IEIIT-BO / DEIS. Consiglio Nazionale Ricerche, Università degli Studi di Bologna Consorzio Nazionale Interuniversitario per le Telecomunicazioni

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1 IEIIT-BO / DEIS Consiglio Nazionale Ricerche, Università degli Studi di Bologna Consorzio Nazionale Interuniversitario per le Telecomunicazioni v.le Risorgimento 2, Bologna BO Italy roberto.verdone@cnit.it Paris, May 20, 2003 alberto.zanella@cnit.it Outline I) Introduction to RRM II) Link Level and System Level Performance Evaluation Break III) Performance of Cellular Systems: Teletraffic vs Statistical Models IV) Directed Retry Break V) Capacity Evaluation for WCDMA: analytical description VI) Capacity Evaluation for WCDMA: semi-analytical approach VII) Capacity Evaluation for WCDMA: dynamic simulations

2 I) Introduction to RRM RRM techniques aim at optimising the use of radio resources while fulfilling the quality requirements of the largest possible number of users Key aspects in Mobile Radio Networks: Limited Spectrum Availability Channel Loss vs Thermal Noise Co-channel Interference Signal Distortion due to Multipath User Mobility Heterogeneous Traffic Radio Channel A signal format allowing the transmission of information at the requested user bit rate t t f FD TD Allocated Radio Channels are orthogonal within one cell Orthogonality can be reached via Frequency (FD), Time (TD), Code (CD), Space Division (SD) or a mixture of them. c t f f CD SD Resource Unit (RU) The minimum amount of radio resource that can be allocated to a user. FD: minimum bandwidth TD: shortest slot

3 Radio Access Network Other Networks Service Area Core Network Cells Base Station BS Controller Mobile Station Radio Link PP Link Where do RRM techniques operate? Power Control MS MS Power Control Load Control BTS BTS Power Control Handover Admission Control Load Control BSC PSTN Power Control UE Node B RNC

4 Decisions to be taken by the RRM entities (C.S. Services) B A Release the call? How many base stations? If one, what base? Accept the call? What base, channel? How many RUs? Decisions to be taken by the RRM entities (C.S. Services) At call set up: Admission control Initial base station assignment Initial channel assignment Initial bandwidth assignment During the call: Power control Base re-assignment Re-assignment of the number of bases Channel re-assignment (whether to accept a new call) (what base) (what channel) (how many RUs) (what power) (what base) (how many bases) (what channel)

5 Decisions to be taken by the RRM entities (P.S. Services) At Packet Data Transfer (PDT) set up: Admission control (whether to accept a new PDT) Initial base station assignment (what base) Initial channel assignment (what channel) Initial bandwidth assignment (how many RUs) During the PDT: Power control Base re-assignment Re-assignment of the number of bases Channel re-assignment Bandwidth re-assignment Call release (what power) (what base) (how many bases) (what channel) (how many RUs) (whether to release a PDT) Decisions to be taken by the RRM entities (P.S. Services) Activity (bit rate) time Activity (bytes) The same procedures as for C.S. services are implemented, but with much faster characteristics

6 I.a) RRM Techniques: Definitions (1) Admission Control The process of determining whether a service request can be admitted to the system Admission Control The call could be rejected for reasons related to capacity, or interference levels

7 RRM Techniques: Definitions (2) Admission Control Directed Retry The process of determining whether a service request can be admitted to the system The process of re-directing a new user toward a base station different from the one providing the best link budget Directed Retry If one base cannot provide service, the call request is re-directed toward a different base (if within range).

8 RRM Techniques: Definitions (3) Admission Control Directed Retry Channel Assignment The process of determining whether a service request can be admitted to the system The process of re-directing a new user toward a base station different from the one providing best link budget The process of choosing the channel (and the number of RUs) to be allocated to the user Distinction: 1) assignment of channels to the cells (Channel Allocation) 2) assignment of channels to the users within a cell (Channel Assignment) Channel Assignment Channel Allocation Techniques Fixed (FCA): a predefined (sub-)set of channels is assigned to a base; the channel to be allocated to the user is selected among these pre-assigned channels Dynamic (DCA): channels are in a pool, and can be selected by every base for each link Hybrid (HCA): part of channels are allocated via FCA, part via DCA

9 RRM Techniques: Definitions (4) Admission Control Directed Retry Channel Allocation Power Control Distinction: The process of determining whether a service request can be admitted to the system The process of re-directing a new user toward a base station different from the one providing best link budget The process of choosing the channel (and the number of RUs) to be allocated to the user The process of setting the transmission power level fast PC and slow PC RRM Techniques: Definitions (5) Admission Control Directed Retry Channel Allocation Power Control Hard Handover The process of determining whether a service request can be admitted to the system The process of re-directing a new user toward a base station different from the one providing best link budget The process of choosing the channel (and the number of RUs) to be allocated to the user The process of setting the transmission power level The process of changing serving base and/or channel

