Nhiều giao thức truy cập đối với truyền thông di động P7

Multiple Access Protocols for Mobile Communications: GPRS, UMTS and Beyond Alex Brand, Hamid Aghvami Copyright  2002 John Wiley & Sons Ltd ISBNs: 0-471-49877-7 (Hardback); 0-470-84622-4 (Electronic) 7 MD PRMA WITH LOAD-BASED ACCESS CONTROL Chapter 5 provided descriptions of channel and traffic models used for investigations on the MD PRMA protocol, which was defined in detail in Chapter 6. Starting with this chapter, and continuing in Chapters 8 and 9, the outcomes of our research efforts on MD PRMA will be discussed. In this chapter, the focus is on load-based access control (for MD PRMA), a technique adopted to protect reservation-mode users from multiple access interference generated by contending users. Only voice traffic is considered. We are investigating an interference- limited scenario, where code-slots are not distinguished, and random coding is assumed instead, such that ‘classical’ code-collisions cannot occur. However, users may still suffer ‘collisions’ due to excessive MAI, which will cause packet erasure. With access control, the overall packet-loss probability P loss is composed of the packet-dropping ratio P drop and the packet-erasure rate P pe . Load-based access control is applied to trade off packet dropping against packet erasure in a manner which minimises P loss . To assess the benefits of load-based access control through so-called channel access functions (CAFs), several benchmarks are introduced. After a section defining the system considered, both analytical and simulation results for the first benchmark, a random access protocol, are presented. The analysis is expanded to underpin some of the comments made in the introductory chapter of this book on multiplexing efficiency. Other bench- marks include one used as a reference to assess multiplexing efficiency, and an ideal backlog-based access control scheme. Following considerations on channel access func- tions used for load-based access control, performances of the different schemes considered are compared for various scenarios. This includes a study of the impact of power control errors and the choice of the spreading factor. 7.1 System Definition and Choice of Design Parameters 7.1.1 System Definition and Simulation Approach MD PRMA for frequency division duplexing as defined in Section 6.2 is considered, assuming immediate acknowledgements and using load-based access control as described in Section 6.4. Physical layer performance is accounted for assuming random coding and applying the standard Gaussian approximation to assess the error performance, as outlined in Section 5.2. When intercell interference is considered, all cells are assumed to be 280 7 MD PRMA WITH LOAD-BASED ACCESS CONTROL equally loaded, that is, K in Equation (5.16) is the average load per time-slot experienced in the test cell, as defined below, and I intercell is taken to be 0.37 and 0.75, for values of the pathloss coefficient γ pl of 4 and 3 respectively. Code-slots are not considered. Therefore, in Subsection 6.2.3, the specific considerations provided for the random-coding case apply. In other words, we are considering a purely interference-limited system, where, however, instantaneous interference levels are only considered for interference generated within the test cell, while intercell interference is assumed to be constant at its average level. To assess the benefit of load-based access control, MD PRMA performance is compared with that of various benchmarks, which are defined below. The only traffic considered in this chapter is packet-voice traffic, using the two-state voice model specified in Section 5.5 with parameters D spurt = 1s and D gap = 1.35 s, which results in a voice activity factor α v = 0.426. The number of conversations M supported simultaneously determines the system load. P loss performance as a function of M is of interest here, and particularly, M 0.01 and M 0.001 , the number of conversations which can be supported at tolerated maximum P loss values, (P loss ) max , of 1% and 0.1%, respectively. A static scenario is considered, where P loss is established as a function of M,andM remains fixed over the relevant period of observation. Therefore, the average number of users per time-slot K can be obtained through K = M · α v N .