Radio Frequency Coverage: The Cell

Abstract

The FCC (Federal Communications Commission) provides licenses to operate cellular communication systems over given band of frequencies. These bands of frequencies are finite and have to be reused to provide services to other geographic areas. Since a number of different technologies are available, the reuse of frequencies must also differ. Therefore, techniques are needed to support these competing technologies so that they can coexist and offer services to a wide geographic area without interfering each other. In order to provide a comprehensive overview, this chapter begins with the description of cell geometry followed by the concept of cell reuse with the evaluation of carrier to interference ratio (C/I). The classical cell reuse plan is described next, with examples of various frequency plans related to OMNI and Sectorization schemes. The associated channel capacity and C/I performances are also evaluated.

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

6.1 Introduction

The FCC (Federal Communications Commission) provides licenses to operate cellular communication systems over a given band of frequencies. These bands of frequencies are finite and have to be reused to provide services to other geographic areas. Since a number of different technologies are available [1, 2], the reuse of frequencies must also differ. Therefore, techniques are needed to support these competing technologies so that they can coexist and offer services to a wide geographic area without interfering each other. In order to provide a comprehensive overview, this chapter begins with the description of cell geometry followed by the concept of cell reuse with the evaluation of carrier to interference ratio (C/I). The classical cell reuse plan [3] is described next, with examples of various frequency plans related to OMNI and Sectorization schemes. The associated channel capacity and C/I performances are also evaluated.

6.2 The Concept of Cell

A cell, also known as the Radio Frequency (RF) footprint, is the basic building block in wireless communication. There are two types of cells:

• OMNI Cell and

• Sectorized cell

OMNI means all directions and uses OMNI directional antenna at the center of the cell as shown in Fig. 6.1a. Sectorized cells use directional antennas. Typically, there are three sectors, 120° per sector. Each sector uses a directional antenna as shown in Fig. 6.1b. Also shown in Fig. 6.1c is an alternate version of a sectorized cell known as tri-cellular plan. We will further discuss these cell structures later in this chapter.

Fig. 6.1

Illustration of OMNI and sectorized cells. a OMNI cell, b three sectored cell, c sectorized cell (Tri-cellular plan)

Each OMNI and sectorized cell has a base station, where the transmitter is located at the center of the cell. The shape and size of the cell depends on transmit power, antenna height, antenna gain, Propagation environment, pathloss characteristics and the signal strength at the cell edge. The signal strength, also known as Received Signal Level (RSL is the same all around the cell edge. These cells are distributed over land areas, offering services to tens of thousands of mobile phone users in a given service area. Also, each cellular base station is connected via the Network Operation Center, which provides today’s land-mobile communication all over the world.

Since the RF environment is fuzzy and unpredictable, a practical cell is highly irregular and not useful for analytical purposes. An ideal cell, on the other hand, is a perfect sphere, which applies to free-space only. Considering all these shortcomings, the cellular industries have adopted the hexagonal cell as the basis for the analysis and design of all cellular systems. To illustrate, we Consider Fig. 6.2, where,

Fig. 6.2

The analytical hexagonal OMNI cell

R:

Cell Radius of the ideal cell (circle)

r :

Effective radius of the analytical cell (center to vertex)

Using plane geometry, we obtain:

$$ Cos({{{30}^0}}) = \frac{r}{R} = \frac{{\sqrt 3 }}{2} $$

(6.1)

Solving for r,

$$ r = \frac{{\sqrt 3 }}{2}R = 0.866R $$

(6.2)

We shall use this geometrical configuration for analysis throughout this chapter.

6.3 The Distance Between Two Hexagonal Cells

The distance between two hexagonal cells (D) can be obtained by placing two hexagonal cells as shown in Fig. 6.3. This is given by,

Fig. 6.3

Distance between two hexagonal cells

$$ D = 2r = 2\frac{{\sqrt 3 }}{2}R = 1.732R $$

(6.3)

The performance metric, known as D/R ratio, can be obtained from Eq. 6.3 as:

$$ \frac{D}{R} = 1.732 $$

(6.4)

This parameter will be used to calculate carrier to interference ratio C/I, as we shall see later.

