Tài liệu Adaptive WCDMA (P12) docx

12 Adaptive CDMA networks 12.1 BIT RATE/SPACE ADAPTIVE CDMA NETWORK This section presents a throughput delay performance of a centralized unslotted Direct Sequence/Code Division Multiple Access (DS/CDMA) packet radio network (PRN) using bit rate adaptive location aware channel load sensing protocol (CLSP). The system model is based on the following assumptions. Let us consider the reverse link of a single-cell unslotted DS/CDMA PRN with infinite population and circle cell coverage centered to a hub station. Users communicate via the hub using different codes for packet transmissions with the same quality of service (QoS) requirements [e.g. the target bit error rate (BER) is 10 −6 ]. The radio packets considered herein are of medium access control (MAC) layer (i.e. MAC frames formed after data segmentations and cod- ing). Packets have the same length of L (bits). The scheduling of packet transmissions, including the retransmissions of unsuccessful packets at mobile terminals, is randomized sufficiently enough so that it is possible to approximate the offered traffic of each user to be the same, and the overall number of packets is generated according to the Poisson process with rate λ. In the sequel, we will use the following notation: ζ – the path-loss exponent of the radio propagation attenuation in the range of [2, 5] r – the distance of a mobile terminal from the central hub that is normalized to the cell radius, thus in the range of [0, 1] R 0 – the primary data rate for given system coverage and efficiency of mobile power consumption; T 0 – the packet duration (i.e. the time duration needed for transmitting a packet com- pletely) of the primary rate T 0 = L/R 0 . The cell area is divided into M + 1 rings (M is a natural number representing the spatial resolution) centered to the hub. Let M ={0, 1, ,M};andforallm ∈ M, r m – the normalized radius of the boundary-circle of ring (m +1) given by r m = 2 −m/ζ , r 0 = 1 for the cell-bounding circle and r M+1 = 0 for the most inner ring; R m – the rate of packet transmissions from users in ring (m + 1) given by R m = 2 m R 0 , that is, packets from the more inner ring will be transmitted with the higher bit rate; Adaptive WCDMA: Theory And Practice. Savo G. Glisic Copyright ¶ 2003 John Wiley & Sons, Ltd. ISBN: 0-470-84825-1 422 ADAPTIVE CDMA NETWORKS T m – the corresponding packet duration T m = 2 −m T 0 and also the mean service time of a packet transmission using rate R m . For a fixed packet length L, the closer the mobile terminal to the hub, the higher is the bit rate and the shorter is the packet transmission time. In order to ensure the optimal operation of transceivers, the packet duration should be kept not too short, for example, minimum of around 10 ms as the radio frame duration of the 3GPP standards for WCDMA cellular systems. Therefore, a proper trade-off between L, R 0 and M is needed. For example, with L = 2560 bits, R 0 = 32 kbps and M = 3, there are four possible rates for packet transmissions: 32, 64, 128 and 256 kbps with 80, 40, 20 and 10 ms packet duration, respectively. In the absence of shadowing, for the same mobile transmitter power denoted by P from any location in the network, approximated with the spatial resolution described above, the received energy per frame denoted by E is the same: E = PT m r ζ m = P 2 −m T 0 (2 −m/ζ ) ζ = PT 0 (12.1) This significantly reduces the maximum radiated power into the user direction, reducing the health risk and the interference level produced in the adjacent cell and therefore increasing capacity in the cell. The bit-energy E b = E/L is also constant. Let W – the CDMA chip rate, for example, 3.84 Mcps; g m – the processing gain of a transmission using rate R m that is given by g m = W/R m ; η – the ratio of the thermal noise density and maximum tolerable interference (N 0 /I 0 ); γ m – the local average signal to interference plus noise ratio (SINR), also denotes the target SINR for meeting the QoS requirements of transmissions with rate R m . The transmitter power control (TPC) is assumed sufficient enough to