(7.1) Simulations were performed using a commercial, event-driven and object-oriented tool for network simulations. Each simulation-run with fixed M covered 1000 s conversation time. Where required, several simulation-runs were performed for the same value of M, in which case the P loss reported is the averaged result over these simulation-runs. 7.1.2 Choice of Design Parameters The starting point for the choice of design parameters is to be found in Reference [146]. In this reference, a voice source rate R s of 8 kb/s and a frame length D tf of 20 ms are considered, yielding 160 information bits per packet 1 , to which 64 header bits are added. With a PRMA channel rate R p of 224 kbit/s, neglecting guard periods, a slot duration D slot of 1 ms is required to accommodate a packet. A frame is therefore composed of N = 20 time-slots. The dropping delay threshold D max issetto20ms,whichishalfthe value considered in Reference [146]. This is to keep the total transfer delay low, to which also other sources of delay contribute, such as framing delay and processing delay. It remains to specify the FEC code-rate r c and the spreading factor X. In Section 5.2, the optimum value for r c was established for packets with 224 message bits, applying the Gilbert–Varshamov bound. It was found that, irrespective of X, the bandwidth-normalised throughput was maximised when r c was between 0.4 and 0.6. A suitable BCH code with a code-rate in this range of values is the (511, 229, 38) BCH code. It supports five more message bits than required (they will be attributed to the header), and has a code-rate r c of 0.45. With this choice, R p increases to 229 kbit/s before error coding, while the channel-rate after error-coding R ec is 511 kbit/s. Interleaving is not applied, every packet 1 In other Goodman publications, such as References [8] and [142], the voice source rate assumed was 32 kb/s, which is rather high for a basic voice service in cellular systems. 7.2 THE RANDOM ACCESS PROTOCOL AS A BENCHMARK 281 Table 7.1 Parameters relevant for the physical layer, protocol operation and traffic models Description Symbol Parameter Value TDMA Frame Duration D tf 20 ms Time-Slots per Frame N 20 Message bits per Packet B 160 information bits + 69 header bits Channel-Rate before Error-Coding R p 229 kbit/s Channel-Rate after Error-Coding R ec 511 kbit/s Chip-Rate R c 3.577 Mchip/s Dropping Delay Threshold D max 20 ms Voice Terminal Source-Rate R s 8 kbit/s Mean Talk Gap Duration D gap 1.35 s Mean Talk Spurt Duration D spurt 1s is separately error-coded, and contention and reservation-mode packets have the same packet format. This also implies that contention packets contain the same amount of user data as those sent on reserved resources. No dedicated request bursts are generated. In order to limit computer resource requirements for simulations, a rather low spreading factor of X = 7 was chosen when we started our investigations on PRMA-based protocols back in 1994. The resulting chip-rate R c of 3.577 Mchip/s is surprisingly close to the one having been chosen for UTRA. Most of the results presented in the following are for X = 7. If larger spreading factors are considered, this is explicitly mentioned. The complete set of parameters used is listed in Table 7.1. 7.2 The Random Access Protocol as a Benchmark 7.2.1 Description of the Random Access Protocol In References [28–31] we established the benefits of load-based access control through a performance comparison with what was referred to there as random access CDMA. Strictly speaking, the name ‘random access CDMA’ is somewhat misleading, since the same hybrid CDMA/TDMA channel structure as in MD PRMA is used. A more generic name will therefore be used for this protocol; it will be referred to here as random access protocol (RAP). In RAP, every user may access the channel at will. In other words, the access permission probability p is always set to one. For a voice user, this simply means that the next time-slot after the arrival of a talk spurt will be accessed. In Reference [31], it was assumed that a voice terminal needed to retransmit the first packet of a spurt until it was successfully received and acknowledged by the base station. This can be viewed as MD PRMA with p = 1. Here, in order to have completely unconstrained channel access, packets are never retransmitted, and the time-slot number used for all packets in a spurt depends only on the arrival instance of the first packet in that spurt. Therefore, P drop is always zero, and the P loss performance is entirely determined by P pe . 282 7 MD PRMA WITH LOAD-BASED ACCESS CONTROL 7.2.2 Analysis of the Random Access Protocol According to Section 5.5, the steady-state distribution for the number of simultaneously active terminals v given M voice sources is Pr{V = v}=P V (v) =  M v  · α v v · (1 − α v ) M−v (7.2) with mean V = M · α v .Thesev simultaneously active users will be distributed in some fashion over the N available time-slots. With completely unconstrained access as discussed above, there is no reason to expect that some time-slots are more likely to be chosen by any one of the users than others are. Furthermore, with exponentially distributed spurt and gap duration, any particular user will choose time-slots for successive spurts independently of each other. It can therefore be assumed that each slot in a TDMA frame is chosen with equal likelihood, i.e. P slot = 1/N. The probability of k users accessing a slot conditioned on v active users is then Pr{K = k|V = v}=P K|V (k|v) =  v k  · P k slot · (1 − P slot ) v−k ,(7.3) and the unconditional probability can be calculated through Pr{K = k}=P K (k) = M  v=k P V (v) · P K|V (k|v). (7.4) Note that the summation starts