Propagation measurements and analysis on MF and HF bands in urban areas in The Netherlands

Using a new propagation measurement set-up, which produces a high number of data, enabling a proper statistical analysis, and resulting in very concise results, propagation measurements were performed and analized at 16 residential locations in The Netherlands in the frequency range from 1.8 to 28 MHz. In the whole frequency range the propagation loss appear to be higher than according the International Telecommunication Union ground-wave propagation model might be expected. Also typical characteristics of that model are not present, but instead the propagation shows a constant roll-off in dBs per decade, which slope is increasing with frequency. A regression curve could be established, and constants filled in. This statistical information may be used for building an accumulation model to lay a causality between source powers, source densities, and local Man-Made Noise levels.


I. INTRODUCTION
In a study on the accumulation of man-made radio noise (MMN) by large numbers of noise sources, the propagation of the EM waves from individual noise sources to a point of aggregation is very relevant. MMN in the frequency range of 0.47 to 50 MHz was investigated earlier [1]. A further statistical study of the measurement results revealed that there is a strong correlation between the measured noise floor and the density of habitation [2]. These results raise the question of how does the radio noise propagate in these populated areas, and what is the propagation loss with distance. In the earlier mentioned frequency range, the wavelength vary from 6 to 600 m. As the field strength measurements were done at an antenna height of 2 meters, and the sources are located in homes mostly at the first, second or third floor, or in more dense areas in higher apartment buildings, these heights are also relative low. So, a very reasonable presumption is that the propagation may be described by the theory of the groundwave (GW) propagation. For a well understanding of this theory we will look into a part of the history. After Marconi had proven the ability of long range radio communication by his transatlantic experiments in 1901 the need for a theoretical explanation was first fulfilled by Zenneck [3] and Sommerfeld [4]. Zenneck introduced a surface wave as a solution for the Maxwell equations. Sommerfeld analyzed the case of a vertical Hertzian dipole over a lossy ground, and came also to the surface wave as described by Zenneck, hereafter called "Zenneck Surface Wave", ZSW. The main property of this ZSW is that the energy is trapped on the surface, and that the roll-off with distance is 10 dB/decade, instead of 20 dB/decade for a wave in free space. From 1936 on Norton showed in [5], [6], [7] that the ZSW could only exist under extreme conditions, and that Sommerfeld had made a mistake in his theory by a faulty interpretation of the square root of a complex variable, this resulting in the so-called "sign controversy". A complete overview of this history can be found in [8] and in [9]. In [10] Norton defined the GW as "A Radio Wave that is propagated through space and is, ordinarily, affected by the presence of the ground", with excluding any other reflections than against ground, as for example the ionosphere. In his solution the field strength at a distance from a transmitting antenna, a vertical dipole or a magnetic loop with the winding in a vertical plane, is given by an equation in [10], showing a sum of three terms. The three terms are corresponding respectively to the direct wave, the ground reflected wave, and the surface wave, generally called the "Norton Surface Wave", NSW. In the derivation by Norton the NSW is mathematically the result of the subtraction of the optically reflected Reflected Wave from the total of wave energy that is interacting with the ground. When the transmitting and the receiving antenna are close to the ground with respect to the wavelength the direct and the reflected wave will cancel, so the NSW is left. It is important to realize that the NSW is not trapped on the surface, in contrast to the ZSW, and that the roll-off with distance is minimal 20 dB/decade of distance. The values of the attenuation can be looked up on graphics in [11], a description is given in [12], and may be calculated by means of [13]. In this study, propagation in urban areas, all three wave paths in the GW theory are involved. The distance varies from 50 to 1000 m, in the measurements the transmitter antenna is at a level of 3 m and the receiving antenna at 2 m. That means that next to the NSW the direct and reflected wave may play a role, especially for the short distances and for the upper part of the frequency range. For all three paths the buildings may damp, reflect, or scatter all three waves. Especially tall vertical constructions as street lamps, towers, etc. may cause scattering, which, depending on conductivity and the ratio between height and wavelength, may cause forward, back, and random scattering. Buried conductors in the earth, like all kinds of cables and metal pipes, may enhance the ground conductivity, so decrease the attenuation of the surface wave. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < This is especially the case at the lower frequencies with the greater skin depth. We must remark here that overhead cabling is not used in The Netherlands, so does not play a role in our measurements. In the last decades propagation studies, theoretically and empirical, [14], [15], are mostly concentrated on VHF and UHF frequencies, especially in urban areas. In this frequency range the wavelength is small to very small with relation to the dimensions of the objects in that environment. For the MF and HF range the wavelengths are larger or equal to these dimensions. This also means that in the VHF/UHF range the wave interaction with the ground is less relevant and that free space, reflected, and scattered paths dominates. As a consequence these studies are not relevant in our case. There is a very limited number of studies about propagation in urban areas on frequencies below 30 MHz, and they are in essence limited to Medium Wave broadcasting signals. In [16] an extensive measurement campaign and theory building has been performed about the propagation from a local MW transmitter site North of London, through the city centre to the South of London, with a total range of 60 km. Three frequencies were involved, and interesting phenomena were recorded and theoretically explained. Herein the built-up environment with its buildings was modelled as a "bed of nails" like structure. However, in our study the relevant frequency range is higher, and the distance much shorter. In [17] field strength measurements were perform on the propagation of a local MW transmitter in São Paulo, Brazil. One of the results that were reported is: "the prediction model of Rec. ITU-R P.368-9 overestimates the measured field during daytime". Consequently the GW propagation losses were higher than expected. In [18] propagation measurements on HF frequencies were reported in open desert areas, as well as in urban environments. The conclusion in this report were that the losses in open areas matched the expectation within a few dB, but in urban areas a diversity of propagation losses was found when measured the GW propagation path, and varied all over the city. A need was concluded to develop a prediction model for urban environments. Reference [19] reports a new MF and HF GW propagation model for urban areas. It includes a fundamental addition to the Norton model by building-complex parameters and height-gain factors. The model applies for areas with high and tall buildings in particular. Only validating measurements at the medium wave frequencies were reported. We conclude that the existing models for propagation below 30 MHz handle urban areas as a local disruption in a wider area, mainly for the purpose of coverage studies of broadcasting transmitters. For our application, being short range intra-urban propagation of man-made noise in the MF and HF range, there is no sufficient scientific information available about measurement data, nor theoretical models, useful for a statistical modeling of accumulation of spatial spreaded noise sources, so leading to a conclusion that a measurement campaign was necessarily. The paper is organized as follows. In section II we describe the measurement methods, in section III the data processing and some theoretical aspects. Section IV describes the statistical analysis and the results thereof. Our conclusions are summarized in section V. In Appendix 1 we describe validation measurements, and in Appendix 2 we calculate the field strength above Perfect Electrical Conducting ground. At the end, Appendix 3 derives the equations to make field strength measurement corrections in the near field.