10 Hard Handover One base station at a time Not seamless Can have a serious impact on the signalling channels RRM Techniques: Definitions (6) Admission Control Directed Retry Channel Allocation Power Control Hard Handover The process of determining whether a service request can be admitted to the system The process of re-directing a new user toward a base station different from the one providing best link budget The process of choosing the channel (and the number of RUs) to be allocated to the user The process of setting the transmission power level The process of changing serving base and/or channel

11 Soft Handover More than one base station at a time Seamless Service Macrodiversity: reduced shadowing margin Microdiversity: MR Combining (downlink) or S Combining (uplink) Can have a serious impact on the network capacity Active set The set of serving base stations Softer Handover More than one cell within the same base station at a time Maximal Ratio Combining both on uplink and downlink

12 RRM Techniques: Definitions (6) Admission Control Directed Retry Channel Allocation Power Control Hard Handover Soft Handover Load Control The process of determining whether a service request can be admitted to the system The process of re-directing a new user toward a base station different from the one providing best link budget The process of choosing the channel (and the number of RUs) to be allocated to the user The process of setting the transmission power level The process of changing serving base and/or channel The process of modifying the set of serving bases The process of controlling the load of the network I.b) RRM Techniques and Radio Network Planning Radio Network Planning is the process of defining - where the bases have to be placed - what HW/SW configurations have to be set Inputs: Coverage Requirements Capacity Requirements Quality Requirements

13 Radio Network Planning Phases 1) Dimensioning rough estimation of the number of bases and other network elements 2) Capacity and Coverage Planning determination of the number of bases and other network elements, their configurations 3) Network Optimisation I.c) Long-term and Short-term Evaluations metres Slow fluctuations Received power [dbm] Fast fluctuations wavelengths (λ / 2 under typical urban conditions)

14 Vehicular User (Urban) 1-10 seconds Slow fluctuations Received power [dbm] s Fast fluctuations Speed: 10 m/s GSM frequency band time Pedestrian User seconds Slow fluctuations Received power [dbm] s Fast fluctuations Speed: 1 m/s GSM frequency band

15 Channel fluctuations are fast or slow depending on the user speed. In any case, one has to define what Fast or Slow means with respect to the figures considered e.g. The quality of voice calls: it is known that human perception is not sensitive to fluctuations faster than a few Hertz, Hence, voice quality has to be averaged over fast fluctuations where fast means with a frequency larger than a few Hertz (for instance, fading for pedestrian or vehicular speeds in the GSM frequency band) This has a strong impact on the way link level and network level issues have to be interfaced when dealing with network simulation modelling.

16 II) Link Level and System Level Performance Evaluation The evaluation of the performance of a cellular network requires consideration of both microscopic and macroscopic (in time and space) aspects: the receiver ability to detect errors at the bit level, the movement of mobiles, etc. All these aspects should be considered simultaneously, but this approach is not feasible for reasons related to its complexity. So, normally the performance evaluation is carried out in two phases: at link and at system level, with suitable interfacing between the two. For the sake of simplicity the description of the subject is given with reference to the GSM standard. With WCDMA some aspects are different due to the much larger power control frequency. Reference to GSM standard frame, 4.7 ms 8 slots speech A codeword is interleaved over 8 bursts transmitted over 8 frames With Frequency Hopping, each burst is transmitted over a separate frequency 104 frames, 480 ms A sequence of 104 frames compose a measurement report interval A measurement report is transmitted to the BSC by the MS and the serving BTS every measurement interval (480 ms): RRM procedures take a decision (power control command, or

17 Macroscopic and Microscopic Issues (with reference to GSM standard) resolution required in space (size of evaluation area) 1000 m 100 m 10 m 1 m 0.1 m 0 m fading receiver performance shadowing user mobility NRT traffic sources RT traffic sources s 0.01 s 1 s 100 s s resolution required in time (duration of periods of observation) Two Phases BER Link level P b, P out,... C/I System level

18 1) Link Level Performance Evaluation Requires consideration of microscopic issues (bit level). The complete transmission chain is considered. Modulation, coding, interleaving, etc. Aims at specifying the receiver performance as a function of suitable figures (e.g. the signal-to-noise ratio, etc) 2) System (also denoted Network) Level Performance Evaluation Requires consideration of macroscopic issues. The complete scenario is considered. Many cells, user mobility, etc. Aims at assessing the final figures (e.g. the outage probability, capacity, etc) starting from the link level evaluations. How to split? Multiframe-oriented link level evaluation resolution required in space (size of evaluation area) 1000 m 100 m 10 m 1 m 0.1 m 0 m fading receiver performance shadowing user mobility NRT traffic sources RT traffic sources

19 How to split? Burst-oriented link level evaluation Only modulation, coding, and the transmission aspects have to be considered. resolution required in space (size of evaluation area) 1000 m 100 m 10 m 1 m 0.1 m 0 m fading receiver performance shadowing user mobility NRT traffic sources RT traffic sources s 0.01 s 1 s 100 s s resolution required in time (duration of periods of observation) [OlAlJoHoKr97] Multiframe-oriented link level evaluation With reference e.g. to GSM, 0.48 sec intervals can be considered, which corresponds to a measurement period, and to the duration of a power control command. All fast effects have to be averaged over an interval of 0.48 sec (e.g. the effect of FH, fading, etc). The results (e.g. average BER vs average C/I) are introduced at system level through look-up tables which depend on user speed, etc. Burst-oriented link level evaluation With reference e.g. to GSM, a burst (0.48 / 104 sec) can be considered, during which the channel is approximately constant.