ensure that the local average SINR can be considered as a lognormal random variable having standard deviation σ in the range of 2 dB. Because the transmitter power of mobile terminals in the rate adaptive system is kept at the norm level (denoted by P above), the dynamic range of TPC can be significantly reduced compared to the fixed rate counterpart for the same coverage resulting in less sensitive operation. Thus, σ of the adaptive system can be expected to be smaller than that in the fixed rate system. Once again, if there were only near–far effects in the radio propagation, due to rate adaptation and perfect TPC, SINR of all transmissions would be the same at the hub. However, the required SINR target of higher bit rate transmissions in DS/CDMA systems tends to be lower for the same BER performance due to less multiple access interference (MAI). For example, the simulation results of Reference [1] show that in the same circumstances the required SINR target for 16-kbps transmissions is almost double that of the 256 kbps transmissions. Thus, less transmitter power is needed for close-in users using higher data rate. The rate/space adap- tive transmissions increase the energy efficiency for mobile terminals. It will be shown later that even when the same target SINR was required regardless of the bit rates, the adaptive system still outperforms the fixed counterpart. In the sequel, we will use the following notation: BIT RATE/SPACE ADAPTIVE CDMA NETWORK 423 n ={n m ,m ∈ M} is the system state or occupancy vector, where n m is the number of packet transmissions in progress using rate R m ; w ={w m ,m∈ M} is the transmission load vector, where w m = g −1 m γ m represents the average load factor produced by a packet transmission with rate R m and target SINR γ m . The higher the bit rate, the more the network resources that will be occupied by the transmission. c = nw is the system load state representing MAI in the steady state condition. It has been shown in Chapter 11 that simultaneous transmissions are considered ade- quate, that is, meeting the QoS requirements, if MAI satisfies the following condition: MAI ≡  m∈M n m w m ≤ (1 − η) (12.2) The task of CLSP is to e nsure that the condition (12.2) is always satisfied. Define  ={n, condition (12.2) is true} the set of all possible system states;  ={c, c = nw and n ∈ } the set of all possible system load states. Because of the TPC inaccuracy, the probability that the condition (12.2) is satisfied and the SINR of each packet transmission is kept at the target level, conditioned on the steady system load state c and lognormal SINR can be determined as in Chapter 11, equation (11.30) P ok (c) = 1 − Q  1 − η −E[MAI|c] √ Var [M AI |c]  (12.3) with E[MAI|c] = c exp[(ln 10/10σ) 2 /2] Var [M AI |c] = c exp[2(ln 10/10σ) 2 ] where Q(x) is the standard Gaussian integral function, and σ is the standard deviation of lognormal SINR in dB. This is because the system load state c defined above uses the mean (target) values of lognormal SINR for calculating the average load factor of each transmission. The Gaussian integral term Q(x) in equation (12.3) represents the total error probability caused by a sum of lognormal random variable composing the load state. The above analysis implies that in the equilibrium condition, for a given system load state c, the system will meet its QoS target (e.g. actual bit error probability is less than the target BER of 1e-5) with a probability of P ok (c). In other words, it will lose its QoS target (actual bit error probability is larger than the target BER of 1e-5) with a probability 1 − P ok (c). As a consequence, each equilibrium system load state c can be modeled with a hidden Markov model (HMM) having two states, namely ‘good’ and ‘bad’, which is illustrated in Figure 12.1. 