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Is it time to rethink frequency reuse formulas?

In the 1980s cellular was in its heyday. Competition existed but did not yet threaten nascent operators, and the threat of network overload was still a consideration for the far-off future. Customers were intrigued and easily enticed.

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The sobering 1990s brought decreasing customer satisfaction, plunging revenue per subscriber, increased churn, rising cell site deployment costs, regulatory intervention and-perhaps most important-competition. The wireless sector was forging a new competitive landscape for the entire telecommunications industry, and personal communication services providers were becoming a very real threat to cellular livelihood.

These issues have now reached a boiling point, and intense competition has spurred cellular operators to take steps toward two core goals: improving customer satisfaction and reducing operating costs. Of course, these are the same two goals PCS operators must achieve from the start.

Cellular systems based on the AMPS standard have not provided the capacity or voice quality for large markets-such as Los Angeles and New York-that customers at one time expected based on initial system testing and performance. AMPS traffic growth methods called for cell splitting, sectoring and controlling base station power to increase the number of channels offered for service while maintaining the quality of service to the customer. The practical implementation of these techniques, however, has proved to be less effective than anticipated.

The last several years have witnessed a flurry of "silver bullet" solutions to allow growth and still maintain quality. Those solutions have taken many forms-enhancers, microcells, smart antennas, stealth antennas, down tilt, up tilt-but no solution has proved completely effective in the field. The principles of cellular system design and the small, logical steps that are required to improve costs, capacity, coverage and quality need to be re-evaluated.

Textbook design The frequency reuse pattern defines the maximum capacity per cell site and the typical system signal-to-interference ratio (S/I), which determines voice quality. This ratio is determined by comparing the energy of the desired signal with all sources of interference.

Typical system S/I performance is defined as the S/I of the mobile user in the doughnut shaped area at the edge of a cell. Uplink performance is usually much better.

In estimating the reuse factors required for a particular system, designers use an S/I and reuse equation that takes into account the effects of antenna height, cell size, the number of interfering sources and other factors.

Cellular systems may be either omnidirectional or sectored. An omnidirectional system involves a circular service area around the cell site. In a sectored system, coverage consists of pie-shaped service areas, or sectors, with the site at the center of the pie.

The most familiar reuse design is the seven-cell (k=7) pattern, which has six close-in reuse sites and three sectors (Figure 1). Using the S/I and reuse equation with a k=7 design, S/I is calculated at 23.5 dB, which exceeds the 17 dB S/I often used as the cellular design specification for good voice quality.

That relationship, however, requires that the following statements are all true.

Each interfering site is the same distance away.

Each site is in the ideal location.

In a sectored system, only two cells interfere.

Each site is at the same height.

Each site has a 40 dB per decade propagation constant.

Each site is always transmitting.

The antenna pattern is ideal.

Reality sets in In a large urban market, 95% of the sites may fall within ±12% of a 3.4 mile radius (Figure 2). This indicates that the cell site location error is at least 10% of the cell site radius.

This places some interfering sites closer than expected, causing system S/I to vary from site to site based on the location of adjacent sites. For smaller reuse patterns, cell site location errors have a greater effect on net S/I because the relative errors are much larger. Systems that use a small k factor-or a lower S/I-are more difficult to design and optimize compared with systems that use higher k factors because of greater sensitivity to location error.

In sectored designs, only two interfering sites are considered in the S/I and reuse equation, which requires a very unrealistic pie slice antenna pattern (Figure 3). In reality, effects of ground clutter, nearby antennas and mounting structures can degrade fielded antenna performance.

The resulting pattern has significant back lobe gain and a broader main lobe resulting in a reduced system S/I. It is not unusual to measure the difference between the three sectors of a k=7 system at less than 10 dB regardless of location within the site coverage area.

