Measures of the Spectrum Utilization



Measures of the Spectrum Utilization

R.H.M. Hafez and G.K. Chan

* Carleton University, Ottawa, Canada

** Industry Canada, Ottawa, Canada

Abstract

In this paper, we summarize the known definitions of the spectrum utilization and discuss their applicability to existing radio services and their practical usefulness. An important parameters that limits the full utilization of the available radio spectrum is the non-uniformity of the user density. We illustrates that when users are clustered in small areas, the available spectrum resources in that area actually shrink. This leads to viewing the spectrum availability as a random process that changes with time and space. The randomness of spectrum availability is rooted in the randomness in the topology and demographic of the service area.

I. Introduction

It is widely recognized that the radio spectrum is defined along three dimensions: space, frequency and time [3]. The term "spectrum utilization" refers to the amount of information (measured in bits) that is being carried by a spectrum unit (measured in m2. Hz. Sec.). Therefore, an appropriate "theoretical" measure for the spectrum utilization is the average bits/m2/Hz/Sec. The maximum achievable rate of information per unit spectrum depends on many factors ranging from the physical propagation conditions to the state of technology and system design.

In general, the measures of spectrum utilization fall into two categories: (1) absolute measures and (2) relative measures. Absolute measures help spectrum managers and government administrators in assessing the overall level of spectrum utilization across a wide rage of radio services. Such measures tend to be either over simplified or very complex. Relative measures, on the other hand, are apply to specific services with known network parameters. They are often expressed in terms of system capacity and are used to guide the system designers in achieving a higher level of spectrum utilization efficiency.

In this paper, we summarize the known definitions of the spectrum utilization and discuss their applicability to existing radio services and their practical usefulness. We also discuss the tools required to monitor and evaluate the spectrum utilization. In most of the discussions presented in this paper, we view the spectrum as a national resource that should be used efficiently and shared fairly among all citizens and organizations. This is the typical view of government administrators trying to access the commercial value of the radio spectrum and allocate it in a way that ensure the highest level of utilization.

The rest of the paper is organized as follow: Section 2 contains some of the known definitions of the spectrum utilization. In section 3, we examine the practicality of proposed definitions by applying them to some known radio services. In section 4, we view the spectrum assignment as a random process and shows the stochastic nature of the spectrum availability. The paper is concluded in section 5.

2. Definitions

The radio spectrum is available in "Hz. m2. Sec.". These spectrum units can be viewed as containers that are filled with useful signals and interference. Therefore, RF signal emitted from a transmitter partially fills many spectrum units with RF energy. This energy can be either "useful signal" or "undesired interference" depending on the presence or absence of an intended receiver. When an intended receiver is present at the location of the spectrum unit, the RF energy received from the desired transmitter is viewed as "useful signal" and all other RF energies of other transmitters are considered " interference". The signal-to-interference ratio encountered at each of the said spectrum unit can be translated into information rate. The utilization level of a spectrum unit is measured by the amount of information it carries.

A) Absolute Measure

One generally accepted definition of the spectrum utilization is based on "The average amount of information per spectrum unit" as follow [1]:

[pic] (1)

where: SUE = Spectrum Utilization Efficiency. M = amount of information transferred (in bits). W = frequency bandwidth. A = geometric space (usually area). T = time. The product: "B.S.T" denotes the total spectrum space under consideration. The definition stated in (1) is in absolute form. In practice, there could be many problems in interpreting the meaning of the absolute SUE as explained in section 2.

B) Relative Measure

The "relative" approach is to compare the utilization of a given system with another system as follow [1]

[pic] (2)

where: RSE = Relative Spectral utilization, which is the ratio between the SUE of the actual system SUEa and that of a reference or standard system SUEs.

A candidate standard system that was mentioned in [1] is an idealized system with a capacity form similar to that of an additive white Gaussian channel.

[pic] (3)

where Fo is the bandwidth of the wanted communications and ρo is the signal to noise (plus interference) ratio at the receiver output.

3. Spectrum Use by Two Radio Services

To illustrate the applicability of the two definitions given above, we will apply them to three different types of radio services.

