Capacity analysis of voice over IP over GERAN with statistical multiplexing

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1 Capacity analysis of voice over IP over GERAN with statistical multiplexing A. Wautier, J. Antoine, L. Husson, J. Brouet, C. Thirouard Supélec, Dpt. Radioélectricité et Electronique, Plateau de Moulon, Gif-sur-Yvette, France, Alcatel CIT, Research & Innovation, Route de Nozay, Marcoussis, France Abstract: Key words: The requirements in terms of service flexibility, spectrum efficiency and speech quality introduce new challenges when voice is transmitted over packet and over wireless. This paper analyses the perceived voice quality when voice frames are transported on packet radio bearers of GSM/EDGE Radio Access Networks (GERAN) and are statistically multiplexed. The resulting quality depends on the link layer quality, on the scheduling and on the header compression algorithms. This paper identifies the range of capacity gain obtained with statistical multiplexing for a given speech quality considering the different radio bearers of GERAN. Voice over IP over Wireless, wireless Internet, statistical multiplexing. 1. INTRODUCTION Today, circuit-switched radio cellular systems like GSM offer good service quality and spectrum efficiency, but provide very little service flexibility. Recently, GPRS (General Packet Radio Service) and its enhanced version EGPRS, which makes use of a modified physical layer EDGE (Enhanced Data Rates for GSM Evolution), have been introduced to support efficient data transmission (e.g. interactive IP Internet Protocol- services like web browsing or WAP) in GSM wireless access. In future all-ip cellular networks, all types of services (real-time or not), will be carried by a unique network infrastructure from the core to the access networks serving the end-users. In particular, in the future releases of GERAN (GSM/EDGE Radio Access Network), end-to-end packet transmission of real-time IP applications is planned to support, for instance,

2 A. Wautier, J. Antoine, L. Husson, J. Brouet, C. Thirouard IMS (Internet Multimedia Services) using GPRS/EGPRS radio bearers. In this context, voice packets of different users can be dynamically multiplexed on the same packet data radio channels (PDCH). They may also be multiplexed with packets coming from other services. When voice is transmitted over IP and over wireless, the requirements in terms of service flexibility, spectrum efficiency and speech quality introduce additional challenges. This paper deals with VoIP over GERAN. In particular, it evaluates the benefit of statistical multiplexing, which exploits silence periods in speech, in the evaluation of the capacity for a quality of service measured by a speech quality estimator and by considering the different packet radio bearers of GERAN. The paper is organized as follows. Section 2 gives an overview of the different aspects of the transmission of voice over IP in the GERAN context. Section 3 presents the simulation models we used for capacity evaluation. Section 4 presents some results followed by concluding remarks. 2. TRANSMISSION OF PACKETIZED VOICE Key features, when designing voice services over IP for cellular radio links, are spectrum efficiency and robustness to transmission errors. This section provides a short overview of VoIP over GERAN specific issues. 2.1 Header compression One of the problems encountered with IP over wireless is the large overheads introduced by IP and other higher layer protocol headers such as UDP (User Datagram Protocol) and RTP (Real-time Protocol). These headers are used to transmit each packet to the correct host with the appropriate application in the correct order and at the right time. In case of real time IP services, IP/UDP/RTP protocol stack is used to convey the media frames. When transporting packet voice frames, the length of an IP/UDP/RTP header (40 bytes for IPv4 and 60 bytes for IPv6) is larger than the payload. Namely, for the GSM Enhanced Full Rate (GSM EFR) codec this corresponds to a payload of 30.5 bytes every 20 ms. Header compression is essential for spectrally efficient transmission of VoIP and is implemented as a three phase process: initial context establishment by exchange of uncompressed header, regular context updates by transmission of compressed headers, context restoration in case of excessive errors in the header decompression. The compression algorithms must be efficient and

