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2. Modelling optimal spectrum quantities
2.2 Scope of the model
2.3 Outline of our methodology
2.4 Assumptions
2.5 Results
2.6 Analysis and conclusion
2.1 Introduction
We have developed a bottom-up Microsoft Excel model1 to determine the optimal amount of spectrum in the 800/900MHz bands to allocate to operators. The optimal spectrum for an operator is the amount of spectrum that results in the lowest cost for that operator. We would normally expect to see network costs decreasing as the amount of spectrum increased, with the rate of decrease slowing as the amounts of spectrum increase, a trend shown in Exhibit 2.1 below.
Exhibit 2.1: Relationship between network cost and spectrum (Source: Network Strategies)
![[image] exhibit 2.1.](http://www.rsm.govt.nz/cms/image-library/images-discussion-paper/network-strategies-report-exhibit2-1.gif "[image] exhibit 2.1.")
The optimal split of spectrum amongst several operators is that at which the total network cost (over all operators) is minimised.
A key assumption in this model is that a variation in spectrum will only affect the wireless access network, which includes the sites and backhaul. The core network (switches and transport network) remains essentially unaffected. To avoid the difficulties of forecasting network costs over the next 25 years, and noting that backhaul is dependent on the number of sites, we have assumed that the number of sites required for coverage can be used as a proxy for the cost of the spectrum-dependent part of the network.
In order to discount the costs of deployment of sites in the future back to the commencement of the licence period (2011), we have assigned a ‘relative cost’ of $1 to each urban site and $2 to each rural site, reflecting that rural sites generally cost more than urban sites. We also assume that each site incurs a capital cost of $0.10 (10 per cent of the urban site cost) each year, to represent the ongoing technology upgrades. This allows us to use an Net Present Value (NPV)2 calculation to find a relative value of the network in 2011.
It is important to note that, apart from costs, there are a number of other factors which will affect the design of a mobile network that extends 25 years into the future. These include take-up rates, traffic rates and network capabilities. We have not attempted to capture realistic forecasts for these factors as we do not believe that the absolute values will have a significant impact on the optimal allocation of spectrum3. Rather, we have focussed on trends and the differences between the operators.
2.2 Scope of the model
Our understanding of the MED’s intention was that we should examine one new entrant in each band: Econet Wireless in the 900MHz band and TelstraClear in the 800MHz band. While more than one new entrant in each band is certainly possible, it cannot be considered cheaper than one new entrant, as each new entrant requires the deployment of a costly new nationwide network. Naturally, the status quo is optimal if considering the total cost: each band only incurs the cost of one nationwide network. The cost of one operator can be obtained from our model as the cost of the incumbent when the full allocation of 20MHz is retained.
The model does not take into account technology transitions in which an operator operates two networks alongside each other. While two networks in a spectrum-constrained environment can be difficult and expensive to deploy, developing a model of a migration may not be meaningful, because we have no reason to believe that any operator will migrate from one technology to another in the 800/900MHz spectrum bands in the timeframe, any more than they will not migrate. For example if Telecom were to migrate to UMTS/LTE4 in its 800MHz band, it is likely to also deploy UMTS/LTE in its 2100MHz band, which it would use in heavily populated areas where it is better suited than the lower-frequency bands, and only roll out UMTS/LTE in the 800MHz band in rural areas where it requires the superior coverage of the lower frequencies. Since networks generally are not spectrum limited in rural areas there is no additional cost or difficulty in deploying two networks in the same spectrum. []. It is therefore difficult to develop a scenario that might represent any realistic migration.
We have not modelled spectrum slack. Indeed we are not aware of any mobile operators specifically reserving spectrum for future technologies (that is, spectrum slack), especially when they already have copious amounts of unused spectrum in higher frequency bands. Even if they did, we doubt it would have any material effect on the results of the model as it would affect all operators.
2.3 Outline of our methodology
To determine the relative cost for an operator, the following calculation steps are used:
| Determine customers |
We have implemented three types of customers: voice, handheld data and modem. |
| Calculate network traffic |
Each customer type contributes to the overall peak-hour network traffic (it is the peak-hour traffic that determines network dimensions and therefore cost). The traffic varies with time, and between urban and rural areas. (Rural traffic is lower than urban traffic mainly because rural network deployment is not as progressive as in urban areas. We expect the network in rural areas to be coverage driven, and capacity driven in urban areas). |
| Calculate traffic density |
The key driver of the number of sites over the period of the licence will be traffic density. This is in contrast to 2G and current 3G technologies which are simply driven by traffic volume. Forthcoming systems, which will be in use over the licence period, such as LTE and EVDO Revision C, are expected to use OFDM (orthogonal frequency-division multiplexing), an adaptive rate system whereby small sites can carry more traffic than large sites because the system makes use of stronger signals (over shorter distances) to transmit at higher data rates. We have assumed that when a cell is at its maximum radius, the capacity is some proportion of its maximum capacity (see the following section on assumptions) and that the capacity increases linearly as the cell radius decreases, until some point where the maximum capacity is reached. This is illustrated in Exhibit 2.2. |
Exhibit 2.2: Variation of capacity against cell radius [Source: Network Strategies]
![[image] exhibit 2.2.](http://www.rsm.govt.nz/cms/image-library/images-discussion-paper/network-strategies-report-exhibit2-2.gif "[image] exhibit 2.2.")
