U.S. patent application number 11/588089 was filed with the patent office on 2007-02-15 for detecting a hidden node in a wireless local area network.
This patent application is currently assigned to AirMagnet, Inc.. Invention is credited to Dean Au, Chia-Chee Kuan, Miles Wu.
Application Number | 20070036091 11/588089 |
Document ID | / |
Family ID | 28039539 |
Filed Date | 2007-02-15 |
United States Patent
Application |
20070036091 |
Kind Code |
A1 |
Kuan; Chia-Chee ; et
al. |
February 15, 2007 |
Detecting a hidden node in a wireless local area network
Abstract
A method and system for detecting a hidden node in a wireless
local area network having a first station, a second station, and an
access point. The first station can send a message, where the
message can be sent as a data frame. After receiving the message,
the access point can send the message to the second station. The
second station can receive the message from the access point. In
response to receiving the message, the second station can send an
acknowledgement to the access point, where the acknowledgement can
be sent as a control frame. The first station can monitor for the
acknowledgement sent from the second station to the access
point.
Inventors: |
Kuan; Chia-Chee; (Los Altos,
CA) ; Wu; Miles; (Fremont, CA) ; Au; Dean;
(Sunnyvale, CA) |
Correspondence
Address: |
MORRISON & FOERSTER LLP
425 MARKET STREET
SAN FRANCISCO
CA
94105-2482
US
|
Assignee: |
AirMagnet, Inc.
Sunnyvale
CA
|
Family ID: |
28039539 |
Appl. No.: |
11/588089 |
Filed: |
October 25, 2006 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
10099222 |
Mar 14, 2002 |
7130289 |
|
|
11588089 |
Oct 25, 2006 |
|
|
|
Current U.S.
Class: |
370/254 ;
370/278 |
Current CPC
Class: |
H04W 84/12 20130101;
H04L 1/188 20130101; H04W 74/08 20130101; H04L 1/1607 20130101 |
Class at
Publication: |
370/254 ;
370/278 |
International
Class: |
H04L 12/28 20060101
H04L012/28; H04B 7/005 20060101 H04B007/005 |
Claims
1-64. (canceled)
65. A method of determining whether a station in a wireless local
area network is a hidden node, the method comprising: at a first
station, receiving a message forwarded from an access point to a
second station associated with the access point; at the first
station, after receiving the message, monitoring to detect an
acknowledgement sent from the second station to the access point in
response to the message forwarded from the access point to the
second station; and if the acknowledgement sent by the second
station to the access point is detected by the first station,
determining that the second station is not a hidden node of the
first station.
66. The method of claim 65, further comprising determining that the
second station is a hidden node of the first station if the
acknowledgement sent by the second station to the access point is
not detected by the first station.
67. The method of claim 65, wherein the message was sent from a
third station to the second station through the access point.
68. The method of claim 65, wherein the message was sent from the
first station to the second station through the access point.
69. The method of claim 68, further comprising: a) repetitively
sending messages from the first station to the second station
through the access point; and b) determining that the second
station is not a hidden node of the first station if the first
station detects at least one acknowledgement sent from the second
station to the access point to any of the messages sent in a).
70. The method of claim 69, further comprising: c) determining that
the second station is a hidden node of the first station if the
first station fails to detect at least one acknowledgement sent
from the second station to the access point to any of the messages
sent in a).
71. The method of claim 65, wherein the first station, the second
station, and the access point operate according to an IEEE 802.11
standard.
72. The method of claim 65, wherein the first station is a
diagnostic tool.
73. The method of claim 65, wherein the first station is an
administrative tool.
74. A computer-readable medium that stores a computer program for
determining whether a station in a wireless local area network is a
hidden node, the computer program includes computer instructions
for: at a first station, examining a message forwarded from an
access point to a second station associated with the access point;
at the first station, after examining the message, monitoring to
detect an acknowledgement sent from the second station to the
access point in response to the message forwarded from the access
point to the second station; and if the acknowledgement sent by the
second station to the access point is detected by the first
station, determining that the second station is not a hidden node
of the first station.
