Ray-tracing data are usually given as angles of arrival and departure, transmitter and receiver coordinates, ray length and delay, received power level, and polarity. Usually, these values are given in raw data with some resolution that covers the area of interest where the simulation is performed. There are two main drawbacks of such approach: first, a huge amount of storage capacity is typically needed and second, although the area of interest is covered by a certain resolution, it is nearly impossible to interpolate between sample points and new time, and memory consuming simulations are necessary in order to increase the resolution of the simulations. This paper addresses the two mentioned drawbacks of ray tracing, suggesting a procedure based on the concept of ray entities both to enable continuous interpolation of ray-tracing data and reduce the memory needed for storing data. Ray entity is a set of rays that all undergo the same series of propagation phenomena (direct ray, diffraction, reflection, or scattering) on the same objects (building walls or edges). The method is given and illustrated for reflection and diffraction phenomena, and diffuse scattering was not included, but discussion is easily extended to this propagation type as well. The paper gives detailed statistics of entities' length and rays' count per simulated receiver point in few illustrative examples and provides an insight on how to interpolate angles of arrival and departure, ray length, and received power level in order to provide a continuous description of the radio environment.
The importance of reference channel models (RCMs) as a distinct kind of radio channel modeling has already been widely realized [Almers et al., 2007]. RCM's purpose is to adequately simulate typical radio environment properties and thus be used as a test platform for the development of new generations of access radios, exploring modulation and coding techniques, different smart antenna and multiple-input multiple-output (MIMO) system designs, etc. Most of the commonly used RCMs are stochastic, or more precisely, geometry-based stochastic channel models (GBSCMs). This means that GBSCM parameters are generated from some stochastic process [Almers et al., 2007; Haneda et al., 2011]. Therefore, these models suffer the risk of unrealistic channel realizations due to their random nature and of inaccuracies of the parameterization extraction approximation.
Current GBSCMs are mostly measurement based, so prior to parameterization, data from real-world measurements are needed. Besides the fact that measurements are time consuming and expensive, additional limitations are caused by antenna properties, phase synchronization, measurement errors, and random events that could be present only while specific measurement is taking place and especially if measurements have not been repeated on the same route or measurement set, which is shown in earlier studies [Molisch et al., 2006; Asplund et al., 2006; Correia, 2006; Sirkova, 2006].
Deterministic RCMs are suggested as a possibility in earlier paper [Katalinić Mucalo et al., 2012], but they are still not explored enough as an achievable option for RCMs, mainly due to their complexity and vast system requirements. The feasible alternative for feeding geometry-based deterministic RCM would be a set of ray tracing (RT) simulated environments. Ray tracing allows high-resolution simulations, thus providing a very detailed description of the radio environment and the propagation phenomena. However, RT is a very time-consuming process with extremely high demands for both CPU time and memory capacities, in order to store and manipulate all the data necessary for a very fine spatial resolution. Also, RT computational burden grows significantly with the number of considered receiver points. In this paper it is elaborated how to decrease stored RT data and enable interpolation of omitted receiver points while ensuring even higher resolution than the ones originally sampled. These, at first hand, contradictive aims are achieved by smart interpolation process using ray entity concept that in the end decreases needed computational time and complexity, while preserving the accuracy of the full ray-tracing model.
The paper analyzes the arrangement of the rays in an urban multipath environment and in particular, virtual sources in cases of reflection and diffraction propagation with up to two interactions. Similar work on ray dynamics in multipath environment has already been done in [Katalinić Mucalo and Zentner, 2011] and showed that due to the nature of diffraction, there is no common stationary virtual source of neighboring rays even when ending very close (below 1 m) to each other and in spite of undergoing identical multipath interactions. In that work, any considerable visibility length could be obtained only by approximation using tolerance, basically approximating VTx locus, which is part of a circle, by a point. The motivation for that was to obtain parameters for stochastic based reference channel models that incorporate stationary clusters, i.e., virtual sources, but no virtual sources that move in correlation with user movement. Further in the paper, ray entity definition will be given and will be different from one in [Katalinić Mucalo and Zentner, 2011].