A) Specialized Mobile Radio (SMR)

SMR is one of the oldest types of mobile communications. SMR licenses are granted to small businesses individually and give them the right to use one or few frequencies on an exclusive or shared basis. In a given band, the primary frequencies (channels) have fixed bandwidth and fixed frequency spacing. Some frequencies could be assigned at half the frequency spacing between two primary carriers. Those frequencies are called interstitial channels. SMR systems are used mainly for voice dispatch applications and operate in an autonomous mode (except for shared licenses).

In order to apply the SUE model of Eq. (1) to the SMR service, one must interpret the information rate and spectrum units in a way compatible with the SMR system model. This can be done as follows:

[pic] (4)

1) The information rate (M/T) is converted into spectrum occupancy, Occ, which is further defined as : [pic]. N is the number of voice channels in the area and Ck is the fraction of time the voice channel # k is active

2) The denominator (W.A) is interpreted as the total spectrum units Hz. m2/s in the area of interest.

The spectrum occupancy varies across the area of interest. In [2], the spectrum occupancy was estimated as follow:

- Divide the total area of interest into M small sub-areas (cells),

- Form a matrix of sub-areas and voice channels,

- Estimate the presence of each of the voice channels in each of the cells

- Estimate the occupancy of each voice channel by accumulating its presence in all cells

- Substitute the results in the occupancy definition given above.

The maximum number of assignments, N, depends on the space distribution of the individual radio systems and the frequency assignment strategy. Figure 1 graphically illustrates a typical interference model applicable to SMR. Within the area of interest, each frequency is assigned once. Frequency reuse within a city is very rare. The single cell system creates three circles of interference limits. The large circle is the co-channel interference limit, a smaller circle represents the interference limit for interstitial channel and the smallest circle sets the adjacent interference limit.

Figure 1- A model for SMR interference areas

B) PCS Cellular Systems

PCS follow a different spectrum utilization model. In PCS, a band of frequencies is assigned to an operator. The government responsibility is to coordinate the spectrum usage among different services sharing the band or operating in adjacent bands. The service provider, on the other hand, refers to the spectrum utilization efficiency as the system capacity and is measured in terms of how many customers (users) can simultaneously use the system. In a voice-only system, the SUE is interpreted as:

[pic] (5)

Where N is the number of voice connections, W is the total bandwidth and A is the total area. Notice that according to this definition, the control and signaling in the network lower the utilization, and increasing the complexity of the infrastructure (i.e. more cells and/or sectors) increases the utilization. Notice also that the area topology affects the utilization. For example, indoor cellular systems have much higher utilization than outdoor systems.

4. The Effect of User Density

The demand for radio services is never uniform in space. Radio users tend to be clustered in given areas that are usually referred to as “hot spots”. The operating transmitters within a “hot spot” create high interference field that eliminates other users from using the assigned frequencies as well as adjacent frequencies. The eliminated channels are referred to as the “denied spectrum” which is larger than the spectrum being utilized. In cellular systems, the channels are assigned in space in an interleaved way that ensure low co-channel and adjacent channel interference. Unfortunately, the spectrum resources that are available outside the “hot spots” have less practical value simply because there is little demand for it. This means that while spectrum resources continue to be available in low demand areas, the band, cell or system has already been saturated.

Therefore, the available spectrum is a random variable that varies from one location to location. The SUE definition given in (1) does not account for this fact. In (1), we assume that the total available spectrum (W.A.T) is constant, and we compute the utilization efficiency as a fraction of this “constant” amount of resources. A more accurate definition is:

[pic] (6)

The double integration in the demodulator replaces the constant frequency-space resources. In the expression the available bandwidth is explicitly expressed as a function of location as it should be. In voice-only systems, M/T can be replaced by the number of voice connections, N, and in a heterogeneous network (voice, data and other forms of information), M/T can be replaced by the aggregate throughput data rate. The denominator in (5) less than or equal the nominal spectrum [W.A] and the actual spectrum utilization can be written as:

[pic] (7)

where g is a factor (( 1) dependent on the variance of user density in the area of interest. It is important to note that g is not constant. It is a non-linear function of the traffic load as well as the user distributions. To illustrate the significance of this modification we constructed a frequency assignment simulation for areas of different user distribution densities. The simulation details are described in the next section.

