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)
8
MD PRMA ON
CODE-TIME-SLOTS
This chapter is concerned with MD PRMA on perfect-collision code-time-slot channels.
The simple and abstract channel model used, representative for a blocking-limited system,
allows one to consider an arbitrary number of code-slots E per time-slot, without having to
worry about the spreading factor required to meet a certain packet erasure performance. In
this framework, the scope of investigations can conveniently be extended to two extreme
cases, namely only one code-slot per time-slot, but numerous time-slots N per TDMA
frame, and only one time-slot per frame carrying numerous code-slots. In the first case, the
CDMA feature is relinquished, and MD PRMA degenerates to pure PRMA. In the second
case, the TDMA feature is relinquished. While this configuration (and in fact also PRMA
itself) can simply be viewed as a special case of MD PRMA, it actually corresponds to
the Reservation-Code Multiple Access (RCMA) protocol proposed in Reference [35].
As in Chapter 7, only voice-traffic will be considered. However, the focus shifts from
load-based access control to fixed permission probabilities and backlog-based access
control (the latter in the shape of Bayesian broadcast). The performances of pure PRMA,
MD PRMA and RCMA will be compared, all with the same number of resource units
U = N · E. For MD PRMA with N = 8andE = 8 (i.e. the original UTRA TD/CDMA
parameters), the impact of acknowledgement delays and TDD operation on voice dropping
performance is also studied. Furthermore, the code-time-slot channel model is enhanced
to account for multiple access interference (MAI). In this scenario, unlike the perfect-
collision case, load-based access control can make sense. Therefore, on top of ‘conven-
tional’ Bayesian broadcast, a scheme combining Bayesian broadcast with a channel access
function is considered.

Subsection 6.2.6. This parameter determines how many time-slots a terminal must wait for
an acknowledgement following the time-slot in which it sent a packet in contention mode.
While waiting, it is not allowed to contend again. In the case of Bayesian broadcast, if x>
0 (i.e. acknowledgement is not immediate), the Bayesian algorithm needs to be modified,
that is, p
v
needs to be calculated through Equation (6.7). Unlike the acknowledgements,
p
v
is assumed to be broadcast immediately at the end of each time-slot. For the same
configuration of resource units, the performance of MD FRMA for TDD with a single
switching-point per frame, as specified in Subsection 6.3.3, is assessed. From one to eight
time-slots per TDMA frame are assumed to be assigned to the uplink direction, where the
last case is obviously only of academic interest, since no resources would be available
for the downlink in this case.
In the following two sections, when more than one code-slot is considered, these slots
are assumed to be mutually orthogonal, which means that MAI is ignored. If dedicated
channels were used, the system would exhibit hard-blocking, but owing to the PRMA
element, it features soft-blocking or soft-capacity. In Section 8.4, on the other hand, MAI
is accounted for in the manner specified therein, in order to assess the impact of the
loss of orthogonality on access control. In this case, depending on the quality of service
requirements, we are dealing with an interference-limited system; that is, excessive packet
erasure may prevent all U resource units from being used. In the terminology used in
Subsection 7.5.3, ‘U is soft up to an upper limit of N · E’. When interleaving is applied,
it is rectangular interleaving over the length of a voice frame, which in turn is carried
on four bursts (see Subsection 6.2.4). In this case, request bursts sent in contention mode
are dedicated signalling bursts, transmitted on a single code-time-slot. By contrast, when
interleaving is not applied, they carry not only signalling, but also user data, namely the
same amount as carried by information bursts.
For the basic scheme without interleaving, the delay threshold D

the next subsection, all parameters mentioned so far are summarised in Table 8.1.
8.1.2 Simulation Approach, Traffic Parameters and Performance
Measures
As in the previous chapter, the only traffic considered in the following is packet-voice
traffic, using the two-state voice model specified in Section 5.5. Two different parameter
sets are considered. The first set, namely D
spurt
= 1.4sandD
gap
= 1.74 s, is from the
RACE ATDMA project [46], and results in a voice activity factor α
v
of 0.448, which is
slightly higher than that in Chapter 7. As a second set, D
spurt
= D
gap
= 3 s taken from
Reference [56] is used. This is to establish a link with Chapter 9, where mixed voice and
data traffic is considered, and parameters from Reference [56] are used for both voice
and Web browsing traffic.
The system load is determined by the number of conversations M simultaneously
supported, and we are interested in P
drop
performance as a function of M. Analogous
to Chapter 7, M
0.01
and M
0.001
stand for the number of conversations which can be