Appreciating the finding that diffraction causes virtual source of rays to move in correlation to moving of receiver [Zentner et al., 2013], this paper analyzes a new method for detection of visibility area and virtual sources for moving receivers. The paper elaborates the method for determining trajectories of virtual sources and how those trajectories can be utilized for the interpolation of RT results. The paper is limited by taking into account only direct rays and reflected and diffracted rays up to two interactions per ray. Although a 3-D RT tool [Degli-Esposti et al., 2004; Fuschini et al., 2008.] used for feeding the interpolation engine is calculating both diffuse scattering and over-the-roof diffraction, in this paper these two propagation modes are not considered. However, the discussion and presented concepts are easily extensible to these propagation phenomena as well.
The paper is organized as follows: In section 2, the concepts of reflection and diffraction propagation phenomena, ray entities, and virtual sources will be shown as well as using those concepts for the interpolation of RT results. In section 3, ray entity detection will be explained for three examples in an urban scenario, and the statistics of ray entity lengths will be given. Section 4 will discuss receiver and virtual source trajectories that are needed so that interpolation of ray length, angles, and power can be interpolated for enhancing RT performance and as a building block of deterministic RCM. The paper ends with conclusions given in section 5.
2 Ray Entities and Virtual Sources
Figures 1 and 2 give 3-D view and top view (ground plan) of a simple setting of one transmitter (Tx), three buildings, and a receiver route of interest. Figure 1 describes reflection points, virtual source, and ray entity for reflection, and Figure 2 describes the same for diffraction. In Figure 1, rays reflected from the building wall will, due to geometry reasons, be present only at the portion of the receiver route (red line) from Rx1 to Rx2 (green line). The set of rays from Rx1 to Rx2 is called ray entity (RE), in which all rays undergo the same propagation phenomenon, here reflection from the building wall. Another property of this RE is that all rays arriving at the receivers come from the identical stationary virtual source, VTxR.
Figure 2 depicts a ray entity which occurs due to a single diffraction at the vertical edge A. Due to the shadowing from edges B and C, this ray entity is also present at the receiver route from point Rx3 to Rx4 (green line). Here, in case of diffraction, virtual transmitter is not a single point for the whole entity but a section of a circle, from VTx1 to VTx2, and slides circularly as the receiver slides along the route section, where entity rays are present. The diffracted ray incidence angle to the edge equals the Keller's  cone semiangle which is described in Keller ; McNamara et al. .
Virtual source for diffraction from vertical edges is often considered to be the last interaction point on the building edge. However, looking from the receiver's perspective, it is much more convenient to extend the ray with the same spatial angle in the direction of the interaction point on the edge for the length of the ray from that interaction point to the transmitter. Thus, the locus of virtual sources for diffraction ray entity is not a line along the interaction edge but a section of a circle at the height of the transmitter and parallel to the ground as can be seen in Figure 2. Since VTx circle is defined with any three points, it is possible to interpolate any virtual source and from calculated VTx to obtain ray properties for any receiver point along the route by extending the ray through the building edge to the route with straight line. Thus, rays at the receiver points along the receiver route that were not previously simulated using RT can be easily calculated using the existing Tx coordinates, edge coordinates, initial ray length, and VTx circle virtually at no computational cost. For pure reflections, there is no need for interpolation of virtual source, since the virtual source is stationary for this kind of propagation as can be seen in Figure 1. For multiple interactions, i.e., double diffraction, reflection with diffraction, and diffraction with reflection, the situation is a bit more complex. Figure 3 shows double diffraction in 2-D and 3-D, where it can be seen that moving the receiver changes only the length and angle ∠ TxRxE, so virtual sources for double diffraction are also sections of circles that can be easily calculated by extending the ray with the same elevation angle from Rx through point B to Tx; i.e., the triangle RxETx can be unfolded as depicted in Figure 3b. It should be noted that in Figure 3, Rx route and all three buildings have the same ground level. However, even when the elevation of point E is different from the elevation of point Rx, the triangle stays the same; only the vertical cathetus length is now hTx + Δh, where Δh is the difference in ground level heights between the receiver and Tx. For events where the first interaction is diffraction and the second interaction is reflection, if we mirror the receiver route in relation to the reflecting wall, the interpolation is simplified to the one diffraction case. For events where the first interaction is reflection and the second interaction is diffraction, if we mirror the transmitter in relation to the reflecting wall, the interpolation is again simplified to the one diffraction case.