3 Capacity analysis of VoIP over GERAN with statistical multiplexing robust against errors to be used on the air interface. The CRTP (Compressed RTP) algorithm [1], which is used for wireline VoIP, is not robust enough for wireless links: if a compressed header is lost, the decompressor is not able to reconstruct the subsequent headers (error propagation). Then, a single packet error causes several consecutive lost packets (headers + voice payloads). Some more adequate algorithms as ROHC (RObust Header Compression) have been proposed [2]. ROHC is significantly less sensitive to radio link errors thanks to repair mechanisms in the decompressor (no error propagation) and reduces IP/UDP/RTP-packet header sizes down to only 2 bytes most of the time [3]. In this paper, it is assumed that the additional frame error rate due to header compression is negligible compared to the other sources of errors further discussed in the following. 2.2 EGPRS Radio link layer EGPRS is an evolution of GSM. Its air interface uses main basic physical layer parameters of GSM (carrier spacing, TDMA frame and burst structure), with the additional possibility of adaptive modulation: 8PSK modulation is used instead of GMSK modulation when the radio link conditions are favorable, which significantly increases the throughput. Besides, different transmission rates are available. Depending on the chosen modulation and coding scheme (MCS), the data rates range from 8.8 kbit/s (MCS-1) to 59.2 kbit/s (MCS-9) per time-slot (cf. Table 1). Modulation RLC Data Unit (bytes) Maximum bitrate (kbit/s) Code Rate Number of 30.5 byte-speech frames per block MCS-9 8-PSK 2x MCS-8 2x MCS-7 2x MCS MCS MCS-4 GMSK MCS MCS MCS Table 1 GERAN: EGPRS radio bearers The channel coding schemes are derived from the same convolutional code, having a rate of 1/3 and constraint length of 7 by applying different puncturing schemes [4]. It should be noted that all information bits are equally protected. The transmission on the radio interface in EGPRS is based on radio blocks transported by 4 bursts (time-slots) in 4 consecutive TDMA frames. The interleaving scheme is rectangular and limited to a depth of 4 frames. This structure in radio blocks enables a highly dynamic resource

4 A. Wautier, J. Antoine, L. Husson, J. Brouet, C. Thirouard sharing on each PDCH: from one radio block to the next one, the resource can be used by different users. 2.3 Mapping voice on GERAN bearers GSM voice codecs implement variants of LPC (Linear Predictive Coding). It consists in analyzing voice frames of 20 ms in order to identify the parameters of the model (e.g. autoregressive filter coefficients and source samples), which are themselves coded in a very efficient way to reduce the bit rate. The bits of a coded frame have different degrees of importance and are divided in 2 classes, namely class I and class II. Class I is further divided into two sub-categories: class Ia and class Ib. The error free reception of class Ia bits is essential for reconstructing the original speech frames. Class Ib bits can tolerate some residual errors, and class II bits tolerate higher error rate. In a circuit-switched GSM voice transmission, the protection provided by channel coding is hierarchical and adapted for each bit class. If GSM EFR voice frames are transported by an EGPRS bearer, the same protection is provided for all the bits (MCS-3 provides a 0.85 code rate for example). Then, class Ia bits may not be enough protected and class II bits may be over-protected. An improvement may consist in splitting the bits over different radio blocks having different levels of protection [5]. Actually, the mapping strategy has a significant impact on perceived speech quality as exposed in [5]. EGPRS radio bearers provide a wide range of data rates on the air interface. Therefore, several voice frames from the same user can be transported on the same radio bearer. This number is a function of the MCS and of the codec as indicated in Table 1 for HR (Half Rate), FR and EFR codecs. Obviously, this enables to increase the number of serving channels on the same time slot. For instance, MCS6 bearer conveys 2 EFR voice frames (equivalent to 40 ms) per radio block (i.e. 20 ms) and then, the available number of serving channel is Bursty nature of voice and statistical multiplexing It is well-known that voice consists of a succession of talk-spurts and silences. If the voice codec has means to quickly detect transitions from talkspurts to silences and vice versa, then, voice packet streams become bursty. GSM vocoders deliver 20 ms frames regularly during talk-spurts and no frames (or few silence description frames) during silences. In a wireless

