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) 5 MODELS FOR THE PHYSICAL LAYER AND FOR USER TRAFFIC GENERATION In general, sophisticated communication systems are designed according to the concept of layering, often adhering to the OSI layering approach. The designer of a certain layer can then consider other layers as black boxes, which provide certain services defined in terms of functional relations between their respective inputs and outputs. She does not have to worry about the details of implementation of the next lower layer, but must only be aware of the services it provides. Conversely, she has to be sure that the layer being designed will cater for the services required by the next higher layer. As we want to investigate the performance of multiple access protocols, we are inter- ested in the MAC sub-layer, which will make use of the services provided by the physical layer. We must therefore assess the performance of the latter, or indeed, establish the rele- vant functional relations. Several options on how to model physical layer performance will be discussed and the models chosen for the performance assessment of a few multiple access protocols presented in Chapters 7 to 9 outlined in the following. Regarding the relationship between the MAC sub-layer and higher (sub-)layers, of major concern here is the traffic coming from the latter, which has to be handled by the MAC making the best possible use of the available physical link(s). Where exactly (in terms of layers) this traffic is generated depends very much on the service considered, but is not of interest here. What is relevant is only the quantity and the temporal characteristics of this traffic as seen by the MAC sub-layer (and hence as delivered by the RLC sub-layer). For this purpose, traffic models are defined, which will then be used for the performance assessment of the MAC solutions investigated in later chapters. These include a model for packet-voice as an example of real-time packet data traffic, and models for Web browsing and email transfer as examples for non-real-time traffic. Furthermore, some aspects relating to video traffic are discussed. 5.1 How to Account for the Physical Layer? 5.1.1 What to Account For and How? To carry traffic across the air interface, the MAC layer will use the services provided by the physical layer. The fundamental question that arises is: under what conditions can 222 5 MODELS FOR THE PHYSICAL LAYER AND FOR USER TRAFFIC GENERATION the physical layer be expected to deliver this traffic successfully to the peer MAC entity? This may not only depend on the input from the MAC layer (e.g. the number of bursts or packets to be carried at any one time), but also on conditions not directly under the influence of the MAC layer, e.g. the current state of the radio channel. As far as the latter is concerned, one would expect the physical layer designer to include means that allow provision of the required degree of reliability, such as appropriate FEC protection in combination with interleaving to combat the effects of fast fading. Since increased reliability comes at the cost of reduced capacity, certain reliability problems will almost always prevail at the physical layer of a mobile communications system due to the typically adverse propagation conditions experienced on radio channels. It is possible to include these effects in the functional relations to be established by appropriate statistical modelling. However, for MAC layer performance optimisation of primary concern are the direct interdependencies between MAC and physical layer, and the main focus will be on modelling these. All the same, one has to be aware that the physical layer may fail to deliver information over the air irrespective of the behaviour of the MAC layer. The physical layer model established in the following will predominantly be used for investigating MD PRMA performance on a hybrid CDMA/TDMA air interface. The fundamental functional relation of interest in this case is the error performance of the physical layer as a function of the number of bursts or packets carried in a time-slot. The error performance may also depend on particular spreading codes selected by the terminals (in particular, code collisions will affect error performance) and on the distribution of the power levels, at which the different bursts or packets are received by the base station. The latter is actually something that can only partially be controlled by the system, and is significantly affected by propagation characteristics. There are two fundamental approaches to establish these functional relations: • through use of appropriate mathematical approximations of the error performance; or • through detailed assessment of physical layer performance, often via simulation. 