20 And WCDMA? i.e. Power Control With WCDMA power control commands have a maximum frequency of 1500 KHz (fast power control). Therefore, the fluctuations of power control have to be considered as average values if the time resolution is kept around 0.5 sec, (only pathloss and shadowing should be considered); explicitly modelled if the time resolution has to be at the slot level (1/1500=0.667 ms) (a more complete model with pathloss, shadowing and fast fading should be considered). Generally, WCDMA systems require smaller simulation time step compared to GSM large number of steps have to be simulated (time consuming); performance evaluation of link quality is more complex and requires additional off-line computation to be used by network level simulator. WCDMA: How can be evaluated link quality when a slot (frame)-oriented analysis is required? look-up table with values coming from link level simulations is still necessary but <BER> vs. <Eb/No> cannot be used Slot-oriented analysis requires: Eb/No should be evaluated slot by slot; several link level simulations with a small number or transmitted bits; pre-processing phase, to collect statistics from link level results;

21 References [MaRyMo94] E. Malkamaki, F. de Ryck, C. Mourot, "A Method for Combining Radio Link Simulations and System Simulations for a Slow Frequency Hopped Cellular System", IEEE Veh. Technol. Conf (VTC'94), pp , Phoenix, AZ, May [OlAlJoHoKr97] H. Olofsson, M. Almgren, C. Johansson, M. Hook, F. Kronestedt, "Improved Interface Between Link Level and System Level Simulations Applied to GSM", IEEE Int. Conf. On Univ. Pers. Comm. (ICUPC'97), Page(s): 79-83, vol.1, S. Diego, CA, Oct

22 III) Performance of Cellular Systems: Teletraffic vs. Statistical Models The term Teletraffic in this context normally denotes those aspects jointly related to user mobility and source traffic in cellular networks. It involves the study of the performance of mobile radio systems in terms of blocking, forced termination and handover failure probability. Many papers can be found in the Literature dealing with teletraffic issues and analytical modelling of the performance of cellular networks; a reference Author in this case is S. S. Rappaport, from the State University of New Jork, who published many works on the subject. Other Authors, like S. Nanda, B. Jabbari, A. Noerpel, etc, issued well known papers. A common aspect of these works is the absence of any consideration regarding the physical aspects (shadowing, or fading, the link level performance, etc). To introduce the field, in this Section one of the most cited papers is considered, to give an idea of the approaches used in teletraffic analyses, and to make reference to a very simple case: a tutorial paper issued in 1996 by Jabbari [Ja96]. A non-queuing, non prioritised system is considered. Teletraffic Modelling: Typical Assumptions η The users are uniformly distributed in the service area and have uniformly distributed directions. The new calls arrival process is Poisson, with rate per cell λ. The handover arrival process is Poisson, with rate per cell λ h. µ λ λ h Therefore, the total arrival process per cell is Poisson with rate per cell λ tot = ( λ + λ h ). The call (natural) duration (also denoted as call holding time), τ, is exponentially distributed with rate per cell 1/µ. Hence E[τ] = 1/µ. The residing time inside a cell (also denoted as cell sojourn time, or dwell time), τ h,

23 Is Handover Traffic Really Poissonian? [ChLu97] E. Chlebus, W. Ludwin, "Is Handoff Traffic Really Poissonian?" IEEE ICUPC'97, Florence, I, Sept Total Offered Traffic, Handover Rate and Probability The total offered traffic is A = (λ + λ h ) / (µ + η) Very Low mobility: µ >> η, λ >> λ h. The offered traffic A λ / µ = A s Very High mobility: µ << η, λ << λ h. The offered traffic A λ h / η Handover rate per call (average number of handovers per call): Nho = η / µ In most teletraffic papers, Nho (or η) is fixed as a parameter, with no relation to the user average speed v. In [Ja96], η is estimated as η= 2 v / π R for circular cells of radius R.

24 Handover Traffic The Handover arrival rate λ h is proportional to the offered traffic λ : denote as Then Pb Pf the (new call) blocking probability the handover failure probability λ h = Ph [ (1 - Pb) λ + (1 - Pf) λ h ] λ h = λ Ph (1 - Pb) / [ 1 - Ph (1 - Pf) ] = λ Nho (1 - Pb) / (1 + Nho Pf) If Pb, Pf << 1 then λ h = λ. Nho [Ja96] Probability of Blocking and Handover Failure (non queuing, non prioritised system) Blocking - The following assumption is normally made: Pb = B[n, A] where n is the number of channels per cell B [ ] is the Erlang B formula Handover Failure - The following assumption is normally made: Pf = B[n, A] = Pb Note that Pf depends on A which depends on λ h that depends on Pf. Normally, an iterative process is needed to evaluate Pf.