II. DESCRIPTION OF THE MEASUREMENTS
The goal of the measurement campaign is to gather statistical data about transmission loss as a function of distance, frequency, and of density of habitation. Thereto we need measurements on several locations in diverse environments. From the list of measurement locations, earlier used in [1], we selected a number of 16, and enumerates them in Table I. They all belong to contributing radio amateurs, the locations are coded in the table and further on in accordance with their radio call signs. Also the city is given and numbers of homes around that locations. The type of environment is given as defined in [1]. According these environments three groups of locations, I, II and III, are created with increasing density of habitation.
The principle of the measurements is based on placing a low power beacon transmitter at a fixed location and drive with a mobile field strength (FS) measurement system in a fixed traject from that location away up to a distance of about 1 kilometer and back via different path, depending on the local topography, and selectively measuring the field strength generated by that beacon transmitter. This drive is repeated for all test frequencies over the same traject: 1.85 (160 m band), 3.57 (80 m band), 7.07 (40 m band), 14.07 (20 m band), 21.07 (15 m band), and 28.07 MHz (10 m band). During the drive repeatedly measurement samples are taken at random varying distances 8 -16 meters between themselves, resulting in a high number of samples. The special designed beacon transmitter consists of a 19 inch cabinet, a 4 m high rod antenna, and two metal plates forming a counterpoise grounding, see Photo 1. Next to the transmitter, a commercial Elad FDM-DUO SDR transceiver, the cabinet contains an antenna matching circuit and a Morse code ID generator, which modulates the transmitter carrier in Frequency Shift Keying with a shift of 100 Hz. That is well within the bandwidth of the measurement receiver, so that the measurement is not disturbed by the ID transmission. The transceiver output power is set at 1 Watt. The RF carrier is measured at the measurement receiver. In principle this includes noise within the receiver bandwidth, but during the measurements the level of the beacon signal is that strong that external and internal noise does not contribute to the measurement result significantly. > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < Photo 1. View of the beacon transmitter.
For calibration the field strength has been measured at a distance of 25 m on a flat and undisturbed piece of grass land by using a calibrated magnetic antenna, the Rohde & Schwarz Z2 loop antenna. For the near field (lower frequencies) corrections were made according correction factors, derived in Appendix 3. Also for ground losses (upper frequencies, very small) compensations, calculated with GRWAVE, [13], has been calculated and applied. From these measurements the actual effective isotropic radiated power (eirp) has been calculated for each test frequency. The eirp values are to be used as calibration numbers in the postprocessing of the field strength measurements. The mobile FS measurement system was build in a passenger car. On the roof an active E-field antenna system is mounted, see Photo 2. The antenna groundplane as shown is well grounded on the roof and the bodywork of the car by a low impedance capacitive coupling through two self-adhesive copper strips on the roof, behind the luggage carrier strips. The capacitance per strip is 10 nF. Fig. 1 shows the principle diagram of the measurement system, and Photo 3 the equipment inside the car. The calibration of the mobile FS measurement system has been carried out for the system as a whole, including the car. arrival of the beacon signal during the measurement drives from the GPS data, using the stored location of the beacon, so to compensate for directional variations in the antenna-factor in real time.
For validating the measurement system and method measurement drives has been performed in flat and open areas as described in Appendix 1. Concerning seasonal effects on the propagation loss, monthly measurements were carried out throughout a full year, from September 2019 to November 2020, on a fixed traject, partly in populated area, and partly over open land. A clear relation with seasonal variation in soil humidity was found, but the maximal deviation from the median on the loss measurement, as caused by a total of 10 % to 90 % spread, was very limited, and varied from 1 (1.8 MHz) up to 3 dB (28 MHz). As a result no corrections were applied in our urban measurements.

