Tài liệu Adaptive WCDMA (P8) docx

8 CDMA network In this chapter, we initiate discussion on CDMA network capacity. The issue will be revisited again later in Chapter 13 to include additional parameters in a more comprehen- sive way. 8.1 CDMA NETWORK CAPACITY For initial estimation of CDMA network capacity, we start with a simple example of single cell network with n users and signal parameters defined as in the list above. If α i is the power ratio of user i and the reference user with index 0, and N i is the interference power density produced by user i defined as α i = P i /P 0 ,i= 1, .,n− 1 N i = P i /R c = P i T c = α i P 0 T c (8.1) then the energy per bit per noise density in the presence of n users is  E b N 0  n = E b N 0 + n−1  i=1 N i (8.2) If (E b /N 0 ) R is the required single-user E b /N 0 necessary to make the n-user signal-to- noise ratio (SNR), namely, (E b /N 0 ) n equal to (E b /N 0 ) 1 ,thenwehave  E b N 0  n = (E b /N 0 ) R 1 + G −1 (E b /N 0 ) R  n−1  i=1 α i  =  (E b /N 0 ) −1 R + G −1  n−1  i=1 α i  −1 (8.3) Adaptive WCDMA: Theory And Practice. Savo G. Glisic Copyright ¶ 2003 John Wiley & Sons, Ltd. ISBN: 0-470-84825-1 218 CDMA NETWORK where G  = T b /T c = R c /R b is the so-called system processing gain. At the point where (E b /N 0 ) n = (E b /N 0 ) 1 , equation (8.3) gives  E b N 0  R = (E b /N 0 ) 1 1 − G −1 (E b /N 0 ) 1  n−1  i=1 α i  (8.4) and the degradation factor DF can be represented as DF = (E b /N 0 ) R (E b /N 0 ) 1 = 1 1 − G −1 (E b /N 0 ) 1  n−1  i=1 α i  (8.5) For n equal-power users, and no coding we have α i = 1foralli, and equation (8.5) becomes DF = 1 1 − (n − 1)G −1 (E b /N 0 ) 1  E b N 0  n = (E b /N 0 ) R 1 − (n − 1)G −1 (E b /N 0 ) R (8.6) For large values of (E b /N 0 ) R , lim (E b /N 0 ) R →∞  E b N 0  n = G (n − 1) ,n≥ 2 (8.7) This is the largest value that the SNR = (E b /N 0 ) n can attain. With this motivation, we define the multiple-access capability factor (MACF) as G/(n − 1) normalized by the SNR, (E b /N 0 ) n . MACF  = G (n − 1)  E b N 0  −1 n (8.8) which can also be expressed as MACF  = G (n − 1)  E b N 0  −1 n = G (n − 1)  E b N 0  −1 R (8.9) As long as the desired SNR, namely, (E b /N 0 ) n , is such that the left-hand side is greater than or equal to one, we can achieve that SNR by appropriately adjusting (E b /N 0 ) R in the right-hand side. If the left-hand side is less than one, however, no value of (E b /N 0 ) R will give the desired value of (E b /N 0 ) n . An example of the system performance is shown in Figure 8.1. One can see that for G = 100 and 1000 the maximum number of users that can be accommodated with finite DF is 10 and 100, respectively. In other words, the CDMA NETWORK CAPACITY 219 2 10 100 0 2 4 6 8 10 12 14 0 4 8 12 16 20 24 28 DF (Degradation factor) (dB) P b = 10 −6 P b = 10 −5 uncoded DF G = R c / R b = 10 3 = 30 dB G = R c / R b = 10 2 = 20 dB MACF for P b = 10 −6 MACF (Multiple-access capability factor) (dB) Total number of users n Figure 8.1 System performance for n equal-power users. 1 10 100 0 2 4 6 8 10 12 14 0 4 8 12 16 20 24 28 DF (Degradation factor) (dB) Power ratio a = P 1 / P 0 MACF (Multiple-access capability factor) (dB) P b = 10 −6 P b = 10 −5 uncoded DF G = R c / R b = 10 3 = 30 dB G = R c / R b = 10 2 = 20 dB MACF for P b = 10 −6 Figure 8.2 System performance for two users of unequal power. system capacity C (maximum number of users) is about 10% of the processing gain in the system, C ∼ = 0.1G. If we now assume n = 2 users of different powers, and set α = P 1 /P 0 The DF becomes DF = [1 − αG −1 (E b /N 0 ) 2 ] −1 (8.10) 220 CDMA NETWORK 0 1 2 3 4 5 6 7 8 9 10 11 12 DF (Degradation factor) (dB) 2 10 100 1000 Total number of users n Coded R c / R b = 200 P b = 10 −6 10 −5 10 −4 10 −3 R c / R b = 2000 P b = 10 −6 10 −5 10 −4 10 −3 Figure 8.3 Degradation factor versus total number of users with K = 7,R= 1/2 convolutional coding and Viterbi decoding with soft decisions. It shows that the performance is equivalent