Definitions

electrical line of force

Non-line-of-sight propagation

Non-line-of-sight (NLOS) or near-line-of-sight is a term used to describe radio transmission across a path that is partially obstructed, usually by a physical object in the Fresnel zone.

Many types of radio transmissions depend, to varying degrees, on line of sight between the transmitter and receiver. Obstacles that commonly cause NLOS conditions include buildings, trees, hills, mountains, and, in some cases, high voltage electric power lines. Some of these obstructions reflect certain radio frequencies, while some simply absorb or garble the signals; but, in either case, they limit the use of many types of radio transmissions, including most of those used for Wi-Fi.

How to achieve effective NLOS networking has become one of the major questions of modern computer networking. Currently, the most common method for dealing with NLOS conditions on wireless computer networks is simply to place relays at additional locations, sending the content of the radio transmission around the obstructions. Some more advanced NLOS transmission schemes now use multipath signal propagation, bouncing the radio signal off other nearby objects to get to the receiver.

Non Line-of-Sight (NLOS) is a term often used in radio communications to describe a radio channel or link where there is no visual line of sight (LOS) between the transmitting antenna and the receiving antenna. In this context LOS is taken

  • either as a straight line free of any form of visual obstruction, even if it is actually too distant to see with the unaided human eye
  • as a virtual LOS i.e. as a straight line through visually obstructing material, thus leaving sufficient transmission for radio waves to be detected.

There are many electrical characteristics of the transmission media that affect the radio wave propagation and therefore the quality of operation of a radio channel, if it is possible at all, over an NLOS path.

The acronym NLOS has become more popular in the context of wireless local area networks (WLANs) such as WiFi and wireless metropolitan area networks such as WiMax because the capability of such links to provide a reasonable level of NLOS coverage greatly improves their marketability and versatility in the typical urban environments in which they are most frequently used. However NLOS contains many other subsets of radio communications.

The influence of a visual obstruction on a NLOS link may be anything from negligible to complete suppression. An example might apply to a LOS path between a television broadcast antenna and a roof mounted receiving antenna. If a cloud passed between the antennas the link could actually become NLOS but the quality of the radio channel could be virtually unaffected. If, instead, a large building was constructed in the path making it NLOS, the channel may be impossible to receive.

Radio waves as plane electromagnetic waves

From Maxwell's equations we find that radio waves, as they exist in free space in the far field or Fraunhofer region behave as plane waves. In plane waves the electric field, magnetic field and direction of propagation are mutially perpendicular. To understand the various mechanisms that allow successful radio communications over NLOS paths we must consider how such plane waves are affected by the object or objects that visually obstruct the otherwise LOS path between the antennas. It is understood that the terms radio far field waves and radio plane waves are interchangeable.

What is line-of-sight?

By definition, line of sight is the visual line of sight, that is determined by the ability of the average human eye to resolve a distant object. Our eyes are sensitive to light but optical wavelengths are very short compared to radio wavelengths. Optical wavelengths range from about 400 nanometer (nm) to 700 nm but radio wavelengths range from approximately 1 millimetre (mm) at 300 GHz to 30 kilometres (km) at 10 kHz. Even the shortest radio wavelength is therefore about 2000 times longer than the longest optical wavelength. For typical communications frequencies up to about 10 GHz the difference is more like 60,000 times so it is not always reliable to compare visual obstructions, such as might suggest a NLOS path, with the same obstructions as they might affect a radio propagation path.

Caution, please respect: Runtime measurements for determining the distance between pairs of transmitters and receivers generally require line-of-sight propagation for proper results. The desire to have just any type of propagation to enable communication does not coincide with the requirement to have strictly line of sight at least temporarily as the means to obtain measured distances.

NLOS links may either be simplex (transmission is in one direction only), duplex (transmission is in both directions simultaneously) or half-duplex (transmission is possible in both directions but not simultaneously). Under normal conditions all radio links including NLOS are reciprocal which means that the effects of the propagation conditions on the radio channel are identical whether it operates in simplex, duplex or half-duplex.

