Maritime fading revisited

A long while ago I wrote a piece about surface multipath interference over the sea and recently, I had to explain that theory to someone. It was regarding their C band microwave access system which was not performing to their expectations. This system had one end station on the land and the other in the form of a tracking antenna mounted on a ship. Being a modern system, the signal level data could be recalled and graphed. In front of me I observed a great example of the fading phenomenon, so I dug out the old Excel model, tweaked the parameters for the atmospheric state of the day et voila:

The sea was a little unsettled on the day in question and the boat had several metres of heave. The multipath effects are clearly visible including impact of the heave that can be observed in the little oscillations in the last measured lobe. Beyond that, the signal diffracts due to the sea state causing the horizon to fall short of the smooth sea prediction.

Rician fading calculator

In setting a challenging project for a very bright physics and mathematics student, I had to stay one step ahead and go back to fundamentals to work out the availability of a fading path as a function of direct and indirect signals.

This is useful in many applications where the fade margin required for reliable communications in narrowband channels can be characterised as a function of the amplitude of indirect scattered components relative the direct line-of-sight component.

This led me to develop this little fading calculator based upon Marcum’s Q function, which I have implemented as a custom function in a spreadsheet to resemble the Nakagami-Rice distribution as expressed in ITU-R P.1057-4 and plotted in figure 4.

I chose the numerical approximation of the Q function based upon ‘Another Recursive Method of Computing the Q Function’ by W F McGee (IEEE Transactions and Information Theory, July 1970).

The complete example is available for download here.

Well done Callum for solving the problem set and keeping me on my toes!

LTE Crossing Borders

An activity in radio network planning that is all too often left till last, is that of assessing the radiated contribution spilling over international borders to see if the level exceeds the threshold requiring formal coordination. This can be a problem if not tackled up front, because coordination activities can be lengthy.

Within CEPT this situation is anticipated, and there are various criteria agreed to allow radiation either side of a border without extraordinary activity. Typically these agreements permit an administration to implement a station that radiates towards a border, as long as the field strength incident at and beyond the border do not exceed defined limits for not more than 10% of the time. The criteria include common methods for predicting propagation which include long term statistics to satisfy the time criterion.

To expedite network roll-out, it is often interesting to engineer the network design to meet the limits. This can be done by limiting sites close to the border, omitting sectors pointing towards the border, using terrain to screen radiation towards the border, or optimisation of power delivered to the antenna and sector pointing. Often these measures need to be used in combination. For example, a site on a hill close to a border will probably require more than antenna down-tilting to be satisfactory. Of course if a configuration causing these limits to be exceeded is essential, classic coordination activities are still possible, but plenty of time must be allowed, hence it is best to identify sites requiring coordination early on in network planning.

In respect of LTE, there are several recommendations for the various harmonised bands in CEPT including the ECC recommendations (08)02 for 900/1800 MHz, (11)04 for 800 MHz, (11)05 for 2600 MHz and (14)04 for 2300 MHz. The attached CEPT LTE cross border coordination spreadsheet gives an example of how to assess if a site requires coordination for the 800/900/1800 MHz bands, but could be easily extended to cover others.

Summing up the unwanted

At a receiving antenna system we generally find a series of signal vectors that arrive and aggregate in positive and negative ways. Often we have a significant wanted signal and multiple unwanted ones from other co-channel users that lead to the planned service being limited by interference rather than noise. The question arises, how to aggregate these signals so that we can compute a wanted to unwanted ratio such that we can ultimately determine the availability of the desired service as we vary location? This post examines some of the approaches and gives a practical spreadsheet example.

Simple summing of the means of these signals does not suffice, because generally they will fade independently due to the diversity of the interference paths, so a meaningful prediction will require a method that takes account of their stochastic nature. To simplify matters these signal are generally characterised by a mean and variance assuming a log-normal distribution, and they will also have that distribution in aggregate. A straight-forward approach is to use Monte-Carlo method to sum many random samples to compute the aggregate mean and variance. With modern computing power this can be done with a high degree of confidence, however, this may require a significant number of samples. If pixel plotting techniques are used to predict the service at a huge number of locations, then the simulation times can be significantly long, this can be limiting when network plans are being evaluated.

However, there are many alternative techniques using numerical approximations to help estimate the sum of log-normal variates that require substantially less computing power. This includes the seminal method by L F Fenton which is often known as Fenton-Wilkinson method. Fenton’s approach has the benefit of being simple, but suffers from  significant accuracy issues which are quite limiting when dealing with a large number of different vectors. The Schwartz-Yeh method is an improvement under most circumstances and is especially useful for summing uncorrelated sources, but it is more complex. Other techniques improve upon these methods and may offer better fidelity in dealing with correlation  and larger numbers of signals, but there is no perfect method, and Schwartz-Yeh stands as a good general purpose method for a small number of uncorrelated signals.