A. Decimation of samples and the statistical approach thereof
For the purpose of the accumulation study an estimator is required in this experiment that is representing the propagation loss. We take here the expected value from the probability distribution function (pdf) of the propagation loss, thus the mean value in the pdf. µ But samples of FS levels are actually measured, which levels are normalized for an effective isotropic radiated power of 1 Watt, transmitted by the beacon transmitter. These FS levels are used as an intermediate result, they can be used to compare with the FS levels that are resulting from calculations according the ITU GW propagation model. In the post processing the measurement samples are grouped into bins, representing ranges of distances. The samples, inputted in those bins, can be measured on a single location, on a group of locations, or on all locations. They may be combined during the post processing in those bins. In this way a kind of parallel processing is achieved from: 1st the individual locations, 2nd the three groups of locations with comparable density of habitation, and 3rd from all measurement locations totalized together. From each bin an average value and a median value from samples can be calculated. Generally, appear to equal nearly in the measurement results. For higher numbers of and approach the pdf mean, and so the mean value, . In this case we use the linear values of the field strength for the statistical calculation, and the results are converted back in logarithmic values [dBµV/m]. In here the statistical processing complicates by the fact that in this field of engineering, basically, FS values are measured in a linear quantity, µV/m, on which the statistics apply, but the further arithmetics and presentations are done in logarithmic quantities, e.g. in dBµV/m (FS) or dB (propagation loss). For the average and median values this is not a problem as they can be converted from linear quantities into dBs and vice versa unambiguously. But deviations translate from linear into logarithmic values for a negative and for a positive deviation differently. This makes it necessarily to define and describe the complete processing procedure.
Herein is ≥0, , and because of the asymmetry in the ratios . The median FS value has to be normalized for an effective radiated power from the beacon transmitter of 1 Watt: To calculate the propagation loss the FS median is subtracted from the FS that would be measured when the ground is Perfect Electrical Conducting, PEC: l Me,j = 10 (LMe,j/20) Because of the sign in (4) the standard errors in will be reversed: Inversely, the linear standard error in the propagation loss is: l In this way we arrive at the same value for both polarities of , so one calculation suffice. In the graphics we use a dB scale, so there the both dB values and are used.