How are plane waves affected by the size and electrical properties of the obstruction?

In general, the way in which a plane wave is affected by an obstruction depends on the size of the obstruction relative to its wavelength and the electrical properties of the obstruction. For example, a hot air balloon with multi-wavelength dimensions passing between the transmit and receive antennas could be a significant visual obstruction but is unlikely to affect the NLOS radio propagation much assuming it is constructed from fabric and full of hot air, both of which are good insulators. Conversely, a metal obstruction of dimensions comparable to a wavelength would cause significant reflections. When considering obstruction size we will assume its electrical properties are the most common intermediate or lossy type.

Obstruction Size

Broadly, there are three approximate sizes of obstruction in relationship to a wavelength to consider in a possible NLOS path. Those which are:

  • (a) much smaller than a wavelength
  • (b) of the same order as a wavelength
  • (c) much larger than a wavelength

If the obstruction dimensions are much smaller than the wavelength of the incident plane wave, the wave will be essentially unaffected. For example, low frequency (LF) broadcasts, also known as long waves, at about 200 kHz has a wavelength of 1500 m and is not significantly affected by most average size buildings which are of much smaller dimensions.

If the obstruction dimensions are of the same order as a wavelength, there will be a degree of diffraction around the obstruction and possibly some transmission through it. The incident radio wave could be slightly attenuated and there might be some interaction between the diffracted wavefronts.

If the obstruction has dimensions of many wavelengths, the incident plane waves will be heavily dependent on the electrical properties of the material forming the obstruction which are described below.

The electrical properties of obstructions that may cause NLOS

The electrical properties of the material forming an obstruction to radio waves could range from a perfect conductor at one extreme to a perfect insulator at the other. Most materials have both conductor and insulator properties. They may be mixed: for example, many NLOS paths result from the LOS path being obstructed by reinforced concrete buildings constructed from concrete and steel. Concrete is quite a good insulator when dry and steel is a good conductor. Alternatively the material may be a homogeneous lossy material.

The parameter which describes to what degree a material is a conductor or an insulator is known as tan delta, or the loss tangent, given by

tan delta =frac{sigma}{omegaepsilon_0epsilon_r}
where
sigma is the conductivity of the material in siemens per metre (S/m)

omega=2pi f is the angular frequency of the RF plane wave in radians per second (rad/s) and f is its frequency in hertz (Hz).

epsilon_0 is the absolute permittivity of the material (the permittivity of free space) in farads per metre (F/m)

and

epsilon_r is the relative permittivity of the material (also known as dielectric constant) and has no units.

Good conductors (poor insulators)

If sigma gg omegaepsilon_0epsilon_r the material is a good conductor or a poor insulator and will substantially reflect the radio waves that are incident upon it with almost the same power. Therefore virtually no RF power will be absorbed by the material itself and virtually none will be transmitted, even if it is very thin. All metals are good conductors and there are of course many examples that cause significant reflections of radio waves in the urban environment, for example bridges, metal clad buildings, storage warehouses, aircraft and electrical power transmission towers or pylons.

Good insulators (poor conductors)

If sigma ll omegaepsilon_0epsilon_r the material is a good insulator (or dielectric) or a poor conductor and will substantially transmit waves that are incident upon it. Virtually no RF power will be absorbed but some could be reflected at its boundaries depending on its relative permittivity compared to that of free space, which is unity. This uses the concept of intrinsic impedance which is described below.There are few large physical objects that are also good insulators, with the interesting exception of fresh water icebergs but these do not usually feature in most urban environments. However large volumes of gas generally behave as dielectrics. Examples of these are regions of the Earths atmosphere which gradually reduce in density at increasing altitudes up to 10 to 20 km. At greater altitudes from about 50 km to 200 km various ionospheric layers also behave like dielectrics and are heavily dependent on the influence of the Sun. Ionospheric layers are not gases but plasmas.
Plane waves and intrinsic impedance
Even if an obstruction is a perfect insulator, it may have some reflective properties on account of its relative permittivity epsilon_r differing from that of the atmosphere. Electrical materials through which plane waves may propagate have a property called intrinsic impedance (eta) or electromagnetic impedance which is analogous to the characteristic impedance of a cable in transmission line theory. The intrinsic impedance of a homogeneous material is given by:

