Abstract
The direct link communication between STAtions (STAs) is one of the techniques to improve the MAC performance of IEEE 802.11 infrastructure networks. For the efficient direct link communication, in the literature, the simultaneous polling method was proposed to allow the multiple direct data communication to be performed simultaneously. However, the efficiency of the simultaneous polling method is affected by the interference condition. To alleviate the problem of the lower polling efficiency with the larger interference range, the hybrid polling method is proposed for the direct link communication between STAs in IEEE 802.11 infrastructure networks. By the proposed polling method, we can integrate the sequential and simultaneous polling methods properly according to the interference condition. Numerical examples are also presented to show the medium access control (MAC) performance improvement by the proposed polling method.
maintains the sets, 
and 
which are the sets of STAs of which the transmission signal can be heard by STA 
, and can interfere with the data reception of STA 
, respectively. STA 
can obtain the MAC address of STA 
(
) from the polling frame transmitted by the AP before the transmission of STA 
. For this purpose, the polling frames should be received by the STAs. When STA 
hears the transmission signal of other STA 
not in 
, STA 
adds STA 
to 
. When STA 
has not heard the transmission signal of other STA 
in 
during recent three PIs, STA 
deletes STA 
from 
. In this manner, each STA can maintain the set, 
. STA 
can also maintain the set, 
as follows. When STA 
finds the reception power level of the transmission signal of other STA 
not in 
to be above that of the background noise, STA 
adds STA 
to 
. When STA 
has not found the power level of the transmission signal of other STA 
in 
to be above that of the background noise during recent three PIs, STA 
deletes STA 
from 
. Actually, each STA 
can piggyback the MAC addresses of the STAs that are deleted from or added to 
and 
on the response null or data frames transmitted to the AP. Considering the case when transmission errors occur, we modified the method in [
from 
or 
.
to obtain the connectivity and interference information between STA 
and STA 
(
), the following two events should sequentially occur in a PI:
is successfully received by STA 
and STA 
;
is successfully received by STA 
when STA 
is within the transmission range of STA 
. STA 
can detect the interference by the reception power level of the response frame transmitted by STA 
when STA 
is within the interference range of STA 
.
and 
, we can compute the probability that STA 
can successfully obtain the connectivity and interference information between STA 
and STA 
within three PIs as 
. When the failure probabilities of the two events are less than or equal to 0.05, that is, 
and 
, 
, therefore, we can infer that it is quite reasonable to wait for three PIs before deleting STA 
from 
or 
.
and 
for 
and 
, and 
and 
for 
, which are collected in the PI to specify the connectivity and interference information, and the information of the STAs' requests for the direct link communication, respectively, are defined as follows:
if STA 
. Otherwise, 
;
if STA 
. Otherwise, 
;
: the MAC address of the recipient of the direct data transmission that STA 
requested on a packet basis in the recent PI. If STA 
did not request the direct data transmission, 
.
, STA 
and STA 
in the group 
attempt to transmit their frames simultaneously to the recipients, STA 
, STA 
and STA 
, respectively, an SIFS period after receiving the multipolling frame. For the simultaneous transmissions to be performed properly without interference, STA 
should hear the transmission of STA 
for 
, and the interference among the transmissions should be ignorable. Therefore, we need the following connectivity and interference condition:
STA 
, STA 
STA 
and the group 
STA 
, STA 
STA 
. The STAs in the sequence 
transmit their frames sequentially after the multipolling frame is received. An SIFS period after receiving the multipolling frame, STA 
first attempts to transmit its frame. An SIFS period after sensing the end of the transmission of STA 
, STA 
attempts to transmit its frame. STA 
attempts to transmit its frame an SIFS period after sensing the end of the transmission of STA 
. In this manner, the STAs transmit their frames sequentially. An SIFS period after sensing the end of the transmission of STA 
, the STAs in the group 
transmit their frames simultaneously. In order for the sequential transmissions to be performed properly, STA 
, which is the recipient for STA 
, should hear the transmission of STA 
for 
, and STA 
should sense the end of the transmission of STA 
for 
. The STAs in the group 
should sense the end of the transmission of STA 
. Therefore, in addition to the conditions of (1), the following connectivity condition should be satisfied for the proposed polling method:
fails to respond to the multipolling frame or the transmission of the previous STA in the sequence within an SIFS period following the transmission of the AP or the previous STA, for the error recovery the AP will transmit the multipolling frame to repoll the next STAs in the sequence 
and the group 
after a PIFS period, which is an SIFS period plus a slot time, from the end of the previous transmission. The format of the multipolling frame is shown in Figure 
and 
indicate the MAC addresses of the STAs in the sequence 
, 
and 
the MAC addresses of the STAs in the group 
, and 
and 
are the numbers of the STAs in the sequence 
and the group 
, respectively. The other fields are from [
or 
. When 
(or 
) is omitted in the multipolling frame, the simultaneous (or sequential) polling method is only specified.