from k, since in order that k users access a certain time-slot, there must be at least k users active in total. Finally, P loss can easily be calculated according to P loss = 1 K M  k=0 k · P K (k) · P pe [k],(7.5) with K from Equation (7.1). To establish the packet erasure probability P pe [k], depending on the circumstances considered, Equations (5.7) and (5.3) together with either Equa- tion (5.6) or Equation (5.16) are used 2 . Alternatively, Equation (5.20) may be used. The steady-state distribution (Equation (7.2)) is a binomial distribution with parame- ters M and α v . The Poisson distribution with mean V = M · α v is a good approximation of the binomial distribution, provided that α v  1andM large (e.g. α v < 0.05 and M>10). The first condition must hold for the variance of the binomial distribution, M · α v · (1 − α v ), to match roughly that of the Poisson distribution, V . Here, α v is signif- icantly larger than 0.05, and thus, the variances of the two distributions cannot match, irrespective of M. Assume for now all the same, that Equation (7.2) can be approximated by a Poisson distribution with mean V . In this case, since every slot is selected indepen- dently with probability P slot , the probability distribution per slot is again Poisson with 2 The attentive reader will have noticed that upper case ‘K’ was used for the number of users per time-slot in Chapter 5, while ‘k’ was used as an index for a particular user out of these K users. For consistency of notation in this chapter, ‘k’ is here the number of users per time-slot, and ‘K’ the respective random variable. Instead of  K , we can write P K (k) for the probability distribution of this random variable. 7.2 THE RANDOM ACCESS PROTOCOL AS A BENCHMARK 283 mean V/N= K owing to the ‘splitting property’ of the Poisson process discussed in Section 6.5. Therefore, P K (k) = K k e −K k! .(7.6) This approximation is useful for the discussion on multiplexing efficiency provided in Subsection 7.2.4. Its accuracy is assessed below. 7.2.3 Analysis vs Simulation Results In Figure 7.1, P loss values resulting with the random access protocol are reported as a function of M for two cases, namely an isolated test cell and a test cell in a cellular environment, in both cases assuming perfect power control. In the single-cell case, there is no intercell interference, and Equation (5.6) is used for the average SNR which determines P pe [k]. For the results shown for the cellular environment, a pathloss coefficient γ pl of 4 is assumed, and average intercell interference is accounted for by using Equation (5.16), with I intercell = 0.37, instead of Equation (5.6). The curves with markers represent simulation results, whereas the solid and the dashed curves refer to analytical results with the binomial steady-state distribution according to Equation (7.2) and the Poisson approximation for the steady-state distribution respectively. Two conclusions can be drawn from this figure. Firstly, judging from the P loss values reported, the Poisson approximation models the P loss performance obtained with the binomial distribution quite well for large values of M, regardless of the variance mismatch. With decreasing M, however, the gap between the P loss values calculated widens. Secondly, in general a very good agreement between analysis and simulation results can be observed. Normally, even simulation results obtained from individual 1000 s simulation-runs closely match the analytical results, although most points shown in the 0.0001 0.001 0.01 0.1 90 110 130 150 170 190 210 230 250 Simultaneous conversations M Packet loss ratio P loss Simulation Binomial Poisson Perfect power control spreading factor X = 7 Cellular environment, g pl = 4 Single cell Figure 7.1 Performance of the random access protocol with perfect power control 284 7 MD PRMA WITH LOAD-BASED ACCESS CONTROL simulated curves represent results averaged over several simulation-runs. As a result of this averaging, fairly smooth curves were obtained, but in rare occasions such as M = 130 in the single-cell case, even averaging over more than 50 simulation results did not allow the curve to smooth out perfectly. Figure 7.2 shows equivalent results for the case when power control errors are accounted for through Equation (5.20). Here, due to the flatter P pe [k]-slopes, the errors made with the Poisson approximation of the binomial steady-state distribution have a much smaller impact on the calculated P loss values than in the case considered above. Correspondingly, the two analytical curves almost match even for small values of M. Again, a very good agreement between analytical and simulation results can be observed, which validates the simulation platform. Figure 7.3, showing only simulation results, summarises all cases considered for X = 7. Note that the impact of the intercell interference decreases with increasing error variance (which is partially due to the fact that fluctuations of the inter- cell interference level are not captured here). The two