In Fig. 6.3, we also notice that two adjacent hexagonal cells are equivalent to two overlapping circles. This overlap region is the well-documented “Hand-Off” region.

6.4 Frequency Reuse and C/I

6.4.1 C/I Due to a Single Interferer

In cellular communications, frequencies are reused in different cells, which mean that another mobile can use the same frequency, thereby causing co-channel interference or carrier to interference (C/I) [4–6]. As an illustration, we consider Fig. 6.3, where the same frequency is used in Cell-A and Cell-B. Therefore, a mobile communicating with Cell-A will also receive the same frequency from the distant Cell-B. This is analogous to the “Near-Far” problem, causing co-channel interference. We use the following method to determine this interference Fig. 6.4.

Fig. 6.4

Carrier to Interference ratio (C/I) due to a single interferer

Let,

RSL_A :

Received signal level at the mobile from Cell-A

d_A :

Distance between the mobile and Cell-A

RSL_B :

The received signal level at the mobile from Cell-B

d_B :

Distance between the mobile and Cell-B

γ :

Pathloss exponent

Then we can write,

$$ \begin{gathered}RS{L_A}\propto {({{d_A}})^{- \gamma }}\hfill\\RS{L_B}\propto {({{d_B}})^{- \gamma }}\hfill\\ \end{gathered}$$

(6.5)

The ratio of the signal strengths at the mobile will be:

$$ \frac{{RS{L_A}}}{{RS{L_B}}}= {\left({\frac{{{d_A}}}{{{d_B}}}}\right)^{- \gamma }}= {\left({\frac{{{d_B}}}{{{d_A}}}}\right)^\gamma } $$

(6.6)

In Eq. 6.6, RSL_A is the RF signal received from the serving cell. Therefore, this is the desired signal and we redefine this signal as the carrier signal C. We also assume that the mobile is at the cell edge from the serving cell-A, which is the cell radius R. On the other hand, RSL_B is the undesired signal received from Cell_B and we redefine this signal as the interference signal I. The corresponding interference distance d_B = D; D being the reuse distance. Therefore, Eq. 6.6 can be written as a carrier to interference ratio (C/I), due to a single interferer, as:

$$ \frac{C}{I} = {\left({\frac{D}{R}}\right)^\gamma } $$

(6.7)

In decibel, it can be written as:

$$ \frac{C}{I}({dB}) = 10Log{\left({\frac{D}{R}}\right)^\gamma } $$

(6.8)

6.4.2 C/I Due to Multiple Interferers

In hexagonal cellular geometry, each hexagonal cell is surrounded by six hexagons. Therefore, in a mature cellular system, there can be six primary interferers. The total interference from all six interferers will be

$$ \begin{gathered}6RS{L_B}\propto {({{d_B}})^{- \gamma }}\hfill\\or \hfill\\RS{L_B}\propto \frac{1}{6}{({{d_B}})^{- \gamma }}\hfill\\ \end{gathered}$$

(6.9)

Therefore, the effective interference ratio is:

$$ \frac{C}{I} = \frac{{RS{L_A}}}{{RS{L_B}}}= \frac{1}{6}{\left({\frac{{{d_A}}}{{{d_B}}}}\right)^{- \gamma }}= \frac{1}{6}{\left({\frac{{{d_B}}}{{{d_A}}}}\right)^\gamma } = \frac{1}{6}{\left({\frac{D}{R}}\right)^\gamma } $$

(6.10)

And in decibel,

$$ \frac{C}{I}({dB}) = 10Log\left[{\frac{1}{6}{{\left({\frac{D}{R}}\right)}^\gamma }}\right] $$

(6.11)

Therefore, by knowing the reuse distance, the C/I ratio can be determined. Or, by knowing the C/I requirement, the reuse distance can be determined in a given propagation environment. The reuse distance D can be determined from plane geometry and the cell radius can be obtained from the propagation model Fig. 6.5.