be the set of STAs that requested the direct data transmissions, which are determined to be feasible using the connectivity information, in the recent PI. Then 
can be obtained as follows:
using the proposed polling method.
with as few groups as possible in such a way that no two STAs, 
and 
with 
or 
, are in the same group. Note that the connectivity and interference conditions as shown in (1) are satisfied for each group. Therefore, the AP can grant the simultaneous direct transmission opportunities to the STAs in each group using the simultaneous polling method. This grouping problem can be formulated as graph coloring problem (GCP), where the STAs in 
are vertices and two STAs, 
and 
in 
, are connected only when 
or 
. We can use the simple heuristic for GCP, which is based on the degree-descending order of the vertices [
for 
[
polling frame transmissions to poll the STAs in the groups in 
using the simultaneous polling method. The first phase of the algorithm was considered in the simultaneous polling method in [
. The AP can poll the STAs in the groups in the sequence 
with 
for 
by transmitting a multipolling frame, the format of which is as shown in Figure 
for 
, and the following connectivity condition is satisfied:
indicates that the STAs in 
can hear the transmission of the STA in 
. We will call such a polling sequence satisfying the condition of (4) sequentially connected. For convenience of explanation, we will also call the sequence H having only one group sequentially connected.
have only one STA, that is, the simultaneous polling method cannot be actually applied to some of the groups, we can further reduce the number of polling frame transmissions by finding the sequentially connected polling sequences and applying the proposed polling method to the sequentially connected polling sequences. The problem of finding the optimal polling sequence of the groups in 
that minimizes the multipolling frame transmissions can be formulated as the asymmetric traveling salesman problem (TSP), where the groups in 
are 
cities, and the distance, 
from 
to 
, is binary valued:
, and the corresponding total distance by 
. If 
, that is, 
is sequentially connected, only one multipolling frame transmission is sufficient to grant the direct transmission opportunities to the STAs in the groups in 
. If 
, we can cyclically reorder the groups in 
to obtain the sequentially connected polling sequence, 
, and only one multipolling frame transmission is sufficient to poll the STAs in the groups in 
. If 
, we can cyclically reorder the groups in 
to obtain two sequentially connected polling sequences, 
and 
. (For instance, let 
, 
, 
, and 
. Then we can reorder 
to obtain two sequentially connected polling sequences as 
, 
.) Generally, if 
, we can cyclically reorder 
to obtain 
sequentially connected polling sequences, 
and 
, and 
multipolling frame transmissions are sufficient to grant the direct transmission opportunities to the STAs in the groups in 
.
)).
(the number of the groups having two or more STAs in 
).
Bounding_Cost + 1, and go to Step 2.
is the number of the groups having two or more STAs in 
, at least 
multipolling frame transmissions are needed to poll the STAs in the groups in 
. The preceding algorithm first tries to obtain the solution with 
. If the algorithm does not succeed to get the solution within time of Time_Limit, the algorithm relaxes the constraint for the cost of the solution by increasing Bounding_Cost by 1 and tries to get the solution with 
. If the algorithm fails again, the algorithm again increases Bounding_Cost by 1 and tries to get the solution with 
. In this manner, the algorithm continues until the solution with 
Bounding_Cost is obtained. By the branch and bound techniques, if a part of tour has a cost higher than or equal to the current optimal cost or higher than Bounding_Cost, all tours including this part of tour are skipped.