(A) Simulation Model

We consider the problem of assigning 50 channels (consecutive frequencies) to different locations within a square area of 100 km x 100 km. Within that area, each frequency is assigned once (SMR model). The area resolution is one sq. km. The adjacent channel interference area is 12 km x 12 km centered at the position of the transmitter. There are no interstitial channel assignments and the frequency assignments are made at random provided that they satisfy the adjacent channel interference criterion.

The user distribution, f(x,y),was modeled as a truncated, bi-variate Gaussian random variable with the variance as a parameter:

[pic] (8)

where 2b is the side length of a squared service, s is the standard deviation of the model probability density function and

[pic]

The simulation is conducted as follow:

(1) A user location is generated at random according to the density of (8). This will point to (x,y) location in the service area.

(2) A frequency is selected at random from the set of un-assigned frequencies [each frequency is assigned once in the area]

(3) The selected frequency is checked for the ACI condition. If it passes the test , it gets selected and removed from the set of remaining frequencies; otherwise, another frequency is selected. If all candidate frequencies are tested and rejected, the request for assignment at (x,y) is rejected.

(4) After n assignments are made, we stop an further assignments and keep generating new requests to see if any of them will be rejected. Using that technique we can estimate the probability of rejection (saturation) as a function of the spectrum utilization level.

The purpose of this simulation is to confirm the hypothesis that the spectrum resources in an area with skewed user distribution (small variance) is less than the nominal value of the resources. In this model, the assignable frequencies are less than the total available of 50. If we simply view the utilization as the fraction of assigned frequencies (relative to the total available), we encounter saturation at very low level of utilization when the user density function has a small variance.

Some simulation results are shown in Figures 2 and 3. In Figure 2, the probability of rejecting a request for assignment is plotted against the fraction of assigned frequencies. The dashed line is an upper bound on this probability and the solid line is a lower bound. The bounds are obtained from [4]. The circle points are the simulation results when the standard deviation is 7.1.

Figure 3 illustrates the case when the standard deviation has a higher value of 14.3. In this case the users are more widely spread out and as a results it was less probable to reject a new request.

Simulation runs were also conducted for a much higher standard deviation of 27.3. In that case, the users were almost uniformly distributed throughout the area and as a result, there were no measurable probability of rejection and all 50 frequencies were successfully assigned.

(B) Discussion

The simulation results confirm the view that the available spectrum resource is a random variable that is related to the variance of the user distribution. For example, Figure 2 suggests that the spectrum is nearly saturated when only about 50% of the frequencies are assigned. This may vary somewhat with different assignment strategies, but the fact remains that not all frequencies can be assigned. In other words, at 50% assignment level, the spectrum is fully utilized.

The same argument can be extended to other factors. For example, an area with high attenuation and dividers can support higher level of frequency re-use and therefore the spectrum can be utilized at higher level than in flat areas.

5. Conclusions

The ratio of the total information communicated to the total available bandwidth is universally acceptable as a measure for the spectrum utilization. The communicated information can be expressed as bits/sec of Erlang units for voice only networks.

In This paper we illustrated briefly how can this simple concept be applied to practical systems. We also argue that the amount of spectrum resources available in any given area is a random variable that depends on the user distribution as well as the topological characters of the area of interest. In some places it becomes impossible to attain full utilization. But if we modify the utilization definition to be the ratio between information and the actual spectrum availability, we would have a more accurate view of the spectrum utilization level.

References

[1] Radio Communication Study Group, "Definition of Spectrum Use and Efficiency of Radio Systems", International Telecommunication Union (ITU). Document 1/4-E February 1996.

[2] G.K. Chan and B.A. Brown, "A measure of Spectrum Utilization in Land Mobile Bands", Canadian Conference on Electrical and Computer Engineering, 1996

[3] CCIR Report Rep.662-1 (Mod.F),. Dubrovnik, 1986.

[4] H.M. Hafez, S.Towaij and R.A. Goubran, "The Effect of User's Geographical Distribution on the Utilizayion of Radio Spectrum", IEEE Trans. on Electromagnetic Compatibility, vol. 32, No.4, November 1990

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Adjacent

channel

interference

Coordination area

Fn+1/2

Fn

Fn

Fn+1

Co-channel

interference

(interstitial)

Co-channel

interference

(primary)

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