Domain of Actual Small-Cell Propagation Variations

The definition of field strength variations depends on the chosen reference. Often the actual variations and the ability to describe the field from measurements and calculations (often of insufficient resolution) are confused.

The field strength variations in many instances would be quite predictable or measurable to small error, if sufficient information were available regarding clutter, and morphology. Remaining variations would be those which really do vary with time and are never the same again.

The domain of actual variations for cellular and PCS applications, from close-in to cell-edge regions, is estimated to be within standard deviations (sigmas) of:

* 6 to 12 dB, referenced to a single log-linear regression line fit to the data, or
* 6 to 10+ dB, referenced to a dual log-linear regression line fit to the data, or
* 7 dB referenced to the area mean, determined with about 200-meter resolution
* 5 dB, referenced to a running local mean, determined with about 30-meter resolution

The question arises of how much information about cell/sector C/I variations is needed and what degree of prediction (or measurement) accuracy is required to accomplish a good GSM design?

We have just seen that the expected C/I sigma near threshold is 8 dB. This assumes a link without severe diffraction shadowing. In the cell fringe area having a great deal of shadowing; that is, a poorly-designed cell, the standard deviation with respect to the local mean C/I may be as high as 12 - 14 dB. Using different logic of mitigating full Rayleigh fading and also putting variations within the range of call processing parameters to correct, the greatest acceptable sigma in design is about 8.5 dB.. Note the closure with the 8 dB value.

The 5 dB individual link sigma upon which the composite C/I threshold sigma argument is based comes from the prediction accuracy of a wave-front method RF tool having a true 100-meter range resolution against an extensive body of accurate measurements.

It then follows that the minimum requirements for design should involve a technique with resolution sufficient to determine that the cell edge variations are no more than about sigma = 8.5 dB, and also to assess longer paths from which interference is expected. The more stringent requirement is that within the target cell/sector.

Well calibrated modified COST 231 Hata empirical models within target cell areas coupled with ITS/ITM or TIREM models for distant interference computation have been sufficient for cellular design using 3-arc-second (100 meter resolution) terrain data when the cell radii were about 2 miles or more. Simply scaling range down to PCS cell radii of the order of 1 kilometer, the required resolution for PCS target cell computation may well be of the order of 30 meters. 30 meter data is now available for about 60% of the continental United States.

Summarizing,

* A well designed cell will have no more than an 8 - 8.5 dB C/I sigma near threshold, which will occur in the cell fringe area
* A prediction or measurement accuracy referenced to a running (local) mean of about 5 dB or better is needed to determine the 8 - 8.5 dB
* At PCS frequencies, a range resolution no greater than about 30 meters is needed to achieve this accuracy
* For GSM, a threshold design C/I of about 14 dB should be used, which will require a fringe area C/I of about 28 dB to assure the threshold 90% of the time.

As the range resolution of empirical models is about 200 meters at best due to terrain height averaging and the far-field requirement, the use of such models require extensive companion field measurements. As sufficient measurements over interference zones may be impractical, as they were in cellular drive testing, the use of predictive model computation of interference is required. Such predictive models should at least be of the quality of Longley Rice, ver. 1.2.2 as stipulated by the FCC for computing PCS-to-microwave path loss

REVIEW OF MODELING METHODS

The most significant differentiation is between predictive and empirical models. Predictive models use algorithms derived from electromagnetic theory; thus, only require terrain and land-use-land-cover information to predict propagation performance. Empirical models are mathematical formulas, embodying no inherent physical significance, with constants that require field test data to calibrate the formulas for a particular physical environment.

Since 1993, many RF tools have used the empirical Cost 231 modified Hata model; a simple slope/intercept equation for computing propagation in the far-zone of the base station. Some tools allow two or more such slopes to be calibrated. Such models are combined with an additional diffraction algorithm good for up to two widely-spaced obstacles; radios and obstacles must be in each others far-zone for the algorithm to work, and the algorithms do not account for intermediate ground reflections. Terrain effects are modeled as a height-gain correction factor over average intervening height (HAAT).

For a street-level mobile/portable at PCS frequencies, the far-zone begins at a range of about one(1) kilometer for every 100 feet of antenna or obstacle height...and the distance is even greater when the mobile is elevated. At cellular, the zone boundary is roughly 0.5 kilometers.

Computer predictive modeling has been available for land mobile since 1967, by virtue of Longley-Rice [ESSA tech. Rep. ERL 79 ITS-67]. A similar government model developed by ECAC, TIREM, has been available since the early 1970's. These models worked well for cellular for cell radii greater than about two miles in relatively uncluttered environments. This is because although predictive, they still used geometrical-optics (ray) models for diffraction, which are far-zone limited.

Any model, empirical or predictive, using a multiple knife-edge or rounded obstacle diffraction algorithms will not experience greater accuracy with greater terrain data resolution than 3-arc-second (100-meter). Better resolution requires a physical optics based model.