be the set of existing simplex direct link connections. A duplex connection can be realized by two simplex connections. We propose a two-phase scheduling algorithm for granting the direct transmission opportunities to the transmitting STAs of the direct link connections in 
. We will denote the transmitting and receiving STAs of direct link connection, 
in 
by 
and 
, respectively.
with as few groups as possible in such a way that no two connections, 
and 
with 
or 
, are in the same group. This grouping problem can be also formulated as GCP, where the connections in 
are vertices and two connections, 
and 
in 
, are connected only when 
or 
. We can use the simple heuristic for GCP, which is based on the degree-descending order of the vertices [
for 
. We need 
polling frame transmissions to poll the transmitting STAs of the connections in the groups in 
using the simultaneous polling method.
. The AP can poll the transmitting STAs of the connections in the groups in the sequence 
with 
for 
by transmitting a multipolling frame, the format of which is as shown in Figure 
for 
, and the following connectivity condition is satisfied:
indicates that the transmitting STAs of the connections in 
can hear the transmission of the transmitting STA of the connection in 
. We will call such a polling sequence satisfying the condition of (6) sequentially connected.
have only one connection, that is, the simultaneous polling method cannot be actually applied to some of the groups, we can further reduce the number of polling frame transmissions by finding the sequentially connected polling sequences and applying the proposed polling method to the sequentially connected polling sequences. The problem of finding the optimal polling sequence of the groups in 
that minimizes the multipolling frame transmissions can be also formulated as the asymmetric TSP, where the groups in 
are 
cities, and the distance, 
from 
to 
, is binary valued:
, and the corresponding total distance by 
. If 
, that is, 
is sequentially connected, only one multipolling frame transmission is sufficient to grant the direct transmission opportunities to the transmitting STAs of the connections in the groups in 
. If 
, we can cyclically reorder 
to obtain 
sequentially connected polling sequences, 
and 
, and 
multipolling frame transmissions are sufficient to grant the direct transmission opportunities to the transmitting STAs of the connections in the groups in 
. To solve the asymmetric TSP, we can employ a dynamic search algorithm similar to the one of the packet-level scheduling algorithm with Time_Limit of 10 seconds.
consists of a single connection, the transmitting STA of the connection can transmit its direct data frame to any receiving STA of the established direct link connections in its transmission range when polled by the AP. When the transmitting STA of the connection has no direct data frame to transmit, the STA should use the granted transmission opportunity to transmit its null or data frame to the AP when polled by the AP. The AP can optionally modify the derived polling sequence to insert the AP's polling frame transmissions before the transmissions of the nonsimultaneous polling groups when the AP has the data frames, which are actually piggybacked on the polling frames, destined for the nonsimultaneous polling groups. When no direct link communication through the connections in a simultaneous polling group in 
was requested, the AP will modify the derived polling sequence to remove the group from the polling sequence that is actually delivered to the STAs. This is for avoiding wasting the wireless bandwidth. When all connections with a transmitting STA are separately in the different simultaneous polling groups, the STA can choose only one connection to transmit its direct data frame when polled by the AP. Note that the first phase of the algorithm avoided the case that two or more connections with a transmitting STA are separately in the nonsimultaneous polling groups, and the case that two or more connections with a transmitting STA are scattered in both the simultaneous and nonsimultaneous polling groups.
, and 40, we generated ten IEEE 802.11a wireless LANs, where the APs are located at the centers of the circular service areas, and twenty, thirty, or forty STAs are randomly located in the service areas, including the one consisting of one AP and thirty STAs in Figure 
and STA 
. 
will denote the number of simultaneous full-duplex VoIP traffic streams between two STAs of each pair. The STAs perform a good uplink power control in PIs so that the null or data frames transmitted by each STA can be received by the STAs including the AP in the circular transmission range with the radius 
of the distance between the STA and the AP, and the STAs out of the transmission range cannot hear the transmission signal of the STA.
in each wireless LAN [
, that is, the interference ranges are set to the same as the transmission ranges. 
is set to 1.3 
, 1.5 
, and 1.8 
in the second, third, and fourth cases, respectively. According to [
bytes/second = 240 bps is required for this overhead.
