The Cellular Concept Cellular radio systems accommodate a large number of users (subscribers) over a large geographic area, within a limited frequency.

The Cellular Concept Cellular radio systems accommodate a large number of users (subscribers) over a large geographic area, within a limited frequency spectrum. High capacity is achieve by limiting the coverage area of each base station transmitter to a small geographic area called a cell. The cellular structure allow the re-use of frequency across the network. Top of Cellular Radio tower

Cells Different Frequencies or Codes
Basics: Structure Single antenna for Tx and Rx, a device called duplexer is used to separate. Multiple Access Division Duplexing Separate Tx and Rx antennas Downlink, forward direction Handoff Handover Uplink, reverse direction Cell Mobile Station (MS) Distributed transceivers Base Station (BS) Fixed transceiver Cells Different Frequencies or Codes To differentiate between different transmissions in the same direction (share the same broadcast channel) Multiple access technique is used, e.g., FDMA, TDMA, CDMA, OFDMA. To differentiate between the downlink and the uplink (provide full-duplex system), use Frequency division duplexing (FDD) or Time division Duplexing (TDD).

Duplexer principle Rx Tx

FDD: Uplink Downlink Allocated Frequency Spectrum for a cell X Hz Y Hz
1 … 1 … 2 … 2 … 1 … k 1 … 1 … 2 … 2 … 1 … k Allocated Frequency Spectrum for the whole cellular system

Allocated Frequency Spectrum for a cell
TDD: Downlink Uplink Allocated Frequency Spectrum for a cell X Hz Y Hz

Basic Multiple Access Methods
Frequency CMDA: Code Division Multiple Access TDMA: Time Division Multiple Access Codes FDMA: Frequency Division Multiple Access Time

Allocated channels for one cell
Channels allocation Assume that a cell is allocated 𝑘 full-duplex channels. At least one full-duplexed channel is use for control (call setup, call request, call initiation, and beacon) called Control Channel or Setup Channel. The other channels are used for voice and data. uplink downlink RCC 1 2 3 4 … … … FCC 1 2 3 4 … … … K-1 K-1 RVC FVC Allocated channels for one cell

Terminology Subscriber: A user who pays subscription charges for using a mobile communication system. Mobile Station (MS): A station in the cellular radio service intended for use while in motion at unspecified locations. Base Station: a fixed station in a mobile system used for radio communication with mobile station. Base stations are located at the center or on the edge of a coverage region. Mobile Switching Center (MSC) or Mobile Telephone Switching Office (MTSO): Switching center which coordinates the routing of calls in a large service area. It connects the cellular base stations and the mobiles to the PSTN. Handoff: the process of transferring a mobile station from one channel or base station to another. Hard handoff: break before make. Soft handoff: make before break. Page: A brief message which is broadcast over the entire service area, by many BS at the same time. Roamer: A subscriber which operates on a service area (market) over than that from which service has been subscribed.

Make a cellular Call Communication between MS and BS is defined by:
Standard Common Air Interface (CAI): FVC: forward voice channel. RVC: reverse voice channel. FCC: forward control channel. RCC: reverse control channel. Called Setup channels

Mobile Terminated call
Power level downlink Mobile Terminated call uplink downlink RCC 1 2 3 4 … … … FCC 1 2 3 4 … … … K-1 FCC K-1 RVC FVC FCC Page MIN#1 Alert Move MS to U VC Page MIN#1 Page MIN#1 On MIN#1 FCC RCC FCC FVC3 FCC Ack Ack Page MIN#1 MSC PSTN Page MIN#1 Move MS to U VC

Mobile Originated call
uplink downlink RCC 1 2 3 4 … … … FCC 1 2 3 4 … … … K-1 K-1 RVC FVC Move MS to U VC tone FVC4 FCC RCC request request Move MS to U VC MSC PSTN