25 The impact of user speed on Pb and Pf 1) If Pb, Pf << 1 then λ h = λ. Nho 2) Nho = η / µ Then, A = (λ + λ h ) / (µ + η) λ. (1 + Nho) / µ. (1 + Nho) = λ / µ = As Pb = B[n, A] If Pb, Pf << 1 (normal operating conditions) the impact of mobility on Pb and Pf is negligible (see also [FoGoMi93]) The impact of user speed on Pb and Pf Simulation Results Uniform distribution of users and directions, hexagonal cells As = 10.3 Erl/cell n = 15 Reuse 4/12

26 The impact of user speed on Pb and Pf Simulation Results Uniform distribution of users and directions, hexagonal cells As = 10.3 Erl/cell n = 15 Reuse 4/12 v [Km/h] v [m/s] Pb (FCA) Pb (FCA/DR) If Pb, Pf << 1 (normal operating conditions) the impact of mobility on Pb and Pf is negligible CONFIRMED BY SIMULATION Probability of Call Dropping (non queuing, non prioritised system) A call is assumed to be dropped if a handover attempt fails. In this case the probability of call dropping can be estimated as Pdo = Ph Pf / [ 1 - Ph (1 - Pf) ] = Nho Pf / ( 1 + Nho Pf) Very Low mobility: Nho << 1 Pdo Pf = Pb Very High mobility: Nho Pf >> 1 Pdo 1

27 The impact of user speed on Pdo Numerical Results Pf = 0.02 R = 500 m 1/µ = 120 [s] Nho = 2 v / µ π R = 0.15 v v [Km/h] v [m/s] Nho Pdo Even if Pb, Pf << 1 (normal operating conditions) the impact of mobility on Pdo can be not negligible The impact of user speed on Pdo Simulation Results Uniform distribution of users and directions, hexagonal cells As = 10.3 Erl/cell n = 15 Reuse 4/12 (FCA) Reuse 1 (DCA) Pb = 0.08 (FCA) or (FCA/DR) R 450 m 1/µ = 120 [s]

28 The impact of user speed on Pdo Simulation Results Uniform distribution of users and directions, hexagonal cells As = 10.3 Erl/cell n = 15 Reuse 4/12 (FCA) Reuse 1 (DCA) Pdo = Prob[ C/I < th1 or C < th2 ] Even if Pb, Pf << 1 (normal operating conditions) the impact of mobility on Pdo can be not negligible THE BEHAVIOR IS CONFIRMED BY SIMULATION Main Remark This kind of modelling assumes a call is dropped if a handover is failed because of the lack of channels in the new base. This is not true in actual networks, due to - the overlap between cells: mobiles can attempt several handovers to the new base before the call is dropped; some enhancement of the teletraffic model proposed take this effect into account through a queing process; - the possibility to attempt handovers toward several candidate cells, depending on

29 Probability of Call Non Completed (non queuing, non prioritised system) A call is non completed if it is dropped or blocked. The probability of call non completed can be estimated as Pnc = 1 (1 Pb) (1 Pdo) = 1 - (1 - Pb) / (1 + Nho Pf) For a non-queuing system the following assumption is normally made: Pb = Pf. Hence Pnc = 1 - (1 - Pf) / (1 + Nho Pf) Very Low mobility: Nho << 1 Pnc Pb Very High mobility: Nho Pf >> 1 Pnc 1 [HoRa86] Final Remark This kind of modelling assumes the quality of the network can be assessed through the call dropping and call blocking probabilities. The outage probability (the probability that the link quality is below a specified threshold) is not investigated, as the link and physical aspects (propagation, etc) are not considered. This makes uncertain the generalisation of the results.

30 Statistical Models The typical Teletraffic Models assume the cell is an integral entity that can be described by means of a suitable state, and the mobile users can connect or not to a base depending on the cell state. These models normally do not take physical aspects into account, such as the randomness of channel fluctuations or the dependence on the cell size, etc. A Statistical Model is discussed in this Section, that under specified conditions can be useful to describe some aspects of cellular systems by taking the main physical phenomena (shadowing, path loss) into account. This model can be useful e.g. for Radio Network Dimensioning phases, where the precise definition of the base station sites, etc, is not needed. This model was first presented by J. Orriss and S. K. Barton from the University of Manchester within COST259. Then, a collaboration between the group in Manchester and the teachers of this course was set up and several extensions of the model that is presented in this Section have been developed, are under submission in the open literature, and are under current development. A Statistical Model for Connettivity Between Mobiles and Base Stations: Main Assumptions A generic transceiver is considered. Communication is assumed to be possible if the power loss of a signal transmitted from one transceiver (say, T) does not exceed a specified value before reaching the other (say, R). T R T and R can be both mobiles, or one mobile and a base station. The case of mobile-to-base communications is considered here (or viceversa). The transceivers are assumed to be randomly and uniformly distributed over an infinite plane with different densities ρ m (for mobiles) and ρ b (for bases).