Fig. 6.5

C/I due to multiple interferers. Group of frequencies used in the center cell are reused in the surrounding six cells

6.5 Frequency Reuse

6.5.1 Basic Concept

Cellular communication is a multiple access system where several non-interfering channels are combined to form a channel group and assigned to a cell site. Since there are a limited number of channels, these channel groups are reused at a regular interval of distances. This is an important engineering task, which determines system capacity and performance.

Several frequency reuse techniques, generally known as frequency planning or channel assignment techniques, are available. Some of the most widely used frequency planning techniques are given below [5]:

• N = 7 Frequency Reuse Plan

• N = 3 Frequency Reuse Plan

The N- = 7 is the classical cellular architecture, which is based on hexagonal geometry. It was originally developed by V.H. MacDonald in 1979. It ensures adequate channel reuse distance to an extent where co-channel interference is low and acceptable, while maintaining a high channel capacity. These frequency plans are briefly presented to illustrate the concept.

The scheme is shown in Fig. 6.6 where we have a cluster of 7 OMNI cells and a cluster of 7-sectorized cells. OMNI cell use OMNI directional (all directions) antennas. In the sectorized scheme, each cell is divided into three sectors, 120° each. Directional antennas are used in each sector. According to the art of channel assignment technique, all the available channels are grouped into 21 frequency groups as follows:

Fig. 6.6

The classical 7-cell cluster. a OMNI pattern and b 3-Sectored pattern.

G1, G2, G3, G4, G5, G6, G7, G8, G9, G10, G11, G12, G13, G14, G15, G16, G17, G18, G19, G20, G21.

Each frequency group has several frequencies (known as channels). These 21 frequency groups are equally distributed among the cells/sectors. Notice that each OMNI cell gets three frequency groups or a total of 21 frequency groups in the 7 cell cluster. On the other hand, a sectorized cell gets one frequency group per sector for a total of three frequency groups per cell. The total number of frequency groups per cluster is still the same as in the OMNI scheme.

6.5.2 Example of N = 7 OMNI Frequency Plan

In the N = 7 frequency reuse plan, the available channels are equally divided among 7 cells known as a 7-cell cluster. As an illustration, we will consider the classical North American 1G and 2G standards [1, 2]. According to these standards, the channel assignment is accomplished by forming 21 frequency groups per band (Band-A and Band-B) as shown in Tables 6.1 and 6.2 respectively [5]. Frequency assignment is then based on a distribution plan described earlier in the previous section. The corresponding N = 7 cell cluster is shown in Fig. 6.7 having three frequency groups per cell.

Table 6.1 N = 7/21 A-Band Frequency Chart

Table 6.2 N = 7/21 B-Band Frequency Chart

Fig. 6.7

N = 7, Frequency reuse for OMNI plan showing re-appearance of adjacent channels

The total number of frequency groups per cluster is 7 × 3 = 21. Channel assignment is based on the following sequence: (N, N + 7, N + 14) where N is the cell number (N = 1, 2, 7). The channel-grouping scheme is shown in Table 6.3. Figure 6.7 gives two versions of channel assignments. Notice that adjacent channels appear within the cluster, causing adjacent channel interference. It indicates that the total elimination of channel adjacency is practically impossible in the N = 7 plan, which gives rise to adjacent channel interference throughout the network.

Table 6.3 N = 7/21 OMNI, channel grouping

6.5.3 Evaluation of Co-Channel Interference

Co-Channel Interference (CCI), also known as Carrier to Interference ratio (C/I, arises from multiple uses of the same frequency. For OMNI sites (see Fig. 6.6), C/I is given by [5, 6]:

$$ \frac{C}{I} = 10\log \left[{\frac{1}{k}{{\left({\frac{D}{R}}\right)}^\gamma }}\right] $$

(6.12)

Where

k =:

Number of Co-Channel Interferers

γ :

Propagation constant

D :

Frequency reuse distance

R :

Cell radius

The distance ratio (reuse distance) D/R is given by

$$ \frac{D}{R} = \sqrt {3N}$$

(6.13)

For N = 7 frequency plan

$$ \frac{D}{R} = \sqrt {3x7}= 4.58 $$

(6.14)

The distance ratio can also be determined geometrically.