Cell planning segmentation of the area into cells cell
Actual radio coverage of the cell segmentation of the area into cells idealized radio coverage of the cell cell hexagon shape of the cell cell Ameba shape use of several carrier frequencies not the same frequency in adjoining cells cell sizes vary from some 100 m up to 35 km depending on user density, geography, transceiver power etc. hexagonal shape of cells is used (cells overlap, shapes depend on geography) Actual radio coverage of a cell is known as the footprint, is determined: From field measurement or, Propagation prediction models

Circular Coverage Areas
Original cellular system was developed assuming base station antennas are omnidirectional, i.e., they transmit in all directions equally. Users located outside some distance to the base station receive weak signals. Result: base station has Ideally circular coverage area. Weak signal Strong signal

Tessellation Some group of small regions tessellate a large region if they overlay the large region without any gaps or overlaps. There are only three regular polygons that tessellate any given region.

Tessellation (Cont’d)
Three regular polygons that always tessellate: Equilateral triangle Square Regular Hexagon Triangles Squares Hexagons

Circles Don’t Tessellate
Thus, ideally base stations have identical, circular coverage areas. Problem: Circles do not tessellate. The most circular of the regular polygons that tessellate is the hexagon. Thus, early researchers started using hexagons to represent the coverage area of a base station, i.e., a cell.

Circles to Hexagons

Thus the Name Cellular With hexagonal coverage area, a cellular network is drawn as: Since the network resembles cells from a honeycomb, the name cellular was used to describe the resulting mobile telephone network. Base Station

Regular Hexagon ℎ= 𝑅 2 − 𝑅 2 2 = 3 2 𝑅 Area of one triangle is:
ℎ= 𝑅 2 − 𝑅 = 𝑅 Area of one triangle is: 𝐴= 𝑅 2 ℎ= 𝑅 2 Area of the hexagon: 3 4 𝑅 2 ×6= 𝑅 2 R R R h triangle R

Frequency Reuse (Frequency Planning)
Cellular structure allows carrier frequencies to be re-used High frequency re-use will lead to: Short distance between same carriers High traffic capacity Low C/I ratio (i.e. worse interference) Frequency planning involves a compromise between requirements for capacity and interference Digital systems like GSM can cope with lower values of C/I than analog systems Simple frequency plans assume a homogeneous distribution of carriers and equal sized cells. A cell-cluster is a group of adjacent cells, which are allocated all the frequency channels without duplication

Cell Cluster Cluster size N, Frequency reuse Factor = 1 𝑁 .
𝑁= 𝑖 2 +𝑖×𝑗+ 𝑗 2 , 𝑖=𝑗=1, ⇒𝑁=3 Let 𝑠 be the total number of Duplex channels in this cellular system.  Each cell is allocated 𝑘= 𝑠 𝑁 channels. To cover the whole area, the clusters are replicated 𝑀 times within the system  the total no. of duplex channels (the Capacity of the system) 𝐶=𝑀𝑘𝑁=𝑀𝑠 𝑀=39, 𝐶=39𝑠 tier2 Frequency reuse factor 1 3 60 𝑜 tier1 To find tier 1 co-channel neighbors of a particular cell: 1) Move 𝑖 cells along any chain of hexagons 2) Then turn 60 𝑜 counter-clockwise and move 𝑗 cells. The no. of tier1 co-channel neighbors is 6 always regardless of N.

7 Cell Cluster 𝑁= 𝑖 2 +𝑖×𝑗+ 𝑗 2 , 𝑖=1,𝑗=2, ⇒𝑁=7
As N increase the system capacity decrease, while the distance between co-channel neighbors will increase i.e. co-channel interference will decrease. tier1 𝑀=16, 𝐶=16𝑠 Frequency reuse factor 1 7

