Tài liệu Adaptive WCDMA (P10) doc

10 Resource management and access control 10.1 POWER CONTROL AND RESOURCE MANAGEMENT FOR A MULTIMEDIA CDMA WIRELESS SYSTEM 10.1.1 System model and analysis In this section we assume N different classes of users in the system characterized by the following set of parameters [1] Transmitted power vector P = [P 1 ,P 2 , .,P N ] Vector of rates R = [R 1 ,R 2 , .,R N ] Vector of required E b /N 0 s  = [γ 1 ,γ 2 , .,γ N ] Power limits p = [p 1 ,p 2 , .,p N ] Rate limits r = [r 1 ,r 2 , .,r N ] Channel gains vector h Energy per bit per noise density E b /N 0 of each user can be represented as  E b N 0  i = W R i h i P i  j=i h j P j + η 0 W (10.1) The resource management has to provide quality of service (QoS) for each user that can be represented as W R i h i P i  j=i h j P j + η 0 W ≥ γ i i = 1, .,N (10.2) Adaptive WCDMA: Theory And Practice. Savo G. Glisic Copyright ¶ 2003 John Wiley & Sons, Ltd. ISBN: 0-470-84825-1 296 RESOURCE MANAGEMENT AND ACCESS CONTROL Power and rate constraints can be defined as 0 <P i ≤ p i R i ≥ r i i = 1, .,N (10.3) As optimization criteria, we can have 1. Minimum total transmitted power. For this criterion we also find the maximum num- ber of users of each class that can be simultaneously supported while meeting their constraints. 2. Maximum sum of the rates (overall throughput). 10.1.2 Minimizing total transmitted power For a single cell system, let P be the transmitted power vector. The problem we are looking at is defined by Minimize P,R N  i=1 P i (10.4) subject to constraints P, given by equation (10.3). An easily proven observation about the solution is 1. at the optimal solution all QoS constraints are met with equality, 2. the optimal power vector is one that achieves all rate constraints with equality. The optimum rate vector is R ∗ = [r 1 ,r 2 , .,r N ]. If we write equation (10.2) for each user with equality, we have W r i h i P ∗ i  j=i h j P ∗ j + η 0 W = γ i ∀ i = 1, .,N (10.5) By using r  i = r i γ i , this yields the matrix equation AP ∗ = η 0 W 1 (10.6) where A =              Wh 1 r  1 −h 2 . −h N −h 1 Wh 2 r  2 . −h N . . . . . . . . . −h 1 −h 2 . Wh N r  N              (10.7) POWER CONTROL AND RESOURCE MANAGEMENT FOR A MULTIMEDIA CDMA WIRELESS SYSTEM 297 [P ∗ 1 ,P ∗ 2 , .,P ∗ N ] T is the optimal power vector and 1 = [1, 1, .,1] T is an all-ones vec- tor. By elementary row operations (subtraction of each row from the next), this reduces to the following equation in P ∗ 1  W r  1 + 1  h 1 P ∗ 1      1 − N  j=1 1 W r  j + 1      = η 0 W(10.8) Positivity of P * implies the following condition: N  j=1 1 W r  j + 1 < 1 (10.9) If this condition is satisfied for a set of rates and E b /N 0 requirements, the powers can be obtained. By solving for the powers and imposing power constraints, equation (10.8) gives N  j=1 1 W r  j + 1 ≤ 1 − η 0 W min i  p i h i  W r  i + 1  i = 1, .,N (10.10a) This equation now determines feasibility of a set of rates, QoS requirements and power constraints. By solving for the powers and imposing power constraints, equation (10.8) gives N  j=1 1 W r  j + 1 ≤ 1 − η 0 W min i  p i h i  W r  i + 1  i = 1, .,N (10.10b) This equation now determines feasibility of a set of rates, QoS requirements and power constraints. 