eta=sqrt{frac{mu_0mu_r}{epsilon_0epsilon_r}}

where

mu_0 is the absolute permeability in henries per metre (H/m) and is a constant fixed at 4 pi x 10^{-7} H/m

mu_r is the relative permeability (unitless)

epsilon_0 is the absolute permittivity in farads per metre (F/m) and is a constant fixed at 8.85 x 10^{-12} F/m

epsilon_r is the relative permittivity or dielectric constant (unitless)

For free space mu_r = 1 and epsilon_r = 1, therefore the intrinsic impedance of free space eta_0 is given by

eta_0=sqrt{frac{mu_0}{epsilon_0}}

which evaluates to approximately 377 Omega.

Reflection losses at dielectric boundaries
In an analogy of plane wave theory and transmission line theory, the definition of reflection coefficient Gamma is a measure of the level of reflection normally at the boundary when a plane wave passes from one dielectric medium to another. For example, if the intrinsic impedances of the first and second media were eta_1 and eta_2 respectively, the reflection coefficient of medium 2 relative to 1, Gamma_{21}, is given by:

Gamma_{21} = frac{eta_2-eta_1}{eta_2+eta_1}

The logarithmic measure in decibels (T_r) of how the transmitted RF signal over the NLOS link is affected by such a reflection is given by:

T_{ref} = 10log_{10}(1-left|Gamma_{21}right|^2) dB

Intermediate materials with finite conductivity

Most materials of the type affecting radio wave transmission over NLOS links are intermediate: they are neither good insulators nor good conductors. Radio waves incident upon an obstruction comprising a thin intermediate material will be partly reflected at both the incident and exit boundaries and partly absorbed, depending on the thickness. If the obstruction is thick enough the radio wave might be completely absorbed. Because of the absorption, these are often called lossy materials, although the degree of loss is usually extremely variable and often very dependent or the level of moisture present. They will often be heterogeneous and comprise a mixture materials with various degrees of conductor and insulator properties. Such examples are hills, valley sides, mountains (with substantial vegetation) and buildings constructed from stone, brick or concrete but without reinforced steel. The thicker they are the greater the loss. For example a wall will absorb much less RF power from a normally incident wave than a building constructed from the same material.

Means of achieving non-line-of-sight radio transmission

Passive random reflections

Passive random reflections are achieved when plane waves are subject to one or more reflective paths around an object which makes an otherwise LOS radio path into NLOS. The reflective paths might be caused by various objects which could either be metallic (very good conductors such as a steel bridge) or relatively good conductors to plane waves such as large expanses of concrete building sides, walls etc. Sometimes this is considered a brute force method because, on each reflection the plane wave undergoes a transmission loss which must be compensated for by a higher output power from the transmit antenna compared to if the link had been LOS. However the technique is cheap and easy to employ and passive random reflections are widely exploited in urban areas to achieve NLOS. Communication services which use passive reflections include WiFi, WiMax, WiMAX_MIMO MIMO, mobile (cellular) communications and terrestrial broadcast to urban areas.

Passive repeaters

Passive repeaters may be used to achieve NLOS links by deliberately installing a precisely designed reflector at a critical position to provide a path around the obstruction. However they are unacceptable in most urban environments due to the bulky reflector requiring critical positioning at perhaps an inaccessible location or at one not acceptable to the planning authorities or the owner of the building. Passive reflector NLOS links also incurr substantial loss due to the received signal being a 'double inverse-square law' function of the transmit signal, one for each hop from the transmit antenna to the receive antenna. However, they have been successfully used in rural mountainous areas to extend the range of LOS microwave links around mountains thus creating NLOS links. In such cases the installation of the more usual active repeater was usually not possible due to problems in obtaining a suitable power supply.