12 Cell Cluster 𝑁= 𝑖 2 +𝑖×𝑗+ 𝑗 2 , 𝑖=2,𝑗=2, ⇒𝑁=12 tier1 𝑀=12, 𝐶=12𝑠
Frequency reuse factor 1 12

Frequency Re-use Distance
From the cosine law: 𝐷 2 = 2ℎ𝑖 ℎ𝑗 2 −2 2ℎ𝑖 2ℎ𝑗 cos 120 𝑜 ℎ= 𝑅, ⇒𝐷= 3 𝑖 2 +𝑖𝑗+ 𝑗 2 𝑅 2 = 3𝑁 𝑅 ⇒ 𝐷 𝑅 = 3𝑁 𝑄= 𝐷 𝑅 2ℎ𝑗 D 120 𝑜 R 2ℎ𝑖 𝑄 is called co-channel reuse ratio

Interference and System Capacity
Interference is the main limiting factor in the performance of cellular radio system. Interference has been recognized as a major bottleneck in increasing capacity and is often responsible for dropping calls. Sources of interference: Another mobile in the same cell. A call in progress in a neighboring cell. Other base stations operating in the same frequency band The two major types of system-generated cellular interference are: Co-channel interference (C/I). Adjacent channel interference (C/A).

Adjacent Channel Interference
Adjacent channel interference is measured by the carrier to adjacent channel ratio: C/A 𝐶 𝐴 =10 log 𝑃 𝑐 𝑃 𝐴 dB 𝑃 𝑐 :Power from wanted channel 𝑃 𝐴 :Power from adjacent channel GSM specification for minimum working C/A: - 9 dB Some operators plan for C/A as high as 3 dB Ways of improving C/A: More selective receivers Greater distance between adjacent TX frequencies

Co-channel interference
Around each cell, there are 6 cells in adjacent clusters using the same carriers (co-channel cells) These cells will cause mutual co-channel interference The C/I due to these cells can be found from the reuse distance, D 𝐷 𝑅 = 3𝑁 Typical cluster sizes are: 3, 4, 7, 12, 21 Co-channel interference can not be combated by simply increasing the carrier power of the transmitter, this is because an increase in carrier power increases interference to neighboring co-channel cells. Larger cluster sizes give better C/I ratios (large D) However, smaller cluster sizes give higher traffic capacity per cell – more carriers available in each cell (𝑘= 𝑠 𝑁 channels) and higher overall system capacity (C=Ms) 1 2 3 4 5 6 7 1 2 3 4 5 6 7 2 1 2 3 4 5 6 7 1 2 3 4 5 6 7 D 1 2 3 4 5 6 7 1 2 3 4 5 6 7 2 6 nearest interfering (co-channel) cells 2 Serving Cell

Interference Calculations
1 2 3 4 5 6 7 To estimate C/I we assume: Each base station radiating the same power Homogeneous propagation throughout the service area Propagation follows a 1 𝑟 𝑥 law 𝑥 is the propagation (path loss) co-efficient) 𝑟 is the distance between the Tx and Rx Re-use distance, D, is large compared with cell radius, R 1 2 3 4 5 6 7 2 1 2 3 4 5 6 7 1 2 3 4 5 6 7 D 1 2 3 4 5 6 7 1 2 3 4 5 6 7 2 6 nearest interfering (co-channel) cells 2 Serving Cell

Estimating C/I for Re-use Patterns
Let 𝑛 be the number of co-channel interfering cells. Then the carrier-to-interference ratio (C/I) for a mobile receiver which monitors a downlink channel: 𝐶 𝐼 = 𝐶 𝑖=1 𝑛 𝐼 𝑖 C: the desired signal power from the serving BS. 𝐼 𝑖 : interference power caused by the 𝑖th interfering co-channel cell. Let 𝐷 𝑖 be the distance of the 𝑖th interferer from the mobile. Assume a mobile on the edge of the serving cell: 𝐶=𝛼 1 𝑅 𝑥 𝐼 𝑖 =𝛼 1 𝐷 𝑖 𝑥 ⇒ 𝐶 𝐼 = 𝑅 −𝑥 𝑖=1 𝑛 𝐷 𝑖 −𝑥

Estimating C/I for first tier
Consider only the first tier and equal distance 𝐷 from the interferers to the mobile. Under the assumption that D >> R. This is more appropriate for large clusters. 𝐶=𝛼 1 𝑅 𝑥 , 𝐼=6 𝛼 1 𝐷 𝑥 𝐶 𝐼 = 𝐷 𝑅 𝑥 But 𝐷=𝑅 3𝑁 ⇒ 𝐶 𝐼 = 𝑁 𝑥 ⇒ 𝐶 𝐼 =10 log 𝑁 𝑥 dB The value of 𝑥 will depend on the local radio propagation properties, but 3.5 is generally a good estimate.