10.1.3 Capacity (number of users) of a cell in the multimedia case Consider K classes of users. For any class i, γ i the QoS requirement, r i the rate required and p i the upper bound on the power are all fixed. N i represents the number of simulta- neous users of class i. The channel gains for the users of class i are given as h i = [h 1 i ,h 2 i , .,h N i i ] T (10.11) 298 RESOURCE MANAGEMENT AND ACCESS CONTROL Equation (10.10b) in this case becomes K  j=1 N j W r  j + 1 ≤ 1 − η 0 W min i  p i  min j (h j i )  W r  i + 1  (10.12) 10.1.4 Maximizing sum of rates The system tries to give each user the best throughput possible within the specified constraints. For a received power vector Q, this is defined as Maximize Q,R N  i=1 R i (10.13) Subject to W R i Q i  j=i Q j + η 0 W ≥ γ i i = 1, .,N 0 <Q i ≤ q i R i ≥ r i i = 1, .,N (10.14) From equations (10.13 and 10.14), the problem can be written as Maximize Q N  i=1 W γ i Q i  j=i Q j + η 0 W (10.15) subject to 0 <Q i ≤ q i W γ i Q i  j=i Q j + η 0 W ≥ r i i = 1, .,N (10.16) The objective function is nonlinear, whereas the constraints are linear functions of the variables. Efficient methods analogous to linear programming exist for solving such prob- lems. Furthermore, the objective function is convex in each of the variables. This restricts the search to the surfaces of the polyhedron defined by the constraints. One technique that can be used is the gradient projection method, which is well elaborated in textbooks [2]. A solution to the rate maximization problem exists if and only if a solution to the minimum total power problem exists. The equation is first checked. If it is satisfied, the correspond- ing power vector is chosen as the initial iterate to the gradient projection method. The similar rate constraint is the first included in the active set. It was found that the method converges quickly to the solution [3]. However, with initial guesses containing the maxi- mum rate constraint in the active set, the algorithm converged to a local minimum. With other initial guesses, this problem was avoided. POWER CONTROL AND RESOURCE MANAGEMENT FOR A MULTIMEDIA CDMA WIRELESS SYSTEM 299 10.1.5 Example of capacity evaluation for minimum power problem Consider a system with two classes of service, voice and data. The parameters of the system are [1] Item Symbol Value Bandwidth W 1.25 MHz Vo i c e r a t e R v 8 kbps Data rate R d 4, 8, 20 kbps (E b /N 0 ) voice γ v 5(7dB) (E b /N 0 )data γ d 12, 10, 5 Max. power voice p v 0.5 W Max. power data p d 0.3, 0.5, 0.6 W Min. channel gain voice h v 0.25 Min. channel gain data h d 0.25 AWGN spectral density η 0 10 −6 With these parameters and equations (10.4 to 10.12), the maximum number of data users of each class is found for a given number of active voice users in the network. These results are shown in Figures 10.1 and 10.2. These results can be used for data access control in the system. 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 Number of voice users Number of data users R d = 4 kbps R d = 8 kbps R d = 20 kbps Figure 10.1 Capacity curves for unconstrained power case. Parameters R v = 8 kbps, γ v = 5. For data, three cases γ d = 12, R d = 4 kbps; γ d = 10, R d = 8 kbps and γ d = 5, R d = 20 kbps [1]. Reproduced from Sampath, A., Kumar, P. S. and Holtzman, J. M. (1995) Power control and resource management for a multimedia CDMA wireless system. Proc. PIMRC , Vol. 1, pp. 21–25, by permission of IEEE. 300 RESOURCE MANAGEMENT AND ACCESS CONTROL 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 Number of voice users Number of data users R d = 4 kbps R d = 8 kbps R d = 20 kbps Figure 10.2 Capacity curves for constrained power case. Parameters R v = 8 kbps, p v = 0.5W and γ v = 5 for voice. For data, three cases γ d = 12, R d = 4 kbps; p d = 0.3W; γ d = 10, R d = 8 kbps, p d = 0.5W and γ d = 5, R d = 20 kbps, p d = 0.6 W [1]. Reproduced from Sampath, A., Kumar, P. S. and Holtzman, J. M. (1995) Power control and resource management for a multimedia CDMA wireless system. Proc. PIMRC , Vol. 1, pp. 21–25, by permission of IEEE. 10.2 ACCESS CONTROL OF IN DATA INTEGRATED VOICE/DATA CDMA SYSTEMS The problem from the previous section is now elaborated in more detail in the case when only voice and one class of data users are used. Equation (10.9) still holds N  j=1 1 W r j γ j + 1 < 1 (10.17) If we use the following notation for