Coverage prediction for digital mobile systems (Part 1)

The rapid growth in mobile communications systems over the past several years has lead to increasing use of digital modulation techniques to transmit information. Whether it's cellular, PCS, paging, two-way mobile or SMR trunking, essentially every aspect of mobile communication has been affected by the "digital revolution." Digital techniques allow much greater flexibility for encoding and processing information, which makes possible more efficient and robust transmission than previously achieved with analog systems.

In designing any radio system, a fundamental task is to predict the coverage of a proposed system and to determine whether the intended service objectives are met. Over the years a wide variety of approaches have been developed to predict coverage using what are known as propagation models. Propagation in this context simply means the transfer or transmission of signals from the transmitter to the receiver. Propagation modeling is an effort to predict what happens to signals en route from the transmitter to the receiver. Obviously the signal gets weaker, and everyone has experienced other signal impairments such as multipath fading. In large part, the design of modulation techniques and radio system hardware, including antennas, is directed toward combating the signal impairments that happen during propagation.

The traditional approaches to propagation modeling, which have been developed for analog systems, were intended only to predict signal attenuation, or path loss, as the signal traveled from the transmitter to the receiver. While these approaches have been adequate for most analog systems, digital systems need new techniques to produce other information in addition to path loss. This information may actually be the controlling factor on system performance or coverage, even when the signal-to-noise ratio is well above the value otherwise necessary to achieve perfect reception.

In the following sections of this article, various approaches to propagation modeling will be discussed with a view toward their strengths and weaknesses when used with digital systems. The most incisive approach based on ray-tracing techniques will be used to explore some of the propagation factors which specifically affect digital system performance and coverage.

Empirical vs. physical models The most common approaches to propagation modeling are:

*empirical models that use measurement data to define a model path loss equation.

*physical models of path loss that use physical radio wave principles such as free space transmission, reflection or diffraction.

Empirical Models — In the VHF/UHF frequency bands, examples of empirical propagation models are the FCC and ITU-R models (see References). The FCC uses propagation curves that were fitted to a set of signal strength measurements done at several locations in the United States. The propagation model as represented by a set of curves for different frequency bands shows field strength vs. distance for a range of transmit antenna height above average terrain (HAAT) values. The ITU-R has similar curves based on HAAT as set forth in Rec. 370-6. The ITU-R method also provides for corrections to take into account "terrain roughness" or [DELTA]h, the 10% to 90% inter-decile terrain variation over the path. These models make use of measurement data instead of electromagnetic wave principles to define the prediction. As such, the FCC and ITU-R models are classic examples of purely empirical models.

Another model commonly used in mobile radio and cellular work is the Hata model, which is a set of equations based on measurements and graphs developed by Okumura. This is also an excellent example of an empirical model.

Empirical models use what are known as "predictors" or "specifiers" in general statistical modeling theory. Predictors are parameters which have been found through statistical analysis to bear a relationship to (are correlated with) the quantity which is to be predicted. In econometric models, the objective may be to predict gross national product (GNP). In doing so, the model may use values such as unemployment, disposable income or balance of trade as predictors. All of these factors may have been found to be correlated with GNP, but none of them directly causes GNP to go up or down. Similarly, in the field of psychology, one may find a correlation between a child's IQ and the family annual income, but higher family income does not cause the child's IQ to be higher. There are other mechanisms at work. In medicine, misinterpretation of the significance of empirical studies have lead to such absurd headlines as "Coffee causes cancer." The textbook axiom is "Correlation does not prove causality."

In the case of the FCC model, through statistical analysis, a correlation was found between antenna HAAT and signal strength. But this was only correlation, not a causal relationship. Indeed, one could not conceive of a radio propagation mechanism where the simple average elevation value directly changes the magnitude of an electric or magnetic field at the receiver. The consequence of this approach is easily illustrated in Figures 1 and 2 on page 38, which show two terrain profiles along a 25km path separating the transmitter and receiver. The 3km-16 km HAAT values (as specified in the FCC Rules) for the transmit and receive antennas are the same for both terrain profiles in Figures 1 and 2, but the field strength at the receiver will be much lower in Figure 2 due to the obstruction of the nearby hill. A similar example could be constructed for [DELTA]h in which a valley and a mountain along two paths both have the same inter-decile elevation variation, yet the field strength at the receiver on the path with the mountain will be much lower than on the path with the valley. The inability to explicitly account for particular features of the propagation environment is perhaps the greatest limitation of empirical, measurement-based models.

The accuracy and usefulness of such empirical models also depends on the environment where the original data for the model was taken and how universally applicable that environment is. A common problem is trying to use empirical models in areas where the propagation environment is widely different from the environment where the data was gathered. In the Hata model based on the work of Okumura, propagation path loss is defined for "urban," "suburban" and "open" environments. These correction factors in Okumura's work are an effort to refine the predictions, but unless the characteristics of "urban," "suburban," and "open" for your study area are reasonably similar to those in Japan, where the measurement data was taken, these finer-grained classifications may not be of much use.

In spite of their limitations, empirical models such as the FCC, ITU-R, and Hata models are still widely used because they are simple and allow rapid computer calculation. They also have a certain "comfort" factor in that people using them in certain circumstances over time have come to know what to expect and to make their own ad-hoc "corrections" to the prediction values provided by the model. When the propagation environment is fairly homogeneous and similar to the environment where the model measurements were taken, an empirical model can achieve reasonably good prediction results.