31 The Probability Distribution of the Distance Subject to a Maximum Loss (1) Pr = Pt - L [dbm] L = ko + k1 ln d + s [db] s Gaussian r. v. (0, σ 2 ) (shadowing) d L Lm ko, k1 constants (path loss) Pose L Lm The probability distribution of the distance d of a mobile from a base station, subject to the previous position, can be analytically derived. Denote it as p d (d). The Probability Distribution of the Distance Subject to a Maximum Loss (2) p d (d) = 2 K d F(a - b ln d) d L Lm where K = exp [ - (2 / k1). (Lm-ko-σ 2 /k1) ] a = (Lm-ko-2σ 2 /k1) / σ b = k1 / σ

32 The Probability Distribution of the Distance Subject to a Maximum Loss: Physical Meaning This expression gives the probability distribution of the distance of mobiles from a base providing the mobiles with a given minimum received power Prmin = Pt - Lm [dbm] If Prmin is set to the value of the receiver sensitivity of the transceiver (i.e. the minimum level of received power providing a specified BER) and Pt is set to the largest possible transmit power value, from the above expression we get to a value Lm = Pt - Prmin which represents the maximum loss a signal transmitted from the base can suffer to reach a mobile connected to that base. In other words, this probability distribution describes the statistics of the distance between a base and all the mobiles that can be potentially attached to it. In some sense, it gives an indication of the maximum cell size. d L Lm The Probability Distribution of the Distance Subject to a Maximum Loss: Numerical Results d L Lm 0.01 pd(d) k1 = 16.5 ko = 30 Lm = 100

33 The Probability Distribution of the Number of Stations with a given Max Loss 1 2 L Lm It can be shown that the number, N, of stations with a maximum loss Lm that can be heard from a transceiver is a Poisson r.v. with mean L Lm L Lm N Nm = π ρexp[2(lm-ko)/k] exp[2σ 2 /k 2 ] 1 2 where k = k1 ln10. Denote this distribution as p N (N). Hence, p N (N) = exp[-nm] Nm N / N! L Lm L Lm L Lm N The Probability Distribution of the Number of Stations with a given Max Loss: Physical Meaning If the density ρ is set to the value of base station density, the above expression gives the probability distribution of the number of bases that can be heard by a generic mobile. L Lm Hence, 1 2 L Lm L Lm N p N (N=0) = exp[-nm] represents the probability that no base stations can be heard (minimum outage probability) Prob [N > 1] = 1-p N (0)- p N (1) = 1 - exp[-nm] - exp [-Nm] Nm represents the probability that

34 The Probability Distribution of the Number of Stations with a given Max Loss: Numerical Results L Lm L Lm N 0.15 L Lm pn(n) N Nm=3, 4, 5 Assume a transceiver is located in the centre of a circular area H (having radius R), and denote as n the number of transceivers that can be heard belonging to H. The Probability Distribution of the Number of Stations with a given Max Loss in Non-Uniform Conditions (1) It can be shown that the conditional probability of n, given N transceivers that can be heard from the whole plane, can be analytically derived. Denote this conditional probability as Q n N (n,n). n = 1 L Lm R L Lm 1 1 H 2 L Lm L Lm 2 L Lm N

35 The Probability Distribution of the Number of Stations with a given Max Loss in Non-Uniform Conditions (2) Q n N (n,n) = [N! / (N-n)! n!]. [m 1 / (m 1 + m 2 )] n. [m 2 / (m 1 + m 2 )] N-n where m 1 and m 2 are the mean values of n and N-n, respectively, given by m 1 = π ρ{ exp[2a/b+2/b 2 ] + R 2 F(a - b lnr) - exp[2a/b+2/b 2 ] F(a - b lnr + 2/b) } m 2 = π ρ{ - R 2 F(a - b lnr) + exp[2a/b+2/b 2 ] F(a - b lnr + 2/b) } Therefore, one can assume that inside H (the mean m 1 applies) different values of ρ, a and b can be considered with respect to those outside H. IV) Directed Retry Directed Retry (DR) is a RRM technique that has been investigated in the literature for the first time by Eklund in 1986 [Ek86]. Some papers have been dedicated to DR since then; in all cases the number of cells overlapping is considered as deterministic. DR can be investigated more conveniently via the simplified statistical model previously described.

36 Directed Retry Directed Retry The process of re-directing a new user toward a base station different from the one providing the best link budget At call set up, a user can be allocated a channel in one of the R cells providing the user with largest received power; if N is the number of bases that can be heard by the mobile, the true number of potentially serving bases is M = min [N,R] Scenario The users are uniformly distributed over an infinite plane S S The base stations are uniformly distributed over the infinite plane, with density ρ The base stations are equipped with the same amount of channels per cell, n c

37 Propagation Model Pr = Pt - L [dbm] L = ko + k log d + s s Gaussian r. v. (0, σ 2 ) (shadowing) d Pr ko, k constants (path loss) A user is assumed to be heard by a base if the received power at the selected base is larger than a suitable threshold, or, equivalently, if the path loss L is less than a threshold Lm Evaluation of Blocking Probability (1) N 2 P b = E N [P b N (N)] N is a Poisson r. v. with mean Nm 1 Nm = πρexp[2(l m -k o )/k] exp[2σ 2 /k 2 ] Denote as Q N (N) the distribution of N