75. The computer-readable medium of claim 74, further comprising
computer instructions for: determining that the second station is a
hidden node of the first station if the acknowledgement sent by the
second station to the access point is not detected by the first
station.
76. The computer-readable medium of claim 74, wherein the message
was sent from a third station to the second station through the
access point.
77. The computer-readable medium of claim 74, wherein the message
was sent from the first station to the second station through the
access point.
78. The computer-readable medium of claim 77, further comprising
computer instructions for: a) repetitively sending messages from
the first station to the second station through the access point;
and b) determining that the second station is not a hidden node of
the first station if the first station detects at least one
acknowledgement sent from the second station to the access point to
any of the messages sent in a).
79. The computer-readable medium of claim 78, further comprising
instructions for: c) determining that the second station is a
hidden node of the first station if the first station fails to
detect at least one acknowledgement sent from the second station to
the access point to any of the messages sent in a).
80. The computer-readable medium of claim 74, wherein the first
station, the second station, and the access point operate according
to an IEEE 802.11 standard.
81. A detector to be used in a wireless local area network to
determine whether a station is a hidden node, the detector
comprising: an antenna configured to receive a message forwarded
from an access point to a station associated with the access point;
and a computer-readable medium that stores a computer program, the
computer program includes computer instructions for: examining the
received message; and after examining the message, monitoring to
detect an acknowledgement sent from the second station to the
access point in response to the message forwarded from the access
point to the second station; and if the acknowledgement sent by the
second station to the access point is detected by the first
station, determining that the second station is not a hidden node
of the first station.
Description
BACKGROUND
[0001] 1. Field of the Invention
[0002] The present invention generally relates to wireless local
area networks. More particularly, the present invention relates to
detecting a hidden node in a wireless local area network.
[0003] 2. Description of the Related Art
[0004] Computers have traditionally communicated with each other
through wired local area networks ("LANs"). However, with the
increased demand for mobile computers such as laptops, personal
digital assistants, and the like, wireless local area networks
("WLANs") have developed as a way for computers to communicate with
each other through transmissions over a wireless medium using radio
signals, infrared signals, and the like.
[0005] In order to promote interoperability of WLANs with each
other and with wired LANs, the IEEE 802.11 standard was developed
as an international standard for WLANs. Generally, the IEEE 802.11
standard was designed to present users with the same interface as
an IEEE 802 wired LAN, while allowing data to be transported over a
wireless medium.
[0006] Although WLANs provide users with increased mobility over
wired LANs, the quality of communications over a WLAN can vary for
reasons that are not present in wired LANs. For example, stations
in a WLAN can communicate with other stations in the WLAN through
an access point ("AP"). More particularly, each station can have a
transmission range within which the station can transmit signals to
an AP within the WLAN.
[0007] Other stations located within this transmission range can
detect signals transmitted by the station. After detecting signals
transmitted by the station, these other stations can wait to send
their own signals until the wireless medium is free from traffic
generated by the station. However, because a station can have a
limited transmission range, other stations located outside of this
transmission range, typically called "hidden nodes," can exist in a
WLAN. These "hidden nodes" can send signals across the WLAN that
can collide with signals sent by the station. This type of
collision arising from the presence of "hidden nodes" is typically
called the "hidden node problem."
[0008] The collision of messages resulting from the "hidden node
problem" can create unacceptable performance and reliability
problems in a WLAN. For instance, each message that is interrupted
by a collision can be resent according to the IEEE 802.11 standard.
However, resending the message can delay the receipt of the message
at its destination. In addition, each resent message can consume
additional bandwidth in the WLAN. Such delays and bandwidth
consumption can affect other messages being sent across the WLAN,
thereby creating performance and reliability problems in the
WLAN.
SUMMARY
[0009] The present invention relates to detecting a hidden node in
a wireless local area network having a first station, a second
station, and an access point. In one exemplary embodiment, the
first station can send a message, where the message is sent as a
data frame. After receiving the message, the access point can send
the message to the second station. The second station can receive
the message from the access point. In response to receiving the
message, the second station can send an acknowledgement to the
access point, where the acknowledgement can be sent as a control
frame. The first station can monitor for the acknowledgement sent
from the second station to the access point.
