Line-of-sight propagation
Line-of-sight (LOS) propagation is a fundamental mode of radio wave transmission in which electromagnetic signals travel directly from a transmitting antenna to a receiving antenna along a straight path, requiring an unobstructed line between the two points for effective communication.[1] This form of propagation dominates at higher frequencies, particularly in the very high frequency (VHF, 30–300 MHz), ultra high frequency (UHF, 300–3000 MHz), and microwave bands (above 3000 MHz), where waves behave more like light rays due to their shorter wavelengths and reduced diffraction.[2] The effective range is limited by the radio horizon, which extends approximately 4/3 times the optical horizon because of atmospheric refraction bending the waves slightly downward, allowing distances up to several hundred kilometers for elevated antennas but typically tens of kilometers over flat terrain.[3] Key principles of LOS propagation include the direct space wave, which follows the inverse square law for free-space loss—calculated as L_{fs} = 32.44 + 20\log_{10}(f) + 20\log_{10}(d) in decibels, where f is frequency in MHz and d is distance in km—and contributions from ground-reflected waves that can cause multipath interference.[1] Reliable performance demands clearance of the first Fresnel zone, a roughly ellipsoidal region around the direct path with radius r = \sqrt{\frac{\lambda d_1 d_2}{d_1 + d_2}} (where \lambda is wavelength and d_1, d_2 are segment distances), to minimize diffraction losses from terrain or obstacles.[1] Atmospheric factors, such as refractive index gradients (typically N = 301 N-units at sea level), introduce fading through super-refraction or ducting, leading to signal variations of 5–30 dB, while obstructions like buildings or vegetation can cause attenuation exceeding 20 dB.[3] LOS propagation is essential for applications including broadcast television and FM radio, mobile cellular networks, satellite-to-ground links above 450 MHz, and fixed point-to-point microwave relays for telecommunications and military short-haul systems, often operating up to 40 GHz with careful path engineering to mitigate impairments.[4] Despite its limitations in non-line-of-sight environments, advancements in antenna height, diversity techniques, and error correction enable robust performance over urban and rural terrains.[3]Fundamentals
Definition and Principles
Line-of-sight (LOS) propagation refers to the direct transmission of radio waves from a transmitter to a receiver along a straight path, requiring an unobstructed view between the antennas, akin to visibility with the naked eye or optical instruments. This mode is fundamental for electromagnetic waves in free space, where the signal follows the principles of geometric optics for high frequencies, minimizing scattering or bending unless influenced by environmental factors.[5] In vacuum, electromagnetic waves propagate at the speed of light, approximately c \approx 3 \times 10^8 m/s, enabling near-instantaneous travel over the LOS path.[6] The behavior is frequency-dependent: at lower frequencies below about 30 MHz, waves can diffract around obstacles or reflect off the ionosphere for beyond-horizon communication, but above 30 MHz—encompassing VHF, UHF, microwaves, and mm-waves—LOS becomes the dominant mode due to reduced diffraction and negligible ionospheric reflection, as shorter wavelengths interact more directly with the path.[5] Higher frequencies thus impose stricter LOS requirements, limiting range to the optical horizon unless augmented by relays or other techniques, assuming familiarity with the electromagnetic spectrum where these bands align with line-of-sight viability.[7] The concept traces back to early optical telegraphy systems in the 1790s, pioneered by Claude Chappe's semaphore network in France, which relied on visual signals transmitted via towers in direct line of sight for rapid messaging across distances.[8] This principle was extended to radio by Guglielmo Marconi in his 1895 experiments, where he demonstrated wireless telegraphy over increasing ranges limited by line-of-sight paths, laying groundwork for electromagnetic signaling without wires.[9] These foundational efforts established LOS as essential for reliable, direct communication in both optical and radio domains.Electromagnetic Wave Behavior
Radio waves propagating in line-of-sight (LOS) conditions are transverse electromagnetic waves, characterized by oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation.[6] These waves maintain their transverse nature in free space, enabling predictable straight-line travel between transmitter and receiver without significant bending, provided no obstacles intervene.[6] Polarization describes the orientation of the electric field vector in the wave, which can be linear (horizontal or vertical) or circular (right-hand or left-hand).[10] In LOS propagation, proper alignment of transmitting and receiving antenna polarizations is essential for maximizing signal strength, as mismatch—such as between linear and circular polarizations—can result in up to 20-30 dB of polarization loss, severely degrading the received signal.[11] This effect arises because antennas are designed to efficiently couple with waves matching their polarization, emphasizing the need for consistent orientation in LOS links.[11] The fundamental attenuation of radio waves in free space under ideal LOS conditions is quantified by the Friis transmission equation, which relates received power to transmitted power and system parameters: P_r = P_t G_t G_r \left( \frac{\lambda}{4 \pi d} \right)^2 Here, P_r is the power available at the receiver, P_t is the transmitted power, G_t and G_r are the gains of the transmitting and receiving antennas, \lambda is the wavelength, and d is the propagation distance.[12] This equation assumes isotropic free-space propagation and highlights how path loss scales with the square of the distance and inversely with the square of the wavelength, underscoring the importance of antenna gains in compensating for spreading losses over distance.