The interference summing methods compared spreadsheet implements a number of functions that can be called to compare Monte-Carlo, Fenton-Wilkinson and Schwartz-Yeh methods. The spreadsheet contains an example with 20 components that are assumed to be uncorrelated. These components are simply passed as arrays to user defined VBA functions making the worksheet compact and easy to experiment with. Aside from the helper functions, there are only a few core functions whose code is easily modified for re-use in other programming environments.

Are aeronautical paths special?

Why is the aeronautical radio path between the ground and an elevated platform different to say a path between two stations on the surface? Surely the same principles are at play? Well yes they are, but it is more a question that the terrestrial path is often simplified when modelling stations near the surface of the Earth compared to the aeronautical case.

A simplification often applied, is to model of the atmosphere as uniform rather than inhomogeneous. Of course the density of air is greatest at the surface and ‘thins out’ with altitude. This may be fine for short range applications, or for those close to the surface of the Earth, but for a path that is slanted between a terrestrial station on the surface and an aircraft at altitude, the radio wave will encounter different densities of atmosphere, and so it will refract causing the ray to bend with a magnitude that varies with altitude.

To model the ray bending, ray tracing is often used with an exponential model of the atmosphere. An example of this is contained within the ITS IF77 model published in 1983 by Johnson and Gierhart. IF77 is the basis for the ITU recommendation P.528-3 on propagation for aeronautical mobile and radionavigation services using the VHF, UHF and SHF bands. The diagram below depicts an exaggerated example of the ray tracing used to generate key metrics for estimate of propagation losses for IF77.

Aircraft-effective-height

Straight line geometry over estimates the ray bending leading to horizons being predicted as further away, so a longer line-of-sight region and thus smaller propagation losses. In IF77, the ray is traced using iterative methods to find the radio horizons, and then to correct the end station heights to lower effective heights. This is one aspect of the model that is by no means unique to aeronautical, but more significant than for say land mobile over short paths. Other effects that are significant in an aeronautical context include the role of antenna systems in attenuating the Earth reflected path, some of the principles of which were discussed in the post Plane old Earth on the sea!

Despite the age of the Johnson Gierhart work, it is a current topic of discussion in ITU SG3, because it was a well researched piece, and provides a solid basis from which to model the propagation path, which is required to help satisfy the need for improved spectrum planning, mostly for sharing and coexistence studies. This need arises from the relentless pressure for more spectrum to serve both land and aeronautical mobile systems.

Plane old Earth on the sea!

Broadband cellular systems are becoming commonplace in maritime environments, with public and private networks desired over large sea areas to cover needs which were once uniquely served by satellite. To take advantage of economies of scale, land mobile cellular technology is often simply transplanted into the maritime context. In principle that is fine, however, propagation planning principles common in land mobile should not not be applied applied without forethought.

For example, planning methods based upon propagation models such as COST231 Hata that are often used in land mobile for predicting coverage and frequency planning are not suited to the maritime environment. These models account for a combination of physical effects for specific to a particular type of environment, and are not sufficient when taken out of context. Model tuning is the cell planners usual tool to improve validity, but it doesn’t really help, as fundamentally these models account for different physical effects, so a rethink in modelling approach is required.

Of course the maritime environment is not characterised by building or vegetation clutter, hence any approach based upon them is likely to come unstuck. However, whilst the environment is largely uncluttered in terms of obstacles above the surface of the sea which would cause diffraction losses, the sea surface itself is an excellent source of scattering that can lead to undesirable effects, as well as a source of shadowing due to waves in high sea states. Furthermore high seas are the potential source of unstable antenna platforms. These issues and many others are well understood by designers of other types of radio system deployed in a maritime context, and something useful can be learned from them.

In the radar world, designers are familiar with sea clutter, which is the term used to describe the excess information that can appear on a radar display as a function scattering for a given sea state. Other issues include lobing effects limiting range in the elevation plane due to surface reflection in calmer seas. Much of a radar system processor is devoted to alleviating these effects without compromising the ability to detect valid targets. In the fixed link world, paths crossing larger bodies of water may suffer heavy fading, particularly in calm conditions and space diversity in the vertical plane is often used to mitigate fading.

So, for maritime mobile network some of the considerations and techniques can be borrowed from fixed link and radar planning. One of the most basic things is to understand the nature of reflections from the surface, and in fact early planners of land mobile systems were quite aware of this, and simply talked of plane Earth modelling. In this case the effects of a specular refection is considered from the surface, and the interference pattern predicted for typical path geometry. Unfortunately common mobile radio diversity techniques with small displacements between antennas offer less relief than in a cluttered land mobile environment, which means that the antenna height of the mobile system must be carefully considered to avoid the effects of severe fading.

The plot below shows an example of the fading effect from surface multipath for a system with a base  height of 100 m operating at 1.5 GHz to a receiver antenna height in the range 0 – 40 m above the sea surface at a range of 10 km.

Height-gain-over-free-space

In this case significant fades are present at multiples of 10 m, so unless the fades can be tolerated, the antenna configuration would require optimisation to ensure that bad heights are avoided, or a diversity configuration could be chosen with optimal antenna separation. These issues are well understood and have a clear impact that can demonstrated whatever the sophistication of current mobile technology.