Detection of ray entities is rather simple. For each ray obtained by RT, a signature is assigned, that contains subsignatures of identity of the first and second interaction objects (edges and surfaces) at which the ray lands and the types of interactions (diffraction and reflection) that the ray undergoes there. Then all rays with the same signatures and neighboring each other at Rx side are grouped into same entity, and the entity's minimal set of parameters for its description is recorded. A list of these parameters will be given at the end of the paper, in discussion about memory requirements for storing entities.
The virtue of ray entity concept is that a number of rays obtained by ray tracing and belonging to the same ray entity can be stored as one ray entity, and it will be shown how those memory for storing ray-tracing data can be spared.
Once the ray entities are detected and stored, not only the initial RT results at initially simulated discrete Rx points can be retrieved at small computational cost but also the RT results on arbitrary locations between these discrete Rx points can be obtained by interpolation, under assumption that there exist only ray entities present at the adjoining Rx points.
The ray entity record can also offer an estimate of sufficiency or insufficiency of initial Rx resolution, that comes from observing RT results without need for variation in resolution, by counting how many entities were formed only at a single Rx. This criterion will be applied on results in this paper and give resolution of 1 m to be quite reasonable for considered environments.
It is worth noting also that unnecessarily high resolution of receivers during initial RT simulation would not increase memory need if data are stored as ray entities, whereas in conventional storing of all ray data, memory space is roughly proportional to resolution increase.
Therefore, ray entity concept offers users versatility according to their needs and computer capacity. Either they can carefully estimate when initial Rx resolution is sufficient, and then form ray entities for further use of data, or go using “brute force” by having very high initial Rx resolution and then form ray entities for further use. In both cases, results would usually be similar, in former case, sparing some initial computer power on expense of potentially missing some entities and in later case, using excessive computer power for reduced risk of missing some entities.
3 Detection of Ray Entities From RT Results
The analysis is performed on RT-simulated radio environments, where a mobile unit is slid incrementally along a receiver (Rx) route. All rays obtained from simulations are compared by their interaction points (walls or edges) and propagation modes (direct ray, reflection, and diffraction) and then grouped into ray entities, consisting of rays which underwent same types of propagation effects, in the same order, and on the same objects. Rays within the same RE form an entity visibility region, a section of a receiver route.
An example will be given using three RT simulations on a map of Stockholm (Figure 4). The first simulation route is the shortest, a 39 m long straight route 1, the second simulation is 238 m long L-shaped route 2, and the third simulation is 100 m straight route 3. All three simulations have resolution of 1 m; i.e., Rx samples are taken every 1 m. The propagation modes simulated were line of sight: first- and second-order reflection, first- and second-order diffractions, and mixed rays.
Table 1 presents properties of each route, i.e., overall number of rays, range, and average of the number of rays at a single Rx point. All rays regardless of power were included under “raw data (no threshold)” section, but also, same data after applying power threshold of 150 dbW was considered as well, under “power threshold 150 dbW” section. The power threshold was set to −150 dbW since most modern communication systems already have few orders of magnitude weaker receiver sensitivity even for simple modulations like quadrature phase-shift keying.
For routes 1, 2, and 3, the power threshold reduced the total power at the receiver locations on average for negligible 0.0037 dB, 0.00048 dB, and 0.0029 dB, respectively, and the maximal observed reductions at any one Rx were 0.0044 dB, 0.004 dB, and 0.013 dB.
Raw data are interesting because imposing threshold may cut entity into two or several entities, and data after imposed power threshold are interesting since these data are more likely to be relevant in practice.
Figure 5 shows the distribution of entities detected along the straight route 1 by their length. It is given for a case with no power threshold on rays (Figure 3a) and with power threshold (Figure 3b). Observing Figure 3, one can see that a significant portion of entities is of length 1, i.e., was detected only at Rx point in RT simulations. This may suggest that Rx resolution of 1 is not sufficient and that many entities of shorter duration would be lost. However, more fair estimation of single-point entities' contribution would not be from the distribution of entities by their length, but rather from the distribution of rays by entity length, since shorter entities are less significant compared to longer entities, and the distribution of rays by entity lengths will resemble this fact.
