MRN -4 Frequency Reuse
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1 Politecnico di Milano Facoltà di Ingegneria dell Informazione MRN -4 Frequency Reuse Mobile Radio Networks Prof. Antonio Capone
2 Assignment of channels to cells o The multiple access technique in cellular systems allows not only to create sub-channels to different flows/calls o But also to assign channels to different cells in the network o If you think about the thousands of cells covering the service area it is quite surprising that resources can be divided into so many small pieces A. Capone: Mobile Radio Networks 2
3 Frequency reuse o Actually, considering the total number of channels available for different technologies there are not enough channels even assigning one channel per cell o Solution: use the same channel more times for different cells o Channel reuse generates interference among cells using the same channels o Reuse if possible only with cells that are sufficiently apart each other o Frequency is the fundamental characteristic of cellular networks that makes its dimensioning different from other systems A. Capone: Mobile Radio Networks 3
4 Cell shape o Traditionally for describing in a simplified way the structure of cellular systems, the shape of cells is depicted as hexagonal o Obviously, due to base station positions and non uniform propagation of signals due to obstacles, the real shape of cells is usually much different o The use of the regular hexagonal shape is however a good approach to make a rough dimensioning of the system and for us to understand the basic principles of reuse A. Capone: Mobile Radio Networks 4
5 Cluster model o o o o o o After coverage planning, capacity planning is in charge of defining which radio resources can be used by each cell The amount of resources (frequencies) assigned to cells determines system capacity Frequencies can be reused, but SIR (quality) constraints must be enforced A simple didactical model considers F 7 F 3 F hexagonal cells and homogeneous traffic F F 6 F 4 F 6 F 4 F5 Frequencies are divided into K groups and F5 assigned to a group of K cells, named F 7 F 3 cluster. F The cluster is repeated in the area in a regular fashion F 7 F 3 F F 6 F5 F 4 F 6 F5 F 4 F 7 F 3 F F 6 F5 F 4 F 7 F 3 F 7 F 3 F F 6 F5 F 4 F 7 F 3 F F 6 F5 F 4 A. Capone: Mobile Radio Networks 5
6 Cluster model o Only some values of K are admissible K,3,4,7,9,2,3, o Reuse efficiency /K F 3 F F 4 F F 4 F 3 F 4 F F 3 F 4 F 3 F 3 F 3 F 3 F 3 F F F F 3 F 3 F 3 F 3 F F 3 F F F F F 4 F 4 F F 3 F 4 F F 3 F F 3 F F 3 F F K 4 K 3 A. Capone: Mobile Radio Networks 6
7 Cluster model o Given the minimum value of SIR, SIR min, we can determine K the minimum value of K o Received power: P r P G d t -h A. Capone: Mobile Radio Networks 7
8 A. Capone: Mobile Radio Networks 8 Cluster model d r D d d 2 d 3 d 4 d 5 d 6 o Same antennas and same power: å å i i i i t t d d d G P d G P SIR h h h h o Worst case d r o Approxmation d i D h h h ø ö ç è R D r SIR 6 6
9 Cluster model o SIR depends only on the reuse ratio RD/r and not on the power and the cell radius o Geometric consideration provides: K 2 R 3 o And therefore: K min ( 6SIR) 3 2/ h A. Capone: Mobile Radio Networks 9
10 Example o Let us dimension the cluster for a system that tolerate a SIR min 8 db in the case the attenuation exponent h is equal to 3.9 K ( ) 2/ h 6SIR ( 6 63.) 2/3.9 min A. Capone: Mobile Radio Networks
11 Cluster dimensioning Some key comments: o In the model we made several simplifying assumptions n distances n Only first ring of interferers n No thermal noise n Propagation with only path loss o The objective of the dimensioning is to guarantee a good SIR to all users and for this reason we have to consider the most critical cases o For including fast fading and shadowing we can consider a margin on SIRmin (similarly to what we did for the cell dimensioning) A. Capone: Mobile Radio Networks
12 Sectorial antennas o The use of directive antennas allows to modify the cellular layout and reduce interference received o In cellular systems the use of directive antennas with a 2 angle of the main lobe is quite common cella 2 cella cella 3 sito A. Capone: Mobile Radio Networks 2
13 Reuse with sectors A. Capone: Mobile Radio Networks Reuse Pattern 7/2 K7
14 Reuse with sectors o In this scheme the reuse scheme is the same but the base station sites are different F 7 F 3 F F 6 F 5 F 4 F 7 F 3 F F 6 F 5 F 4 F 7 F 3 F F 7 F 3 F F 6 F 5 F 4 F 7 F 3 F F 6 F 5 F 4 F 7 F 3 F F 6 F 5 F 4 F 7 F 3 F F 6 F 5 F 4 F 6 F 5 F 4 A. Capone: Mobile Radio Networks 4