5.1.2 Using Approximations for Error Performance Assessment It would be nice if the physical layer performance could be approximated with reasonable accuracy by a set of formulae readily available from literature, preferably parameterised in a manner that permits different operating conditions to be investigated easily. MAC layer investigations could then be carried out without having to undertake detailed phys- ical layer investigations first. Such approximations of the error performance for CDMA systems, such as the well known standard Gaussian approximation (SGA), have indeed been discussed widely in the literature and will be considered in the next section. The simplest way to detect direct-sequence CDMA signals is to use a simple correlation receiver or matched filter, which detects a single path of the wanted signal. MAI is treated as noise. Multipath propagation does normally not result in undesired signal distortion, since the correlation receiver can lock onto and resolve paths individually 1 . Unfortunately, 1 A path can be resolved by a Rake receiver, if its temporal separation from other paths is at least equal to the chip duration T c . 5.1 HOW TO ACCOUNT FOR THE PHYSICAL LAYER? 223 replicas of the signal to be detected arriving through other paths will manifest themselves as self-interference, which will affect the error performance. To improve performance, Rake receivers are commonly included in CDMA system design concepts (e.g. Refer- ence [12]). In a Rake configuration, several correlation receivers lock each onto a different path, and the individual signals are combined, which allows a path diversity gain to be achieved. Whether simple matched filters or Rake receivers are implemented, MAI is the main limiting factor to the error performance. Thus, to reduce errors further, the level of MAI has to be reduced, for instance through methods such as interference cancellation or joint detection (see below), or through the use of antenna arrays at the base station. It is possible to invest arbitrary effort in error performance approximation, to account for the effect of multipath propagation, use of Rake receivers, and even antenna arrays [242,243]. However, the potential benefits of using such approximations in the context considered here do not justify the added complexity involved. Instead, when assessing the impact of MAI on MD PRMA performance, a standard Gaussian approximation for simple correlation receivers will be used, multipath propagation will be ignored, and it will be assumed that power fluctuations are compensated by power control. However, the impact of power control errors on error performance will be studied. This ‘standard Gaussian model’, which is described in Section 5.2, can be used on its own to establish the error performance of the physical layer, while ignoring code-assignment matters. Alternatively, as outlined below, it can be combined with a ‘code-time-slot model’ to account for code assignment and potential code collisions. 5.1.3 Modelling the UTRA TD/CDMA Physical Layer A very important issue in CDMA systems is power control. In order to avoid capacity degradation due to the near-far effect, the power radiated by the different users on the uplink should be controlled tightly, such that each user’s signal is received by the base station at a power level which correspond as closely as possible to a certain reference power level. Unfortunately, due to the fast power fluctuations caused by fast fading, it is impossible to control the power perfectly. Tight power control is particularly difficult to achieve in a hybrid CDMA/TDMA system, since closed-loop power control cannot be fast enough. In fact, Baier argues that the introduction of a TDMA component in a CDMA system with single-user detection (whether this be a single correlation receiver or a Rake receiver) will be virtually impossible for exactly this reason [109] and that multi- user detection should be used instead. In his research group, physical layer solutions were developed for hybrid CDMA/TDMA systems which incorporate joint detection (JD) of all signals transmitted in a time-slot, such that the near-far problem can be resolved without requiring tight power control (e.g. Reference [13]). Such an approach was also adopted for the UTRA TD/CDMA mode. One could argue that with the fast and accurate open-loop power control possible in TDD configurations with alternating up- and downlink slots (see Section 6.3), joint or multi-user detection would not be required. However, TDD with alternating slots is limited to small cells, and multi-user detection schemes would still be required in all other cell types. Furthermore, according to Reference [86], the accuracy of open-loop power control is in general not very good due to terminal hardware limitations 2 . 