| Capacity of 800/900MHz cell at maximum size |
The capacity of a cell at maximum range depends on the spectral efficiency of the system (bits per second per hertz), the amount of spectrum owned by the operator (at 800 or 900MHz), and the capacity factor (describing how much lower the capacity is when the site is at maximum range than the maximum capacity). The maximum traffic density when the cell is at its maximum range is the capacity at maximum radius divided by the area covered by the cell at maximum radius. |
| Number of 800/900 MHz-only sites |
If the traffic density is less than the traffic density capacity when the cell is at its maximum range then there is no need to extend the cell by using equipment operating at higher frequencies. The number of sites required is the total area to be covered divided by the maximum coverage area per site. |
| Number of all-spectrum sites |
If the traffic density is more than the maximum traffic density when the cell is at its maximum range, then additional capacity is required. This could be achieved either by cell-splitting (adding more sites) or by adding additional capacity to existing sites, in the form of equipment using higher frequencies. We have assumed the latter method on the basis that additional sites will be a last resort because of the high cost of sites. The number of sites is calculated by assuming all sites have equipment to operate using the operator’s higher frequency spectrum. It is assumed that cells are centred around locations of high traffic, such as rural towns in the case of rural coverage. This means that we assume that the traffic in the centre of the site is of sufficient density in order that the higher frequency (1.8 or 2.1GHz) equipment can operate at full traffic density. Any remaining traffic is carried by the low frequency equipment (800 or 900MHz). If the low frequency equipment is not sufficient to carry all the remaining traffic then additional sites are deployed until the are sufficient to satisfy demand. The model does not attempt to model any umbrella/hotspot cell arrangements (for example, macrocells, microcells and picocells). |
| Net present value of sites |
To find a present value of sites installed in the future, urban sites are allocated a simple relative capital cost of $1 and rural sites are allocated a relative capital cost of $25. Relative costs for rural sites are higher because rural sites are significantly more expensive than urban sites. In particular they often have higher civil works, tower and backhaul costs6. All sites are also incur a further annual capital cost of $0.10 which represents ongoing upgrades in technology and capability. Thus future sites can be discounted back to the start of the model period (2011) using an NPV calculation. |
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2.4 Assumptions
We have attempted to make the model as technology-independent as possible. In fact, the only differentiation between the 800MHz case (i.e. Telecom and TelstraClear) and the 900MHz case (i.e. Vodafone and Econet) is the amount of spectrum held by the operators at the higher frequencies (see Exhibit A.2).
| Spectrum |
We have assumed operators in both bands have a maximum of 20MHz (paired). The amount of spectrum was varied in 5MHz blocks from 0MHz to 20MHz. (We recognise that this allows scenarios that are not currently possible in the 900MHz case because not all spectrum is up for renewal, but 5MHz is the basis for UMTS carriers, and is also likely to be the basis for CDMA carriers in the future.) In the higher frequency bands (1.8GHz and 2.1GHz), the actual amount of spectrum for each operator was used. We examine two options for spectrum in the higher bands: the first option is that each operator will be able to use all spectrum it holds in all bands. In particular this means that Telecom will be able to use its 1800MHz and 2100MHz bands, which it cannot currently do with CDMA technology. CDMA may develop so that it can be operated in these bands, or Telecom may migrate to UMTS/LTE which can also use these bands. The second option assumes Telecom cannot use its spectrum in its higher bands (as is the case today). |
| Coverage |
Neither Telecom nor Vodafone publish coverage areas. However both Telecom and Vodafone advertise their coverage as 97% of the population. We combined this information with urban and rural profile data from Statistics New Zealand to estimate the area covered. We have assumed that coverage does not vary over time. |
| Population |
We have used Statistics New Zealand forecast population growth data, and have forecast the population split between urban and rural. We have assumed that there will be no change in the proportions of customers living in urban and rural areas over time. |
| Mobile penetration |
We have assumed three types of usage: voice, handheld data (data on the handheld) and modem (a data card or built in to a laptop). Voice: we have assumed voice penetration will be saturated by 2010, and will remain constant at 120%. Handheld data: penetration will start at 10% in 2010 and increase linearly to 50% in 2031. Modem: penetration will start at 10% in 2010 and increase linearly to 50% in 2031. |
| Migration |
We have assumed that initially customers are split evenly between the two incumbents. Customers start migrating in 2011 to the new operators at a constant rate, and after ten years (2015) customers are split evenly between all four operators. |
| Traffic |
We have made basic assumptions about the peak-hour traffic generated per customer: Voice: We have assumed 0.04 Erlangs in 20107 (similar to current rates), increasing linearly to 0.20 Erlangs in 2031, a trend reflecting mobile phone usage replacing fixed phone usage. We have assumed voice has a data rate of 12kbit/s. Handheld data: Future data rates are entirely speculative as it depends on the applications that find success on the mobile platform. We have assumed different data rates for rural customers and urban customers, which partially reflects the difference in the capabilities of the network between those two areas (that is, operators will roll-out new technologies in urban areas before rural areas). In urban areas we have assumed an average peak data rate of 0.01Mbit/s in 2010 increasing to 0.5Mbit/s in 2031. In rural areas the rate increases from 0.001Mbit/s to 0.1Mbit/s. (This peak rate is the average over all users, taking into account the users’ duty cycles8 and activity rates9). Modem data: We have assumed the same data rate as for handheld data. |
| Site maximum capacity |
We have used an illustration of the trend in growth of capacity provided by Telecom in its submission10 to estimate the maximum capacity of a site. From this we can estimate that the maximum capacity will be about 5bit/s/Hz in 2010 and if we extrapolate linearly, about 10bit/s/Hz in 2031. We assume that this can be applied to all technologies. We have assumed that because technology deployment in rural sites lags that of urban sites, the capacity is less: 0.5bit/s/Hz in 2010, increasing to 2bit/s/Hz in 2031. |
| Capacity versus range |
As discussed in the previous section, it is expected that future range mobile technologies will all use OFDM, which allows adaptive data rates. (It is expected that adaptive data rates will be introduced in EVDO revision C and LTE). WiMAX has already been introduced using adaptive data rates. With the adaptive data rate, as the radius of the cell increases, the capacity drops off. We have assumed that all mobile technologies will have a similar capacity versus range trend as WiMAX. This assumption is reasonable because OFDM will have similar characteristics in all technologies. Using data provided by the WiMAX forum11 , we estimate that full capacity is only possible when the cell’s radius is at 40% or less of its maximum radius, and at full radius the capacity has decreased to 40% of its maximum capacity. |
| Maximum cell radii |
In theory, maximum cell radii can be as large as 30km for GSM and 40km for CDMA in rural areas. However in reality these maximum cell radii will not always be achieved due to terrain, non-ideal site locations etc. We have therefore de-rated12 maximum cell radii to those given in the following table (Exhibit 2.3). We have assumed no difference between the CDMA and GSM families of technologies. We have also assumed the maximum radii do not vary over time as new technologies are introduced. |
Exhibit 2.3: Maximum cell radii [Source: Network Strategies]
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Maximum cell radius (km)
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|
|
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800/900MHz
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1.8/2.1GHz
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Urban sites
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2.5
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1.5
|
|
Rural sites
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15
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12
|
Please see the accompanying spreadsheet model for a full list of assumptions including sources and references.
2.5 Results
The model results are listed below with the four operators all having an equal market share of 25% (after the initial introductory period for the new entrants of 10 years). We also tested the results with varying market shares (see below).
Equal market share
The results of the model are shown in the following tables. Each table shows the relative cost of the access network to each operator against the amount of spectrum the incumbent operator has in the 800/900MHz band (with the new entrant having the remainder). Each operator has an market ultimate market share of 25% For the 900MHz spectrum and option A of 800MHz (where Telecom uses all its spectrum), the lowest overall cost is about the same for all scenarios from a 5MHz:15MHz split (incumbent: new operator) to a 15MHz:5MHz split. For option B of 800MHz, the cost to Telecom is much greater, and so the lowest cost scenario is 15MHz for Telecom and 5MHz for the new operator
The information is also shown in the graphs in Exhibit 2.7 Exhibit 2.8 and Exhibit 2.9 .