38 Evaluation of Blocking Probability (2) N 2 P b N (N) Prob[B 1 ] x x Prob[B M ] Prob [B i ] = B(A, n c ) B(n c, A) Erlang B formula i = 1,, M 1 n c A number of channels per cell offered traffic Evaluation of Offered Traffic A = (λ + λ h + λ r ) / (µ + η) λ new call arrival rate per cell λ r η λ h handover attempts rate per cell λ r new call re-directions rate per cell 1/µ call holding mean time 1/η cell sojourn mean time µ λ λ h

39 Evaluation of Blocking Probability (3) P b = E N [P b N (N)] = Σ N P b N (N) Q N (N) Estimation of η and λ h

40 Estimation of λ r Numerical Results (1) As = λ / µ n c = 15 k = 38 Lm = 125

41 Numerical Results (2) As = λ / µ n c = 15 k = 38 ko = 6 Lm = 125 Numerical Results (3) As = λ / µ Lm = 125

42 Example of application: GPRS vs GSM (1) Ao = λ / µ v = 0 m/s Example of application: GPRS vs GSM (2) Ao = λ / µ v = 0 m/s

43 Example of application: GPRS vs GSM (3) Ao = λ / µ v = 0 m/s m = 0 or 8 channels dedicated to GPRS Extension to the case of non-uniformly loaded environments Superposition on the uniform scenario S of a circular area H characterised by different offered load or radio capacity. Denote the area outside H as L

44 Evaluation of Blocking Probability (Extension) n is the number of bases that can be heard in (x m, y m ) from the circular area H n is a Poisson r. v. P b = Σ Q N N N(N) Σ P b n,n Q n N (n N) =0 n =0 P b n,n = Prob(B 1, B 2,,B M ) Prob(B 1 ) Prob(B 2 ) Prob(B M ) Prob(B j ) = B [n j, A j ] A j = (λ j + λ rj ) / µ j The traffic re-directed is cell-dependent Upper and Lower bounds A j = (λ j + λ rj ) / µ j i) The whole re-try traffic is generated by the cells belonging to H ii) The whole re-try traffic is generated by the cells belonging to L P bh P bl

45 Numerical Results (Extension, 1) Nm = 6 EL is the offered traffic outside the hot spot EH is the offered traffic inside the hot spot Numerical Results (Extension, 2) Nm = 6 EL is the offered traffic outside the hot spot EH is the offered traffic inside the hot spot

46 Let σ range from 0 + to 12. Exercise Implement in a computer program the iterative procedure to evaluate Pf and look at the effects of the Handover Rate Nho. The following numerical values could be considered: 1/µ = 120 [s] λ = 1/72 [Hz] n = 15 Let Nho range from 0 + to 10. Repeat with n = 12. Also evaluate Pdo and Pnc as a function of Nho. Exercise Implement in a computer program the expression of p d (d) and look at the effects of the standard deviation of shadowing. The following numerical values could be considered: k1 = 16.5 ko = 30 Lm = 100

47 σ = 8 Exercise Implement in a computer program the expression of p N (N) and look at the effects of the standard deviation of shadowing. The following numerical values could be considered: k1 = 16.5 ko = 30 Lm = 100 ρ = 1.27 E-6 (average cell radius equal to 500 m) Let σ range from 0 + to 12. Exercise Implement in a computer program the expression of Q n N (n,n) and look at the effects of R. The following numerical values could be considered: k1 = 16.5 ko = 30 Lm = 100 ρ = 1.27 E-6 outside H, ρ = 1.27 E-5 inside H

48 V) Capacity Evaluation for WCDMA: analytical description VI) Capacity Evaluation for WCDMA: semi-analytical approach A comparison between different models, to evaluate capacity in a WCDMA scenario. The comparison has been carried out between three different models: I. a simple analytical model, to give preliminary evaluation of a WCDMA cell dimensioning [Nokia Networks]; II. a more complex semi-analytical model [UniBO]; III. an extension of the analytical model extension of the analytical model previously introduced, to define capacity from a statistical point of view [UniBO]

49 Consider a single cell scenario, where the reference mobile station (MS) is at cell border; The base station (BS) is located in the centre of the cell, using an omni antenna; Traffic distribution is uniform; The presence of other cells is taken into account through the parameter i: Analytical Model [NOKIA] BS OtherCellsInterference i = OwnCellInterference MS Starting from the assumption that, due to fast power control, each MS is able to obtain the [E b /I 0 ] th target, the signal-to-interferenceplus-noise ratio can be written as follows: E I b 0 = R bk W P L [( h+ i ) P+ N W L ] k k k 0 k = [ Eb / I0] th (1) W = 3.84 Mcps is the chip rate, R bk the bit rate of user k, P k the received signal power from MS k and N 0 the noise spectral density. P is the total transmit power of the BS (equal for all BSs) and L k is path loss from serving BS for user k.