2 For completeness, it is reported that a Japanese company proposed a wideband CDMA system with a TDMA element and without mandatory multi-user detection in the early phases of the UTRA standardisation, but also 224 5 MODELS FOR THE PHYSICAL LAYER AND FOR USER TRAFFIC GENERATION Unfortunately, convenient approximations of the error performance of TD/CDMA with JD do not exist yet, since the detection algorithms used are rather complex. An alternative would be to establish the physical layer performance through simulation. The snapshots produced with such simulations, however, are only valid for very specific scenarios, thus not allowing for easy generalisation. It is possible to overcome this limitation, but at the expense of complex interfacing between physical layer simulations and higher layer simulations. These interfacing issues have actually resulted in a string of dedicated publications (e.g. references [227–229]). To adopt such approaches, it is necessary to process the results obtained during physical layer simulations in a particular manner. In TD/CDMA, to perform joint detection, the receiver must be able to estimate reliably the channels of all users transmitting in the same time-slot. This requires inclusion of training sequences in the burst format, and limits the number of users that can simultane- ously access a time-slot and the number of spreading codes available in this slot (note that a single user may transmit on more than one code in a particular time-slot). As a general rule, the fewer the number of users, the more codes are available, but the relationship is not straightforward [90]. Here it is assumed that every user is allocated only one code. This results in a fixed number of codes per time-slot, and thus in a rectangular grid of code-time-slots representing a TDMA frame, as for instance shown in Figure 3.13, each being able to carry a burst or a packet. With the above considerations on the problems of assessing physical layer performance in mind, the simplest possible model is adopted for TD/CDMA in Section 5.3, namely that of the perfect-collision channel. This is probably also the most commonly used approach for MAC investigations. In this model, if only one user accesses a particular code-time- slot, its burst is assumed to be transmitted successfully, but if more than one user accesses that slot, a collision occurs and all bursts involved in this collision are assumed to be corrupted. This model is very basic; in particular it does not account for MAI. However, since JD will at least partially eliminate the dominant source of MAI, namely intracell interference, it is a reasonable approximation, provided that: • strong FEC coding is used; and • the number of code-slots provided per time-slot and the reuse factor are chosen such that the intercell interference level is tolerable even in case of fully loaded cells (i.e. the system is blocking limited). The major drawback of this ‘code-time-slot model’ is that individual code-slots in a time-slot are considered to be mutually orthogonal, and it is assumed that even excessive intracell interference created by contending users in a particular time-slot will not affect users holding a reservation in the same slot. Unfortunately, JD cannot completely remove intracell interference, particularly not that of contending users. To model at least quali- tatively the impact of non-orthogonality on the protocol operation, the models presented in Sections 5.2 and 5.3 will be combined in Section 5.4. Collisions on individual code- time-slots will again result in the erasure of the bursts involved in the collision, but on top of that, the error performance of all bursts in a particular time-slot will depend on the total level of interference in that time-slot. pointed at the power control problem. Presumably, also the hybrid CDMA/TDMA candidate systems submitted in early phases of the GSM standardisation process (see Reference [3]) did not mandate multi-user detection. 5.2 ACCOUNTING FOR MAI GENERATED BY RANDOM CODES 225 5.1.4 On Capture and Required Accuracy of Physical Layer Modelling The possibility of the receiver capturing one of several colliding bursts is ignored in the following. The qualitative behaviour of the protocols to be investigated would not be affected by capture. Quantitatively, protocol performance would improve without any particular precautions being required other than modifying update values in the case of backlog-based access control as outlined in Reference [131] (see also Sections 3.5 and 4.11). On a more general note, it must be repeated that it would be beyond the scope of this book, which is concerned with multiple access protocols, to assess the physical layer performance in various environments in great detail. As long as it is made certain that the suggested protocol can cope conceptually with all possible effects affecting physical layer performance (whether for the better such as capture, or for the worse such as some residual errors), it is justifiable to focus on those effects that have a fundamental impact on protocol operation. These effects are collisions of bursts or packets and, where a CDMA component is considered, the impact of multiple access interference. Correspondingly, while protocol multiplexing efficiency and access delay performance will be investigated, with respect to the limitations of the physical layer models used, it would be unwise to quote any spectral efficiency figures. 