شبکه‌های بی‌سیم ( 873-40 ) شبکه‌های سلولی CDMA

1. شبکه‌های بی‌سیم (873-40)شبکه‌های سلولی CDMA نیمسال دوّم 93-92 افشین همّتیار دانشکده مهندسی کامپیوتر

2. Introduction • One of the two major technologies for second-generation cellular systems is based on CDMA. • Third-generation (3G) cellular access systems that provide high speed data and multimedia access are also based on CDMA. • In this chapter we will study various resource allocation problems in cellular CDMA systems, basing our discussion mainly on SINR analysis.

3. Overview • Universal frequency reuse: The same portion of the spectrum is reused at every BS. • Resource allocationfor telephone quality voice, guaranteed QoS services and elastic services • SINR target for guaranteed QoS services • Admission Control: Some call requests need to be blocked. • Hard handover and soft handover • Multiclass calls:Individual resource requirements • Transmit power allocation: Iterative power control algorithm • Scheduling of downlink elastic transfers: Trade-off between maximizing the total transfer rate over all the MSs (operator revenue), and fairness between the rates assigned to the MSs.

4. Uplink SINR Inequalities (1) • In CDMA cellular systems each active mobile station (MS) is associated with one of the base stations (BSs) in its vicinity. • When an MS is involved in a conversation, then it is assigned a power level with which it should transmit. • in CDMA access networks the link performance obtained by each mobile station (MS) is governed by the strength of its signal and the interference experienced by the MS’s signal at the intended receiver. • For each radio link between an MS and a BS, a SINR target needs to be met. • It is important to associate MSs with BSs, and to assign them transmit powers in such a way that signal strengths of intended signals are high and interference from unintended signals is low.

5. Uplink SINR Inequalities (2) • Increasing the transmit power to help one MS may not solve the overall problem, as this increase may cause unacceptably high interference at the intended receiver (i.e., a BS) of another MS. • An association of MSs with BSs, and an allocation of transmit powers, is feasible if all SINR targets are achieved. • There may be no feasible power allocation. • The analysis of CDMA systems is performed via certain SINR inequalities.

6. Uplink SINR Inequalities (3) • A depiction of the power allocation problem for several MSs in the vicinity of some BSs is shown. • The solid lines indicate signals from MSs to the BSs with which they are associated.

7. Uplink SINR Inequalities (4) • Consider a CDMA system with multiple interfering cells. • The system bandwidth is W (e.g., 1.25 MHz in the IS-95 standard). • The chip rate is Rc≤ W (e.g., 1.2288 Mcps (Mega chips per second)) in IS-95. • There are M MSs and N BSs, with B = {1, 2, 3, . . . ,N} denoting the set of BSs. • Let hi, j , 1 ≤ i ≤ M, 1 ≤ j ≤ N, denote the power gains (i.e., attenuations) from MS i to BS j. • Let A = (a1, a2, . . . , aM), ai∈ B, denote an association of MSs with the BSs. • Thus, in the association A, MSiis associated with BSai.

8. Uplink SINR Inequalities (5) • Let pibe the transmit signal power used by MSi, 1 ≤ i ≤ M. • Uplink received signal power to interference plus noise ratio for MSkis: N0is the power spectral density of the additive noise. W is the radio spectrum bandwidth. • Assume that the interference plus noise is well modeled by a White Gaussian Noise process.

9. Uplink SINR Inequalities (6) • Various types of calls may be carried on the system. • Suppose that a call requires a bit rate Rk. • To ensure a target Bit Error Rate (BER) (which is governed by the required QoS for the application being carried,) we need to lower bound the product of the SINRkand the processing gain Lk:= Rc/Rk. • If desired lower bound is γkthen Γk:= γk/Lk= γk(Rk /Rc)

10. Uplink SINR Inequalities (7) • Total power received at BSjfrom MSs associated with it is: • Total interference power at BS j from MSs associated with other BSs is: • Then SINR inequalities are:

11. Uplink SINR Inequalities (8) • Power control feasibility for two users: • The left panel shows the situation in which there are feasible power controls; then there is a power control that achieves the SINR targets with equality. • The right panel shows a situation in which there is no feasible power control.