Active repeaters

An active repeater is a powered piece of equipment essentially comprising a receiving antenna, a receiver, a transmitter and a transmitting antenna. If the ends of the NLOS link are at positions A and C, the repeater is located at position B where links A-B and B-C are in fact LOS. The active repeater may simply amplify the received signal and re-transmit it un-altered at either the same frequency or a different frequency. The former case is simpler and cheaper but requires good isolation between two antennas to avoid feedback, however it does mean that the end of the NLOS link at A or C does not require to change the receive frequency from that used for a LOS link. A typical application might be to repeat or re-broadcast signals for vehicles using car radios in tunnels. A repeater that changes frequency would avoid any feedback problems but would be more difficult to design and expensive and it would require a receiver to change frequency when moving from the LOS to the NLOS zone. A communications satellite is a good example of an active repeater which does change frequency.

A communications satellite is an example of an active repeater which, in most cases is positioned in geosynchronous orbit at an altitude of 22,300 miles (35,000 km) above the Equator.

Groundwave propagation

Application of the Poynting Vector to vertically polarised plane waves at LF (30 kHz to 300 kHz) and VLF (3 kHz to 30 kHz) indicates that a component of the field is propagated a few metres into the surface of the Earth. The propagation is very low loss and communications over thousands of miles over NLOS links is possible. However, such low frequencies by definition (Nyquist–Shannon sampling theorem) are very low bandwidth, so this type of communication is not widely used.

Tropospheric scatter links

A tropospheric scatter NLOS link typically operates at a few gigahertz using potentially very high transmit powers (typically 3 kW to 30 kW, depending on conditions), very sensitive receivers and very high gain, usually fixed, large reflector antennas. The transmit beam is directed into the troposphere just above the horizon with sufficient power flux density that gas and water vapour molecules cause scattering in a region in the beam path known as the scatter volume. Some components of the scattered energy travel in the direction of the receiver antennas and form the receive signal. Since there are very many particles to cause scattering in this region, the Rayleigh fading statistical model may usefully predict behaviour and performance in this kind of system.

Refraction through the Earth's atmosphere

The obstruction that creates an NLOS link may be the Earth itself, such as would exist if the other end of the link was beyond the optical horizon. A very useful property of the Earth's atmosphere is that, on average, the density of air gas molecules reduces as the altitude increases up to approximately 30 km. Its relative permittivity or dielectric constant reduces steadily from about 1.00536 at the Earth's surface. To model the change in refractive index with altitude, the atmosphere may be approximated to many thin air layers, each of which has a slightly smaller refractive index than the one below. The trajectory of radio waves progressing through such an atmosphere model at each interface, is analogous to optical beams passing from one optical medium to another as predicted by Snell's Law. When the beam passes from a higher to lower refractive index it tends to get bent or refracted away from the normal at the boundary according to Snell's Law. When the curvature of the Earth is taken into account it is found that, on average, radio waves whose initial trajectory is towards the optical horizon will in fact follow a path which does not return to the Earth's surface at the horizon, but slightly beyond it. The distance from the transmit antenna to where it does return is approximately equivalent to the optical horizon, had the Earth's radius been 4/3 of its actual value. The '4/3 Earth's radius' is a useful rule of thumb to the radio communication engineers when designing such a NLOS link.

The 4/3 Earth radius rule of thumb is an average for the Earth's atmosphere assuming it is reasonably homogenised, absent of temperature inversion layers or unusual meteorological conditions. NLOS links which exploit atmospheric refraction will typically operate at frequencies in the VHF and UHF bands including FM sound and TV terrestrial broadcast services.