to n users for the equal-power example when we substitute α = n− 1. In other words, having two users one of which is α times stronger is equivalent to having additional (n − 1) users of the same power. This is to be expected, particularly since we have modeled additional users as adding more broadband noise. This is the first time where we explicitly demonstrate the impor- tance of near–far effect and the role of power control discussed in Chapter 6. These results are demonstrated in Figure 8.2. Figure 8.3 demonstrates the same results for the system with coding. In general, more coding would require less S/N ratio for the same performance, which means that more users can be brought into the system, C ∼ = 0.4G. 8.2 CELLULAR CDMA NETWORK In this section, we extend our analysis on a whole cellular network. In such a network users communicate through a central point, the base station (BS) placed usually in the middle of an area called cell. The link between the mobile and BS is called reverse or uplink and between the BS and mobile is called forward or downlink. These two links may be separated in frequency, which is referred to as frequency division duplexing (FDD) or in time, referred to as time division duplexing (TDD). The basic block diagram of the system transmitter is shown in Figure 8.4 and the network layout, composed of a collection of cells is shown in Figure 8.5. CELLULAR CDMA NETWORK 221 Vocoder FEC Spreader Digital processor f 1 f 2 f 3 f N Modulator Transmitter (a) (b) User #1 digital processor User #2 digital processor User #3 digital processor User # N digital processor Transmitter Pilot signal Digital linear combiner and QPSK modulator Figure 8.4 Cellular system simplified block diagram: (a) reverse link subscriber processor/transmitter, (b) forward link cell-site processor/transmitter. For the initial discussion we assume single cell scenario and existence of: 1. Pilot signal in the forward (cell-site-to-subscriber) direction. 2. Initial power control by the mobile, based on the level of detected pilot signal. The mobile adjusts its output power inversely to the total signal power it receives. This, plus closed loop control, described in Chapter 4, should justify the assumption that at the BS all received signals have the same power S. Under this assumption SNR, and energy per bit per noise density in the network with N users can be expressed as SNR = S (N − 1)S = 1 N − 1 (8.11) E b /N 0 = S/R (N − 1)S/W = W/R N − 1 ∼ = G N (8.12) If the presence of thermal noise is also taken into account, we have E b /N 0 = W/R (N − 1) + (η/S) (8.13) 222 CDMA NETWORK Sector Plus from all other cell sites Sector r m r 0 (a) (b) Figure 8.5 Cell geometrics: (a) reverse link geometry, (b) forward link geometry. For a given E b /N 0 , required for a certain bit error rate (BER), the number of users is N = 1 + W/R E b /N 0 − η S ∼ = G E b /N 0 (8.14) where R is the bit rate, W is the bandwidth proportional to chip rate, G is the processing gain G = W/R and η is Gaussian noise (thermal noise) power density. This very simple expression shows that the system capacity measured in number of users is inversely proportional to E b /N 0 required for a certain quality of service (QoS). This explains why the equipment in a CDMA network should use everything available in the modern signal processing technology to keep this level as low as possible. Powerful coding, antenna diversity and advanced signal processing including multiuser detectors are considered for these applications. In order to extend the previous analysis on a network of cells we make the following assumptions: For the reverse direction, noncoherent reception and dual antenna diversity are used. The required E b /N 0 = 7 dB (constraint length 9, rate 1/3 convolution code) [1]. The forward link employs coherent demodulation by the pilot carrier. Multiple trans- mitted signals are synchronously combined. Its performance in a single cell system will CELLULAR