Since 1986, the Canadian Research Centre in Ottawa (J.H. Whitteker) has employed Fresnel-Kirchoff methods for diffraction in combination with plane-segment modeling. This predictive method employs a chained physical-optics calculation in range. This method is suitable for predictive PCS modeling, and is the most accurate method available today. The accuracy is limited only by the resolution of the terrain and clutter data.

REVIEW OF MODELING METHODS

* Predictive modeling computes performance without field-test calibration
* Empirical modeling requires field test calibration for each different environment
* Cost 231 modified Hata empirical models are in common use in RF tools
* Cost 231 modified Hata models work only in far-zone of base antennas and obstacles
* Empirical and longley-Rice/TIREM models are limited in range resolution
* High range resolution is required for small PCS cells in cluttered environments
* High range resolution requires a physical optics model to compute in near-zones
* Accurate PCS prediction requires a physical-optics-based model
* The Fresnel-Kirchoff method provides such a model

BENEFITS OF PREDICTIVE MODELING

* Field test calibration is not required
* Greater range resolution can be obtained
* Greater prediction accuracy can be obtained
* Potential problem areas are quickly identified
* Alternate solutions to problems can be computer modeled
* Isolation can be "designed-in" by computer
* The network can be computer-optimized

Empirical modeling requires a great deal of field-testing early-on to be useful. For WLL operation, this testing cannot be drive testing as drive testing applies only to operation of the mobile/portable at street level. Conversely, predictive modeling can be accomplished in 3-dimensions.

Empirical modeling, even with careful calibration, is basiclly inaccurate to the extent that only median (averaged) levels are predictable and not the fine detail. High range resolution is needed to predict detail, especially in the near-zones of antennas and obstacles. Predictive modeling can provide this detail; hence, accuracy.

Predictive modeling enables a statistical projection of performance, rather than just deterministic median levels available with empirical modeling. Statistical modeling enables a quick location of potential problem areas within the coverage footprint of one or more base stations. The 3-dimensional modeling capability permits assessment of the potential cures to such problems.

The aim of using predictive modeling is not to design a network wholly on the computer, to the exclusion of field-testing. Indeed, field-testing is an integral part of the design process. The aim is to facilitate testing on a prioritized basis (by exception), and to make it knowable. That is, the scientific method requires prior knowledge of the possible outcomes of an experiment prior to performing it.

PREDICTION ACCURACY: COMPARISON WITH EMPIRICAL

Prediction accuracy using the Fresnel-Kirchoff predictive method has been validated to be within a standard deviation (sigma) of 5 dB. This is compared with a sigma of at least 9 dB for carefully-calibrated empirical modeling, which is more typically 11 or more in cluttered urban environments. The 5dB sigma for Fresnel-Kirchoff is based on 3-arc-second terrain and 100 meter DEM land-use-land-cover (LULC) data. The ultimate accuracy in a PCS environment with supplemental high-resolution clutter data in small cells is yet to be determined.

There is a question if empirical modeling is even feasible at all for the design of an interference-limited PCS network operating under significant traffic load. This is because the sigma of the C/I or C/Nt metric for performance involves the ratio of two computed quantities; each having associated prediction accuracy. For example, a CDMA cell/sector is never more than 6.5 dB away from instability according to C/Nt under power control. Thus it may be difficult to design such a sector (and contiguous sectors) using a tool having a sigma of, say, 12 dB (joint probability of two sigma = 9 dB processes).

PREDICTION ACCURACY: COMPARISON WITH EMPIRICAL

* Predictive modeling via Fresnel-Kirchoff has an accuracy within a sigma
* of 5 dB using 3-arc-second terrain data and 100 meter DEM LULC data
* Prediction accuracy of Cost 231 empirical modeling is about 9 dB at best, and typically 11 dB or more with the same resolution terrain and clutter
* Prediction accuracy of the best Longley-Rice derivative is about 7 dB at best, and is not expected to improve with finer range resolution

DIFFICULTIES WITH EMPIRICAL MODELING

* The initial RF design process takes a long time; thus, constricting the build out process of a network, due to all the field-testing involved
* The empirical modeling is essentially 2-dimensional, and does not apply with a high mobile, such as in a multi-story building
* The accuracy will be insufficient for PCS design under traffic load; thus, network computer optimization is not feasible
* The process requires a great deal of experience on the part of the RF Engineer, thus configuration control of the network design is difficult

DIFFICULTIES WITH EMPIRICAL MODELING

Designing a wireless network should be a predictable convergent process. Design of cellular networks had this feature as traffic load was never immediately an issue; and, the design of cellular networks more-or-less followed a "cook book." PCS design is by it's very nature quick and undisciplined; yet, must provide for high traffic capacity once WLL operation is initiated.

Because of the inherent small-cell high-frequency high-traffic nature of PCS and because of the relative inaccuracy of empirical modeling, getting started with a network design takes a long time even using very experienced RF engineers.

If the network is in an urban area and WLL operation in other than single-family residential neighborhoods is envisioned, it will be almost impossible to obtain enough field test data to calibrate the tool, let alone design the network. In such an environment, field-testing every sector of every potential cell is mandatory using an empirical tool.