6.5.4 Evaluation of Adjacent Channel Interference

Adjacent channel interference arises from energy spillover between two adjacent channels. This can be evaluated with the aid of Fig. 6.8, where we assumed that the adjacent channel is assigned to the adjacent site and the ratio di/dc varies as the mobile moves towards or away from the cell. Moreover, the out-of-band signals are also assumed attenuated by the post-modulation filter at least by 26 dB (EIA Standard) [1, 2]. Then the Adjacent Channel Interference will be:

Fig. 6.8

Adjacent channel interference evaluation scheme

$$ \begin{gathered} \hfill\\ACI =- 10\log \left[{{{\left({\frac{{{d_i}}}{{{d_c}}}}\right)}^\gamma }}\right] + Adj.Ch.Isolation \hfill\\ \end{gathered}$$

(6.15)

Where the adjacent channel isolation is provided by the post-modulation filter, which is generally ≈ 26 dB. As an example, an adjacent channel in the in the adjacent site has di/dc = 1, resulting in ACI ≈ − 26 dB. An adjacent channel in an alternate channel (one cell away) provides much greater than 26 dB isolation due to a higher distance ratio (di/dc > 1).

6.6 120° Sectorization

6.6.1 Basic Concept

The 120° Sectorization is achieved by dividing a cell into three sectors, 120° each, as shown in Fig. 6.9a. Each sector is treated as a logical OMNI cell, where directional antennas are used in each sector for a total of three antennas per cell. Figure 6.9b shows an alternate representation, which is known as Tri-Cellular plan [5, 6]. Both configurations are conceptually identical while the latter is convenient for channel assignment. Each sector uses one control channel and a set of different voice channels. Adequate channel isolations are maintained within and between sectors in order to minimize interference. This is attributed to channel assignment techniques, as we shall see later in this chapter.

Fig. 6.9

Illustration of 120° sectorization. Directional antennas are used in each sector a Conventional representation b an alternate representation

Because directional antennas are used in sectored cells, it allows reuse of channels more frequently, thus enhancing channel capacity. Moreover, multipath components are also reduced due to directionalization, hence enhancing the C/I performance.

6.6.2 N = 7/21, 120° Sectorization Plan

The N = 7/21, 120° sectorization plan is based on the distribution of one frequency group per sector, three frequency groups per cell for a total of 21 frequency groups per cluster. This is shown in Fig. 6.10a for the conventional plan and in Fig. 6.10b for the tri-cellular plan where the sector is represented by hexagon. Channel distribution is based on N, N + 7, N + 14 scheme where N = 1, 2,.., 7. Therefore for N = 1, cell-1 uses frequency group-1 for sector-1, frequency group-8 for sector-2 and frequency group-15 for sector-3. Similarly, cell-2 uses frequency group 2, 9 and 16 for sector 1, 2 and 3 respectively.

Fig. 6.10

a N = 7/21 sectorized configurations based on 120°. Sectorized plan. b N = 7/21 tri-cellular plan

6.6.3 N = 7/21, 120-Deg. Co-Channel Interference

The 120-deg sectorization is achieved by dividing a cell into 3 sectors, while directional antennas are used in each sector. Thus antenna configuration and their directivity play an important role in determining the C/I performances. In order to illustrate this further, let us consider the diagram as shown in Fig. 6.11, where directional antennas are used for the present analysis. Antenna down tilt is also provided for an additional isolation, which must be taken into account.

Fig. 6.11

Illustration of antenna down tilt

The angle of down tilt is related to the cell radius and antenna height. This can be calculated by using plane geometry. It is given by the following equation:

$$ R = \frac{H}{{\tan \theta }}$$

(6.16)

Where,

R =:

Cell radius

H =:

Antenna height

θ =:

Angle of antenna down tilt

These assumptions modify the C/I prediction equation as

$$ \frac{C}{I} = 10\log \left[{\frac{1}{k}{{\left({\frac{D}{R}}\right)}^\gamma }}\right] + \Delta dB (due to antenna down tilt) $$

(6.17)

With k = 6, γ = 3.84, D/R = 4.58 and ∆dB ≈ 6 dB, we now obtain

$$ \frac{c}{I}\approx 23.6dB $$

(6.18)

The performance can be further improved by using antenna having a narrow vertical beam width.