the bit rates for voice (R V ) and data (R D ), respectively, when active, then inequality from the above equation can be written as [3] S = v a V + d a D < 1 (10.18) where v is the number of active voice users and d is the number of data users who transmit and a V = (W/R V γ V + 1) a D = (W/R D γ D + 1) (10.19) ACCESS CONTROL OF IN DATA INTEGRATED VOICE/DATA CDMA SYSTEMS 301 S is called the load. If we discretize the timescale into slots, then equation (10.19) becomes S(n) = V(n) a V + D(n) a D < 1 (10.20) V(n) is the number of active voice users in the nth slot. Through access control, the number D(n) can be dynamically controlled. More data users can be allowed to transmit when the voice load V(n) is low and less when the voice load is heavy. This is the motivation behind access control, and for the same target outage probability, more data calls can be admitted into the system than if no access control scheme was used. The penalty lies in introducing delay for the packets of data since they may have to wait to be transmitted. In practice, power control is not perfect, and also, power control loops are designed to adjust the power of users on an individual basis, on the basis of current conditions for that user. Dynamic range limitations at the base station (BS) receiver require that the total received power be limited. Of interest is to maintain the total received power Z to within around 10 dB of the background noise power. In a probabilistic access control scheme, permission probability for data is varied on the basis of either measuring S or Z.IfS (or Z) is less than the limit, the permission probability is increased, and it is reduced if otherwise. The performance measure presented in the sequel is very much based on Reference [3]. As defined, the probability of outage (P out ) is the fraction of time that the outage condition is violated. Since no retransmission for voice is possible, it is designed to keep this probability low, nominally around 1%. For data users, outage probability is important too since it affects throughput. When the outage condition is violated, data packets are errored but can be retransmitted subsequently. In addition, mean access delay for data (D A ) and goodput for data (G) are also considered. For these purposes the voice activity is modeled with the two-state process shown in Figure 10.3. The system model in the presence of K v voice users is shown in Figure 10.4. P(i /j ) is P {V(n+ 1) = i /V (n) = j} Off On l m Figure 10.3 Two-state model for voice activity. 302 RESOURCE MANAGEMENT AND ACCESS CONTROL 0 1 2 • • • • • • K v l K v K v m K v ( K v – 1)l ( K v – 2)l 2m m P (0/0) P (1/0) P (1/1) P (2/1) P (0/1) P (1/2) P (3/2) P ( K v – 1/ K v ) (a) (b) 01 2 Figure 10.4 (a) Continuous-time Markov chain that represents the cumulative voice process. (b) Approximate discrete-time Markov chain for the cumulative voice process. The time epochs correspond to positive integer multiples of the slot duration d.Itis assumed that d is small compared to 1/λ and 1/µ, so that the probabilities of two or more events in a slot are negligible. Under these assumptions, we can use the Markov model for the process. Time spent in state k before making a transition to state (k + 1) is exponentially distributed with mean 1/ ˜ λ k = 1/λ(K V − k). The transition time to state (k − 1) is exponentially distributed with mean 1/ ˜µ k = 1/(µk). The probability of remaining in state k is one minus the sum of two previous probabilities. From the theory we have P {V(n+ 1) = k|V(n) = k}=exp(−λ k d) · exp(−µ k d) = exp(−( ˜ λ k +˜µ k )d) (10.21) This is the probability that there will now be new arrival or new departure. The probability that there will be exactly one arrival and one departure is neglected. So, we have P [ V(n+ 1) = k + 1|V(n)= k ] = ˜ λ k ˜ λ k +˜µ k {1 − exp[−( ˜ λ k +˜µ k )d]} P [ V(n+ 1) = k − 1|V(n)= k ] = ˜µ k ˜ λ k +˜µ k {1 − exp[−( ˜ λ k +˜µ k )d]} (10.22) ACCESS CONTROL OF IN DATA INTEGRATED VOICE/DATA CDMA SYSTEMS 303 The stationary probability of state k can be obtained from the state equations for the model from Figure 10.4 and the solution is  V (k) =  K V k  (λ/µ) k K V  j=0  K V j  (λ/µ) j (10.23) A simple data model with a fixed number of admitted data calls K D and each offering exactly one packet per slot is used. If a packet is blocked by the access control scheme or errored on the channel, it remains in the buffer to be transmitted. No new packets are generated until that packet is delivered. Transmitted packets are at rate R D bits s −1 .This model would be adequate for services such as file transfer, e-mail and store-and-forward facsimile. The result can be extended to other data models. A Poisson model is believed to represent short message service (SMS) very well. Although the analysis gets complicated in this case, the qualitative results from the simple data model still hold. Interactive data service can be modeled as a queue of packets at each source with an arrival process into the queue. All results from the fixed data model directly apply in this case, with an additional stability condition to ensure that none of the queue lengths become unbounded. 10.2.1 Access control under perfect power control Assumptions There is a slotted system for the reverse link. No processing or feedback delay of the permission probability is considered. All voice users share a common target signal-to- interference ratio (SIR), as do the data users. Whenever power control is feasible, transmit power assignment that gives each user its desired SIR is made. No limits on total received power at the BS or transmit power limits at the mobile station are considered. Other cell interference is incorporated as background noise. With no received power limits at the BS or the transmit power limits at the mobile station, other cell interference only leads to a scaling of the received powers and does not affect the feasibility condition for power control. No access control From equation (10.20) the load in the nth slot is S(n) = V(n) a V + K D a D (10.24) Probability of outage is given by P out = lim n→∞ P {S(n) ≥ 1} (10.25) 304 RESOURCE MANAGEMENT AND ACCESS CONTROL Hence, from equations (10.23 and 10.25) we have P out = K D  j=[a V (1−K D /a D )]  K V j  (λ/µ) j K V  l=0  K V l  (λ/µ) l (10.26) where [x] is the smallest integer greater than or equal to x. Since no access control is used, the mean access delay for data D A is zero. Average throughput A data packet that is transmitted in a slot in which the outage condition is violated is errored and must be retransmitted. A packet transmitted in a slot in which the outage condition is met is received error-free. Let D S (n) be the random variable that represents the number of successful data packets (over all data users) in the nth slot. Then D S (n) =  K D , if S(n) < 1 0, if S(n) ≥ 1  (10.27) The expected value of D S (n) represents the goodput for data G = lim n→∞ E[D S (n)] = K D lim n→∞ P [S(n) < 1] = K D (1 − P out )(10.28) The goodput per user is simply G K D = (1 − P out )(10.29) Access control based on prediction This control is based on the following steps: 1. Measure V(n), the number of active voice users in the nth slot. 2. Predict the number of active voice users in the (n + 1)th slot  V(n+ 1) =      V(n+ 1) for perfect prediction E[V(n+ 1)|V(n),V(n− 1), V (n − 2), .,] for MMSE prediction      (10.30) 3. Compute permission probability for data such that P   V(n+ 1) a V + D(n + 1) a D < 1  = δ(10.31) . represented as W R i h i P i  j=i h j P j + η 0 W ≥ γ i i = 1, .,N (10.2) Adaptive WCDMA: Theory And Practice. Savo G. Glisic Copyright ¶ 2003 John Wiley