Figure 6 shows the distribution of detected rays by entity length along the straight route 1, and it can be seen that a portion of rays allocated to the shortest entity is quite small. This fact suggests that it is, in the case of route 1, reasonable to conclude that Rx resolution of 1 m was quite sufficient.
Regarding difference between data with and without power threshold, Figures 3 and 4 show that an expected proportionate difference in overall number of rays and entities is present, but there is no significant difference in distribution shape. Since for routes 2 and 3, also, no significant difference in distribution shape was observed, for them; only cases with power threshold will be presented.
Figure 7a shows the distribution of entities by length, and Figure 7b shows the distribution of detected rays by entity length, along the L-shaped route 2, for case with −150 dbW power threshold. Although Figure 5a shows that portion of the shortest, 1 m long entity is largest, Figure 5b clearly shows how negligible is the amount of rays that form the shortest entities, comparing to the amount of all rays obtained in RT simulations.
The same can be said for route 3, presented in same way in Figure 8. Therefore, for all routes considered, it is quite certain that the resolution for RT of 1 m was sufficient.
Figures 3, 6, 7, and 8 show that numerous ray entities of considerable length are detected in considered example scenarios.
4 Interpolation of RT Results Using Ray Entities
One entity from L-shaped route (route 2) with the visibility length of 86 m shall be used to illustrate typical relationship between the actual source, interaction points, entity visibility, and virtual sources. Figure 9 gives a ground plan of a scene in Figure 4 (route 2), but with a limited number of elements, only those relevant for this entity: location of transmitter (red triangle), actual raypath (red), entity visibility range (green), and locus of virtual sources for the entity. Figure 9 conveniently shows ray entity that is present along one street of L-shaped route and then disappears shortly after the receiver enters the other street of the route.
Figure 10 gives the ray power at Rx location along the route section where the entity is visible, which can be represented with few-element polynomials. Figure 11 gives the interpolated ray power along the 50 m long entity. Interpolation, i.e., curve fitting was done with fourth- (Figure 11a) and fifth- (Figure 11b) degree polynomial fit. This way for a negligible residual fit error, instead of storing 50 data points, only 4 or 5 polynomial coefficients are stored.
Table 2 gives all values needed and stored for each ray entity for future reconstruction, i.e., interpolation of rays. The procedure of finding rays present at a given arbitrary receiver location using ray entity data is rather simple. First, algorithm finds all entities present at that location. Then from parameters that describe ray entity and from locations of Tx and Rx, all ray properties can be recalculated. For example, through x and y coordinates of the last interaction, entity delay offset, location of Rx, and Tx virtual location can be determined using simple geometry and then angles of departure and arrival and time delay follow. Power is interpolated by finding relative location of desired Tx within the entity (using entity data about its start point) and polynomial interpolation.
Table 2. Comparison of Number of Entities and Number of Rays and Corresponding Number of Values Needed to Describe Them
Number of Rays
Number of Entities
No power threshold example
Power threshold example
Values necessary to describe a ray/entity
Ray length/time delay
Entity start (integer index)
Entity end (integer index)
Entity delay offset (i.e., virtual Tx locus radius)
Ray arrival location (integer index)
Last interaction (edge) x-y coordinates (point E in Figure 8), to ensure calculation of correct virtual Tx on a circle, for each Rx
Entity power polynomial interpolation (five coefficients)
4 real + 1 integer
8 real + 2 integer
The fourth-degree polynomial has SSE (sum of squared errors) 9.81E–29, with R square (coefficient of determination) 0.9906, and RMSE (root-mean-square error) 1.477E–15. The fifth-degree polynomial has SSE 1.557E–29, with R square 0.9985, and RMSE 5.95–16. It should be noted however that the average received power for 50 samples is 1.155E–14 W.
If we exclude the first sample due to Runge's phenomenon, then for the fourth-degree polynomial fit, maximum residual value (difference between polynomial fit and actual value) is 2.576 dB and the minimum residual value is 0.053 dB with average residual value of 0.766 dB. For the fifth-degree polynomial fit, maximum residual value is 0.845 dB and the minimum residual value is 0.0023 dB with average residual value of 0.307 dB. From the given results, it can be seen that it is advisable to use the fifth-degree polynomial fit for the received power interpolation.