5 Capacity analysis of VoIP over GERAN with statistical multiplexing packet transmission, a traffic channel can be assigned to a mobile user only during the talk-spurts. The bursty nature of voice can either be used to pack additional users through statistical multiplexing [6-8], or to convey other data information streams, which can be either real-time or not, from same or other users [8]. In this paper only statistical multiplexing of voice is addressed as in [6]. Actually, the scheduler exploits the silence periods to pack in more users in average than the number of available serving channels, which enhances the offered traffic per cell. However, it may happen that the number of voice frames coming from several users is higher than the available number of serving channels. Those extra frames can then be buffered and transmitted later. Nevertheless, as voice service has very a stringent constraint on the end-to-end transmission delay, the size of the buffer must be limited. If the buffer overflows, packets that could not be delivered in time have to be discarded. With statistical multiplexing, the increase of the number of admitted calls (which gives the offered traffic gain) is then limited by the acceptable speech quality of those calls, which is sensitive to the number of shared serving channels, to the selected MCS, to the chosen buffer size, and to the voice activity factor. Consequently, a tradeoff between the increase of delay and the packet loss rate has to be optimized Finally, overall capacity gain should also take into account the reuse factor, which can be deduced from systemlevel signal-to-noise ratio (SNR) simulations [9]. 2.5 Voice quality evaluation In a GSM circuit-switched transmission, the speech quality is only related to the link level performance, which can measured by the following metrics: the frame error rate (FER), the residual bit error rate (RBER) on class Ib bits, and the BER of class II bits [10]. In a GERAN packet-switched transmission, these metrics cannot be reused for several reasons. First, the physical link configuration is different and is characterized by a plurality of transmission options. Secondly, statistical multiplexing (and header compression to a lower extent) causes additional packet loss and increased delays. Finally, the resulting speech quality also depends on the missing frames processing [11]. We therefore recommend to come back to the actual evaluation of perception of the speech quality to carefully analyze all the impacting parameters in VoIP over GERAN.

6 A. Wautier, J. Antoine, L. Husson, J. Brouet, C. Thirouard Speech perception is a complex process. Subjective and objective methods have been developed. Subjective tests are realized with listening tests, and the most well-known is the MOS (Mean Opinion Score) scale ranging from 1 to 5. Recently, objective methods have also been introduced. They can be divided in three groups. Comparative methods are based on a comparison between the original signal and the delivered signal. Absolute methods are based on the analysis of the delivered signal only. Finally, parametric methods exploit the network transmission parameters to evaluate the quality. The comparative methods require the simulation of the whole transmission link from mouth to ear, whereas the parametric methods allow faster evaluation assuming that the degradations due to the diverse alterations (codec, BER, FER, delay, echo,...) are additive. These alterations can therefore be studied apart and added in the degradation factor. In our study, we resorted to two complementary methods: the PESQ (Perceptual Evaluation of Speech Quality) that belongs to the first category [12], and the E-model [13] that belongs to the last one. They are further detailed in the following section. 3. SYSTEM MODELS The models developed to determine the capacity gain due to statistical multiplexing of voice over GERAN are described below. 3.1 Transmission model In this study, the radio link including modulation, radio channel, demodulation and equalization (DFSE, Decision Feedback Sequence Estimator [14]) has been modeled and replaced by a two-layer hierarchical error-event model using Markov chains. This kind of flexible model permits extensive and fast characterization of wireless channels. With such a model, it is possible to analyze or to simulate burst errors and therefore to compute analytically or by simulation the bit error rate for any channel coding/interleaving scheme [15]. The first model dedicated to channels with memory has been suggested by Gilbert-Eliot, which is a two-state Markov model where the states are called good and bad states. Fritchman extended this model to an M-state Markov model with K good states (with error-free events) and M K bad states (with error events), where there is no transition neither between good states nor between bad states (cf. figure 1) [16].