curves shown for σ 2 pc = 2dB(or σ pc = 1.41 dB) even meet below a packet-loss ratio of 0.1%. A more detailed discus- sion of the performance degradation due to power control errors will be provided in Section 7.6. For completeness, it is reported that simulations were also carried out for a spreading factor X = 15, obtaining similar agreement between simulation and analytical results as in the cases illustrated here. 7.2.4 On Multiplexing Efficiency with RAP In Section 1.4, we claimed that the statistical multiplexing gain depended essentially on the standard deviation normalised to the mean of simultaneously active users (or almost equivalently: the standard deviation of the multiple access interference or MAI). In the following, this claim is first substantiated and, based on this, further observations on 0.0001 0.001 0.01 0.1 20 40 60 80 100 120 140 160 180 200 Simultaneous conversations M Packet loss ratio P loss Simulation Binomial Poisson Lognormal power control errors spreading factor X = 7 isolated cell s pc = 1.41 dB s pc = 1 dB Figure 7.2 Performance of RAP when accounting for power control errors 7.2 THE RANDOM ACCESS PROTOCOL AS A BENCHMARK 285 0.0001 0.001 0.01 0.1 10 50 90 130 170 210 250 Simultaneous conversations M Packet loss ratio P loss Spreading factor X = 7 s pc = 0 dB s pc = 1 dB s pc = 1.41 dB g pl = 4, s pc = 0 dB g pl = 4, s pc = 1 dB g pl = 4, s pc = 1.41 dB g pl = 3, s pc = 0 dB Figure 7.3 Simulation results for RAP obtained with different values for σ pc , both for an isolated cell and two cellular scenarios with γ pl = 4and3 multiplexing efficiency with pure CDMA and hybrid CDMA/TDMA air interfaces are provided. For simplicity, assume a physical layer on which all packets are transmitted success- fully, if no more than K pe max users access the channel simultaneously, and otherwise, all packets are erased. In other words, P pe [k] is approximated by a step-function, P pe [k] =  0,k≤ K pe max 1,k>K pe max , (7.7) and K pe max represents the number of resource units available. With P K (k) describing the distribution of the random variable K, and with P pe [k]as above, P loss = 1 K M  k=K pe max +1 k · P K (k). (7.8) The appropriately weighted and normalised tail of the distribution of K, shaded in Figure 7.4 provided for illustration, determines the packet-loss ratio. Restricting the focus to bell-shaped distributions, at a given offset between K pe max and mean K of this distri- bution, it is obvious that the larger the standard deviation of K, σ K ,thelargerP loss .The more interesting question to ask is what kind of offset needs to be respected in order not to exceed a certain (P loss ) max . Write this offset as a multiple of σ K , K pe max − K = c offset · σ K ,(7.9) 286 7 MD PRMA WITH LOAD-BASED ACCESS CONTROL 0 0.01 0.02 0.03 0.04 0.05 0.06 007 15 20 25 30 35 40 Users K per time-slot 45 50 55 60 65 P K ( k ) K pe max K C offset .s K s K Figure 7.4 Illustration of K and K pe max when K is Poisson with mean K = 40 as shown in Figure 7.4. Next, define multiplexing efficiency η mux as the ratio of K over K pe max , which is the normalised resource utilisation. Using Equation (7.9), η mux =  c offset · σ K K + 1  −1 .(7.10) If c offset were a constant, we could indeed claim that the multiplexing efficiency only depends on the normalised standard deviation σ K /K. The smaller its value, the larger the multiplexing efficiency. But is c offset constant? It would almost be, if the shape of the tail of the distribution of K were fully described by σ K (as for instance with a normal distribution) 3 . Since it has just been found that P loss performance of RAP is modelled accurately if K is assumed to be Poisson distributed, this distribution will be used in the following. If we ignore the fact that a continuous distribution is being compared with a discrete distribution, when K  0, the Poisson distribution resembles the normal distribution. In particular, it is nicely bell-shaped, as shown in Figure 7.4, although not completely symmetric with respect to K. However, there is only one degree of freedom: the Poisson distribution is entirely specified by its mean K, and the variance is equal to the mean, thus σ K = √ K. Figure 7.5 shows c offset as a function of K for a Poisson distribution. Individual points in this graph were obtained by fixing K pe max , imposing (P loss ) max = 1%, and calcu- lating the maximum value of K which is admissible to meet this P loss requirement, as determined through Equation (7.8) together with Equation (7.6). As expected, c offset is almost constant for K above 20, while there are somewhat stronger fluctuations for lower values of K, where the Poisson distribution loses its bell shape. Since σ K increases less than linearly with K, η mux increases with increasing K (the fact that 3 Because of inevitable distortion effects due to the weighting and normalisation in Equation (7.8), c offset will fluctuate slightly, even if a normal distribution is considered. 