5.2 Accounting for MAI Generated by Random Codes 5.2.1 On Gaussian Approximations for Error Performance Assessment In CDMA systems, MAI is usually generated by a large number of users. Applying the Central Limit Theorem (CLT), one would therefore expect its distribution to be Gaussian. If this were the case, and if the variance were known, the approximate bit error rate P e could be calculated using the error function. Pursley proposed to do exactly this in 1977. Furthermore, expanding on a paper from 1976 [244], he provided expressions for the variance in direct-sequence CDMA (DS/CDMA) systems, with random coding and BPSK modulation, as a function of the spreading factor or processing gain X, the number of simultaneous users K and additive white Gaussian noise [245]. This approximation is now commonly referred to as the standard Gaussian approximation (SGA) [246]. The CLT in its strictest form states that the sum of a sequence of n zero-mean inde- pendent and identically distributed (i.i.d.) random variables with finite variance σ 2 will converge to a Gaussian random variable as n grows large. Using random spreading sequences and assuming perfect power control, such that the power level received from each mobile user at the base station is the same, the CLT in its strictest form can indeed be applied, since each user looks statistically the same to the base station. We would therefore expect the SGA to deliver accurate results when the number of simultaneous users K is large, but might have to expect accuracy problems for small K. Indeed, Morrow and Lehnert found that for small K, when the phases and delays of the inter- fering signals are random, the MAI cannot be accurately modelled as a Gaussian random variable. Thus, SGA delivers only reliable P e values when K is large [246]. Particularly 226 5 MODELS FOR THE PHYSICAL LAYER AND FOR USER TRAFFIC GENERATION inaccurate (overly optimistic) results are obtained for large values of the spreading factor X combined with small values of K. The shortcomings of SGA can be overcome by an improved Gaussian approxima- tion (IGA) proposed by Morrow and Lehnert in Reference [246]. In Reference [137], the same authors demonstrate how to reduce the computational complexity of IGA. However, even this simplified approach entails complex calculations to determine P e .IfafixedX and perfect power control are considered, and only the MAI to the wanted user created by K − 1 other users needs to be accounted for to assess P e ,suchP e (K) values can be calcu- lated once for the desired range of K and then simply looked up when required. Courtesy of the authors of Reference [247], Perle and Rechberger, such results were available to us for the investigations reported in References [136] and [31]. In Reference [247], Perle and Rechberger propose an approach to extend IGA for unequal power levels, which requires establishing first the power level distribution, and then involves similar calcu- lations as in Reference [137]. Again, this approach is quite complex, and would require separate calculations for every scenario that results in a different power level distribution. Furthermore, the approach would need to be further extended to account for interference created by users dwelling outside the test cell considered. The interested reader is referred to a fairly recent letter by Morrow, which provides a good summary on the issues discussed above and the relevant results reported in Refer- ence [248]. As a matter of fact, we would have welcomed this letter to appear some years earlier. The letter reports successful endeavours by Holtzmann to simplify IGA greatly for equal power reception without compromising too much on accuracy, and provides further simplifications to this approach. According to the letter, this simplified IGA (SIGA) can also be extended easily to the unequal power case. Such an extended SIGA could have been attractive for our investigations. However, it is perfectly justifiable to use SGA for our purposes for the following reasons. • We are mostly interested in small X, in which case the difference between SGA and IGA is not so large (see Reference [246]). • To maximise the normalised throughput, quite strong FEC coding is applied. In this case, the values of K for which SGA underestimates P e will result in a packet success rate of 1 anyway, whether SGA or IGA is used [31]. • SGA can easily be extended to unequal power reception. While this violates the i.i.d. requirement of the strongest form of the CLT, a weaker form can be invoked, which requires that at least the variances of the individual contributors should be of the same order 3 . Unequal power reception of intracell interferers (which should dominate intercell interferers) will be due to power control errors. If these errors are small, the variances should indeed be of the same order. If they become too large, problems with limited accuracy of SGA will be overshadowed anyway by severe degradation of system performance to the point where the system being considered becomes useless. • Finally, physical layer models in investigations dedicated to the MAC layer will always be subject to some simplifications (e.g. we are ignoring multipath fading). 