424 ADAPTIVE CDMA NETWORKS good bad Figure 12.1 Two-state HMM of the system load state. The stationary probability of HMM state (‘good’ or ‘bad’) conditioned on the system load state c is given by Pr{‘good’|c}=P ok (c) (12.4) Pr{‘bad’|c}=1 − P ok (c) (12.5) Let us introduce two other parameters for analytical evaluation purposes: P eg – the equilibrium bit error probability over all ‘good’ states of the channel, in which the QoS requirements are met. The target BER is supposed to be the worst case of P eg , for example, 1e-5. P eb – the equilibrium bit error probability over all ‘bad’ states of the channel, in which the QoS requirements are missed to some extent, for example, P eb = 1e − 4whenthe target BER is 1e − 5. The target BER is therefore the upper bound of P eb . In the perfect-controlled system, P eg = P eb and equal to the target BER. This assump- tion is widely used in the related publications investigating the system performance on the radio packet level. In this section, the impacts of channel imperfection are evaluated in the context of SINR errors with total standard deviation σ and P eb as a variable parameter representing effects of ‘bad’ channel condition. Let p(c) – the steady state probability of being in the system load state c ∈ ; P e – the equilibrium bit error probability of the system for the actual QoS of packet transmissions. From the above results, we have P e =   c∈ cp(c)  −1  P eg  c∈ cp(c) Pr{‘good’|c}+P eb  c∈ cp(c) Pr{‘bad’|c}  (12.6) It is obvious that in the perfect-controlled system as mentioned above, P e is also equal to the target BER. Let P c – the equilibrium probability of a correct packet transmission. With employment of forward error correction (FEC) mechanism having the maximum number of correctable BIT RATE/SPACE ADAPTIVE CDMA NETWORK 425 bits N e (N e <Land dependent on the coding method; N e = 0 when FEC is not used), P c is generally given by P c = N e  i=0  L i  P i e (1 − P e ) L−i (12.7) In the fixed rate system with the same coverage, the primary rate R 0 is used for all packet transmissions. From equation (12.2) under perfect TPC assumption, the channel threshold or system capacity defined as the maximum number of simultaneous packet transmissions can be determined by C 0 =(1 − η)/w 0  (12.8) where x is the maximum integer number not exceeding the argument. Thus, with respect to CLSP, the hub senses the channel load (i.e. MAI, in general, or the number of ongoing transmissions for the fixed rate system) and broadcasts the control information periodically in a forward control channel. Users having packets to send should listen to the control channel and decide to transmit or refrain from the transmission in a nonpersistent way. The feedback control is assumed to be perfect, that is, zero propagation delay and perfect transceivers in the forward direction. The impacts of system imperfection, such as access delay, feedback delay and imperfect sensing have been investigated in Chapter 11 for the fixed rate systems with dynamic persistent control. Let G – the system offered traffic G = λT 0 (the average number of packets per normalized T 0 ≡ 1) is kept the same for both adaptive and fixed rate systems for fair comparison purposes. In the adaptive system, G ≡ λ is distributed spatially among users that are in different rings. For m ∈ M,let λ m – be the packet arrival rate from ring (m +1), which is dependent on λ and the spatial user distribution (SUD) having the probability density function (PDF) f(r,θ).In general, λ m is given by λ m = λ r m  r m+1 2π  0 f(r,θ)dr dθ(12.9) For instance, let us assume that the SUD is uniform per unit area in the mobility equilib- rium condition. Thus, λ m can be determined by λ m = λ(r 2 m − r 2 m+1 )(12.10) For the derivation of the performance characteristics of the rate adaptive C LSP unslotted CDMA PRN, a multirate loss system model of the stochastic knapsack-packing prob- lem [2] can be used. The analysis presented in this section can therefore be used for investigating PRNs supporting multimedia applications and QoS differentiation, where users transmit with different rates depending on the system load state, their potential subscriber class and the required services. 