7 Capacity analysis of VoIP over GERAN with statistical multiplexing Good states Bad states Fig. 1 - Fritchman channel model A two-layer hierarchical model is more relevant for wireless channels. It consists of an external and of an internal chain sub-models. The external chain gives the time variations of the mean energy per bit for each time-slot (in GSM, the energy is assumed to be constant on a GSM burst). It can either be modeled by a Markov chain [17] or be simply obtained from the random multi-path Rayleigh fading impulse response model. The internal chain models the distribution of the bit errors at the output of the equalizer over a time-slot. This chain can be modeled by a Fritchman Markov model [16], which is characterized by the number of bad/good states associated to error/error-free events and by the matrix [p ij ] giving the probabilities of transitions between states. Such a transition probability matrix must be computed for each state of external chain. Different matrix sets are determined for each channel type with the considered mobile speed (e.g. TU50), and for both GERAN modulations. Then, error events over a burst can be easily determined by generating state occurrences and the associated events and included in a complete transmission link. TU 50, GSM/EFR TCH/EFR MCS 3 MCS 6 MCS 1+5 FER (%) 1 0, SNR (db) Fig. 2 FER due to transmission channel

8 A. Wautier, J. Antoine, L. Husson, J. Brouet, C. Thirouard Figure 2 illustrates the results obtained with a TU50 channel model with different coding schemes encountered in GSM (TCH/EFR), in GERAN (MCS3, MCS6), and with the coding scheme (MCS1+5) proposed in [5]. The Markov model represents a transmission including modulation, radio channel, DFSE receiver structure with perfect channel impulse response estimation. The Fritchman model has 2 bad states and 2 good states. Besides, soft decisions at the output of the demodulator are considered [18, 19]. Moreover, perfect detection of erroneous frames is assumed. 3.2 Voice activity model While it is difficult to model the voice activity of a single user, Weinstein found that the number of active lines could be modeled by a continuous-time birth-death process [20]. He showed that this model is quite valid when the number of users is superior to 25. The parameters that govern the transition rates are the mean talk-spurt duration α 1 and the mean silence duration β 1. The voice activity factor η is defined by the ratio of mean talk-spurt duration to the sum of mean talk-spurt and mean silence duration: 1 α η = 1 β + α 1 Typical values encountered in the literature for the voice activity factor are (obtained with α 1 = 1.41 s and β 1 = 1.74 s ) or 0.36 (obtained with α 1 = 0.96 s and β 1 = 1.69 s). If b i j (t) is the probability of having i active lines at time t assuming that we have j admitted voice communications, the steady-state probability of having i active lines among j admitted lines is given by: b i j j = ) i i j i η ( 1 η for 0 i j 3.3 Traffic model Speech traffic is modeled by a Poisson process for call arrival and by an exponential distribution for call duration. The parameters of the model are the call rate λ and the mean call duration µ -1. The mean offered traffic intensity is equal to the product λµ 1, which is denoted by ρ in the following.

9 Capacity analysis of VoIP over GERAN with statistical multiplexing 3.4 Statistical multiplexing model The statistical multiplexing model considered in this paper, is assumed to be UAS (Uniform Arrival and Service) as in [5]. With such a model, an analytical study can be conducted as proposed in [5, 6]. The parameters of the scheduler is the number of shared serving channels c and the size of the buffer m (introducing a maximal delay D). In GERAN, the number of serving channels shared in a cell by a set of active users is restricted. Indeed, the capacity of processing of the terminals is limited. One terminal can only handle a maximum number of time-slots per TDMA frame. Besides, if the terminal has a multi-slot capability, those slots must be on the same radio frequency if multiple slots are actually used in the same TDMA frame. Therefore, depending on the terminal capabilities, either it has access to a single physical channel for the whole duration of the call or to a pool of physical channels but located on the same transceiver (TRx). The maximum feasible values for the number of serving channels c per TRx is given in Table 2 for various MCS of GERAN with GSM FR or EFR codecs assuming that all communications use the same physical link configuration. MCS type bearer c/trx MCS-9 32 MCS-6 16 MCS-3 8 MCS-1/MCS-5 8 Table 2 Maximum values for the number of serving channel per bearer The size of the pool and the number of pools per TRx will impact the statistical multiplexing capacity gain. Table 3 summarizes the number of pools p of size c per TRx (p x c) for different codecs and physical link configurations versus the mobile station (MS) multi-slot capability. MS multi-slot capability GSM FR or EFR MCS3 8x1 4x2 2x4 1x8 MCS6 8x2 4x4 2x8 1x16 GSM HR MCS3 8x2 4x4 2x8 1x16 MCS6 8x4 4x8 2x16 1x32 Table 3 Possible values for the number serving channels per TRx (pxc)