C/I for Typical Cluster Sizes
𝐶 𝐼 =10 log 𝑁 𝑥 dB Propagation Coefficient (𝑥) 2 3 3.5 4 Cluster Size (N) 1.76 6.53 8.92 11.3 3.01 8.41 11.1 13.8 7 5.44 12.05 15.36 18.66 9 13.68 17.27 20.85 12 7.78 15.56 19.45 23.34 21 10.21 19.21 23.71 28.21 Analog systems require a minimum C/I of about 20 dB Digital systems can cope with C/I as low as 9 dB

Cell Splitting To increase the capacity decrease the cell size (more users per unit area) 𝑅 𝑜𝑙𝑑 : radius of old cell. 𝐴 𝑜𝑙𝑑 =𝜋 𝑅 𝑜𝑙𝑑 2 : area of old cell Let 𝑅 𝑛𝑒𝑤 = 𝑅 𝑜𝑙𝑑 2 ⇒ 𝐴 𝑛𝑒𝑤 =𝜋 𝑅 𝑜𝑙𝑑 = 𝐴 𝑜𝑙𝑑 4 𝑃 𝑟(𝑜𝑙𝑑) =𝛼 𝑃 𝑡(𝑜𝑙𝑑) 𝑅 𝑜𝑙𝑑 −𝑥 𝑃 𝑟(𝑛𝑒𝑤) =𝛼 𝑃 𝑡(𝑛𝑒𝑤) 𝑅 𝑛𝑒𝑤 −𝑥 Let 𝑃 𝑟(𝑛𝑒𝑤) = 𝑃 𝑟(𝑜𝑙𝑑) ⇒ 𝑃 𝑡(𝑛𝑒𝑤) 𝑃 𝑡(𝑜𝑙𝑑) = 2 −𝑥 Two choices: Keep the old site (“Umbrella” overlay cell) Get rid of the old site Disadvantage: costly

Cell Splitting Techniques
To increase capacity, split each cell into 3 using sectored antennas Center-excited cell: omnidirectional antennas Edge(corner)-excited cell: sectored directional antennas tri-sectored site antenna systems with space diversity Top view

Further Splitting As the network grows, capacity can be further increased by another 3 way split as shown

1:4 Cell Split Alternative way of further splitting the cells
No re-alignment of antennas needed Increases traffic capacity, frequency re-use and number of sites by a factor of 4

Effect of Cell Splitting on Interference
Directional pattern of sectored antennas reduces response to interference Increases C/I significantly Allows greater frequency re-use, i.e. smaller cells If cells A and B use the same carrier: B will cause co-channel interference in A A will cause very little co-channel interference in B  Interference is no longer mutual

Transition Zones Problems may occur at the boundaries between high and low traffic areas Large cells in rural areas will use higher power - can cause interference with smaller urban cells nearby Requires careful frequency planning - possibly reserve carriers for use in such transition zones Alternatively, hierarchy of cells (e.g. overlay / underlay) may be used

GSM Frequency Patterns
Two common re-use patterns in GSM are 3/9 and 4/12 3/9 consists of 3 sites, each of which has been tri-sectored giving a cluster of 9 cells

Interference in the 3/9 Pattern
3/9 pattern allows frequencies to be allocated so no physically adjacent cells use the same frequency C/I is about 9 dB, which is the minimum specified for GSM with frequency hopping Cells A1 and C3 are physically adjacent and are allocated adjacent carriers On the boundary of A1 and C3: C/A = 0 dB GSM specifies a minimum C/A of -9 dB