Instead of the familiar k=7 reuse pattern, systems using code division multiple access (CDMA) or GSM, the Pan-European digital cellular standard that is now being adopted in North America, often use a k=1 or k=3 pattern. For k=1 and k=3 reuse patterns, there are actually three interfering sources in the main antenna beam of a sectored system, even for the ideal pie shape pattern.

Tower height and local topography dramatically affect propagation characteristics, and the propagation constant has a very strong effect on S/I. Deployed systems must use a variety of tower heights because of terrain, available sites, local regulations and coverage concerns.

In the histogram of antenna height, for a deployed system, the mean height is 195 feet with a standard deviation of 90 feet (Figure 4).

Research conducted by Hata has demonstrated that the typical propagation constant for a 195 foot tower is 33 dB per decade. To achieve the 40 dB per decade propagation constant, a tower height of roughly 20 feet, or towers below all surrounding structures, is required. Clearly this is not the typical situation for any deployed system.

Achievable reuse A more realistic estimate of network performance would factor in the effects of tower height, cell site location and antenna patterns. Using a more pragmatic estimate yields a different optimal reuse pattern.

Achieving even a minimal 17 dB S/I in a realistic omnidirectional system requires a pattern of greater than 13 (Figure 5).

In a sectored design, a reuse design of at least k=9 is needed to achieve 17 dB S/I. With a k=7 design, the S/I is reduced to 16 dB (Figure 6).

Designers should also reconsider the 17 dB S/I criteria for voice quality, as most users have become accustomed to a higher quality level with an S/I near 21 dB (see sidebar).

A design goal of 21 dB S/I would call for even higher k values.

These issues are important to the system designer who must plan for growth, capacity and costs. An overly optimistic estimate of achievable reuse will result in either dissatisfied customers because of the reduced S/I or reduced return on investment because of the additional cell sites needed to provide the required capacity.

Another important distinction between AMPS and most digital standards is that AMPS systems require only the control channel to be continuously broadcasting. AMPS systems enable traffic channels only when they are required. Net system downlink and uplink S/I changes with the loading and activity in the system.

At times of low system traffic, S/I is significantly greater than predicted. An estimate of the change in S/I can be made by using the Erlang equation and system blocking requirements.

For example, at 2% blocking with 10 transmitters in a sector, each transmitter is in use 50% of the time. With 50% use per channel, the resulting average S/I improvement is 3 dB (Figure 7).

At the same blocking, the use per channel increases and the average S/I decreases as the number of channels increases. This is a very important observation with respect to the deployment of "idle channel technologies" such as cellular digital packet data. These technologies degrade the delivery of voice services because they fill idle channels with data carriers. Thus, the overall S/I and the voice quality in the network decreases.

This slow degradation in delivered quality of service is occurring, or has occurred, in most AMPS systems with the increase in subscribers and transceivers being added to each cell site. System performance suffers during busy hours and improves as traffic and the number of active channels decrease. With most time division multiple access and GSM technologies, the base site transmitters are always active. In these cases, only the uplink S/I will improve as system activity decreases.

Frequency reuse in analog cellular systems is not a simple textbook issue. Environment-including actual antenna location and height above average terrain-along with trunking efficiencies and system usage must be closely studied and understood.

With so much competition, system quality and cost are of paramount importance to the system engineers and operating staff. The reality is that no "silver bullet" solution exists for system quality or cost. The designer must understand each individual market by using local information describing the topography, sites, structures and customer expectations. Each market will require unique design rules to provide the required service quality at the lowest capital cost.

Traditional design rules are optimistic, particularly for the tight reuse patterns that are used in GSM and CDMA design. A more realistic S/I, frequency reuse and capacity estimate should incorporate tower height, reuse distance, antenna patterns and trunking efficiency. The resulting relationship more accurately reflects system performance as experienced in the field.

Ron Rudokas is the President of Wireless Engineering and Systems Technologies in Littleton, Colo., and Terry Benz is Director of Engineering and Technical Operations for Western Wireless in Issaquah, Wash. Rudokas' e-mail address is

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© 2014 Penton Media Inc.

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