: (STAs 4 and 25), (STAs 27 and 14), (STAs 7, 15 and 1), (STAs 8 and 30), and (STAs 16 and 23);
: (STAs 4 and 30), (STAs 7 and 25), (STAs 14 and 15), (STAs 8 and 1), (STA 23), (STA 27), and (STA 16);
: (STA 7), (STA 8), (STA 14), (STAs 15 and 1), (STAs 16 and 30), (STAs 25 and 23), (STA 4), and (STA 27);
: (STA 4), (STA 7), (STA 25), (STA 8), (STA 16), (STA 15), (STA 14), (STAs 23 and 30), and (STAs 1 and 27);
: (STA 30), (STA 27), (STA 25), (STA 23), (STA 16), (STA 15), (STA 14), (STA 8), (STA 7), (STA 4), and (STA 1).
: (STAs 4 and 25), (STAs 27 and 14), (STAs 7, 15 and 1), (STAs 8 and 30), and (STAs 16 and 23);
: [STA 23, STA 27], (STA 16), (STAs 4 and 30), (STAs 7 and 25), (STAs 14 and 15), and (STAs 8 and 1);
: [STA 8, STA 4, STA 27], (STA 14), (STAs 15 and 1), (STAs 16 and 30), (STAs 25 and 23), and (STA 7);
: [STA 25, STA 14], (STAs 23 and 30), (STAs 1 and 27), [STA 8, STA 16, STA 15, STA 4], and (STA 7);
: [STA 27, STA 23, STA 8, STA 16, STA 15, STA 4], [STA 7, STA 1, STA 25, STA 14, STA 30].
, we could obtain each hybrid polling sequence for 414 combinations of wireless LANs, interference conditions, and selected values of 
out of 450 = 30 (wireless LANs) 
(interference conditions) 
(selected values of 
) combinations within 1 microsecond. The three selected values of 
represent the light, medium, and heavy traffic loads carried on wireless LAN. We applied the connection-level scheduling algorithm to the remaining 36 combinations, and could obtain each hybrid polling sequence for 33 combinations within 10 seconds. The connection-level polling scheduling algorithm took about 117 seconds to derive each hybrid polling sequence for 3 combinations of a wireless LAN with 40 STAs and the interference condition of 
. From these observations, it was determined that we can perform the simulation analysis of the performance of our proposed polling method applying the packet-level and the connection-level scheduling algorithms to the 414 and 36 combinations, respectively.
1.5 seconds/88 bits = 82, where 4.8 Kbps is the speech coding rate of the IMBE speech coder [
time slots using the specialized simulator developed in 
code by the author. One slot time is 9 microseconds in IEEE 802.11a wireless LANs. In Figures 
) is imposed on IEEE 802. 11a wireless LAN with 20 STAs.
) is imposed on IEEE 802. 11a wireless LAN with 20 STAs.
) is imposed on IEEE 802. 11a wireless LAN with 20 STAs.
) is imposed on IEEE 802. 11a wireless LAN with 30 STAs.
) is imposed on IEEE 802. 11a wireless LAN with 30 STAs.
) is imposed on IEEE 802. 11a wireless LAN with 30 STAs.
) is imposed on IEEE 802. 11a wireless LAN with 40 STAs.
) is imposed on IEEE 802. 11a wireless LAN with 40 STAs.
) is imposed on IEEE 802. 11a wireless LAN with 40 STAs.
, and becomes the same as that of the PCF polling method under the severe interference condition of 
. However, with the hybrid polling method, the decrease in the MAC performance is relatively small even in the interference conditions of 
and 
. Compared with the simultaneous polling method, the hybrid polling method decreases the mean delay bound by about 7.6%, 11.0%, 18.5%, 27.8%, and 40.5% under the interference conditions of 
, and 
, respectively. Compared with the PCF polling method, the hybrid polling method decreases the mean delay bound by about 58.8%, 45.1%, 39.1%, 38.0%, and 38.9% under the interference conditions of 
, and 
, respectively. From the simulation results, we can see that the hybrid polling method outperforms both the PCF protocol and the simultaneous polling method in maximum delay especially under the severe interference condition.