50 Solving in P k we obtain: P L k [ E / I ] [( h+ i ) P+ N W L ] b 0 th_ k bk k = k 0 W R k (2) Multiplying equation (2) for the activity factor µ k and summing up over all N contributions we obtain the expression of the total transmit power of the BS: N [ E b / I 0 ] th _ k N 0 W µ k L k k = 1 W / R bk P = N [ E ] (3) b / I 0 th _ k 1 µ k ( h + i k ) W / R k = 1 The denominator of equation (3) is the downlink load factor η DL. bk Path loss L and the parameter i depend on users position, which is not considered by the model; to ward off it we can average out each parameter on user position, obtaining: P N 0 1 W = N k = 1 L µ k N k = 1 [ E / I ] b W µ k / R [ E / I ] 0 th _ k bk b W 0 / R th _ k bk ( h + i) (4)

51 The scenario is composed of 19 hexagonal cells; One or three BSs are located in the centre of each cell, depending on use of omni or three sectorial antennae; Each BS transmits at the maximum power P max : a portion γ < 1 is devoted to to the traffic, while the rest is for signalling; Mixed service scenario: speech users and a fraction D of data users. Semi-analytical Model [UniBO] x x x x x x x x x BS 1 x x x x x x x x x x R max A single slope propagation model is considered, with an amplification factor K and a path loss exponent n; the average signal power received at MS i from BS j is then: (7) Sr ji = K P ( r ) n ji max Sh ji, the shadowing sample for mobile i with respect to BS j is a log-normally distributed variable. Taking also shadowing into account the received signal power is thus: Pr ji = Sr ji Sh ji (8)

52 This expression relates to the case of Omnidirectional case Being Φ ji the portion of total transmit power at BS j and devoted to Ms i we can establish the following system constraint, with reference to BS 1 : N k= 1 µ kφ1k 1 (9) The expression of Φ jk can be derived directly from the following equation, representing the E b /I 0 value, related to no soft handover case, received by a generic MS: E b W / Rbk γ Φ1 k Pr1 k = J I0 nho Pr + N ( 1 γ Φ1 k ) hpr1 k + j= 2 jk 0 W (10) With perfect downlink power control, the received E b /I 0 of all mobiles are kept at the target value [E b /I 0 ] th ; therefore, by reversing (10) we carry out the variable Φ jk with reference to BS 1 : Φ 1k = Φ 1k _ nho = h + J Pr Pr γ h + jk N0W + KP Pr j= 2 1k max 1k W / R bk [ E ] b / I0 th_ k (11)

53 Soft handover In a WCDMA system, a mobile in soft handover mode is connected to several BSs which constitute the Active Set (AS). m max : maximum number of BSs that can be in the AS; m: instantaneous number of BSs in the AS. Moreover, we assume that: BSs belonging to the effective AS are ranked according to their respective receive power at the mobile. The MS performs Maximal Ratio Combining (MRC) [E b /I 0 ] = [E b /I 0 ] th_soft Owing to the microdiversity effect provided by MRC, a diversity factor α must be taken into account α = & E I 0 b th _ soft < 1

54 The above expression requires knowledge of the percentage of mobiles requiring speech and data services, and the distinction between users in and We assume that all BSs in the active set provide the same E b /I 0 contribution (denoted by [E b /I 0 ] link ). Therefore, the [E b /I 0 ] th_soft value is given by: [ E / I ] α = [ E / I ] = [ E / I ] = m [ E I ] b 0 th b 0 th soft b 0 link_ j b / _ j= 1 m 0 link (12) Where the [E b /I 0 ] link_j is the received bit energy-to-interference power spectral density ratio of a mobile in Soft Handover connected to BS j. From equations (11) and (12) the expression of Φ jk for mobiles in Soft Handover can be obtained. Since the aim of the model is to evaluate the maximum capacity of the system, the fundamental equation (9) can be rewritten as follows: ( N (1 D)% nho ) ( ND% µs Φs + µ d k 1k _ nho k= 1 k= 1 nho ) k Φd 1k _ nho + ( N (1 D)% soft ) ( ND% soft) µs kφs1 k _ soft + µ dkφd1 k _ soft = 1 k= 1 k= 1 (13)

55 Soft handover algorithm Pr jk Pr 1k Pr jk >M SH <=M SH <=M SH Class A users (% Aclass ): Connected only to BS 1, Best Server Class B users (% Bclass ): Connected to BS 1, Best Server and to BS K HO users Class C users (% Cclass ): Connected to BS K, Best Server and to BS 1 k Numerical Results Class A users Class B users Percentage di users in class A % Aclass m max =1 m max =2 m max =3 m max =4 m max =5 Percentage of users in class B % Bclass m max =1 m max =2 m max =3 m max =4 m max =