3 Actually, according to Reference [249], the weakest form of the CLT requires that every single contributor shall only make an insignificant contribution to the sum of contributions. 5.2 ACCOUNTING FOR MAI GENERATED BY RANDOM CODES 227 Small accuracy problems within the framework of the simplified model are negligible compared to the inaccuracies caused by these simplifications. In the following, the physical layer performance is assessed in terms of the bit error rate or BER and of the packet success probabilities. SGA is used to evaluate the BER. 5.2.2 The Standard Gaussian Approximation The standard Gaussian approximation for DS/CDMA systems is derived in detail in Refer- ence [245] and makes use of results from Reference [244] to provide a value for the MAI variance for the case of random coding and equal power reception. Extending SGA to unequal power reception is fairly straightforward. Here, the system model consid- ered is briefly introduced and the SGA expression used for performance assessment is reported. A detailed derivation of SGA in the unequal power case was provided in Reference [31]. The transmitted signal of user k, using BPSK modulation, is written as s k (t) =  2P k a k (t)b k (t) cos(ω c t + θ k ), (5.1) with spreading sequence (also called direct or signature sequence) a k (t), data sequence b k (t), carrier frequency ω c , transmitted power level P k and carrier phase θ k . The data sequence b k (t) is made up of positive or negative rectangular pulses of unit amplitude and bit duration T b . The sequence a k (t), on the other hand, is also made up of rectan- gular pulses of unit amplitude, but now with duration T c , the so-called chip duration. Random direct sequences are used, i.e. Pr{a (.) j =+1}=Pr{a (.) j =−1}=0.5, where a (.) j is an arbitrary chip j of the direct sequence. This is why the section title refers to random codes. The length of the sequence is equal to the spreading factor or processing gain 4 X = T b /T c , with X ∈ℵ. In other words, the sequence is randomly chosen to spread the first bit, but repeated for subsequent bits. In a system in which K simultaneous mobile users transmit according to Equation (5.1), the total signal received at the base station can be written as r(t) = n(t) + K  k=1  2 P k α k a k (t − τ k )b k (t − τ k ) cos(ω c t + ϕ k )(5.2) where τ k is the propagation delay, α k is the propagation attenuation experienced, such that the received power level amounts to P k /α k ,andn(t) is the additive white Gaussian noise (AWGN). Here, ϕ k = θ k − ω c τ k + ψ k with 0 ≤ θ k < 2π and ψ k the phase-shift due to fading. If user i is to be detected, we can assume ϕ i = τ i = 0, as only relative delays and phase angles need to be considered. On the other hand, on the uplink of a mobile communication system it is rather difficult to achieve ϕ k = τ k = 0fork = 1 .K, k = i. Instead, carrier phases ϕ k are assumed to be uniformly distributed in the interval [0, 2π), and chip delays τ k in the interval [0,T b )fork = i. 4 If FEC coding is used, the redundancy introduced through coding may be considered as part of the processing gain, in which case spreading factor X and processing gain are not equal. 228 5 MODELS FOR THE PHYSICAL LAYER AND FOR USER TRAFFIC GENERATION In the following, it is assumed that the dominant interference contribution is MAI, and AWGN is ignored. The average BER or probability of bit error P e can then be calculated using P e ≈ Q(SNR), (5.3) with Q(x) = 1 √ 2π  ∞ x e −u 2 2 du, (5.4) and the short-term average signal-to-noise-ratio SNR =      3X · P i α i  K k=1 k=i P k α k (5.5) For equal power reception, that is if P k /α k = P for k = 1, 2, .,K, Equation (5.5) reduces to the well known SNR =  3X K − 1 .(5.6) Similar expressions reported in Reference [246] and summarised in Reference [248] can be obtained, if either phases, or chips, or both together are aligned. These cases are not relevant for the uplink considered here, but may be of interest for the downlink of a mobile communications system and, with limitations, for the uplink of synchronous CDMA systems such as the synchronous UTRA TDD mode envisaged to be introduced as part of further UMTS developments. 