6.7 N = 3 Tri-Cellular Plan

6.7.1 Alternate Channel Assignment

The N = 3 tri-cellular plan is based on a cluster of three tri-cells for a total of 9 logical cells [5]. Channel assignment is based on a 3 × 3 array of 9 frequency groups, distributed alternately among 9 logical cells as shown in Fig. 6.12. Because of alternate channel assignment, this arrangement completely eliminates adjacent channels from adjacent sites, thus reducing adjacent channel interference.

Fig. 6.12

The N = 3, tri-cellular plan having 9 logical cells as sectors

The growth plan is based on repetition of vertical and horizontal patterns in sequence as shown in Fig. 6.13. As can be seen, adjacent channel isolation is maintained throughout the network. It may be noted that only vertical and horizontal expansions are possible in this scheme; this is due to the rhombic pattern of the cluster. The N = 7 mapping is also evident in Fig. 6.13, which can be shown to expand throughout the network.

Fig. 6.13

N = 3, Tri-Cellular growth plan showing N = 7 mapping

6.7.2 N = 3 Cyclic Distribution of Channels

In this plan, the channel distribution is based on (N, N + 3, N + 6) where N = 1,2,3, N being the cell number. Using this scheme, we obtain

$$ \begin{gathered}{\text{Cell - 1 frequency group: 1, 4, 7}}\hfill\\{\text{Cell - 2 frequency group: 2, 5, 8}}\hfill\\{\text{Cell - 3 frequency group: 3, 6, 9}}\hfill\\ \end{gathered}$$

(6.19)

The corresponding N = 3 cell cluster is given in Fig. 6.14, where the growth plan is already established. For example, if cell-1 is assumed to be in the center, the surrounding pattern would be 2, 3, 2, 3, 2, 3. Similarly, if cell-2 is in the center, the surrounding pattern would be 1, 3, 1, 3, 1, 3. Likewise, if cell-3 is in the center, the surrounding pattern would be 1, 2, 1, 2, 1, 2. This is shown in Fig. 6.15 where each distribution pattern is free of adjacent channels.

Fig. 6.14

N = 3 tri-cellular plan

Fig. 6.15

Principle of cyclic distribution

Figure 6.16 shows a complete distribution pattern for case-1 where cell-1 is assumed to be in the center. we also see a mapping similarity between N = 3 plan and N = 7 plan. Therefore existing N = 7 cell sites can be easily translated into N = 3 plan simply by channel reassignment. Other distribution patterns can be obtained from the distribution principle according to Fig. 6.15.

Fig. 6.16

N = 3 growth plan showing N = 7 mapping

6.7.3 N = 3 Co-Channel Interference

Because of antenna directivity, it can be shown that there are three effective interferers in this scheme.

Therefore the Co-Channel Interference can be estimated as:

$$ \frac{C}{I}\approx 10\log \left[{\frac{1}{3}{{\left({\frac{D}{R}}\right)}^\gamma }}\right] + \Delta dB{(}ave.) $$

(6.20)

$$ \frac{D}{R} = \sqrt {3x3}= 3 $$

With γ ≈ 3.84, D/R = 3 and ∆dB(ave.) ≈ 6 dB we get

$$ \frac{C}{I}\approx 13.55 + 6 = 19.55dB $$

(6.21)

Problem 6.1

Given: The received signal strength at the cell edge: RSL (dBm) = − 90 dBm

Find: The corresponding RSL in watts

Solution 6.1

RSL (dBm) = 10 Log [RSL(mW) = − 90 dBm

Log [RSL (mW) = − 90/10 = − 9 mW

[RSL (watts) = 10⁻¹² Watts

[NOTE: 1 milli watt = 10⁻³ Watts]

Problem 6.2

Given: The received signal strength at the cell edge: RSL (W) = 10⁻¹² W

Find: The corresponding RSL in dBm.

