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Coverage-Capacity Tradeoff in the Reverse Link

Simple capacity models of the reverse link show that RF power rises with loading. There is a theoretical limiting, or pole, capacity, achieved when all users are transmitting infinite power. Beyond the pole capacity no station achieves its SNR target, no matter what the power.

Real systems must operate below the capacity pole because real user stations have an upper bound to the their transmitter power. When the marginal users are transmitting at maximum power, loading should not be permitted to increase. Conversely, if the loading is allowed to increase, then the marginal user stations can no longer close their power control loops. That is, their SNRs will fall below target. In effect, the cell shrinks due to loading.

This phenomenon couples coverage and loading. The pole capacity of a cell depends only on the average SNR target, the processing gain, and voice activity factor. The coverage area of a cell, that is, the area over which all users obtain the target SNR, depends on the loading relative to the pole capacity. This relationship between loading and coverage area is a factor in the choice of cell locations. For minimum cost, one would like to use the minimum number of cell sites. Sparsely dispersed cells may be appropriate for a new system, or a location with low user population density. However as the load density increases cell density must be increased. Cell spacing must high enough that the all users can be serviced within the design limits of transmitter power. And in reality, loading is a random variable, measured in Erlang density. Grade of service can only be measured in a statistical sense. System design is, just as in wireline telephone systems, a compromise between the competing requirements of low cost and good grade of service.

Detailed analysis of the interaction of coverage and Erlang capacity is a complex question, involving power control, soft handoff, fading, the mobility mix of subscribers, and other factors, as well as the differences between forward and reverse link. Other pages go into more detail on Reverse Link Erlang Capacity and Forward Link Erlang Capacity. But even at an elementary level, the reverse link is easy to analyze, and the simple model elucidates some basic phenomena.

It is convenient to rewrite the capacity equation in terms of a dimensionless load parameter. Start from the reverse link capacity equation

(1)
where
The pole capacity is the loading which is the solution to this equation when the user station power approaches infinity.
(2)

The pole capacity for Eb/N0 = 6 dB and the 9.6 kbps rate set, other parameters as above, is about Npole = 40.

The relationship between loading and power takes a particularly simple form if we make the substitutions: dimensionless power
(3)
and dimensionless load
(4)
The capacity equation, in terms of these dimensionless parameters, becomes
(5)
There are two important observations from these equations:

1. The pole capacity depends only on the target Eb/N0, the processing gain, the voice activity factor and the effective frequency reuse F. It does not depend on the receiver noise figure.

2. The receiver noise figure sets the sensitivity of the receiver, and hence the spatial scale of the system. It does not affect the capacity.

This analysis neglects the effects of imperfect power control and the dynamics of the system. It would not be prudent to run a system too close to the capacity pole because the load fluctuations will grow in amplitude as the pole is approached. Load excursions will adversely affect the service given to marginal subscribers, possibly causing intermittent failures to close their power control loops and excessive frame erasures. Loadings of 50% to 75% (Z = 3 to 6 dB) are an appropriate compromise between loading and coverage.


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Copyright © 1996-1999 Arthur H. M. Ross, Ph.D., Limited