426 ADAPTIVE CDMA NETWORKS 12.1.1 Performance evaluation Fixed-rate CLSP The performance characteristics of the unslotted CDMA PRN using fixed-rate CLSP under perfect TPC is given in Chapter 11. Herein, we consider the system with imperfect TPC. Define n – the number of ongoing packet transmissions in the system or the system state; p n – the steady state probability of the system state n; P succ – the equilibrium probability of successful packet transmissions; S – the system throughput as the average number of successful packet transmissions per T 0 ; D – the average packet delay normalized by T 0 ; Using the standard results of the queuing theory for Erlang loss formula [3] with the number of servers set to the channel threshold C 0 , the arrival rate of λ and the normalized service rate of 1/T 0 ≡ 1, we have for the steady state solutions: p n = G n /n! C 0  i=0 G i /i! for 0 ≤ n ≤ C 0 (12.11) The equilibrium probability of a successful packet transmission consists of two factors. The first factor is the probability that the given packet is not blocked by the CLSP given by (1 − B), where B is the packet blocking probability: B = p C 0 (12.12) The second factor is the equilibrium probability of correct packet transmissions P c given by equation (12.7) with a modification of equation (12.6) as given below: P e =  C 0  n=0 np n  −1  P eg C 0  n=0 np n Pr{‘good’|n}+P eb C 0  n=0 np n Pr{‘bad’|n}  (12.13) where similarly to equations (12.4) and (12.5)we have Pr{‘good’|n}=1 −Q  C 0 − ne (ln 10/10σ) 2 /2 √ ne 2(ln 10/10σ) 2  (12.14) Pr{‘bad’|n}=1 −Pr{‘good’|n} (12.15) The equilibrium probability of a successful packet transmission, P succ , is now given by P succ = (1 − B)P c (12.16) BIT RATE/SPACE ADAPTIVE CDMA NETWORK 427 The system throughput is given by S = GP succ (12.17) The average packet delay is decomposed into two parts: D b the average waiting time of a packet for accessing the channel including back-off delays and D r the average resident time of the given packet from the instant of entering to the instant of leaving the system successfully. Formally, the average packet delay (normalized to T 0 )isgivenby D = D b + D r (12.18) with D b = ∞  i=0 B i = B 1 − B (12.19) and according to Little’s formula [3] D r = S −1 C 0  n=0 np n (12.20) Thus, the performance characteristics can be optimized subject to trade-off of the packet length and the transmission rate. This can be achieved by using adaptive radio techniques for link adaptation. Rate adaptive CLSP This system, as mentioned above, can be modeled with a multirate loss network model. It is well known that the steady state solutions of such a system have a product form [2] given by p(n) = 1 G 0  m∈M α n m m n m ! n ∈ (12.21) with G 0 =  n∈  m∈M α n m m n m ! where p(n) is the steady state probability of having n transmission combination in the system, n ∈ ; α m is the offered traffic intensity from ring (m + 1) using rate R m . Thus, α m = λ m T m ,whereλ m and T m are defined above. For large state sets, that is, large M and C 0 , the cost of computation with the above for- mulas is prohibitively high. This problem has been considered by many authors, resulting in elegant and efficient recursion techniques for the calculation of the steady system load state and blocking probabilities. The steady state probability p(c) of system load state 428 ADAPTIVE CDMA NETWORKS c ∈  defined above can be obtained by using the stochastic knapsack approximation described in R eference [2] p(c) = q(c)  c∈ q(c) (12.22) with q(c) given in recursive form as q(c) = 1 c  m∈M w m α m q(c − w m ) for c ∈  + ,q(0) = 1andq(−) = 0 The equilibrium probability of successful transmissions using rate R m can be determined similarly to equation (12.16) as P succ m = (1 − B m )P c (12.23) where P c is given by equation (12.7) with P e given by equation (12.6) and B m is the packet blocking probability of transmissions using rate R m from ring (m + 1) B m =  c∈:c>C 0 w 0 −w m p(c) (12.24) The system throughput can be given by S =  m∈M λ m P succ m (12.25) Note that G = λT 0 ≡  m∈M λ m because of normalized T 0 ≡ 1. The average packet delay of this system, similar to equation (12.18), can be obtained by D =  m∈M D b m T m + D r (12.26) with the components D b m = B m 1 − B m (12.27) D r =   m∈M λ m P succ m w m  −1  c∈ cp(c) (12.28) For illustration