7.2 THE RANDOM ACCESS PROTOCOL AS A BENCHMARK 287 3.5 3 2.5 2 01020304050 Mean number of users K per time-slot c offset 60 70 80 90 100 Figure 7.5 c offset as a function of K c offset decreases with increasing K further amplifies this effect). K can obviously only be increased, if K pe max is increased as well, that is, more bandwidth or resources must be provided. Summarising, the multiplexing efficiency increases with increasing size of the popula- tion multiplexed onto a common resource. This is very similar to the so-called trunking efficiency in blocking-limited circuit-switched systems discussed in Section 4.6: the larger the number of channels provided, the higher the average channel utilisation at a given admissible blocking level. Next, we need to ask how the relevant common resource is determined. In Section 1.4, we stated that the relevant resource for multiplexing was an entire carrier in wideband CDMA, but only a time-slot in hybrid CDMA/TDMA with unconstrained channel access. Consider a hybrid CDMA/TDMA system with N time-slots and K pe max = E,andawide- band CDMA system with an equivalent amount of resources, but no time-slots (or rather, only one ‘time-slot’ per frame), i.e. K pe max = N · E. In the latter case, the steady-state distribution of the total number of users on the carrier being considered, which is approx- imately Poisson with mean V C , determines the packet-loss probability. Therefore, the trunking efficiency is determined by the total number of users. In the hybrid case, as just seen, the relevant distribution is the distribution per time-slot with mean V CT /N, thus the trunking efficiency is determined by the average number of users accessing a single time-slot. If the total amount of resources is the same as in the pure CDMA case, the trunking efficiency will be lower and, thus, the hybrid solution will support fewer users at a given (P loss ) max ,i.e.V CT < V C . For quantitative considerations on these matters, based on Gaussian approximations for physical layer modelling rather than the simple step function as per Equation (7.7), refer also to Section 7.6. These findings would suggest that a pure CDMA air interface is a better choice than a hybrid CDMA/TDMA air interface from a pure multiplexing point of view. However, if the load is balanced out between time-slots through access control, the relevant population becomes the total number of terminals admitted to this carrier in the hybrid CDMA/TDMA case as well. This is shown below. 288 7 MD PRMA WITH LOAD-BASED ACCESS CONTROL 7.3 Three More Benchmarks 7.3.1 The Minimum-Variance Benchmark Suppose M simultaneous conversations are to be supported on N time-slots, such that the average load per slot amounts to K = M · α v /N packets. Assume further that it is possible to schedule packets perfectly on the uplink, that is, the base station could have full control over how many users access any given time-slot, through whatever means may be necessary. Consider the case where the base station schedules either k 1 =K or k 2 =K packets per slot (in other words, k 1 and k 2 are the two consecutive integers embracing K). Of all possible discrete distributions for K with mean K, this is the one with minimum variance. In Reference [30], to find the highest theoretically possible number of conversations which can be supported at a given (P loss ) max , the analysis focussed on such minimum- variance distributions, for which Equation (7.5) can be rewritten as P loss = P K (k 1 ) · k 1 · P pe [k 1 ] + P K (k 2 ) · k 2 · P pe [k 2 ] P K (k 1 ) · k 1 + P K (k 2 ) · k 2 .(7.11) In the above equation, the denominator is the mean K or expectation E[K]ofthe distribution of K.SinceP K (k 1 ) + P K (k 2 ) = 1, it can easily be shown that P K (k 1 ) = K − k 2 k 1 − k 2 .(7.12) P loss (M) can now be calculated using Equation (7.1) to establish K, then Equa- tions (7.12) and (7.11) with P K (k 2 ) = 1 − P K (k 1 ). Note that these formulas imply perfect statistical multiplexing. In other words, it is assumed that arbitrary distributions of K can be shaped by scheduling and thus delaying packets as necessary, without having to drop packets. We claimed in Reference [30] that M x found at a given (P loss ) max of x through the formulas above is a strict upper limit for M x , and this benchmark was referred to as perfect scheduling. While we still believe that it will be rather difficult to exceed M x with any other distribution than this minimum-variance distribution for the typical P pe [k] curves found in Chapter 5, which are the ones of interest here, we have invested no further efforts to prove this conjecture. On the other hand, if P pe [k] is approximated by the step-function (7.7), the distribution maximising M x at a (P loss ) max of x is not the distribution considered above with minimum variance, as shown in Reference [61, Appendix C]. Since ‘perfect scheduling’ may not only refer to the ability of the base station to schedule precisely the wanted number of packets in each time-slot, but could potentially also imply an optimum distribution for K, caution suggests that this benchmark should be referred to in the following as the minimum-variance benchmark (MVB) rather than the ‘perfect-scheduling benchmark’. Throughout the remainder of this chapter, the packet erasure rate P pe [k] will be model- led by Gaussian approximations and random coding is assumed, such that the number of code-slots E per time-slot is in theory unlimited. Equation (6.1) given in Subsection 6.2.8 can therefore not be used to assess multiplexing efficiency, since the number of available resource units is not clearly specified. However, U = N · K can be used instead of N · E [...]