15 Reuse with sectors o For the SIR we can use the same formula: -h -h r æ ö -h ç 6D 6 è R ø o With a small modification r MD -h -h -h o Where M is the number of interferers (first ring) visible form a single sector (M6/#sectors) o And therefore: K min M æ ç è ( M SIR) 3 R 2/ h ö ø A. Capone: Mobile Radio Networks 5
16 Assignment constraints o Once cluster size is selected, the assignment of channels to cells is usually subject to additional constraints o Adjacent frequencies have often slightly overlapped spectrum and therefore can generate mutual interference (adjacent channel interference) o The problem can be more complex due to sectors that usually have secondary lobes in the antenna diagram that generate interference in the neighboring cells o As a results it is not usually possible to assign adjacent frequencies to cells of the same site A. Capone: Mobile Radio Networks 6 f
17 Cellular layouts o Important observation: The simplified formula for cluster dimensioning does not depend on the cell radius but only on the distance ratios o Varying the cell radius we can vary the number of channels available per unit area o This gives us the freedom to plan the cellular layout (cell sizes) based on the traffic density estimated in different areas A. Capone: Mobile Radio Networks 7
18 Cellular layouts A. Capone: Mobile Radio Networks 8
19 Cellular layouts o We need however to take into account that with small cells some of the assumptions do not hold n With small distances the propagation formula may change o Moreover with small cells the number of handovers increases o In some cases the coverage and mobility management can be guaranteed with an umbrella cell Umbrella cell A. Capone: Mobile Radio Networks 9
20 Models and algorithms for frequency assignment A. Capone: Mobile Radio Networks 2
21 Graph based models o Unfortunately cells are not hexagonal and traffic is not homogeneous o Other models have been proposed for practical cases o Some popular models are based on graph coloring problems A. Capone: Mobile Radio Networks 2
22 Graph based models o Compatibility graph G(V,E) n Vertices are base stations n Two vertices are connected by an edge if the two base stations cannot reuse the same frequencies A. Capone: Mobile Radio Networks 22
23 Graph based models o o o o Any coloring of the vertices of G (i.e., assignment of colors such that adjacent vertices have different colors) is an assignment of frequencies to the network such that no mutual interfering BSs receive the same frequency. A minimum cardinality coloring of G is a minimum cardinality non-interfering frequency assignment of the network. Graph coloring problem is NP-hard and several exact algorithms and heuristics have been proposed. This simple model assumes: n n One frequency per BS Two distinct frequencies do not interfere A. Capone: Mobile Radio Networks 23
24 Graph based models o Generalized graph coloring models: n Compatibility matrix: C { cij} i, j Î S n Frequencies are numbered according spectrum position f A. Capone: Mobile Radio Networks 24
25 A. Capone: Mobile Radio Networks 25 Graph based models o Generalized graph coloring models: n Sets F j defines assignments of frequencies to BSs n Traffic constraints: n Compatibility constraints: j j i i ij j i F f F f S j i c f f Î Î Î ³ -,,, S j m F j j Î "
26 Graph based models: Frequency Assignment Problem (FAP) o o o if c ij i and j can reuse the same frequencies if c ij i and j cannot use the same frequencies if c ij 2 i and j cannot use either the same frequencies and adjacent frequencies i o Optimization objective: c ij j n Min Span(G) n number of frequencies used MS-FAP (Minimum Span Frequency Assignment Problem) A. Capone: Mobile Radio Networks 26
27 How to find a solution? o FAP is an NP-complete problem o For small instances ILP solvers can provide the optimum solutions in reasonable time o For large instances we need heuristics to get a good quality solution in short time o Among the simplest heuristics we have a greedy algorithm: n The solution is built sequentially ordering cells and assigning frequency according to a simple merit function A. Capone: Mobile Radio Networks 27
28 Greedy algorithm A. Capone: Mobile Radio Networks 28 o The Greedy algorithm assume a single frequency per cell must be assigned o In case m i > we need to split cell i into m i copies o Example: { } { } { } û ù ë é,2,2,, ij i c C m M
29 Greedy algorithm A. Capone: Mobile Radio Networks 29 o example: { } { } û ù ë é Þ û ù ë é Þ û ù ë é Þ û ù ë é,,,2,, m i M
30 Greedy algorithm A. Capone: Mobile Radio Networks 3 { } { } û ù ë é Þ û ù ë é Þ û ù ë é,,,,,, m i M