4/12 Re-use Pattern 4 sites, each tri-sectored to give a 12 cell cluster Numbering of D cells allows carriers to be allocated so that no adjacent carriers are used in physically adjacent cells

Interference in the 4/12 Pattern
4/12 pattern has no physically adjacent cells with co-channel or adjacent channel carriers C/I is about 12 dB This is adequate in GSM without frequency hopping C/A is higher than in 3/9 pattern Traffic capacity is lower than 3/9 as there are fewer carriers per cell

Adjustments for Capacity
Simple re-use patterns assign same number of carriers to each cell Practical traffic may not be evenly distributed Moving carriers to other cells to handle traffic will introduce new interference problems This can be avoided by reducing base station power - e.g. introduce an overlay cell If there are several possible under loaded cells from which a carrier can be moved, consider carefully the interference implications (for both C/I and C/A) of each possible move. Select the carrier which causes the least increase in interference.

Multiple Reuse Patterns (MRP)
A technique to vary the reuse pattern for different channels and different levels of quality of service (QoS) Combines conservative control channel reuse with aggressive traffic channel reuse to achieve a tighter average reuse Frequency Hopping, Power Control and DTX are necessary: These techniques reduce the impact of interference on calls and allow close reuse distances to work more reliably Frequencies can be reserved for microcells and picocells Best used with lots of spectrum Performance results with 15 MHz (75 GSM carriers) are better than for 5 MHz (25 GSM carriers) because there are more frequencies to hop across

MRP BCCH: N=12, i=2, j=2 TCH1:N=7, i=1, j=2 TCH2: N=3, i=1, j=1 TCH1

Frequency Hopping in GSM
When using frequency hopping, the actual carrier frequency used by a TRX changes on each frame (8 timeslots) The frequency follows either a sequential or pseudo-random pattern One frame is 4.6 ms long Rate of hopping = 1/ (4.6 x 10-3) = 217 hops / second This is also known as Slow Frequency Hopping (SFH) to distinguish it from Fast Frequency Hopping used in CDMA systems

Frequency Hopping at the BTS
If the BTS has implemented SFH: TRXs used only for traffic channels will hop through set sequences TRX used for the BCCH carrier will not hop - mobiles must be able to access this for periodic signal level measurements 64 hopping sequences are available in GSM: 1 sequence is cyclic - 1,2,3 …, 1,2 … 63 others are pseudo random patterns Hop Sequence Number (HSN) defines the sequence in use HSN = 0 indicates the cyclic sequence The set of carrier frequencies assigned to the sequence (Mobile Allocation) may be the same for each TRX provided the sequence starts at a different point (Mobile Allocation Index Offset, MAIO)

Frequency Hopping at the Mobile
Base stations need not implement frequency hopping Mobile must be capable of SFH in case it enters a cell in which it is implemented In addition to hopping in step with the BTS, the mobile must also make measurements on adjacent cells This is why the rate of hopping is limited to SFH in GSM The mobile needs to know: Frequencies used for hopping (Mobile Allocation) - coded as a subset of the Cell Allocation frequencies Hop Sequence Number (HSN) Start frequency (Mobile Allocation Index Offset, MAIO)

Traffic Theory and Channel Dimensioning

Traffic Capacity Capacity is the ability of the network to handle traffic, i.e. calls made by subscribers Traffic theory is based on the concept of trunking, where the links between potential callers are routed through a limited number of channels or trunks Cellular radio systems rely on trunking to accommodate a large number of users in a limited radio spectrum This leads to the concepts of blocking and grade of service which must be considered when dimensioning the channels

Trunking Without trunking: With trunking:
In wireless networks trunks correspond to traffic channels

Terminology used in Trunking Theory
Setup Time: The time required to allocate a trunked channel to a requesting user. Blocked Call: Call which cannot be completed at time of request, due to congestion. Also referred to as a lost call. Holding Time: Average duration of a typical call. Denoted by H (in seconds). Traffic Intensity: Measure of channel time utilization, which is the average channel occupancy measured in Erlangs. Denoted by A. Load: Traffic intensity across the entire trunked system, measured in Erlangs. Grade of Service (GoS): A measure of congestion which is specified as the probability of a call being blocked (Erlang B), or the probability of a call being delayed beyond a certain amount of time (Erlang C). Request Rate: The average number of call requests per unit time. Denoted by 𝜆 𝑠𝑒𝑐 −1 .