... curves Finally, again for perfect power control, Figure 7.20 illustrates how the performance difference between MVB and RAP decreases As already discussed earlier, for M0.001 , this difference amounts to a mere 20% at X = 63 More representative of the capacity gain realistically obtainable through access control, the difference between worst-case MVBwd and RAP (not shown in the figure) is only 14% The Figure... control-slot split into minislots, followed by twenty 0.9 ms information slots Each admitted terminal indicates at the beginning of every frame through the sending of a tone in its request mini-slot whether it has a packet to transmit or not, allowing the base station to schedule every packet individually according to the most appropriate policy The idea of power grouping is that the base station measures... R[t] = R[t − N ] + Cs [t − N ] Furthermore, as shown in Chapter 8, the backlog estimation algorithm described in Chapter 6 allows an accurate estimation of the number of contending terminals Y [t], if distinct code-slots are discriminated and feedback in terms of number of code-collisions in each time-slot is available Kpe max calculated through Equation (7.20) depends on (Ppe )max , which in turn... shows that KBAC, while providing good results, is not the optimum approach (in terms of minimising packet loss) to probabilistic access control In particular, even with optimised Kpe max , access control with KBAC can be too generous in certain conditions With Equation (7.20), load is controlled in a ‘symmetric manner around Kpe max ’, that is, if Kpe max − R[t] < Y [t], the conditioned probability that... two linear segments backlog according to Equation (7.19), statistics were collected to determine p v [R], that is, pv [t] values were first classified according to the observed R[t] values, and these classified values were subsequently averaged Like this, backlog-based pv [t] values were mapped to load-based pv [t] values One could be tempted to use these p v [R] values directly for access control However,... for which the number of contending terminals happens to be high, to be heavily overloaded In such slots, both the reserved packets will be erased and no new reservations can be granted This will cause a temporary accumulation of contending terminals, which increases the probability for subsequent time-slots to suffer from overload, too Eventually, the number of contending terminals will have grown... CAFs used here for the single-cell case could be applied directly This would also allow intercell interference fluctuations to be taken into account, to react for instance to congestion in neighbouring cells Strictly speaking, the BS would have to be able to distinguish between interference stemming from reservation-mode users and that from colliding contentionmode users not only in the test cell, but... of MD PRMA using the semi-empirical channel access functions depicted in Figure 7.10 Table 7.3 summarises the performances of the different schemes considered in terms of M0.01 and M0.001 The substantial performance improvement, in certain cases exceeding 100%, is immediately apparent and clearly justifies channel access control in the scenario considered, that is, with the given set of design parameters... with the small modification compared to PRMA that users in the MINI SILENCE state keep their reservation, but otherwise under exactly the same conditions as considered here Such an approach would not make sense in conventional PRMA, since Pdrop can only be decreased if users relinquish their resource during mini-gaps In a CDMA environment, on the other hand, at least when random coding is assumed, it... standard deviation σpc of 1 dB according to the model outlined in Subsection 5.2.6 and with CAFs (both heuristic and semi-empirical) optimised for this specific value of σpc Figure 7.16 shows these results, together with the respective results for MVB and the ones for RAP, the latter corresponding to those in Figure 7.2 Note that in case of SECAF and σpc = 1 dB, three different access functions were used . Poisson distributed, this distribution will be used in the following. If we ignore the fact that a continuous distribution is being compared with a discrete distribution,. binomial distribution, provided that α v  1andM large (e.g. α v < 0.05 and M>10). The first condition must hold for the variance of the binomial distribution,