12. Uplink SINR Inequalities (9) • The SINR inequalities are: • Lines labeled 1 and 2, for MS1 and MS2. • The region to the right of, and below, the line labeled 1 is feasible for MS1. • The region to the left of, and above, the line labeled 2 is feasible for MS2. • There is a nonempty feasible region if • Equivalently, if Γ1Γ2< 1.

13. Uplink SINR Inequalities (10) • It can easily be checked that this is equivalent to: • In the left panel, we also see a power vector p∗, which is feasible, and uses the least power in order to satisfy the SINR constraints.

14. Uplink SINR Inequalities (11) • An important step in analyzing cellular CDMA systems is to determine the conditions under which a set of MSs, with given locations and given demands, is admissible in the sense that an association of MSs and BSs, and corresponding power allocations, can be found so that the SINR constraints shown earlier are met. • Given that a set of users is admissible, distributed algorithms are needed in order to determine which BSs they should associate with, and the transmission powers that should be used.

15. Two BSs and Collocated MSs (1) • Assume: • One call class • The SINR target for this class is denoted by Γ. • Two BSs and M MSs associated with each BS. • The MSs are collocated. • All of the MSs use the same transmit power p. • Then:

16. Two BSs and Collocated MSs (2) • If Mhp=Q (Total received power at a BS from the MSs associated with it) and Mh’p=νQ(Total received power at a BS from the MSs not associated with it)then: • Re-arranging: • We need to assign a transmit power pto each MS so that this inequality is satisfied.

17. Two BSs and Collocated MSs (3) • Summing the inequalities for all of M MSs associated with a BS: • A necessary condition is: • Thus the number of admitted calls M should satisfy:

18. Two BSs and Collocated MSs (4) • If the condition holds, then we have positive powers that satisfy the power constraints with equality: • And the value of Q is given by:

19. Multiple BSs and Uniformly Distributed MSs (1) • Now assume: • One call class (same SINR Target Γ) • Multiple BSs and M MSs associated with each BS • The MSs are uniformly distributed. • The radio propagation is spatially homogeneous. • The BSs are uniformly loaded: each BS receives the same total power Q from the MSs associated with it. • Total interference is Io=νQfor every BS. • Then SINR inequalities are: for each k, 1 ≤ k≤ M, where hkis the channel gain of MSkto the BS with which it is associated.

20. Multiple BSs and Uniformly Distributed MSs (2) • Summing of inequalities, we have: • All the terms on the right are positive, and hence lower bounding this expression, it is necessary that: • Thus necessary condition for the existence of a set of powers pk, that satisfy the SINR inequalities is: 

21. Multiple BSs and Uniformly Distributed MSs (3) • Power allocation: • By setting: we have:

22. Discussion (1) • Admission control permitting feasible power allocation for single class case (with the spatial homogeneity): • A connection request is characterized by its effective resource requirement (Γ/1+Γ). • The connection is added to the existing calls at a BS if and only if the following inequality is satisfied: Number of existing connections × Γ/(1+Γ) +Γ/(1+Γ)< 1/(1+ν) Where ν is a spatial parameter that captures other cell interference. (We will discuss how νcan be derived later in this chapter.) • A large value of Γ reduces the number of calls we can carry. How is the value of Γ determined?

23. Discussion (2) • Suppose we wish to carry a new enhanced quality voice call, streaming audio call, or streaming video call using the CDMA access system just described. • The source coding scheme that is used will determine the aggregate bit rate R that needs to carried. • Also, sophisticated source coders will encode the source into bit streams of varying degrees of importance . • When bit errors occur, a radio link layer protocol can recover the CDMA bursts containing the errored bits, but this recovery takes time, which adds to the end-to-end delay for the connection.

24. Discussion (3) • After some number of attempts, bits may need to be discarded, in the hope that the decoder can reconstruct the speech or audio with some desirable quality using the received bits. • For each coder, there will be a threshold bit error rate above which the speech (or audio or video) quality will not be acceptable. • Finally, the PHY layer techniques employed (e.g., exploitation of multipath diversity,) will determine the Eb/N0, γ, required to provide the desired bit error rate to the connection. • More sophisticated PHY layer techniques will result in a lower value of γ, hence a lower value of Γ=γR/Rc, and thus a lower resource requirement Γ/1+Γ for the connection.