B. Estimation of the propagation pdf
Next step is to estimate the propagation pdf from the measurement samples. We use the t-statistics for an estimation as educated in [21]. For the point estimate µ we calculate: L µ,j = 20 * l µ,j (12) log [dB] From the estimated standard error in the propagation loss, we want to determine the Confidence Interval, CI, wherein . Accepting the middle 90% of the distribution, 10% is left on both trails together, so , two trails. For a degrees of freedom we look up a value for in the t-distribution table in [21]. The lower and upper end of the CI of is now given by: L µ_lower,j = 20 * l µ_lower,j Reference [20] defines several kinds of transmission loss. However, for calculating interference risks as in relevant CISPR EMC standards often the propagation characteristics of free space is used, resulting in a 20 dB roll-off per decade of the distance. So for reference it is relevant to know the increase of transmission loss with distance for the free space condition. Under far field condition, assuming an electrical dipole as transmitting antenna, we calculate the free space power density and the field strength as: The free space propagation loss 4 we calculate from equation (20): (22) log log = 20 * (d) (23) log From our measured FS levels we want to calculate the "Excess Propagation Loss" by comparing with the FS calculated for PEC ground and with ITU ground type "Land" [11] [12] with a mediate conductivity of 3 mS/m and relative permittivity of 22. From equation (4): Limited to the far field ranges, we may calculate the full propagation loss by:

IV. STATISTICAL RESULT ANALYSIS
Applying the foregoing calculations on the measurement results result in Figures 2, 3 and 4 for resp. 1.85, 7, 14 and 28 MHz. In those plots the processing results are collected for the three groups of location with increasing density of habitation and for all locations totalized. Remark that the excess propagation curves related to "Land" show a transition from increasing to constant at a distance related to the wavelength. We find this transition distance back in GW field strength curves in [11], where a transition in the roll-off from 20 dB/ dec. to 40 dB/dec. takes place. This transition is characteristic for GW propagation model, see [5] and [11]. We may conclude from the plots in

A. Regression analysis: Correlation to a straight line and its slope
Inspecting the measurement results leads to the conclusion that the extra path loss above the loss according to GW propagation over PEC, in relation to the logarithmic value of the distance, is well approached by a straight line. For considering a correlation with a straight line we may write: Now we arrive at a linear relation between in dB and . With this relation we assume a case of interval measures, implying we may apply the Pearson correlation test, using the Pearson product-momentum L f ull D = 20 * (d) log 6 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < coefficient, [21]. Here a measurement ensemble consists of the measurement results on a single frequency band on a number of distances as samples to . In this study varies from 3 to 11.  As mentioned before we want to compare our measurement results with the free space roll-off with distance of 20 dB/ decade, starting at the reference distance of 10 meter. This means that we must force the regression line going through the point dB and . So for (= 20 dB/dec.). We can arrange that by, instead of the average values for and (13), substitute and in the formula for the slope of the regression line (31): The degrees of freedom is now given by , one higher than in the standard Pearson correlation test, as one fixed sample point has been added. is the number of bins involved.
The calculations has been performed for all three groups of locations and for all locations totalized. We show here the results for all locations totalized only and for four frequencies. Figures 5 -8 are resulting. We find a high correlation coefficients and roll-off slope of 26.6 to 43.1 dB/decade of the distance. r All resulting values for the Roll-Off slope are shown in Fig. 9 as a function of the frequency. Also here a regression line can be drawn, which leads to a general approximation of the ield strength roll-off with distance for frequencies between 1 and 30 MHz. The result is sumarized in Table 2 Fig. 9. Roll-Off slope as a function of frequency. Results from the three groups and all locations together.