Solution 6.2

$$ \begin{gathered}{\text{RSL}}({{\text{dBW}}}) = 10\ {\log{}}\ {\text{<ct>[<ot>RSL}}({\text{W}})\\= 10\ {\log{}}\ ({10 - 12})\\=- 120\ {\text{dBW}}\\= --90({{\text{dBm}}})\\ \end{gathered}$$

[NOTE: 0 dBW = 30 dBM]

Problem 6.3

Show that 0 dBW = 30 dBm.

Solution 6.3

1 W = 1000 mW

Therefore, in decibel:

10 Log (1 W) = 10 Log (1000 mW)

Or

0 dBW = 30 dBm.

Problem 6.4

Given:

• N = 7 OMNI and sectorized frequency reuse plans

• Pathloss slope γ = 4

Find:

• a. The carrier to interference ratio C/I for the OMNI Plan.

• b. The carrier to interference ratio C/I for the sectorized Plan.

Solution 6.4

• a. For the OMNI plan:

$$\frac{C}{I} = 10\log \left[ {\frac{1}{k}{{\left( {\sqrt {3xN} } \right)}^\gamma }} \right]$$

With N = 7 OMNI, k = 6. Using γ = 4, the C/I becomes,

$$ \frac{C}{I} = 18.6\ {\text{dB}}$$

(6.22)

• b. For the N = 7 sectorized plan, the C/I is written as:

$$\frac{C}{I} \approx 10\log \left[ {\frac{1}{k}{{\left( {\sqrt {3xN} } \right)}^\gamma }} \right] + \Delta dB{\rm{(}}ave.)$$

Where k = 3. ΔdB is an additional dB margin due to directional antennas with down tilt. This value ranges from 6 to 8 dB depending on bean width and amount of down tilt. Using γ = 4 for dense urban environment and ΔdB = 6 dB, the C/I can be derived from the previous problem. This is given by:

C/I (N = 7, Sectorized) = 18.6 dB + 6 dB = 24.6 dB.

Problem 6.5

Given:

• N = 3 OMNI and sectorized frequency reuse plan

• Pathloss slope γ = 4

Find:

• a. The carrier to interference ratio C/I for the OMNI Plan.

• b. The carrier to interference ratio C/I for the sectorized Plan.

Solution 6.5

• a. For the OMNI plan:

$$\frac{C}{I} = 10\log \left[ {\frac{1}{k}{{\left( {\sqrt {3xN} } \right)}^\gamma }} \right]$$

With N = 3 OMNI, k = 6. Using γ = 4, the C/I becomes,

$$ \frac{C}{I} = 14\ {\text{dB}}$$

(6.23)

• b. For the N = 3 sectorized plan, the C/I is written as:

$$\frac{C}{I} \approx 10\log \left[ {\frac{1}{k}{{\left( {\sqrt {3xN} } \right)}^\gamma }} \right] + \Delta dB{\rm{(}}ave.)$$

Where k = 3. Δ dB is an additional dB margin due to directional antennas with down tilt. This value ranges from 6 to 8 dB depending on bean width and amount of down tilt. Using N = 3, γ = 4 for dense urban environment and ΔdB = 6 dB, the C/I can be derived from the previous problem. This is given by:

C/I (N = 3, Sectorized) = 14 dB + 6 dB = 20 dB.

6.8 Conclusions

• Discussed radio Frequency coverage and provided the concept of cell

• Rationalized the use of hexagonal cell geometry and calculated cell radius

• Provided the concept of OMNI and Sectorized cells

• Provided the concept of Cell cluster

• Presented N = 7 frequency reuse plan and carrier to interference ratio (C/I)

• Presented N = 3 frequency reuse plan and carrier to interference ratio (C/I)

• Discussed the benefit of antenna down tilt and calculated the down tilt angle