failures.

Reliable design combines antenna selection, path profiling, diversity, adaptive modulation, interference coordination, safety controls, regulatory compliance, and commissioning measurements. Contemporary AI-enabled optimization is useful when constrained by validated physical models and engineering governance.

Key Terms

Antenna gain: Directivity multiplied by total antenna efficiency.

Aperture efficiency: Ratio describing how effectively a physical aperture produces directive radiation.

Array factor: Pattern contribution produced by the geometry and excitation of an antenna array.

Beamwidth: Angular width of a specified portion of an antenna radiation pattern.

Effective aperture: Receiving area that relates incident power density to available received power.

Fade margin: Difference between clear-sky received power and minimum required receiver input power.

Fresnel zone: Region around the direct path in which obstacles can cause diffraction and phase effects.

Free-space path loss: Ideal propagation loss between isotropic points in unobstructed free space.

Gain: Antenna directivity reduced by antenna efficiency.

Link budget: Accounting of transmitted power, gains, losses, and receiver requirements.

Multipath: Arrival of multiple signal components through different propagation paths.

Polarization mismatch: Loss caused by incomplete alignment of transmitting and receiving polarizations.

Rain attenuation: Microwave signal loss caused by absorption and scattering by raindrops.

Radiation pattern: Directional distribution of radiated field or power.

Reciprocity: Equality of transmit and receive antenna characteristics under corresponding conditions.

Sidelobe: Secondary radiation lobe outside an antenna’s main beam.

Specific attenuation: Propagation loss per unit distance, commonly expressed in dB/km.

VSWR: Ratio of maximum to minimum voltage in a standing-wave pattern on a transmission line.

Review Questions

Short Answer Questions

1. Define antenna gain and distinguish it from directivity.
2. State the assumptions underlying the Friis transmission equation.
3. What is the purpose of the first Fresnel-zone clearance criterion?
4. Explain polarization mismatch loss for two linearly polarized antennas.
5. Name four techniques used to improve microwave link availability.

Long Answer Questions

1. Explain the operating principles, advantages, and limitations of horn, parabolic reflector, microstrip patch, and phased-array antennas.
2. Derive the relationship between antenna gain and effective aperture, stating all assumptions.
3. Discuss free-space propagation, atmospheric absorption, rain attenuation, multipath fading, and ducting.
4. Describe a complete microwave link-budget procedure, including receiver noise and fade margin.
5. Critically evaluate diversity and adaptive modulation as propagation-mitigation techniques.

Analytical / Application Questions

1. A 15 GHz, 30 km link uses 30 dBi antennas at both ends, 18 dBm transmitter power, and 5 dB total equipment loss. Calculate free-space loss and clear-sky received power, then identify additional data required to assess availability.
2. A proposed 26 GHz link crosses a ridge near the path midpoint. Explain how you would calculate the first Fresnel-zone radius, determine clearance, and decide whether antenna heights or route geometry must change.
3. An operator must choose between a lower-frequency narrowband link with modest gain and a higher-frequency high-capacity link exposed to heavy rain. Develop a decision framework including capacity, fade margin, regulation, antenna size, availability, and adaptive operation.

Multiple Choice Questions with Answers

Question 1

Which relationship connects antenna gain to effective aperture under matched polarization and impedance conditions?

A. A_e = Gλ²/(4π)

B. A_e = 4πG/λ²

C. A_e = Gλ/(4π)

D. A_e = 4πλ/G

Correct Answer: A. A_e = Gλ²/(4π)

Question 2

A microwave link has a transmitter power of 20 dBm, antenna gains of 35 dBi at each end, total feeder loss of 4 dB, other clear-sky losses of 2 dB, and free-space loss of 142 dB. What is the received power?

A. −58 dBm

B. −93 dBm

C. −54 dBm

D. −18 dBm

Correct Answer: A. −58 dBm

Question 3

Which condition is most directly associated with Rayleigh fading?

A. A strong unobstructed direct component dominates

B. There is no dominant direct component

C. Only atmospheric absorption is present

D. The signal is transmitted through a matched load

Correct Answer: B. There is no dominant direct component

Question 4

For a circular reflector, which change generally produces a narrower beamwidth?

A. Increasing wavelength while keeping diameter fixed

B. Decreasing reflector diameter

C. Increasing reflector diameter while keeping wavelength fixed

D. Reducing aperture efficiency to zero

Correct Answer: C. Increasing reflector diameter while keeping wavelength fixed

Question 5

The free-space path-loss formula in dB increases with distance according to which dependence?

A. 10log₁₀(R)

B. 20log₁₀(R)

C. R² without a logarithm

D. 1/R

Correct Answer: B. 20log₁₀(R)

Question 6

What is the principal purpose of adaptive modulation in a fading microwave link?

A. To eliminate all antenna losses

B. To maintain service by reducing modulation demands during poor channel conditions

C. To increase atmospheric absorption

D. To remove the need for frequency licensing

Correct Answer: B. To maintain service by reducing modulation demands during poor channel conditions

Question 7

For two linearly polarized antennas misaligned by angle ψ, the polarization coupling factor is

A. sin²ψ

B. tanψ

C. cos²ψ

D. 1 + cosψ

Correct Answer: C. cos²ψ

Question 8

Which phenomenon can extend apparent microwave range but also cause interference and severe fading?

A. Atmospheric ducting

B. Perfect impedance matching

C. Antenna reciprocity

D. Reduced receiver bandwidth

Correct Answer: A. Atmospheric ducting

Question 9

If clear-sky received power is −58 dBm and receiver sensitivity is −72 dBm, the fade margin is

A. −130 dB

B. 14 dB

C. −14 dB

D. 130 dB

Correct Answer: B. 14 dB

Question 10

Why is a first Fresnel-zone clearance check required even when geometric line of sight exists?

A. Because geometric line of sight does not prevent diffraction and phase-related obstruction loss

B. Because it determines receiver noise figure

C. Because it replaces antenna polarization analysis

D. Because it measures transmitter spectral regrowth

Correct Answer: A. Because geometric line of sight does not prevent diffraction and phase-related obstruction loss