Blocking Since there are fewer trunks (channels) than potential calls, some calls will be blocked Grade of Service (GoS) is a measure of the ability of a user to access a trunked system during the busiest hour. % of calls blocked % of calls experiencing a delay greater than a certain queuing time So a low figure for Grade of Service is good for the subscriber Low Grade of Service may not be good for the network, as channels will be under-used at times Trunking efficiency describes the percentage usage that is made of the channels Offered Traffic = Carried Traffic + Blocked Traffic Offered Traffic : Total traffic offered to channel by all users Carried Traffic : Traffic successfully carried by the channel Blocked Traffic: Traffic which is blocked at call setup

Grade of Service (GoS) Grade of Service is the fraction of incoming calls (offered traffic) allowed to be blocked due to congestion in the channel Typical Grade of Service is 0.02 (2%) Grade of Service is also called blocking probability or loss probability

Traffic Channel Dimensioning
To dimension the network for traffic capacity: Find the total traffic generated by the subscribers in the network area Find the traffic that can be handled by one TRX at a base station Divide to find the number of base station TRXs needed

Traffic Measurement The fundamentals of trunking theory were developed by Erlang, a Danish mathematician. The measure of traffic intensity bears his name.  Unit of traffic measurement: Erlang (E) One Erlang represents the amount of traffic intensity carried by a channel that is completely occupied. Traffic in Erlangs is the number of call-hours per hour: e.g. A radio channel that is occupied for thirty minutes during an hour carries 0.5 Erlang of traffic

Cont. The traffic intensity offered by each user is equal to the call request rate multiplied by the holding time. Each user generates a traffic intensity of 𝐴 𝑢 Erlangs. 𝐴 𝑢 =𝜆𝐻 𝜆: the average number of call requests per unit time for each user. 𝐻: the average duration of a call. For a system containing 𝑈 users, the total offered traffic intensity 𝐴 is: 𝐴=𝑈 𝐴 𝑢

Cont. Typical traffic per subscriber during the busy hour is 25 mE which corresponds to a mean call holding time of 90 sec (How?). Another traffic unit, used mostly in the USA, is the Call Centum Second (CCS): 1 CCS = 100 call seconds per hour 1 Erlang = 3600 call seconds per hour 1 Erlang = 36 CCS

Erlang Models of Traffic
Two commonly used models of trunked systems are: Erlang B and Erlang C Erlang B (Blocked calls cleared)- blocked calls are lost or cleared Erlang C (Blocked calls delayed)- calls that cannot be handled are put in a queue until a channel becomes available

Erlang B Formula Calls arrive following Poisson distribution: there is a memoryless arrival of requests, implying that all users, including blocked users, may request a channel at any time. The probability of a user occupying a channel is exponentially distributed, so that longer calls are less likely to occur. Finite number of channels Infinite number of users M/M/m/m queuing problem. ⇒𝑃𝑟 𝑏𝑙𝑜𝑐𝑘𝑖𝑛𝑔 = 𝐴 𝐶 𝐶! 𝑘=0 𝐶 𝐴 𝑘 𝑘! =𝐺𝑂𝑆 𝐴: total offered traffic 𝐶: number of trunked channels offered by the trunked system

Erlang B Calculations Tables based on the Erlang B model allow calculations to be made relating: Offered traffic Grade of Service Number of channels Structure of Erlang B table: Example: at 2% blocking (0.02 GoS), 2 traffic channels can carry Erlangs of traffic C