31 Greedy algorithm o For each cell i we calculate its degree: N å g i c ij j j¹ i o Then we sort cells according to a decreasing degree order in a list L o Let us denote with f i the frequency assigned to cell i A. Capone: Mobile Radio Networks 3
32 Greedy algorithm o Algorithm: n For each cell i in L and for each frequency f in F o For each cell j i a cost function is calculated ( c ) ij - f - f j cij o The cost function is cumulated for all j o Note that if f is compatible the cost will be zero! n The frequency f i with the minimum cost is assigned to i A. Capone: Mobile Radio Networks 32
33 Greedy algorithm BestCost For i Î L do For f Î F do End End End cost : For j Î N If : f ( f j ¹ ) AND ( f-f j < cij ) : cost + ( c - f-f ) cost do End End If BestCost ³ cost then BestCost : cost f i i A. Capone: Mobile Radio Networks 33 ij j c then ij
34 Greedy algorithm: Example A. Capone: Mobile Radio Networks 34 { } { } { } { } { },2,4,7,3,6,5,...,3,,,,,, û ù ë é L c C F m M ij i
35 Greedy algorithm: Example A. Capone: Mobile Radio Networks 35 o Step : i n tutte le frequenze j hanno costo n quindi f 3 o Step 2: i2 n costi(,,) n quindi f 2 2 o Step 3: i4 n costi(,,) n quindi f 4 { } { } { } { } { },2,4,7,3,6,5,...,3,,,,,, û ù ë é L c C F m M ij i
36 Greedy algorithm: Example o Step 4: i7 n costi(,,) n quindi f 7 3 o Step 5: i3 n costi(,,) n quindi f 3 2 o Step 6: i6 n costi(,,) n quindi f 6 3 o Step 7: i5 n costi(,,) n quindi f 7 2 M F C L { mi} {,,,,,, } {,...,3} { c } ij é ë {,2,4,7,3,6,5 } ù û A. Capone: Mobile Radio Networks 36
37 Greedy algorithm: Example A. Capone: Mobile Radio Networks 37 o A compatibility graph can help with the algorithm { } { } { } { } { },2,4,7,3,6,5,...,3,,,,,, û ù ë é L c C F m M ij i
38 Graph based models o Comments: n Graph based models do not consider SIR constrains explicitly n The cumulative effect of interference is not accouter for Compatible? A. Capone: Mobile Radio Networks 38
39 Interference based models o Minimum Interference Frequency Assignment Problem (MI-FAP) n Generalization of the max k-cut problem on edge-weighted graphs n penalty p vwfg v, wî S, f, g Î F representing the interference (cost) generated when v is assigned with f and w is assigned with g. n Decision variables: x vf ì í î if f is assigned to otherwise v A. Capone: Mobile Radio Networks 39
40 Interference based models o Objective function: z vwfg min å å p v, wîs f, gîf if f vwfg o The problem can be linearized: x vf wg is assigned vwfg x vf to x v wg and g is assigned ì í î otherwise + x + z " v, wî S f, g Î F to w A. Capone: Mobile Radio Networks 4
41 Interference based models o Linear MI-FAP: min å å v, wîs f, gîf p vwfg z vwfg s.t. x vf + x + z " v, wî S f, wg vwfg g Î F å f ÎF x vf m( v) " vîs A. Capone: Mobile Radio Networks 4
42 Interference based models o MI-FAP with interference constraint: n Interference generated by w on v when f is assigned to v and g to w: I vwfg n Interference constraints: v, wî S, f, g Î F å å wîs w¹ v I f, gîf vwfg x vf x wg L v vî S Note: linearization like in previous case A. Capone: Mobile Radio Networks 42
43 Dynamic Frequency Assignment A. Capone: Mobile Radio Networks 43
44 Dynamic Channel Assignment o With models considered so far assignment is fixed and decided during planning phase (FCA Fixed Channel Allocation) o This is approach is not flexible in case of non homogeneous and variable traffic A. Capone: Mobile Radio Networks 44
45 Dynamic Channel Assignment o For improving performance Dynamic Channel Allocation (DCA) techniques can be used o These techniques does not assign a fixed set of channels to a cell n But they allow to assign channels dynamically only when needed n Guaranteeing at the same time quality and reuse constraints A. Capone: Mobile Radio Networks 45
46 Geometric DCA n In this popular scheme channels are in a common pool and are assigned o At call request arrival o Considering reuse constraints o Selecting compatible channels according to some criteria n The most interesting geometric schemes are distributed o Each cell knows the status of neighboring base stations and select autonomously the channels when calls arrive A. Capone: Mobile Radio Networks 46
47 Geometric DCA n Each base station has a occupancy matrix which is updated with exchange of control information wit the other cells stazione numero di canale canali base N disponibili x x x 2 x 4 3 x x 2 4 x 5 9 ki x x 2 A. Capone: Mobile Radio Networks 47
48 Geometric DCA n The occupancy matrix can be created considering the compatibility constraints c ij stazione numero di canale canali base 2 3 k N disponibili x x x 2 x 4 x x 2 j x x x x 5 9 ki x x 2 Example: - c ij 2 A. Capone: Mobile Radio Networks 48
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