Exhibit 2.4: Relative costs of 800 MHz operators (option A: with Telecom using spectrum in higher bands) [Source: Network Strategies]
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Telecom
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New operator
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Total cost
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||
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Spectrum (MHz)
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Relative cost of access network
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Spectrum (MHz)
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Relative cost of access network
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|
|
0
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2721
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20
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1234
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3956
|
|
5
|
671
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15
|
1248
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1919
|
|
10
|
642
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10
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1265
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1907
|
|
15
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619
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5
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1286
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1905
|
|
20
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601
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0
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3328
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3929
|
Exhibit 2.5: Relative costs of 800 MHz operators (option B: with Telecom using 800MHz spectrum only) [Source: Network Strategies]
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Telecom
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New operator
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Total cost
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||
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Spectrum (MHz)
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Relative cost of access network
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Spectrum (MHz)
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Relative cost of access network
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|
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0
|
n/a
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20
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1234
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n/a
|
|
5
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6777
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15
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1248
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8026
|
|
10
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3411
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10
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1265
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4676
|
|
15
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2322
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5
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1286
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3608
|
|
20
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1781
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0
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3328
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5108
|
Exhibit 2.6: Relative costs of 900 MHz operators [Source: Network Strategies]
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Telecom
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New operator
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Total cost
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||
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Spectrum (MHz)
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Relative cost of access network
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Spectrum (MHz)
|
Relative cost of access network
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|
| 0 | 3081 | 20 | 1391 | 4472 |
| 5 | 950 | 15 | 1438 | 2238 |
| 10 | 858 | 10 | 1500 | 2358 |
| 15 | 791 | 5 | 1583 | 2374 |
| 20 | 740 | 0 | 3710 | 4450 |
Exhibit 2.7: Relative costs of access networks of 800MHz operators (Telecom using higher band spectrum) [Source: Network Strategies]
![[image] exhibit 2.7.](http://www.rsm.govt.nz/cms/image-library/images-discussion-paper/network-strategies-report-exhibit2-7.gif "[image] exhibit 2.7.")
Exhibit 2.8: Relative costs of access networks of 800MHz operators (Telecom not using higher band spectrum) [Source: Network Strategies]
![[image] exhibit 2.8.](http://www.rsm.govt.nz/cms/image-library/images-discussion-paper/network-strategies-report-exhibit2-8.gif "[image] exhibit 2.8.")
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Exhibit 2.9: Relative costs of access networks of 900MHz operators [Source: Network Strategies]
![[image] exhibit 2.9.](http://www.rsm.govt.nz/cms/image-library/images-discussion-paper/network-strategies-report-exhibit2-9.gif "[image] exhibit 2.9.")
Varying market share
In the results above, it was assumed that each operator ultimately had an equal market share (that is, 25%). The graphs below show the results if the market share obtained by the new operators is varied, first increased to 35% and then decreased to 15%. The remaining market share is split equally between the incumbents (15% and 35%, respectively). The graphs show that having more spectrum is more valuable to the operators with higher market share.
Exhibit 2.10: New entrant with 15% market share (800MHz network) [Source: Network Strategies]
![[image] exhibit 2.10.](http://www.rsm.govt.nz/cms/image-library/images-discussion-paper/network-strategies-report-exhibit2-10.gif "[image] exhibit 2.10.")
Exhibit 2.11: New entrant with 15% market share (900MHz network) [Source: Network Strategies]
![[image] exhibit 2.11.](http://www.rsm.govt.nz/cms/image-library/images-discussion-paper/network-strategies-report-exhibit2-11.gif "[image] exhibit 2.11.")
Exhibit 2.12: New entrant with 35% market share (800MHz network) [Source: Network Strategies]
![[image] exhibit 2.12.](http://www.rsm.govt.nz/cms/image-library/images-discussion-paper/network-strategies-report-exhibit2-12.gif "[image] exhibit 2.12.")
Exhibit 2.13: New entrant with 35% market share (900MHz network) [Source: Network Strategies]
![[image] exhibit 2.13.](http://www.rsm.govt.nz/cms/image-library/images-discussion-paper/network-strategies-report-exhibit2-13.gif "[image] exhibit 2.13.")
2.6 Analysis and conclusion
From the model results we conclude that:
- It is very expensive for an operator to provide nation-wide coverage without 800 or 900MHz spectrum.
- As an operator’s spectrum in the 800 or 900MHz band increases from 5MHz to 20MHz, the cost to that operator continues to decrease slightly. In other words, if the incumbents lose spectrum in the 800 and 900MHz bands, their costs will increase slightly, assuming they can use their spectrum in higher bands. In particular, if Telecom is unable to use its spectrum in its higher band (that is, if it stays with its CDMA technology and CDMA does not evolve to use 1.8GHz and/or 2.1GHz spectrum), the cost of having lower spectrum is significant.
- The lowest overall cost (for both operators in a spectrum band together) is obtained when both operators have equal amounts of that spectrum, although there is not much difference overall between splitting the spectrum evenly (10MHz:10MHz) and providing 5MHz to one operator and 15MHz to the other (5MHz:15MHz).
- The actual costs of the individual operators varies between the operators for two reasons:
- it is assumed that the incumbents already have a number of sites at the start of the licence period. These sites are not included (they are treated as sunk costs). It is assumed all new operators’ sites are included.
- The amount of spectrum in the higher 1.8GHz and 2.1GHz bands has an effect on the total cost, especially in later years when the traffic levels increase.
![[link to New Zealand government website].](http://www.rsm.govt.nz/cms/image-library/link-to-new-zealand-government-website.gif/image_thumb)