V. CONCLUSIONS
In the study of accumulation of man-made noise on MF and HF frequencies in urban areas propagation may play a significant role. Information from foregoing propagation studies appear to be unsatisfying, so a new experiment had to be set-up wherein a mobile field strength measurement system, in combination with a stationairy beacon transmitter, performed propagation measurements at a small scale with hundreds of measurement points at propagation distances up to 1000 meter. This method produces a high number of data and allows to run a proper statistical analysis, giving very concise results. From these measurements at sixteen locations in The Netherlands at six frequencies from 1.8 to 28 MHz the conclusion can be drawn that propagation in urban areas do not follow the ITU GW propagation model, but show higher propagation losses, increasing with frequency, and show a constant roll-off with distance. The slope of this roll-off is frequency dependant according a linear regression as depicted in Fig. 9 and numerically displayed in Table II. Stochastically there is a small dependency on the density of habitation, as shown in the table and visible in Fig. 9, but at individual locations the local topography is strongly relevant. The so found statistical information about propagation loss in residential areas may be used for building an accumulation model to lay a causality between source powers, source densities, and local MMN levels. We would recommend others to do propagation experiments in other urban places, using equivalent methods, to verify and broaden our results.

APPENDIX 1. VALIDATION MEASUREMENTS
To validate this method of measurement of the propagation loss a number of validation measurement has been carried out. By definition these measurements should be done outside residential areas in open fields where the ITU GW propagation model according [11], [12], [13] should apply. As the ground in residential areas has been paved for a large part, also for the reference measurements two traject with a concrete surface were sought. The three trajects, all in the Netherlands, were: 1 A 3 km long, nearly straight, farmer's road near Kloosterhaar, brick road, vast open area, grown crops, only two trees halfway the road. Groundwater level: -1.2 m. 2 A 1000 m long, 25 m wide, runway of the general aviation airstrip near Drachten, asphalt concrete. Small airport building 150 m from the beacon location, business area at 150 m distance next to the runway at the far end. 3 A 2 km long, 50 m wide, decommissioned part of the 3 km runway of the military airbase Deelen, asphalt concrete, forest at 400 m distance at one side next to the runway. Dry sandy soil. The measurement results are shown as normalized field strength levels next to calculated field strength levels according the ITU GW propagation model for a series of standardized types of ground, and for Perfect Electrical Conducting ground (PEC), all for an isotropic effective radiated power of 1 Watt. The measurements are performed at ten frequencies in the range from 1.8 to 28 MHz. Because of limited space we will show the plots of three frequencies here, showing the three locations together. A few observations we will mention here. In the measurements at Kloosterhaar we see a good propagation for lower frequencies and bad propagation for the higher frequencies. We explain that by the influence of the groundwater causing an enhanced conductivity deeper in the ground, having influence at the longer wavelength. At the higher frequencies the extra losses caused by vegetation is having an effect, especially the effect of the 2 meter high crops in the distance range of 200 to 700 m is visible. At Deelen the underground is sandy and dry, so bad propagation for low frequencies, but for the high frequencies the effect of > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < the runway pavement appear to be relevant. In the measurement on the runway of Drachten the conducting effect of buried cables from decommissioned runway lighting is showing up on the lower frequencies. We conclude that these measurements show results being well inside the range we might expect, and so validate the measurement system and method.