Anomalous propagation

The phenomenon described above that the atmospheric refractive index, relative permittivity or dielectric constant gradually reduces with increasing height is on account of the reduction of the atmospheric air density with increasing height. Air density is also a function of temperature which ordinarily also reduces with increasing height. However, these are only average conditions; local meteorological conditions can create phenomena such as temperature inversion layers where a warm layer of air settles above a cool layer. At the interface between them exists a relatively abrupt change in refractive index from a smaller value in the cool layer to a larger value in the warm layer. By analogy with the optical Snell's Law, this can cause significant reflections of radio waves back towards the earth's surface where they are further reflected, thus causing a ducting effect. The result is that radio waves can propagate well beyond their intended service area with less than normal attenuation. This effect is only apparent in the VHF and UHF spectra and is often exploited by amateur radio enthusiasts to achieve communications over abnormally long distances for the frequencies involved. For commercial communication services it cannot be exploited because it is unreliable (the conditions can form and disperse in minutes) and it can cause interference well outside of the normal service area.

Temperature inversion and anomalous propagation can occur at most latitudes but they are more common in tropical climates than temperate climates, usually associated with high pressure areas (anticyclones).

Ionospheric propagation

The mechanism of ionospheric propagation in supporting NLOS links is similar to that for atmospheric refraction but, in this case, the radio wave refraction occurs, not in the atmosphere but in the ionosphere at much greater altitudes. Like its tropospheric counterpart, ionospheric propagation can sometimes be statistically modelled using Rayleigh fading.

The ionosphere extends from altitudes of approximately 50 km to 400 km and is divided into distinct plasma layers denoted D, E, F1 and F2 in increasing altitude. Refraction of radio waves by the ionosphere rather than the atmosphere can therefore allow NLOS links of much greater distance for just one refraction path or 'hop' via one of the layers. Under certain conditions radio waves that have undergone one hop may reflect off the Earth's surface and experience more hops, so increasing the range. The positions of these and their ion densities are significantly controlled by the Sun's incident radiation and therefore change diurnally, seasonally and during Sun spot activity. The initial discovery that that radio waves could travel beyond the horizon by Marconi in the early 20th century prompted extensive studies of ionospheric propagation for the next 50 years or so which have yielded various HF link channel prediction tables and charts.

Frequencies that are affected by ionospheric propagation range from approximately 500 kHz to 50 MHz but the majority of such NLOS links operate in the 'short wave' or high frequency (HF) frequency bands between 3 MHz and 30 MHz.

In the latter half of the twentieth century, alternative means of communicating over large NLOS distances were developed such as satellite communications and submarine optical fiber, both of which potentially carry much larger bandwidths than HF and are much more reliable. Despite their limitations, HF communications only need relatively cheap, crude equipment and antennas so they are mostly used as backups to main communications systems and in sparsely populated remote areas where other methods of communication are not cost effective.

Finite absorption

If an object which is responsible for changing a LOS link to NLOS is not a good conductor but an intermediate material it will absorb some of the RF power incident upon it. However, if it has finite thickness the absorption will also be finite and the resulting attenuation of the radio waves may be tolerable and an NLOS link may be set up using radio waves that actually pass through the material. As an example, wireless local area networks (WLANs) often use finite absorption NLOS links to communicate between a router and clients in the typical office environment. The radio frequencies used, typically a few gigahertz (GHz) will normally pass through a few thin office walls and partitions with tolerable attenuation. After many such walls though or after a few thick concrete or similar (non-metallic) walls the NLOS link will become unworkable.

How is positioning accuracy affected by NLOS conditions?

In most of the recent localization systems, it is assumed that the received signals propagate through a LOS path. However, infringement of this assumption can result in inaccurate positioning data . For Time of Arrival based localization system, the emitted signal can only arrive at the receiver through its NLOS paths. The NLOS error is defined as the extra distance travelled by the received signal with respect to the LOS path. The NLOS error is always positively biased with the magnitude dependent on the propagation environment.

References

Further reading

Bullington, K.; "Radio Propagation Fundamentals"; Bell System Technical Journal Vol. 36 (May 1957); pp 593-625. "Technical Planning Parameters and Methods for Terrestrial Broadcasting" (April 2004); Australian Broadcasting Authority. ISBN 0-642-27063-5

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