With the recent advent of automated field strength measurement systems with GPS position logging, it is now relatively easy to acquire vast amounts of measurement data. This has lead to the use of custom empirical propagation models that are path-loss equations or formulas "tuned" for a given system, or even for a given transmitter or cell base station within a system. With such extensive use of measurement results, however, it is appropriate to question whether these models are really prediction methods at all, when in essence the answers are used to "predict" the answers. In spite of their heavy reliance on measurement data, such customized models will still fail to adequately account for propagation environment features such as the hill in Figure 2.

Digital communication systems require a wider variety of information from propagation models than just signal strength to predict coverage and performance. With empirical models, each new category of information represents another set of measurements that has to be taken. As an example, RMS delay spread (defined later) has recently become a routinely used factor in predicting the performance of wideband digital communication systems. For an empirical model to be useful for such systems, another set of measurement data using a channel sounder would have to be acquired and appropriate statistical analysis would have to be done to determine statistically significant predictors of RMS delay spread. All the same limitations of empirical modeling pointed out above would still apply, but when signal strength and RMS delay spread predictions are both considered as separate dimensions in the prediction problem, the difficulties of the empirical approach multiply. This problem is aggravated as other information types such as signal fading statistics are added. As the amount of data increases, the attraction of the empirical modeling approach diminishes.

Physical Models — Unlike empirical propagation models, physical models don't use measurement data for predictions but instead rely on physical laws governing the interaction of electromagnetic waves with the physical elements of the propagation environment. Fundamentally, all of these interactions can be derived from Maxwell's equations (see Balanis, References).

To be effective, physical models require detailed descriptions of the elements of propagation environment for their predictions. For this reason, the weakness of physical models is that they require extensive databases of information (such as terrain elevations, building wall locations or surface material characteristics) that in turn require significant computer resources to take all this information into account to perform the required propagation calculations. To reduce this problem, simplified descriptions of the propagation environment are usually employed. A typical example is representing an obstructing mountain ridge like that shown in Figure 2 as a single isolated "knife-edge." The effect of a single knife-edge on the signal is readily found from classic diffraction theory to provide a field strength prediction at the receiver. The problem is whether a real mountain ridge can be accurately modeled as a knife-edge. Clearly, no mountain ridge is really a knife-edge. Other methods to more accurately represent the mountain ridge have been used. In each case where a new model of the obstacle was employed, the physical principles governing the effect of the "model" obstacle on the radio waves were known.

The important aspect of physical propagation models, and their primary distinction from empirical models, is that they attempt to predict the field strength at a precise point in space by considering the specific propagation environment circumstances involved. For this reason, they can be regarded as site-specific models. Given a particular transmitter and receiver location, and the propagation environment, a site-specific physical model will provide a tailor-made prediction of the field strength at that point and, as will be shown, other channel response characteristics. Site-specific physical propagation modeling is the approach used here to explore coverage prediction for digital mobile radio systems.

Traditional single path models Commonly used propagation models attempt to predict the signal strength at the receiver by calculating the path loss for a single radio propagation path from the transmitter via a great circle route to the receiver. Models such as TIREM and Longley-Rice are examples of physical models that predict signal strength using a single propagation path. (Footnote: Strictly speaking, TIREM and Longley-Rice are not pure physical models, since measurement results have been used to establish certain parameters in each model.)

Even using the assumption that signal energy arrives at the receiver via a single path only, useful results can still be obtained. Figure 3 on page 41 shows a map of predicted received power levels for a five-transmitter system using the TIREM model. With receiver signal power predicted, and knowing the system noise, digital modulation type and data rate, it is straightforward to display maps of bit error rate (BER) as shown in Figure 4 on page 42. By taking into account relative propagation path length delays from various transmitters, and their relative signal strengths, maps of simulcast delay spread can also be readily created as shown in Figure 5 on page 46. Such maps are especially useful for digital paging systems where time delay and frequency offsets can be assigned to each transmitter to re-locate and control the interference areas. Prediction tools, such as EDX SignalPro software, that provide this capability, allow the system designer to quickly evaluate many different offset configurations from a notebook or desktop computer without making time-consuming and expensive field measurements to interactively assess and adjust these parameters.

Although single path prediction methods are a useful starting point, for modern digital systems the answers can sometimes be inadequate or even misleading as will be shown in the concluding part of this article series.

References Anderson, H.R. "A Ray-tracing Propagation Model for Digital Broadcast Systems in Urban Areas," IEEE Transactions on Broadcasting, Sept. 1993. Anderson, H.R. "Site-specific BER Analysis in Frequency-selective Channels Using a Ray-tracing Propagation Model," Proceedings of the 1994 Globecom Conference, San Francisco, Dec. 1994. Balanis, C.A. Advanced Engineering Electromagnetics. John Wiley, New York, NY, 1989. Code of Federal Regulations Title 47, FCC Rules, Part 73.313, U.S. Government Printing Office. Hata, M. "Empirical Formula for Propagation Loss in Land Mobile Radio Services", IEEE Transactions on Vehicular Technology, Sept. 1981. Jakes, W.C. Microwave Mobile Communications. IEEE Press, Piscataway, NJ, 1994 (re-published). Okumura, Y. et al. "Field Strength and its Variability in VHF and UHF Land-mobile Radio-service," Rev. Elec. Commun. Lab., Sept.-Oct. 1968. VHF and UHF propagation curves for the frequency range 30 MHz and 1000 MHz. ITU-R, Recommendation 370-6, 1994 PN Series Volume, Propagation in Non-Ionizing Media, 1994.