25. Discussion (4) • To get a feel for the numbers, let us consider telephone quality voice over the IS-95 CDMA system. • A commonly used speech coder has R=9.6Kbps. • Wsystem=1.25 MHz, and Rc=1.2288 Mcps,thus the processing gain is 1.2288×106/9.6×103=128 ≈21dB. • For the PHY layer techniques employed in the IS-95 standard, the target Eb/N0for this speech coder is 6dB. • Thus the target SINR is 6−21=−15dB (Γ=1/32). • The target SINR of −15dB should be contrasted with narrowband systems such as FDM-TDMA, where the target SINR could be as high as 8 to 10 dB.

26. Discussion (5) • The interference Io=νQ can be reduced by exploiting voice activity detection; the voice call transmits only when carrying actual speech, and turns off during silence periods, thereby reducing the other cell interference for a given number of accepted calls. • Thus, the factor (1+ν) getting multiplied by the voice activity factor. • The voice activity factor is typically 0.4 to 0.5, and thus this technique results in the capacity being increased by a multiplicative factor of 2 to 2.5.

27. Handover (1) • Cell: A BS and the region in which MSs will normally associate with the BS. • In the one class case, with homogeneous interference at each cell, the received powershkpkare all equal at every BS. • Thus, when the entire system carries just one type of call, the powers of all MSs, in any cell, need to be controlled in such a way that the received powers at their respective BSs are all equal. • If the power to be received at each BS from any MS has to be the same, then, in order that an MS uses the least transmit power, it should associate with the geographically nearest BS.

28. Handover (2) • For a location with coordinates (x, y) let rj(x, y) denote the distance of BSjfrom the location (x, y). • The default coverage area of BS j is all (x, y) such thatrj(x, y) < rk(x, y) for every other BS k. • Then the coverage areas are actually so-called Voronoi cells, which are uniquely determined by the BS locations. • The power allocation actions in one cell, affect the other-cell interference seen by other cells. • For example, if MS k is at the fringe of the coverage area of the BS with which it is associated, then the value of hkwill be small, thus requiring a large value of pk. • But this large value of pkwill result in a higher level of other-cell interferenceat neighboring BSs.

29. Handover (3) • An MS may have a better channelto a neighboring BS than to the one with which it is associated. • Soft handover: MS is handed over on the basis of this better channel to the neighboring BS. • Hard Handover: MS is handed over on the basis of path loss measurements, and is associated with a BS so long as it is in the BS coverage area. • An interference analysis, assuming that all calls are of the same type, and hence the target received power from an MS is the same at every BS, will yield the value of νfor hard handover and for soft handover.

30. Hard Handover (1) • First: hard handover • Let Srdenote the target uplink received powerat a BS from any MS associated with it. • The distance of the MS located at (x, y)to BS 1is r1(x, y), and to BS 0is r0(x, y).

31. Hard Handover (2) • Modeling the power law path loss and shadowing, it can be seen that the interference power, say, S0, at BS 0 due to the MS at location (x, y) is given by: where η is the path loss exponent. • An MS is power controlled by BS 1, and the power it radiates causes uplink interference at BS 0. • The local shadowing terms cancel out, and, further, we assume that the distributions of ξ1(x, y) and ξ0(x, y) do not depend on the MS location (x, y). • Then denoting these generic random variables by ξ1 and ξ0, we get:

32. Hard Handover (3) • The total expected other-cell interference at BS 0is obtained by adding up the interference from all the other cell MSs and taking the expectation of this sum. • This computation is done by assuming a uniform distribution of MSs over the coverage area, with density d MSs per unit area, and then integrating over the area outside of the cell covered by BS 0. • This yields:

33. Hard Handover (4) • Where we use the fact that ξ1−ξ0 is normally distributed with mean 0 and variance σ2. • σ = 8dB , η = 4  ν = 0.44 × exp( σ2/2 (ln10/10)2) = 2.38 • Thus the other-cell interference is 2.38 times the power received from MSs within the cell. • Notice: σ = 0 , η =4  ν = 0.44

34. Soft Handover (1) • Second: Soft handover, an MS is power controlled by the best of two or more BSs. • The diagram shows an MS located at location (x, y) being power controlled by the best of BS 1 or BS 0. • Each diamond shaped area, with a BS at each end of its long diagonal, shows the area in which an MS would be power controlled by either of those two BSs. • By ♦i,j we will mean the diamond between BS iand BS j; as an illustration, ♦0,3 is shown shaded.