5.2.3 Deriving Packet Success Probabilities Transmitting a packet of length L bits over a memoryless binary symmetric communica- tion channel with average probability of data bit success Q e = 1 − P e yields a probability of packet success Q pe of Q pe = e  i=0  L i  ( 1 − Q e ) i ( Q e ) L−i ,(5.7) when a block code is employed which can correct up to e errors. At this point, a problem ignored until now pertaining to both SGA and IGA needs to be addressed. Normally, phys- ical layer design parameters will be chosen such that, at least for mobiles at moderate speed, the channel is quasi static during the transmission of a burst or packet 5 . Because of this, the assumption underlying these approximations, that delays and phases of the interfering users are random, is violated. While they may be randomly selected at the start of a packet, they will essentially remain constant over its duration. This in turn will introduce dependencies between bits in errors or, put differently, the channel will have memory. If one bit is in error, there is an increased likelihood that the next bit 5 In the physical layer context, a packet is equivalent to a burst, i.e. a data unit transmitted in a single (code-)time-slot. 5.2 ACCOUNTING FOR MAI GENERATED BY RANDOM CODES 229 will also be in error, which has also implications on the calculation of the success rate of packets that are protected by error coding. Use of SGA or IGA to establish P e and subsequent use of Equation (5.7) to establish Q pe could therefore cause inaccurate results. Such issues are addressed in detail in Reference [246], where a method for calcu- lating packet success probabilities using IGA, which correctly accounts for bit-to-bit error dependence, is introduced. It is shown that, in systems appling error correction coding, the techniques that ignore error dependencies are optimistic for a lightly loaded channel and pessimistic for a heavily loaded channel. In other words, if error dependencies were correctly accounted for, the slope of Q pe [K] depicted in Figure 5.2 (see next subsec- tion) would be flatter. For two reasons, these issues are ignored in the following and Equation (5.7) is resorted to for the calculation of Q pe : application of interleaving and coding over several bursts should at least partially eliminate error dependencies 6 .Further- more, the impact of flatter slopes on system performance will be investigated anyway in the context of power control errors. 5.2.4 Importance of FEC Coding in CDMA According to Lee, coding is always beneficial and sometimes crucial in CDMA applica- tions [6]. Results reported in References [137,247,250,251] confirm this statement 7 . In digital cellular communication systems currently operational, a combination of convo- lutional coding and block coding is often used. Typically, a Viterbi decoder carries the main burden of error correction at the receiving end, thus convolutional coding is applied for error protection. Block coding is then applied in the shape of cyclic redundancy checks, i.e. some parity bits are added, which allow in GSM for instance detection of whether a voice frame is bad or good. For mathematical convenience, the focus here is on block FEC coding only. As in References [137] and [247], the Gilbert–Varshamov-Bound is used to account for the redundancy required to correct a certain number of errors and assess the code-rate r c which maximises the normalised throughput S.Oncer c is determined, a BCH code [252] with appropriate parameters is selected. The bandwidth-normalised throughput S is defined as S = r c · K pe max X ,(5.8) with K pe max = max K=1,2, .  K   P pe [ K ] ≤  P pe  max  ,(5.9) where P pe [K] = 1 − Q pe [K]isthepacket error probability,andK pe max is the number of users supported at a certain tolerated maximum packet error probability (P pe ) max . Equal power reception is assumed to determine P pe [K] using Equation (5.7). 6 For a detailed discussion on coding, channel memory, and interleaving, see e.g. Chapter 4 in Reference [3]. 7 Prasad identified certain scenarios in which it makes more sense to increase the processing gain through increase of the spreading factor X rather than to introduce FEC redundancy [26, p. 128]. However, in most scenarios considered, his investigations also underlined the benefits of FEC coding. 230 5 MODELS FOR THE PHYSICAL LAYER AND FOR USER TRAFFIC GENERATION The Gilbert–Varshamov bound is employed to account for redundancy. According to Reference [253], for any integer d and L with 1 ≤ d ≤ L/2, there is a binary (L, B) linear code with a minimum Hamming distance d min ≥ d, such that r c ≥ 1 − h  d − 1 L  ,(5.10) where h(p) =−p log(p) − (1 − p) log(1 − p) is the binary entropy function, L is the size of the packet and r c the code-rate. Such a code will correct at least e = d min − 1 2 (5.11) errors and have B = r c · L message bits. Figure 5.1 shows S as a function of r c for X = 7andX = 63, and values of one per cent and one per thousand for (P pe ) max , respectively. For reasons outlined in Chapter 7, the number of message bits B is kept at 224. The steplike behaviour of the effective throughput can be explained by the fact that K pe max can only be increased by steps of one user at a time, hence decreasing the code-rate will reduce S in spite of increasing e, as long as no additional user can be supported. The reason why the throughput is higher for X = 7 is because self-interference is ignored. Subtracting the desired user, e.g. in the denominator of Equation (5.6), increases the SNR the more, the lower X. Irrespective of X, the optimal code-rate is in the range of 0.4 to 0.6. BCH codes are efficient block codes and therefore often used. A possible BCH code with r c = 0.45 which supports around 224 message bits is one with L = 511 bits, B = 229 bits Normalised throughput S 0.9 0.7 0.5 0.3 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 Code-rate r c B = 224 bits for Gilbert-varshamov bound ( L , B , e ) = (511,229,38) for BCH code X = 7, ( P pe ) max = 0.01 X = 63, ( P pe ) max = 0.01 X = 7, ( P pe ) max = 0.01, BCH X = 63, ( P pe ) max = 0.01, BCH X = 7, ( P pe ) max = 0.001 X = 63, ( P pe ) max = 0.001 X = 7, ( P pe ) max = 0.001, BCH X = 63, ( P pe ) max = 0.001, BCH Figure 5.1 Impact of the code-rate on the normalised throughput [...]