Table 1 System parameters and symbols used in the equations
Notation | Definition |
|---|---|
R | Total random access opportunities (RAOs) |
M | Total UE in the paged group |
I max | Total RA slots in a group paging interval |
\(T_{\textit {RA\_REP}}\) | Interval between successive RA slots (unit: sub-frame) |
T RAR | Processing time required by eNB to detect transmitted preambles (unit: sub-frame) |
W RAR | Window of random access reply (RAR) (unit: sub-frame) |
N RAR | Maximum number of acknowledgement that can be carried in a RAR message |
N UL | Maximum acknowledged UE in one RAR window |
W BO | Window backoff (unit: sub-frame) |
N PTmax | Maximum attempt by each UE to transmit preamble in one group paging interval |
T CR | Contention resolution timer (unit: sub-frame) |
T HARQ | Interval for receiving HARQ acknowledgment (unit: sub-frame) |
T M3 | Gap for Msg3 retransmission (unit: sub-frame) |
N HARQ | Maximum attempt of HARQ transmission of Msg3 and Msg4 |
\(T_{A\_M4}\) | Gap of monitor Msg4 (unit: sub-frame) |
T M4 | Gap for Msg4 retransmission (unit: sub-frame) |
W PBO | Window of pre-backoff (unit: sub-frame) |
M i | Total number of UE that transmit their preambles in the ith RA slot |
M i [ n] | Number of contending UE that transmit the nth preamble at the ith RA slot |
M i,S [ n] | Portion of M i [ n] that successfully complete its preamble transmission |
M i,F [ n] | Portion of M i [ n] that fail in its preamble transmission |
P P | Probability of an UE to correctly receive paging message |
α k,i | The portion of backoff interval of the kth RA slot (K min =k=K max <i) that overlap with the transmission interval of the ith RA slot |
P n | The detection probability of the nth preamble transmission due to power-ramping effect |
P C | The ratio between the total number of collided preamble and to all allocated preamble |
P S | The ratio between total UE that successfully access the network and the total number of UE in the paged group |
\(\overline {D_{A}}\) | The total access delay for all successfully accessed UEs normalized by the total successfully accessed UEs |
T i | The access delay for successfully accessed UEs from the transmitting preamble at the ith RA slot |
\(\overline {T_{\textit {MSG}}}\) | The average time for one UE to finish the message-part transmission |
P f | HARQ retransmission probability for Msg3 and Msg4 |