Erlang C Formula If a channel is not available immediately, the call request may be delayed until a channel become available. GoS: probability that a call is blocked after waiting a specific length of time in the queue. Probability of a call not having immediate access to a channel is: 𝑃𝑟 𝑑𝑒𝑙𝑎𝑦>0 = 𝐴 𝐶 𝐴 𝐶 +𝐶! 1− 𝐴 𝐶 𝑘=0 𝐶−1 𝐴 𝑘 𝑘! Probability that the delayed call is forced to wait more than 𝑡 seconds: 𝑃𝑟 𝑑𝑒𝑙𝑎𝑦>𝑡 =𝑃𝑟 𝑑𝑒𝑙𝑎𝑦>0 𝑃𝑟 𝑑𝑒𝑙𝑎𝑦>𝑡|𝑑𝑒𝑙𝑎𝑦>0 =𝑃𝑟 𝑑𝑒𝑙𝑎𝑦>0 𝑒 − 𝐶−𝐴 𝑡/𝐻 Average delay 𝐷 for all calls in queued system is: 𝐷=𝑃𝑟 𝑑𝑒𝑙𝑎𝑦>0 𝐻 𝐶−𝐴

Channel Dimensioning - Example
In GSM channel dimensioning, the number of channels must be related to the number of carriers (frequencies) available: 8 channels (timeslots) per carrier Some channels will be required for signalling Example - in a particular cell: Mean call holding time = 90 seconds Grade of Service = 1 % Total number of available carriers = 4 3 timeslots allocated for signaling How many subscribers can this cell support ?

Channel Dimensioning - Solution
Mean call holding time of 90 s implies the average traffic per subscriber is 25 𝑚𝐸= 𝐴 𝑢 Number of channels available is given by: (carriers x 8) - signalling channels = 4 x = 29 channels Using Erlang B tables for GoS = 0.01 and 𝐶 = 29 channels, gives traffic that can be offered as ⇒A= 𝐸 = 𝑚𝐸 Number of subscribers that can be supported is: 𝑈=𝐴/ 𝐴 𝑢 19487 / 25 = 𝟕𝟕𝟗

Trunking Efficiency Trunking efficiency or channel utilisation is given by: carried traffic / number of channels In the Erlang B model: Trunking Efficiency = A (1- GoS) / C Using the previous example: A = E, GoS = 0.01, C = 29 Trunking Efficiency = ( ) / 29 =0.665 = 66.5 %

Example2: A certain city has an area of 1300 square miles and is covered by a cellular system using a seven-cell reuse pattern. Each cell has a radius of four miles and the city is allocated 40 MHz of spectrum with a full duplex channel bandwidth of 60 kHz (each channel serves only one subscriber). Assume a GoS of 2% for an Erlang B system is specified. If the offered traffic per user is 30 mE, compute: The number of cells in the service area. The number of channels per cell. Traffic intensity of each cell. The maximum carried traffic. The total number of users that can be served for 2% GoS. The number of mobiles per unique channel. The theoretical maximum number of users that could be served at one time by the system.

Solution: Total area = 1300 square miles, 𝑅=4 𝑚𝑖𝑙𝑒𝑠
Area of hexagon cell = 𝑅 2 =41.57 square miles ⇒ total number of cells 𝑁 𝑐 = =31 cells. The number of channels = 40𝑀 60𝑘 =666 Total number of channels per the cell: 𝐶= =95 𝑐ℎ𝑎𝑛𝑛𝑒𝑙𝑠 𝑝𝑒𝑟 𝑐𝑒𝑙𝑙. 𝐶=95, 𝐺𝑜𝑆=0.02, from Erlang B tables ⇒𝐴=84 𝐸𝑟𝑙𝑎𝑛𝑔 𝑝𝑒𝑟 𝑐𝑒𝑙𝑙 Maximum carried traffic =𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑒𝑙𝑙𝑠×𝑡𝑟𝑎𝑓𝑓𝑖𝑐 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑝𝑒𝑟 𝑐𝑒𝑙𝑙=31×84=2604 𝐸. Total number of users = 𝑡𝑜𝑡𝑎𝑙 𝑡𝑟𝑎𝑓𝑓𝑖𝑐 𝑡𝑟𝑎𝑓𝑓𝑖𝑐 𝑝𝑒𝑟 𝑢𝑠𝑒𝑟 = =86800 𝑢𝑠𝑒𝑟𝑠. Number of mobiles per channel = number of users/number of channels = =130 mobile per channel. The theoretical maximum number of users that could be served at a time =𝐶× 𝑁 𝑐 =95×31=2945 users.