[12] Frequency significantly influences wave behavior in LOS propagation. At higher frequencies in the ultra high frequency (UHF, 300 MHz–3 GHz) and super high frequency (SHF, 3–30 GHz) bands, radio waves demonstrate enhanced directivity, with antenna gain scaling proportionally to the square of the frequency (G \propto (f/c)^2, where f is frequency and c is the speed of light), allowing for narrower, beam-like radiation patterns that concentrate energy toward the receiver. However, these frequencies suffer increased atmospheric absorption, primarily from oxygen (peaking around 60 GHz) and water vapor (peaking around 22 GHz and 183 GHz), which can add several dB/km of loss under standard conditions. In contrast, lower very high frequency (VHF, 30–300 MHz) waves, while still dominated by LOS paths, permit slight diffraction around minor obstacles due to their longer wavelengths, though this effect diminishes reliability compared to the stricter LOS requirement at higher bands. Even in LOS scenarios, signal fading can arise from multipath propagation, where minor reflections from ground or nearby structures create secondary paths that interfere with the direct wave, causing constructive or destructive interference. This multipath fading is generally less severe in LOS than in obstructed environments, often manifesting as flat fading with depths of 10–20 dB, and can be mitigated through antenna height adjustments or diversity techniques.Propagation Path and Geometry
Direct Wave Path
In line-of-sight (LOS) propagation, the direct wave path refers to the unobstructed, straight-line trajectory of electromagnetic waves from the transmitter to the receiver, requiring optical visibility between the antenna apertures. This geometry is determined by the heights of the transmitter (h_t) and receiver (h_r) antennas above the local terrain, ensuring that the line connecting the antennas does not intersect significant obstacles. The optical visibility criterion is established by drawing tangent lines from each antenna to the Earth's surface, confirming that the path remains above the horizon and clear of intervening terrain.[13] The fundamental signal attenuation along this direct path in free space is quantified by the free-space path loss (FSPL), which arises from the geometric spreading of the wavefront and the inverse relationship with wavelength. The FSPL in decibels is given by: \text{FSPL (dB)} = 20 \log_{10}(d) + 20 \log_{10}(f) + 20 \log_{10}\left(\frac{4\pi}{c}\right) where d is the distance between antennas in meters, f is the frequency in hertz, and c is the speed of light (approximately $3 \times 10^8 m/s). This formula, derived from the Friis transmission equation, highlights the quadratic dependence on both distance and frequency, meaning higher frequencies (e.g., microwave bands) experience greater loss over the same path length, necessitating careful link budgeting for reliable communication.[12][14] To maintain the integrity of the direct wave path, terrain clearance is essential, requiring the line-of-sight to avoid interruptions from natural or man-made obstacles such as hills, buildings, or vegetation. Path profiles, constructed using digital elevation models or site surveys, graphically depict the vertical cross-section of the propagation path, allowing engineers to identify potential blockage points and adjust antenna heights or locations accordingly. For instance, in microwave links, profiles ensure that the direct ray clears terrain by at least the first Fresnel zone radius to minimize diffraction losses, though full details on zone clearance are addressed elsewhere.[15] Antenna design plays a critical role in optimizing the direct wave path by concentrating transmitted energy and enhancing reception along the intended trajectory. Directional antennas, such as parabolic dishes commonly used in microwave LOS systems, provide high gain (typically 20–40 dBi) and narrow beamwidths (e.g., 1–10 degrees), focusing power to overcome path loss and reduce interference from off-path directions. These antennas align precisely with the line-of-sight geometry, enabling reliable point-to-point links over tens of kilometers in clear conditions.[16]Fresnel Zone Considerations
In line-of-sight (LOS) propagation, Fresnel zones are a series of concentric ellipsoids surrounding the direct wave path between transmitter and receiver, within which secondary wave paths can interfere constructively or destructively with the primary signal.[17] These zones arise from the diffraction of electromagnetic waves around obstacles, with each successive zone representing paths where the path length difference from the direct path is an integer multiple of half the wavelength; the first Fresnel zone is the innermost and most critical for maintaining signal integrity, as it encompasses the majority of the energy contributing to the received signal.[17] Visually, these ellipsoids are widest at the midpoint of the path and taper toward the endpoints, forming a football-like shape in three dimensions that expands with increasing wavelength and path length.[18] The radius r of the first Fresnel zone at any point along the path is given byr = \sqrt{\frac{\lambda d_1 d_2}{d_1 + d_2}},
where \lambda is the wavelength, d_1 is the distance from the transmitter to the point, and d_2 is the distance from the point to the receiver (with d_1 + d_2 as the total path length).[17] Higher-order zones have radii scaled by \sqrt{n} for the n-th zone, but obstructions primarily affect the first zone, with secondary impacts from outer zones in longer paths where cumulative interference becomes significant.[17] In microwave links, which operate at frequencies typically between 1 and 40 GHz, these zones are particularly relevant due to the directive nature of the antennas and the need for reliable high-capacity transmission over distances up to tens of kilometers.[17] Obstructions encroaching into the Fresnel zones disrupt the phase coherence of arriving waves, leading to destructive interference and signal attenuation through diffraction.[17] Partial blockage of the first zone causes phase cancellation, weakening the LOS signal and potentially introducing fading; for instance, full obstruction can result in losses exceeding 20 dB, while even minor intrusions degrade the signal-to-noise ratio in sensitive applications like point-to-point microwave relays.[17] To mitigate this, clearance criteria require that at least 60% of the first Fresnel zone remain unobstructed, which results in negligible diffraction loss (typically less than 1 dB) under normal atmospheric conditions and ensures near-free-space propagation performance.[17] Full clearance (100%) is ideal for minimal attenuation, especially in paths longer than 30 km, though reduced clearance (down to 0% for grazing incidence over isolated obstacles) may be acceptable with predictive modeling to account for tolerable loss; for grazing incidence (0% clearance), the diffraction loss is approximately 6 dB.[17]