... Pareto distributed with parameters eβ and λ, then ln(X) − β is distributed according to an exponential distribution with parameter λ The mean of the Pareto distribution is µ= λ(eβ ) , λ−1 λ > 1, (5.27) and the variance is only finite for λ > 2 In Reference [56], eβ is equal to 81.5 and λ is chosen to be 1.1, which would result in an infinite variance In order to ensure finite variance, a truncated Pareto distribution... for an email log file with 15 000 samples in Figure 5.12 with Sd up to 5.6 Mbytes, normally feature a distinctly elongated tail Correspondingly, mean email sizes are large Therefore, a prime candidate distribution to model email size is the Pareto distribution There are, however, some problems First, according to Equation (5.25) both minimum size and mode are equal to eβ , whereas from histograms with... of packet call requests per session Npc is a geometrically distributed random variable with a mean number of packet calls µNpc = 5 The reading time, Dpc , between two consecutive packet call requests in a session, which starts when the last packet of a call is completely received by the receiving side, is distributed according to a geometrical distribution (in terms of simulation time steps, here Dslot... slightly different with PRMA on hybrid CDMA/TDMA, as discussed in Chapter 7 244 5 MODELS FOR THE PHYSICAL LAYER AND FOR USER TRAFFIC GENERATION give up their reservations during a mini-gap and therefore have to contend for every mini-spurt, leading to increased dropping during a principal spurt, offsets the lower activity factor in certain cases [142] For a complete description of the voice model, the distribution... considered for the overall performance assessment of the different UTRA candidates Among the traffic models, a model for Web browsing was proposed in which a session is made up of several packet calls that in turn contain multiple packets or datagrams (Figure 5.10) This model was suggested for both link directions, and will therefore be used for the uplink direction in our investigations The number of packet... the spatial distribution of mobiles in the cell, the pathloss coefficient γpl , and the shadowing standard deviation σs In particular, since γpl is assumed to be distance-independent, I intercell does not depend on the cell radius r0 It is therefore possible to account for the average intercell interference without having to consider more than one cell by evaluating I intercell for the distribution... Dslot µDpc , an exponential distribution with mean µDpc can be used instead The number of packets in a packet call Nd is again geometrically distributed and has a mean µNd of 25 packets For the time interval Dd between the start instances of two consecutive packets inside a packet call, again an exponential distribution is used here with mean µDd = 0.5 s instead of the geometric distribution suggested in... packets or datagrams in bytes is modelled using a Pareto distribution with probability density function Instant of successful completion of transfer Instants of arrival of datagrams at RLC Packet call with Nd = 5 datagrams Sd Reading time Dpc t Dd Session with Npc = 3 packet calls Figure 5.10 Session, packet calls, reading time between calls, and individual packets or datagrams with size Sd and interarrival... possible reason for these discrepancies could be the exact spatial distribution of the interference considered Although in all references, uniform distribution is considered, it is not clear from References [9] and [251] whether this is on a per-cell-basis or over all cells If Monte Carlo snapshot simulations are performed to assess the interference, during which mobiles are repeatedly redistributed over the... browsing model is with regards to the reading time distribution Anderlind and Zander suggest an exponential distribution with a mean value of 10 s While values observed in practice may often be significantly longer, they state that ‘the chosen value is sufficiently long to necessitate a release of unused resources and short enough to be practical for simulation studies’ In fact, the value first chosen for . any one time), but also on conditions not directly under the influence of the MAC layer, e.g. the current state of the radio channel. As far as the latter. by a set of formulae readily available from literature, preferably parameterised in a manner that permits different operating conditions to be investigated