considered design parameters, a full Markov analysis is rather challenging. In Refer-
ence [61], we provided an EPA for MD PRMA, which expanded on the EPA for PRMA
provided in Reference [143] and adopted a few elements of Reference [149]. In certain
314
8 MD PRMA ON CODE-TIME-SLOTS
scenarios, we found EPA to be satisfactory, in others not. In the following, we focus on
protocol performance assessment through simulation studies.
8.2 Comparison of PRMA, MD PRMA and RCMA
Performances
8.2.1 Simulation Results, No Interleaving
Figures 8.1 to 8.3 show P
drop
performance of MD PRMA, PRMA, and RCMA respec-
tively, with different fixed p
v
values (in the figures simply referred to as p) on one hand,
and p
v
calculated through the Bayesian algorithm on the other. In all cases, the basic
scheme without interleaving and a very short packet dropping delay threshold D
max
equal
to D
tf
, namely 4.615 ms, was considered.
With MD PRMA (Figure 8.1) and Bayesian Broadcast (BB), M
0.01
= 131 and η
mux
=

more, if p
v
is too large, MD PRMA can become unstable. With the values considered
here for M, this was experienced for p
v
≥ 0.6andM = 140.
In cases in which instability is experienced, P
drop
results established through simula-
tions are heavily affected by the instance in time in which the system first experienced
congestion. Once caught in a congested equilibrium point, it is almost certain that the
system remains in this state for the remainder of the simulation run and, from then on,
1.0E-8
1.0E-6
1.0E-4
1.0E-2
1.0E+0
60 70 80 90 100 110 120 130 140 150
Simultaneous conversations
M
Packet dropping ratio
P
drop
p
= 0.1
p
= 0.2
p
= 0.3
p

Choosing p
v
= 0.5 offers the best compromise between capacity (M
0.01
= 128) and
low dropping at low load, while appearing to allow for stable operation up to M = 140
(that is, the FET is much larger than the duration of an individual simulation-run). BB on
the other hand allows for stable operation at high load while ensuring low packet dropping
at low load and performs at least as well as the fixed p
v
approach over the entire range
of M considered.
One could argue that the performance of BB could be met by choosing a semi-adaptive
approach, i.e. selecting p
v
depending on M. However, such an approach cannot easily
be extended to a mixed traffic scenario, possibly with unknown traffic statistics, whereas
BB adapts automatically to different traffic mixes. Furthermore, it would also require
regular signalling of p
v
, leaving reduced computational complexity as the only potential
argument in its favour. In view of the very small complexity of BB, this advantage is of
no relevance in practice, though.
Similar considerations apply in the case of pure PRMA. In fact, looking at Figure 8.2,
to avoid stability problems, p
v
has to be selected even more carefully. Here, with BB,
M
0.01
= 129 (η

M
Packet dropping ratio
P
drop
p
= 0.05
p
= 0.07
p
= 0.1
p
= 0.15
p
= 0.2
p
= 0.3
p
= 0.4
Bayes
PRMA,
N
= 64,
E
= 1
D
max
= 4.615 ms
Figure 8.2 Simulated PRMA performance, overview
316
8 MD PRMA ON CODE-TIME-SLOTS

= 4.615 ms
Figure 8.3 Simulated RCMA performance, overview
Finally, with RCMA, the situation is slightly different, as illustrated in Figure 8.3. Note
first that, since D
max
= D
tf
, there is only one contention opportunity for a terminal until
the first packet in a spurt is dropped, such that there will be significant dropping irrespec-
tive of the load, as soon as p
v
< 1. In fact, for p
v
< 0.98 and M ≤ 100, P
drop
is almost
uniquely determined by the waiting probability 1 − p
v
, which explains the flat segment
of the respective curves. On the other hand, even if there is a temporary accumulation of
contending terminals, they will normally be able to choose between numerous code-slots
available for contention, such that the collision risk is small. Therefore, stability is not
an issue even for p
v
= 1. This in turn means that there is limited benefit in controlling
access dynamically, e.g. through Bayesian broadcast, which is also shown in the figure.
This is very much in contrast to pure PRMA (and to a lesser extent to MD PRMA), where
the accumulation of a few contending terminals C, such that C>1/p
v
, can result in a