35. Soft Handover (2) • An MS at location (x, y) is power controlled by either BS 1or BS 0. • In the situation of random shadowing, this will result in the MS causing less interference than if it was dedicated to the more proximate of the two BSs. • Thus, with random shadowing, an MS may get power controlled by a geographically farther away BS. • For two neighboring BSs i and j (e.g., BS 1and BS 0), and for a location (x, y). in the region where an MS chooses between either of them, define: where ri(x, y) and rj(x, y) are the distances of (x, y) from BS iand BS j, respectively, and ξi(x, y) corresponds to log-normal shadowing near BS i(resp. BS j).

36. Soft Handover (3) • The distributions of these shadowing random variables will be taken to be independent of the location (x, y). • let d be the density of mobiles per unit of the system coverage area. • The total power received at BS 0(i.e., intra-cell power and other-cell interference) is given by:

37. Soft Handover (4) • There are six first tier diamonds that include BS 0, the one between BS 1and BS 0being denoted by ♦0,1. Each of these yields a term given by the first integral in the expression. • Considering BS 1, if α0,1(x, y) ≤ 1, then an MS at (x, y) is power controlled by BS 0, and hence BS 0receives power Sr from such an MS. • On the other hand, if α1,0(x, y) < 1, then an MS at (x, y) is power controlled by BS 1, and then BS 0receives interference power Srα1,0(x, y). • This integral is over ♦0, 1, and dA(x,y) denotes the infinitesimal area around (x, y). Then there are terms for every other pair of neighboring BSs, not involving BS 0.

38. Soft Handover (5) • Each such neighboring BS pair gives an integral of the form shown in the second term. • Using the fact that ξi(x, y) − ξj(x, y) is normally distributed with 0 mean and variance σ2, the expectation of the preceding expression can be numerically evaluated to yield Q + Ioat BS 0. • σ = 0 , η = 4  ν= 0.44, the same as obtained for hard handover, earlier, because, without shadowing, the most proximate BS always power controls an MS. • σ = 8dB , η = 4  ν= 0.77, very smaller than the value for hard handover. • It follows that there is a substantial reduction in inter-cell interference if soft handovers are employed. • We have assumed that an MS is power controlled by either of two BSs. This idea can be generalized.

39. System Capacity for Voice Calls (1) • If power control can be accurately performed, and voice activity is not exploited, then the number of calls, M, that can be admitted into a cell is bounded as follows: • Assume: Γ = 1/32, σ = 8dB, and η = 4. • Then for hard handover, M < 9, and for soft handover, M < 18. • In practice, power control is performed in a feedback loop between the MSs and the BSs. Thus, there are inaccuracies due to feedback delay and coarse control. • This results in the bound on M being reduced by a power control inaccuracy factor.

40. System Capacity for Voice Calls (2) • When a call is admitted, it obtains the desired bit rate and BER; the in-call performance is assured. • The Erlang capacity is defined as the Erlang load up to which the blocking probability is less than some target, say 0.01. • There are two alternatives: • We can admit arrivals into the cell until the number of calls is K and then block any additional arrivals. • Alternatively, if we want to exploit the fact that voice calls alternate between speech and silence, we can model the activity of the ith admitted call by a 0-1 random variable, Vi, where Vi=1 with probability a (the fraction of time that a voice call is active) and Vi=0, otherwise. When M calls are admitted, we take the random variables V1,V2, . . . ,VMwith the same Bernoulli distribution. Then, since calls generate power only when they are active, we can admit M calls so long as the following criterion is satisfied: where є > 0 is a suitably chosen outage probability.