10 A. Wautier, J. Antoine, L. Husson, J. Brouet, C. Thirouard The packet loss rate can be analytically obtained for a given number of active users denoted by i assuming j admitted users. The considered voice activity model is the one described by Weinstein [20]. A packet is lost when the buffer is full (the actual number of packets in the buffer is q = m), this can of course occur only when i is greater than c. Then, the packet loss rate can be expressed as [5]: j i c Pd ( j) = [ P( n = i N = j) P( n = i, q < m N = j)] j i= c η Considering the traffic model seen in 3.3 and assuming that the maximum number of admitted users is N, the relationship between the blocking probability and the offered traffic ρ is given by the classical Erlang B formula [21]: P( N) = N N ρ N! k ρ k= 0 k! The worst case for the packet loss rate is obtained for j=n, which is given by P d (N). Voice activity model can be combined with the traffic model: the voice activity Markov chain can be viewed as a sub-chain of the traffic chain [6]. Then, assuming that the two models are independent, the mean packet loss rate is given by: P d N = P ( j) P( j) where j= c d P( j) = N j ρ j! k ρ k = 0 k! The criterion to evaluate the capacity (possible offered traffic) must take into account not only the blocking probability threshold of 2% but also a criterion about the packet loss probability, which can be either a worst packet loss rate threshold (1% for example) or a packet loss rate threshold for a given percentage of time (e. g. a threshold of 1% for 95% of time). In the latter case, the distribution of the packet loss has to be considered.

11 Capacity analysis of VoIP over GERAN with statistical multiplexing 3.5 Speech quality evaluation models Two models are used to evaluate the quality of speech: the PESQ model and the E-model. The PESQ method (Perceptual Evaluation of Speech Quality) is dedicated to end-to-end speech quality assessment of narrow band telephone networks and speech codecs [12]. The original speech samples and the same but degraded samples passed through a communication system are compared using a psycho-acoustic model of the human ear. This method is also valid for communication systems introducing distortions (e.g. time misalignment, transmission errors,...). It is thus relevant for assessing the impact of the radio link on voice quality perception. The PESQ delivers MOS scores which is convenient to make the link with other methods. In particular, the PESQ permits to calibrate some factors used in the E-model and both models are thus complementary. The E-model is a parametric model, which assumes that the degradations due to different factors are cumulative and therefore studied separately [13]. The quality measurement R uses a scale between 0 (poor) and 100 (good) which is linked to the MOS scale by the following transformation rule (it should be noted that the degradations are only cumulative in the R scale) [13]: MOS = R R (R 60) (100 R) In this paper, we consider two terms in the quality evaluation: I dd and I e. Original speech quality (Background noise effect) R = R 0 -I e -I dd Degradation due to equipments (Codec, FER) Degradation due to delay The parameter I dd depends on the transmission delay T a due to the size of the buffer and to the interleaving depth of the coding scheme. Figure 3-a plots I dd whose expression is [13]: 0 if Ta 100 ms I = ( ) ( ( ) ) ( ) = > T dd 6 1/ 6 X 6 1/ 6 log a / X with X if Ta 100ms log2