purposes, the system parameters summarized in Table 12.1 are used [4]. Two simple SUDs are considered: the two-dimensional uniform (per unit area) and the one-dimensional uniform (per unit length) distributions. For the first scenario, the packet arrival rate from ring (m + 1) is given in equation (12.6). For the second scenario, the BIT RATE/SPACE ADAPTIVE CDMA NETWORK 429 Table 12.1 System parameter summary [4]. Reproduced from Phan, V. and Glisic, S. (2002) Unslotted DS/CDMA Packet Radio Network Using Rate/Space Adaptive CLSP-ICC’02,NewYork, May 2002, by permission of IEEE Name Definition Values W CDMA chip rate 3.84 Mcps η Coefficient of the thermal noise density −10 dB and max. tolerable interference ζ Path-loss exponent 2, 3, 4 L Packet length 2560, 5120 bits R 0 Primary rate 32 kbps γ 0 SINR target of primary rate 3 dB transmission C 0 Fixed primary rate system capacity 56 M + 1 Number of possible rates 4 R m Rate of ring 2, 3, 4 for m = 1, 2, 3 64, 128, 256 kbps γ m SINR target of R m rate transmission for 3 dB or γ 0 for all rates 1e − 5targetBER σ Standard deviation of lognormal SINR 1, 2, 3 dB P eg Equilibrium bit error probability over 1e − 5 ‘good’ condition P eb Equilibrium bit error probability over 1e − 5, 5e − 4, 1e − 3 ‘bad’ condition packet arrival rate from ring (m + 1) is given by λ m = λ(r m − r m+1 ) with r m = 2 −m/ζ and r M+1 = 0 as defined above. This one-dimensional uniform SUD is often used for modeling the indoor office environment in which users are located along the corridor or the highway. The target SINR is set to 3 dB for all transmissions regardless of the bit rates. This is not taking into account the fact that higher bit rate transmissions need smaller target SINR for the same QoS than the lower bit rate transmissions. The load factor introduced by the transmission is therefore linearly increasing with the bit rate that is compensated by shortening the transmission period with the same factor. Because of this, under perfect-controlled a ssumption (P eb = P eg set to target BER as explained above), the fixed rate CLSP system could have slightly better multiplexing gain than the adaptive counterpart for the same offered traffic resulting in slightly better through- put as shown in Figure 12.2. In reality, the BER is changing because of the random noise and interference corrupting the packet transmissions. The throughput characteris- tic of the fixed system worsens much faster than that of the adaptive system because it suffers from higher MAI owing to larger number of simultaneous transmissions and longer transmission period. Further, when the transmission is corrupted, longer trans- mission period or packet length could cause a drop of the throughput performance and wasting battery energy (Figures 12.2 and 12.6). In any case, the adaptive system has much better packet delay c haracteristics than the fixed counterpart (Figures 12.2–12.7). The same can be expected for the throughput performance in real channel condition or 430 ADAPTIVE CDMA NETWORKS 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 System offered traffic System throughput Fixed perfect-ctrl system Adaptive perfect-ctrl Fixed bad-BER = 5e − 4 Adaptive bad-BER = 5e − 4 Fixed bad-BER = 1e − 3 Adaptive bad-BER = 1e − 3 Figure 12.2 Effects of channel imperfection on the throughput performance (two-dimensional uniform SUD, ζ = 3, σ = 2dB, L = 2560 bits, P eg = 1e − 5). 0 10 20 30 40 50 60 70 80 0 1 2 3 4 4.5 3.5 2.5 1.5 0.5 Average packet delay System offered traffic Fixed perfect-ctrl system Adaptive perfect-ctrl Fixed bad-BER = 5e − 4 Adaptive bad-BER = 5e − 4 Fixed bad-BER = 1e − 3 Adaptive bad-BER = 1e − 3 Figure 12.3 Effect of channel imperfection on the packet delay performance (two-dimensional uniform SUD, ζ = 3, σ = 2dB, L = 2560 bits, P eg = 1e − 5). [...]