CDMA NETWORK 223 be much superior to that of the reverse link. For a multiple-cell system, however, other cell interference will tend to equalize performance in the two directions. Using directional antennas at the cell site both for receiving and transmitting signals is assumed. With three antennas per cell site, each having 120 ◦ effective beamwidths, the interference sources seen by any antenna are approximately one-third of those seen by an omnidirectional antenna. Using three sectors, the number of users per cell is N = 3N S . If voice activity is monitored and a signal is transmitted only if there is a signal at the output of the microphone, the level of interference will be in average reduced, and equation (8.13) becomes E b N 0 = W/R (N S − 1) ∝+(η/S) (8.15) where ‘the voice activity factor’ ∝=3/8. 8.2.1 Reverse link power control Prior to any transmission, each of the subscribers monitors the total received signal power from the cell site. According to the power level it detects, it transmits at an initial level that is as much below (above) a nominal level in decibels as the received pilot power level is above (below) its nominal level. Experience has shown that this may require a dynamic range of control on the order of 80 dB. Further refinements in power level in each subscriber can be controlled by the cell site, depending on the power level it receives from the subscriber (20 dB dynamics). For these purposes a closed loop power control of the type described in Chapter 4 is used. In multiple-cell CDMA the interference level from subscribers in the other cells varies not only according to the attenuation in the path to the subscriber’s cell site, but also inversely to the attenuation from the interfering user to his own cell site. This may increase, or decrease, the interference to the desired cell site through power control by that cell site. 8.2.2 Reverse link capacity for multiple-cell CDMA The generally accepted model for propagation is as follows: • The path loss between the subscriber and the cell site is proportional to 10 (ξ/10) r −4 . • r is the distance from the subscriber to the cell site. • ξ is a Gaussian random variable with standard deviation σ = 8 and with zero mean. • Within a single cell the propagation may vary from inverse square law, very close to the cell antenna, to as great as the inverse of 5.5 power, far from the cell in a very dense urban environment such as Manhattan. The cell geometry is shown in Figure 8.5 In order to reach its own BS with power level S, the user with index m would have to transmit power P m . This can be represented as S = P m  10 ξ m /10 r 4 m  (8.16) 224 CDMA NETWORK This signal will at the same time represent interference at the reference site that can be represented as I(r 0 ,m)= P m  10 ξ 0 /10 r 4 0  (8.17) By substituting P m from equation (8.16) to equation (8.17) we have I(r 0 ,r m ) S =  10 (ξ 0 /10) r 4 0   r 4 m 10 (ξ m /10)  =  r m r 0  4 10 (ξ 0 −ξ m )/10 ≤ 1 (8.18) ξ 0 and ξ m are independent so that the difference has zero mean and variance 2σ 2 . Signal to noise ratio E b /N 0 given by equation (8.13) in the reverse link now becomes E b /N 0 = W/R N s −1  i=1 χ i + (I/S) + (η/S) (8.19) where the first term in the nominator represents intracell interference with χ i =  1, with probability ∝ 0, with probability 1−∝ (8.20) Parameter I represents other (multiple) cell user interference approximated as Gaussian random variable with E(I/S)≤ 0.247N s and var(I/S) ≤ 0.078N s [1]. Parameters W /R and S/η, are constants. Outage probability If we define P = Pr(BER < 10 −3 ) = Pr(E b /N 0 ≥ 5)(8.21) then the system outage probability is defined as 1 − P = Pr(BER > 10 −3 ) = Pr  N s  i=1 χ i + I/S > δ  where δ = W/R E b /N 0 − η S ,E b /N 0 = 5 (8.22) CELLULAR CDMA NETWORK 225 Since the random variable χ i has binomial distribution and I/S is a Gaussian variable, the averaging gives 1 − P = N s −1  k=0 Pr  I/S > δ− k     x i = k  Pr   x i = k  = N s −1  k=0  N s − 1 k  ∝ k (1−∝) N s −1−k Q  δ − k − 0.274N s √ 0.078N s  (8.23) This equation is represented graphically in Figure 8.6 for the system parameters from the standard IS-95. The standard is presented in more detail in Chapter 16. If we accept outage probability of 1%, the system capacity becomes 37 for the sector that repre- sents 37/(W/R) ∼ = 20% of processing gain, 0.2G. For Universal Mobile Telecommuni- cation System (UMTS) standard, this number would be modified by two factors. From equation (8.14) the capacity in UMTS would be three times larger (G w ) owing to the three times larger chip rate. This effectively is not a gain because with three IS-95 systems in the same bandwidth, the capacity would be also increased three times. The real improvement would come from the fact that by using three times larger chip rate, the multipath resolution would be better and the RAKE receiver (with gain G RAKE ) would be more effective, requiring lower E b /N 0 . These issues will be discussed later. At this point it would be worth comparing the capacity of CDMA and time division multiple access (TDMA) system [like global system of mobile communication (GSM)]. GSM uses 200 kHz bandwidth for 8 users. In the band of 1.2 MHz (6 times 200 kHz) it would be possible to accommodate 6 × 8 = 48 ∼ = 50 users. One should be aware that the frequency reuse factor in TDMA network would be 7 as opposed to 1 in CDMA network which makes the normalized equivalent capacity of GSM in 1.2 MHz bandwidth 50/7 ∼ = 7 as opposed to 37 obtained in CDMA network. 30 35 40 45 50 55 60 0.1 0.01 0.001 0.0001 P r ( BER > 0.001) Number of users per sector 37( G w G Rake ) 1234 1 – Surrounding cells full 2 – @ 1/2 capacity 3 – @ 1/4 capacity 4 – Surrounding cells empty Figure 8.6 Reverse link capacity/sector (W = 1.25 MHz, R = 8 kbps, voice activity = 3/8). 226 CDMA NETWORK For a fair comparison, one should be aware that GSM codec uses 13 kbit as opposed to 8 used in the previous calculus for CDMA, which reduces 37 by a factor of 8/13. The intention of this discussion is not to offer at this stage a final statement about the capacity but rather to give some initial elements relevant for this discussion. The numbers will be modified throughout the following chapters. They will be increased by a number of sophisticated algorithms for signal processing and also reduced by a number of sources of degradation, due to imperfections in the implementation of these algorithms. 8.2.3 Multiple-cell forward link capacity with power allocation We assume that measurement by the mobile of its relative SNR, defined as the ratio of the power from its own cell-site transmitter to the total power received, is available. Measurements can be transmitted to the selected (largest power) cell site when the mobile starts to transmit. On the basis of these two measurements, the cell site has reasonably accurate estimates of S T 1 and  K i=1 S T i ,where S T 1 >S T 2 > ··· >S T K > 0 (8.24) are the powers received by the given mobile from the cell-site sector facing it. S T1 is the total power transmitted from the cell site. The remainder of S T1 as well as the other cell-site powers are received as noise. Thus for user i, E b /N 0 can be lower bounded by  E b N 0  i ≥ β∅ i S T 1 /R     K  j=1 S T j   + η   /W (8.25) There is inequality because the interference includes the useful signal too. β is the fraction of the total cell-site power devoted to subscribers (1 − β is devoted to the pilot). ∅ i is the fraction of this devoted to subscriber i. From equation (8.25) we have ∅ i ≤ (E b /N 0 ) i βW/R     1 +     K  j=2 S T j S T 1     i + η (S T 1 ) i     (8.26) where N s  i=1 ∅ i ≤ 1 (8.27) Outage probability The relative received cell-site power measurements are defined as f i  =   1 + K  j=2 S T j /S T 1   i ,i= 1, .,N S (8.28) . n−1  i=1 α i  =  (E b /N 0 ) −1 R + G −1  n−1  i=1 α i  −1 (8.3) Adaptive WCDMA: Theory And Practice. Savo G. Glisic Copyright ¶ 2003 John Wiley