12 A. Wautier, J. Antoine, L. Husson, J. Brouet, C. Thirouard The parameter I e depends on the intrinsic quality of the codec and on the sensitivity to the FER (which includes the processing made to restore lost frames). This degradation does not come from a closed-form formula but is determined through listening tests or objective methods like the PESQ method. For example, the GSM EFR codec has an intrinsic quality of 4,32 in the MOS scale. In this paper, we used the PESQ method to determine I e. Figure 3-b gives I e in case of uniformly distributed packet loss for GSM EFR codec obtained with PESQ simulation and it is compared to the normalized MOS evaluation [13]. This actually reflects the packet dropping due to statistical multiplexing GSM EFR + lost frames processing, random FER 30 MOS norm 25 PESQ note I dd 15 Ie Delay (ms) (a) 0 0, FER (%) (b) Fig. 3 Influence of delay and FER on speech quality degradation with E-model 4. SIMULATION AND RESULTS 4.1 Capacity gain due to statistical multiplexing Achievable capacity gain due to statistical multiplexing is illustrated in figure 4 for a given size of the pool corresponding to MCS-6 radio bearer as depicted in table 3. It gives the packet loss rate P d (j) as a function of the number of admitted users j, when the size of the buffer is set for a delay from 0 to 120 ms (6 speech frame duration). For a given target of the packet loss rate, the capacity can be optimised by resorting to an increase of the buffer delay.

13 Capacity analysis of VoIP over GERAN with statistical multiplexing E[talk]= 1.41s ; E[silence]= 1.74s ; c=16 ; Delay between 0 and 6 speech frames 5% 4% packet loss probability 3% 2% 1% number of users j Fig. 4 Influence of statistical multiplexing Figure 5 illustrates the relative capacity gain as a function of the size of the channel pool for packet loss targets of 1% and 3%. It shows that the benefits of statistical multiplexing strongly depend on the size of the pool. For values of c lower than 4, no gain can be expected (critical size effect). 120% 100% Delay = 0 s, η = 0.445, E[talk]=1.4 s packet loss rate =3% 400% 300% c = 32 Delay = 100 ms Packet loss rate =1% Gain (j-c)/c 80% 60% packet loss rate =1% Gain (j-c)/c 200% 100% c = 16 c = 8 c = 4 40% 20% Fig. 5 Influence of the size of the channel pool on capacity gain for a given FER c 0% Speech activity factor η Fig. 6 Influence of the speech activity factor on the capacity gain Figure 6 depicts the relative capacity gain as a function of the voice activity factor for given sizes of the pool (c = 4, 8, 16, 32). As expected the gain is higher for lower activity factors. Moreover, there are noticeable variations when considering values belonging to the typical agreed scale (i.e. between 0.36 and 0.45, see part 3.2). In order to reduce the impact of voice activity factor in practical implementations, statistical multiplexing could be combined with a real time estimation of the activity factor.

14 A. Wautier, J. Antoine, L. Husson, J. Brouet, C. Thirouard Paket loss rate (%) c=8, j=16 E[talk]=1.41 s, E[sil.]=1.74 s,η=0.44 E[talk]=0.96 s, E[sil.]=1.69 s,,η = delay (ms) Fig. 7 Influence of delay on FER The delay and the packet loss rate are two parameters that induce different effects on the perceived quality. The resulting degradations are separately evaluated in the E-model (refer to figure 3). However, there is a dependency between delay and FER. This relationship is illustrated in figure 7, which confirms that the packet loss rate decreases as the delay is increased. Considering both influences on the quality measurement leads to a tradeoff as shown in figure 8 for the EFR codec. 74 c =32, j = 62 R (E-model) c = 4, j = Buffer delay ( ms) Fig. 8 Trade-off between degradation due to FER and delay on speech quality (EFR codec)