...431 BIT RATE/SPACE ADAPTIVE CDMA NETWORK 2.5 Average packet delay 2 Fixed system Adaptive system with 1-dim uniform SUD Adaptive system with 2-dim uniform SUD 1.5 1 0.5 0 0 5 10 15 20 25 30 35 40 System throughput Figure 12.4 Effects of SUD on the performance trade-off (ζ = 3, σ = 2 dB, L = 2560 bits, Peg = 1e − 5, Peb = 5e − 4) 2.5 Fixed system Adaptive with attenuation-exponent of 2 Adaptive with attenuation-exponent... Fixed T = 40 ms Fixed T = 20 ms Fixed T = 10 ms Adaptive T (A1) Adaptive T (A2) 0.5 0.4 0.3 GammaPDF(a = 2, b = 6) for DfD 0.2 5 10 15 20 25 30 35 40 45 System offered traffic G0 Figure 12.13 Normalized system throughput for comparison 50 448 ADAPTIVE CDMA NETWORKS 3.5 Fixed T = 80 (ms) Fixed T = 40 (ms) Fixed T = 20 (ms) Fixed T = 10 (ms) Adaptive T (A1) Adaptive T (A2) Normalized average packet delay... performance characteristics of both fixed and adaptive packet-length systems To assure the fairness of performance comparison, for the fixed packet-length system, the packet 1 Normalized system throughput 0.9 0.8 0.7 0.6 Fixed T = 40 ms, uniform DfD Adaptive T (A1), uniform DfD Adaptive T (A2), uniform DfD Fixed T = 40 ms, exponential DfD Adaptive T (A1), exponential DfD Adaptive T (A2), exponential DfD 0.5... traffic G0 Figure 12.16 Effects of the mobility or DfD to throughput performance in the flat-fading channel 450 ADAPTIVE CDMA NETWORKS 2.5 Fixed T = 40 ms, uniform DfD Adaptive T (A1), uniform DfD Adaptive T (A2), uniform DfD Fixed T = 40 ms, exponential DfD Adaptive T (A1), exponential DfD Adaptive T (A2), exponential DfD Normalized average packet delay 2 1.5 1 0.5 0 5 10 15 20 25 30 35 40 45 50 System... attenuation-exponent of 3 Adaptive with attenuation-exponent of 4 Average packet delay 2 1.5 1 0.5 0 0 5 10 15 20 25 30 35 40 System throughput Figure 12.5 Effects of propagation model on the performance trade-off (two-dimensional uniform SUD, σ = 2 dB, L = 2560 bits, Peg = 1e − 5, Peb = e − 4) 432 ADAPTIVE CDMA NETWORKS 4.5 Fixed system L = 2560 bits Adaptive L = 2560 bits Fixed system L = 5120 bits Adaptive L... or DfD to packet-delay performance in the flat-fading channel 1 Normalized system goodput 0.9 0.8 0.7 0.6 0.5 Fixed T = 40 ms, uniform DfD Adaptive T (A1), uniform DfD Adaptive T (A2), uniform DfD Fixed T = 40 ms, exponential DfD Adaptive T (A1), exponential DfD Adaptive T (A2), exponential DfD 0.4 0.3 0.2 5 10 15 20 25 30 35 40 45 50 System offered traffic G0 Figure 12.18 Effects of the mobility or... Normalized system goodput 0.8 0.7 0.6 0.5 Fixed T = 80 ms Fixed T = 40 ms Fixed T = 20 ms Fixed T = 10 ms Adaptive T (A1) Adaptive T (A2) 0.4 0.3 0.2 5 10 15 20 GammaPDF(a = 2,b = 6) for DfD 25 30 35 40 System offered traffic G0 Figure 12.15 Normalized system goodput 449 MAC LAYER PACKET LENGTH ADAPTIVE CDMA RADIO NETWORKS normalized T0 ) for the GammaPDF(a = 2, b = 6) DfD scenario These figures clearly... presented in this chapter because of limited space Overall, the adaptive system outperforms the fixed counterpart Figures 12.4 to 12.7 show the effects of design and modeling parameters on the performance characteristics The adaptive system is sensitive to the SUDs (Figure 12.4) and path-loss exponent ζ (Figure 12.5) In the rate/space adaptive systems, spatial positions of the clusters formed by mobile... that represents the TPC errors Although the adaptive system can be expected to have better TPC performance and thus smaller σ , the same value of σ is used for both systems in the numerical examples The throughput-delay performance of unslotted DS/CDMA PRNs using rate/spaceadaptive CLSP is evaluated against the fixed rate counterpart The combination of CLSP and adaptive multirate transmissions not only... 2.5 2 Fixed with 2 dB SINR std deviation Adaptive with 2 dB SINR std dev Fixed with 3 dB SINR std dev Adaptive with 3 dB SINR std dev 1.5 1 0.5 0 0 5 10 20 25 15 System throughput 30 35 40 Figure 12.7 Effects of TPC inaccuracy on the performance trade-off (two-dimensional uniform SUD, ζ = 3, L = 2560 bits, Peg = 1e − 5, Peb = 5e − 4) MAC LAYER PACKET LENGTH ADAPTIVE CDMA RADIO NETWORKS 433 even in . higher bit rate; Adaptive WCDMA: Theory And Practice. Savo G. Glisic Copyright ¶ 2003 John Wiley & Sons, Ltd. ISBN: 0-470-84825-1 422 ADAPTIVE CDMA NETWORKS T m –. traffic Fixed perfect-ctrl system Adaptive perfect-ctrl Fixed bad-BER = 5e − 4 Adaptive bad-BER = 5e − 4 Fixed bad-BER = 1e − 3 Adaptive bad-BER = 1e − 3 Figure