Example3: A hexagonal cell within a four-cell system has a radius of km. A total of 60 channels are used within the entire system. If the load per user is Erlangs, and 𝜆=1 call/hour, compute the following from Erlang C system that has a 5% probability of delayed call: How many users per square kilometer will this system support? What is the probability that a delayed call will have to wait for more than 10 sec? What is the probability that a call will be delayed more than 10 sec?

Solution: 𝑅=1.387 𝑘𝑚, ⇒𝑎𝑟𝑒𝑎 𝑐𝑜𝑣𝑒𝑟𝑑 𝑝𝑒𝑟 𝑐𝑒𝑙𝑙= (1.387) 2 =5 𝑠𝑞𝑢𝑎𝑟𝑒 𝑘𝑚. Number of cells per cluster =4, ⇒𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐ℎ𝑎𝑛𝑛𝑒𝑙𝑠 𝑝𝑒𝑟 𝑐𝑒𝑙𝑙:𝐶= 60 4 =15 𝑃𝑟 𝑑𝑒𝑙𝑎𝑦>0 =0.05, 𝐶=15, ⇒𝐴=9 𝐸𝑟𝑙𝑎𝑛𝑔 Number of users per cell U= 𝐴 𝐴 𝑢 = =310 𝑢𝑠𝑒𝑟𝑠 Number of users per square km = =62 𝑃𝑟 𝑑𝑒𝑙𝑎𝑦>𝑡|𝑑𝑒𝑙𝑎𝑦>0 = 𝑒 − 𝐶−𝐴 𝑡 𝐻 𝐻= 𝐴 𝑢 𝜆 =0.029 ℎ𝑜𝑢𝑟=104.4 𝑠𝑒𝑐. ⇒𝑃𝑟 𝑑𝑒𝑙𝑎𝑦>10|𝑑𝑒𝑙𝑎𝑦>0 = 𝑒 −(15−9)(10)/104.4 =56.29% Probability that a call is delayed more than 10 sec. 𝑃𝑟 𝑑𝑒𝑙𝑎𝑦>10 =𝑃𝑟 𝑑𝑒𝑙𝑎𝑦>0 𝑃𝑟 𝑑𝑒𝑙𝑎𝑦>10|𝑑𝑒𝑙𝑎𝑦>0 =0.05×0.5629=2.81%

UL/DL capacity limitation
UL/DL capacity limitation Scenario 1: Capacity limitation due to UL interference The cell can’t serve UE1 because the increase in UL interference by adding the new user would be too high, resulting in a high risk of drops Scenario 2: Capacity limitation due to DL power The cell can’t serve UE2 because it’s using all its available power to maintain the connections to the other UEs Scenario 1 Scenario 2 UE1 UE2

Cell breathing The more traffic, the more interference and the shorter the distance must be between the RBS and the UE The traffic load changes in the system causes the cells to grow and shrink with time RBS 1 RBS 2 Fully loaded system Unloaded system

The Cellular Concept Cellular radio systems accommodate a large number of users (subscribers) over a large geographic area, within a limited frequency.

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The Cellular Concept Cellular radio systems accommodate a large number of users (subscribers) over a large geographic area, within a limited frequency.

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Presentation on theme: "The Cellular Concept Cellular radio systems accommodate a large number of users (subscribers) over a large geographic area, within a limited frequency."— Presentation transcript:

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