Representation of ray-tracing simulations by ray entities can reduce memory usage, and interpolation by virtue of rays sorted in ray entities enables more refined results at small additional computational cost. Reduced memory requirement can be argued in Table 2, which gives comparison of the two examples of L-shaped route scenario with and without power threshold imposed on rays. It shows that storing ray-tracing simulation as ray entities would require less than a double memory per entity as per ray. Significant memory reduction is expected since the number of entities is significantly smaller than the number of rays; in the two examples given, the reduction is 19.5–21.4 times. Thus, the overall memory usage reduction is about 11–12 times. Table 2 gives values only for diffraction cases from two reasons. First, because the three simulations considered, as the most of typical urban environments, were dominated by diffraction. Second, REs based on pure reflections have a stationary virtual Tx, thus making their recording even simpler and less memory consuming. Only a dubious and hard to imagine case of environment dominant by many ray entities of very short duration along the receiver path could see no improvement or even disadvantage in memory usage when using RE approach.
Table 3 sums up all features of comparison between classical ray tracing and ray entity based interpolation method. Although reduced memory usage for a factor of 11 may look as an interesting feature, the major advantage of this approach is the ability to interpolate RT results to arbitrary high resolution. This feature is available after initial RT simulation and after postprocessing is performed. This method can be repeated for the customized needs of the user. Thus, ray entity introduction enables simulations of radio channel with arbitrarily moving user, with arbitrary modulation and coding scheme, in wide-frequency band range and with sufficient spatial resolution. This can be used for the deterministic reference channel model of computer efficiency comparable to its stochastic based counterparts, but with much more realistic and standardized performance.
Table 3. Comparison Between Classical Ray Tracing and Ray Entity Based Interpolation Methods
Simple Ray Tracing
Entity Interpolation RT
Higher (11–12 times)
Lower (11–12 times)
Rx resolution (number of receivers at a certain area)
Fixed after initial RT run
Unlimited (can be increased arbitrarily after initial RT run)
Computational burden for increased Rx resolution
Versatility for including other effects (over the rooftop diffraction and diffuse scattering)
YES, with simple adaptation for each effect
The paper introduced a novel concept of ray entities as a versatile interpretation and postprocessing of ray-tracing data simulated in urban, rich multipath environments. It is hypothesized that combining of rays that undergo same propagation phenomenon into one entity can be of some benefit for reduced storage of ray data and may enable interpolation of ray-tracing results.
Examples given in the paper have shown that the memory needed to store ray-tracing results was reduced by a factor of around 11 to 12. Further investigation with more case studies is needed for more accurate value of reduced memory requirements, but it is clear that there will always be some reduction except in cases of large number of short entities, which is physically unfeasible except maybe in rare architectural cases. Since examples in the paper were dominated by diffraction, even more reduction can be expected in reflection-rich environments, where ray entity's virtual source is stationary.
The existence of ray entities and insight into their nature, such as dynamics of their power, angle of arrival, and their visibility area can improve understanding of urban multipath environments and inspire adapting radio system aspects to that understanding. For example, some adaptive beam forming or MIMO system could be designed having in mind the facts about continuous change of arriving ray properties, as mobile user is moving along an entity.
Ray entity concept also enables interpolation of ray-tracing results obtained for sufficiently closely located set of receivers. It enables, at negligible computational cost, obtaining of ray-tracing data of arbitrary high resolution.
Finally, ray entity concept is a step toward feasible deterministic reference channel model, a standardized channel model that would have database of RT-simulated typical environments, recorded in ray entity format. Next step would be to use similar algorithm and detect ray entities as 2-D surfaces, interpolate powers in 2-D, and to simulate a complete urban area with some arbitrary Tx resolution. This would enable users, who want to test and compare various wireless system concepts on a real environment, to do so in more a realistic way than it is the case with currently available stochastic based reference channel models.
The 3-D ray-tracing tool used in this paper was developed at the University of Bologna in a group of Vittorio Degli Esposti. The authors thank him for his kind cooperation.