15 Capacity analysis of VoIP over GERAN with statistical multiplexing 4.2 Incidence of radio bearers The radio link behavior impact on the perceived speech quality has been evaluated by means of simulation. The simulator models a complete transmission chain comprising voice frame generation, coding, channel error model, decoding, and voice frame reconstruction. The channel model that is included in the simulator is a two-layer model replacing the modulationchannel-demodulation as described in 3.1. The output parameters of the simulator are the FER at the output of the decoder and the voice quality measure obtained with the PESQ method. The MOS obtained with PESQ method is converted in the R scale to be further exploited in the E-model through I e factor. Speech quality evaluation with E-model is illustrated in figure 9 for the GSM EFR codec for three different MCS as a function of the SNR. R (E-model) TU50, GSM/EFR + lost frames processing TCH/EFR R 30 MCS 3 R MCS 6 R 20 MCS 9 R 10 MCS 1+5 R SNR (db) Fig. 9 Influence of radio link performance on speech quality (no statistical multiplexing) 4.3 Capacity evaluation Offered traffic for a given quality of service defined by the blocking probability of incoming calls and by the perceived speech quality of admitted calls is calculated. This capacity can be given in a first step in Erlang per TRx, then in Erlang per cell when the number of TRx is fixed and the reuse factor can be deduced with the help of interference propagation model. Finally, once the cell size has been calculated, capacity in Erlang/MHz/km 2 can be evaluated. The design parameters are the MCS, the maximum number of admitted calls per TRx N, and the buffer size

16 A. Wautier, J. Antoine, L. Husson, J. Brouet, C. Thirouard parameterized by the delay D. The choice of a radio bearer is directly linked to the size of the serving channel pool (cf. table 2 & 3). It is indirectly related to the frequency reuse factor. Without statistical multiplexing (i.e. the maximal number of admitted calls per TRx is equal to the size of channel pool per TRx: N = c), the offered traffic is obtained by the Erlang B model and it depends on the target blocking rate. For example, for c = 16, the offered traffic is 9.8 Erlang per TRx for a blocking rate of 2%. Then, the reuse factor can be taken into account by considering the perceived quality related to a SNR threshold (cf. figure 9). For example, if we consider an acceptable speech quality threshold of 60 in the E-model scale (3 in the MOS scale), the SNR threshold is 16 db with MCS-6 for the GSM EFR codec (cf. figure 9). In a typical cellular network with a reuse factor of 3x4, this minimum SNR value is reached for 80% of a cell. Here a propagation attenuation factor of 3.5 and a standard deviation for the shadowing equal to 7 db are assumed [20]. Shared channel per TRx: c Offered traffic per TRx: ρ(n = c) for 2% blocking probability Table 4 Offered traffic per TRx without statistical multiplexing With statistical multiplexing, the offered traffic is a function of N, which in turn is related to the perceived speech quality tradeoff. Table 5 gives the relative capacity gain expressed in Erlang per TRx when considering that the blocking probability is 2% and that the worst packet loss rate induced by statistical multiplexing equals 1% (i.e. P(P d <1%) = 100%). The capacity gain given in table 5 can be further enhanced by tolerating a delay of 100 ms (i.e. 40 ms for interleaving and 60 ms for the buffer) and by accepting variable quality of service between different users. However, in order to compensate for the effect of increased transmission delay and additional packet loss due to statistical multiplexing, the SNR threshold must be increased to ensure that the global perceived speech quality is maintained. For example, for c equal to 16, tables 4 and 5 show that statistical multiplexing is helpful in increasing the offered traffic from 9.8 Erlang per TRx to 20 Erlang per TRx (MCS-6 and voice activity factor of 0.44). Also, 1 % FER for GSM EFR codec (cf. figure 3) corresponds to a degradation of 10 points in E-model. So, if we consider that the global perceived quality must be above 60, it is mandatory that the operating SNR be increased from 16 db to 18 db. For a given reuse factor, this will reduce the percentage of satisfied users (70% of the cell instead of 80%). However, it is shown in [5],

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