41. System Capacity for Voice Calls (3) • This means that if we admit M calls then, over the times during which M calls have been admitted, during less than a fraction of the time the SINR constraints would be violated. • If єis small enough then the infrequent outages may be imperceptible to users. • Evidently, M>Kand hence, the Erlang capacity for a given call blocking probability increases by taking the second approach. The value M is called soft capacity, as opposed to Kbeing called the hard capacity. • If only K calls are admitted, the in-call performance has a hard assurance, but if Mcalls are admitted then the in-call performance has a soft assurance, as the performance can be violated with a small probability.

42. System Capacity for Voice Calls (4) • The SINR analysis assures the QoS within a call in terms of the voice bit rate, and the quality deterioration due to bit errors. • In addition, call blocking probability is also a QoS requirement (e.g., a typical call blocking objective could be 1%), and must be assured by making a good assessment of the expected Erlangload on the system, once it is deployed. • Given the admission control limit Mand the offered Erlang load, if the blocking probability is higher than the objective, then the operator has the following alternatives: • Deploy more BSs, thus reducing the coverage of each BS and thereby reducing the Erlang load on the cells. There is a limit to how much the cells can be shrunk in this way, while retaining the advantages of CDMA. • Cell sectorizationand directional antennas can substantially reduce inter-cell interference, and thereby improve system capacity. • Better CDMA receiver techniques can be employed, thus reducing the value of Γ, and hence the resource requirement per call.

43. Hard Admission Control of Multiclass Calls (1) • Calls with SINR requirements Γ1, Γ2, . . . , Γk, . . . , ΓMcan be associated with BSj, provided: • Thus feasible power allocation is: • These powers are all positive when the condition holds.

44. Hard Admission Control of Multiclass Calls (2) • Suppose there are two classes of calls (Class1 and Class2) that are being handled by the system, and denote their resource requirements as: and • If there are already n1 calls of Class1 and n2 calls of Class2 associated with a BS, then admit a call of Class i∈ {1, 2}, if and only if: • Define:

45. Hard Admission Control of Multiclass Calls (3) • If calls of each class arrive in independent Poisson processes of rates λ1 and λ2, and the times for which calls stay in the system are exponentially distributed, with rates μ1 and μ2, and independent from connection to connection, then (X1(t),X2(t)), t ≥ 0, is a Markov chain on S. • Analysis of this Markov chain yields the probability that a connection of each class is blocked. • If the resulting blocking probability is not acceptable to the customers of the system then the arrival rates will need to be reduced. • This can be achieved, to some extent, by reducing the area covered by each cell.

46. Soft Admission Control of Multiclass Calls (1) • Another approach for capacity enhancement is to employ soft admission control. • When a connection is not active (as, for example, when a party is listening in a speech telephony connection), then the term corresponding to that flow is set to 0 in the left-hand side of equation. • Define, for a connection of type k, the random process Zk(t)= gkwhen the call is active at instant t, and Zk(t) = 0 when the call is inactive. • Assumethat this is a stationary random process, and let Zkdenote a random variable with the marginal distribution of Zk(t).

47. Soft Admission Control of Multiclass Calls (2) • With pk denoting the fraction of time Connection k is active, we have Zk = 1 with probability pk, and Zk= 0 otherwise. • We may then say that a set of connections (1, 2, 3, . . . , n) is admissible if: where є is the probability of outage, the fraction of time that the system violates the connection QoS requirements. • During such times the SINR targets of calls will not be met and users will experience poor in-call QoS.

48. Soft Admission Control (Using Chernoff’sBound) • If nkcalls of Class Kare to be admitted, is equivalent to: where: 1-Zk,iis the resource requirement random variable of Connection i of Class K. 2- We have defined a:= 1/(1+ν), for notational convenience.

49. Soft Admission Control (Using Chernoff’s Bound) • For any θ ≥ 0, let us define: • Then use Chernoff’s Bound to obtain: • This is true for each θ ≥ 0:

50. Soft Admission Control (Using Chernoff’s Bound) • Depiction of the Chernoff’s bound based admission control. • The thick curve is a sketch of , which depends on the vector n of calls admitted. • The slope of this curve at θ = 0 is the mean resource requirement, the asymptotic slope as θ→∞ is the peak resource requirement, and the line with slope a corresponds to the resource.