56 Sectorised case All the assumptions introduced in the omnidirectional case are still valid; Three sector per site are considered; The Soft Handover (between two sectors of different sites) is exactly the same previously described; The Softer Handover is the one between two neighboring sectors of the same site; The radiation pattern we consider is defined as: 1 ω j-y,k 60 + θ G(ω j-y,k ) = (14) 0 ω j-y,k > 60 + θ Similarly to equation (7), the average (over shadowing) signal power received at mobile k from sector y of BS j can be represented as: Sr ji = K ' Pmax G( ω j y, k ( r ) n ji ) (15) Where K = 3K to take antennae gain into account. Therefore, in a sectorized system the signal power received can be represented as: Pr j y, k = Srj y, k Sh jk (16)

57 Assuming sector 1 of site 1 as a reference sector, we denote as Φ 1-1,k the portion of total transmitted power at BS 1-1 devoted to mobile k. In sectorized systems, the extra cell interference term is composed of the interference from other sectors both of the own and of the other sites. Then, the bit-energy-to-interference ratio can be rewritten as: E b W / Rbk γ Φ1 1k Pr1 1k = I 0 nho_sect Pr 3 J 3 ( 1 γ Φ1 1, k ) hpr1 1, k + Pr1 y, k + y= 2 j= 2 y= 1 j y, k + N 0 W (17) Where the second term in the denominator represents the interference power from the second or third sector of the reference site. From equation (17), under the assumption previously introduced, we can obtain the portion of total transmit power at BS 1-1 devoted to mobile k, for users connected only to BS 1-1 : Φ 1 1, k _ nho _ sect h + = 3 Pr1 y, k + Pr1 1 k γ h + y= 2, J j y, k [ ] Eb / I 0 th _ k (18) Since the attenuations and the shadowing to the adjacent sectors are the same, the first term of the extracell interference can be also derived as: Pr y, k 3 Pr Pr 1 ω 1-y,k 60 + θ y = 2, 3 + j= 2 y= 1 1 1, k 1 1, k W / R bk N 0W Pr

58 Now, taking into account both Soft and Softer handover, the portion of total transmit power at BS 1-1 devoted to MS k, can be evaluated as: Φ 1 1, k _ nho_ sect h + = 3 y= 2 G( ω 1 y, k ) + W / R m [ Eb / I0] γ h + α J 3 Pr Pr j y, k N0W + Pr j= 2 y= 1 1 1, k 1 1, k bk th_ k (20) Moreover, in our study we assume that: Φ 1-1,k_softer_sect = Φ 1-1,k_soft_sect (21) Finally, we can introduce two other classes of users: Class D users: all the users in Softer Handover selecting BS 1-1 as Best Server and at the same time BS 1-2 and/or BS 1-3 belong to the AS. The AS is composed by at least the Best Server BS 1-1, BS 1-2 and/or BS 1-3. Class E users: all the users in Softer Handover detecting a different BS (from BS 1-1 ) as Best Server and at the same time either BS 1-1 and BS 1-2, or BS 1-1 and BS 1-3 belong to the AS.

59 Capacity definition N % Aclass N % N % k = 1 Bclass Cclass µφ1k_nho + µ kφ1i_soft + µ kφ1k_soft = 1 k = 1 (% ) * l N Aclass % Bclass k = 1 N = + every snapshot l N M * 1 m = N M l = 1 * l Average capacity over M snapshots N * * s l s = * = Prob { N < N } Statistic capacity Numerical results (1/4) Omnidirectional case, only speech users, average capacity N m* as a function of M SH, with m max = 1, 2, 3, 4, 5; R=1Km; σ=8 db; n= Average Capacity Capacità media N m * SSDT m max =2 m max =3 m max =4 m max =5 HO 50 40

60 30 Numerical results (2/4) Omnidirectional case, only speech users, statistical capacity N s* as a function of M SH, with m max = 1, 2, 3, 4, 5; R=1Km; σ=8 db; n= * * Capacità Capacity N s N s SSDT m max =2 m max =3 m max =4 m max =5 HO Margine di handover M SH [db] Soft Handover Margin M SH [db] Omnidirectional case, average capacity N m* as a function of M SH, with m max = 1, 2, 3, 4, 5; R=1Km; σ=8 db; n=3.76 Average Capacità Capacity * media N * m Numerical results (3/4) SSDT m max =2 m max =3 m max =4 m max =5 HO Mixed traffic - speech users (8Kbit/s) - 5% data users

61 Numerical results (4/4) Three-sectorial case (120 ), speech users only, average capacity N m* as a function of M SH, with m max = 1, 2, 3, 4, 5; R=1Km; σ=8 db; n=3.76, θ= Capacity N* m m max =1 m max =2 m max =3 m max =4 m max = Soft Handover Margin M SH Starting from the probability density function of the normalized position of users ρ = r/r it is possible to obtain the probability density function of the variables i and L; from this relations we carry out the statistic of the parameter P as a function of N, using equation (3). When users are uniformly distributed over a cell, the probability density function of the parameter ρ is known, and can be written as follows: 2ρ 0 ρ 1 P ρ (ρ) = (22) 0 otherwise Extension of the Analytical Model [UniBO] From equation (22) and characterizing the relationship between ρ and the

62 Only speech users (8Kbit/s) Mixed traffic - speech users (8Kbit/s) -5% data users (144Kbit/s)