SEO AND LEUNG: BACKOFF ALGORITHM FOR RANDOM ACCESS CHANNEL IN UMTS-LTE AND IEEE 802.16 SYSTEM 3977
there can be F random access channels in the frequency domain
within one access period, among which an accessing terminal
may randomly select one. At the same time, a terminal picks
one of P RAPs and transmits it in the selected random access
channel. If the same RAP is transmitted by more than one
terminal over the same random access channel, a code collision
occurs, or if the transmitted RAP is not acknowledged by the
BS within a specified time window, e.g., the random access
response (RAR) window in UMTS-LTE, it is also declared as a
collision. This latter condition may occur due to the transmitted
RAP not being successfully decoded under severe MAI. When-
ever the terminals’ RAP transmissions are not successful, they
retransmit after a delay determined by the UB algorithm (in
UMTS-LTE) or BEB algorithm (in an IEEE 802.16 system).
These algorithms will be explained in the next sections. In
both systems, if the number of retransmissions exceeds the
maximum retry limit, the RAP is dropped in the MAC layer.
This is reported to a higher layer. Once the RAP is successfully
transmitted, the terminal can transmit a bandwidth request mes-
sage for bandwidth reservation on the uplink channel that the
BS has granted to it via the RAR message in UMTS-LTE or the
uplink map (UL-MAP) in the IEEE 802.16 system. This proce-
dure is triggered at the time when an end-user makes a phone
call or uses an application that needs to access the Internet.
Accordingly, fast resolution of collisions in RAP transmissions
is expected to enable fast bandwidth reservations. Additionally,
in UMTS-LTE, the window size of the UB algorithm, which
is denoted by U hereafter and is assigned by the BS in the
first RAR message, can be dynamically chosen according to
network congestion. Thus, it is expected that appropriately
controlling U can efficiently resolve collisions under some
time-varying traffic condition.
In what follows, we assume that the transmission power
and timing of RAPs are perfectly known to terminals, which
simplifies the power-ramping scheme in UMTS-LTE. This is
equivalent to the assumption that initial and periodic ranging
processes are sufficiently well performed in an IEEE 802.16
system. We further assume that perfect orthogonality among
RAPs simultaneously transmitted by multiple terminals is pre-
served. Owing to this perfect orthogonality assumption, a sys-
tem with P RAPs and F random access channels is equivalent
to a system with P · F RAPs. Note that, in UMTS-LTE, each
BS provides 64 RAPs, some of which can be reserved for the
use of noncontention-based access. Additionally, in the frame
structure of type-1 frequency-division duplex (FDD) mode, one
random access channel in the frequency domain appears every
two slots [15]. For analytical simplicity, we set F =1 every
slot and assume a slotted system with FDD, in which each slot
corresponds to one RAP transmission (one packet) time. The
number of RAPs will be given later in Section V. Hereafter, we
interchangeably use the terms RAP and packet. In the system
model, we assume a finite population of M terminals. Each
terminal can hold only one packet for transmission or retrans-
mission until it is successfully received. A terminal that has no
packet to transmit is said to be idle. An idle terminal generates a
packet in every slot based on a Bernoulli trial with probability ,
i.e., unsaturated traffic condition. When a terminal has a packet
to send, it immediately becomes backlogged by performing the
backoff algorithm, i.e., it employs a delayed-first-transmission
protocol. We finally assume that terminals can get feedback
information for the RAP transmitted, e.g., success or failure,
from the BS right before the next slot with no error, i.e., no
feedback delay is taken into account.
B. Uniform Backoff Algorithm in UMTS-LTE
Each backlogged terminal randomly draws a backoff counter
between 0 and U − 1. The backoff counter is then decremented
by one at every slot, until it reaches zero. When the backoff
counter is zero, the terminal selects a random real number
between 0 and 1. As in [11], if this number is less than the
persistence probability (or persistence value) p, the terminal
transmits its packet; otherwise, it postpones the packet trans-
mission by repeating the preceding procedure in the next slot,
until the packet is transmitted. When the packet is not success-
fully transmitted, i.e., the transmission encounters a collision,
the terminal delays its retransmission again by a random time
newly chosen between 0 and U − 1. This trial is repeated
up to L times more, until the retransmission succeeds, or the
terminal drops the packet and goes back to idle if the L +1
th
retransmission remains unsuccessful.
C. BEB Algorithm in IEEE 802.16
Upon an unsuccessful packet transmission, the BEB algo-
rithm exponentially increases the backoff window by doubling
its size. Let W
i
denote the backoff window size of the ith
backoff stage, which is determined by
W
i
=2
i
W
0
for 0 ≤ i ≤ K (1)
where W
0
is the minimum backoff window size. At the ith
backoff stage, the backlogged terminal randomly chooses a
backoff counter in the range [0,W
i
− 1] for 0 ≤ i ≤ K. Once
chosen, the backoff counter is decremented every slot as in the
UB algorithm. When it reaches zero, the terminal transmits
its packet. Upon transmission failure, the terminal increments
the backoff stage by one and chooses the next backoff counter
again. Although the retry limit L is independent of K in [1], we
assume here that the BEB algorithm retries L times additionally
at the Kth stage. Thus, upon the retransmission failure after
a total of L +1 retransmissions at the Kth stage, it drops
the packet. One can find more details of the random access
procedure for IEEE 802.16 in [16].
D. Access Prioritization by Persistence Value
To provide access priority, UMTS includes eight access
priority classes [11], each of which has a different persistence
value p = P
i
(N)=s
i
· 2
−(N−1)
for 0 ≤ i ≤ 7. Note that the
value of i can indicate a certain partition of the random access
channels. The persistence scaling factor s
i
is assumed to be
a value between 0.2 and 0.9 by step of 0.1, and the dynamic
persistence level N from 1 to 8 is regularly broadcast. If the
persistence scaling factors are not broadcast, a default value
of one is assumed. Once the backoff counter reaches zero, the