[0010] In another exemplary embodiment, the access point can send a
message to the second station, where the message can be sent as a
data frame. The second station can receive the message from the
access point. In response to receiving the message, the second
station can send an acknowledgement to the access point, where the
acknowledgement can be sent as a control frame. The first station
can detect the message sent from the access point to the second
station. Furthermore, the first station can monitor for the
acknowledgement sent from the second station to the access
point.
DESCRIPTION OF THE DRAWING FIGURES
[0011] The present invention can be best understood by reference to
the following detailed description taken in conjunction with the
accompanying drawing figures, in which like parts may be referred
to by like numerals:
[0012] FIG. 1 shows an exemplary OSI seven layer model;
[0013] FIG. 2 shows an exemplary extended service set in a wireless
local area network ("WLAN");
[0014] FIG. 3 is an exemplary flow diagram illustrating various
states of stations in a WLAN;
[0015] FIG. 4 shows an exemplary embodiment of the hidden node
problem;
[0016] FIG. 5 shows an exemplary sequence of frame exchanges;
[0017] FIG. 6 shows an exemplary flow diagram of a process that can
be used to detect a hidden node;
[0018] FIG. 7 shows an exemplary header that can be included in a
frame; and
[0019] FIG. 8 shows an exemplary sequence of frame exchanges.
DETAILED DESCRIPTION
[0020] In order to provide a more thorough understanding of the
present invention, the following description sets forth numerous
specific details, such as specific configurations, parameters,
examples, and the like. It should be recognized, however, that such
description is not intended as a limitation on the scope of the
present invention, but is intended to provide a better description
of the exemplary embodiments.
[0021] With reference to FIG. 1, an exemplary OSI seven layer model
is shown, which represents an abstract model of a networking system
divided into layers according to their respective functionalities.
In particular, the seven layers include physical layer 102
corresponding to layer 1, data link layer 104 corresponding to
layer 2, network layer 106 corresponding to layer 3, transport
layer 108 corresponding to layer 4, session layer 110 corresponding
to layer 5, presentation layer 112 corresponding to layer 6, and
application layer 114 corresponding to layer 7. Each layer in the
OSI model only interacts directly with the layer immediately above
or below it, and different computers 100 and 116 can communicate
directly with each other only at the physical layer 102. However,
different computers 100 and 116 can effectively communicate at the
same layer using common protocols. For example, in one exemplary
embodiment, computer 100 can communicate with computer 116 at
application layer 114 by propagating a frame from application layer
114 of computer 100 through each layer below it until the frame
reaches physical layer 102. The frame can then be transmitted to
physical layer 102 of computer 116 and propagated through each
layer above physical layer 102 until the frame reaches application
layer 114 of computer 116.
[0022] The IEEE 802.11 standard for wireless local area networks
("WLANs") operates at the data link layer 104, which corresponds to
layer 2 of the OSI seven layer model, as described above. Because
IEEE 802.11 operates at layer 2 of the OSI seven layer model,
layers 3 and above can operate according to the same protocols used
with IEEE 802 wired LANs. Furthermore, layers 3 and above can be
unaware of the network actually transporting data at layers 2 and
below. Accordingly, layers 3 and above can operate identically in
the IEEE 802 wired LAN and the IEEE 802.11 WLAN. Furthermore, users
can be presented with the same interface, regardless of whether a
wired LAN or WLAN is used.
[0023] With reference to FIG. 2, an exemplary extended service set
200, which forms a WLAN according to the IEEE 802.11 standard, is
depicted having basic service sets ("BSS") 206, 208, and 210. Each
BSS can include an access point ("AP") 202 and stations 204. A
station 204 is a component that can be used to connect to the WLAN,
which can be mobile, portable, stationary, and the like, and can be
referred to as the network adapter or network interface card. For
instance, a station 204 can be a laptop computer, a personal
digital assistant, and the like. In addition, a station 204 can
support station services such as authentication, deauthentication,
privacy, delivery of data, and the like.
[0024] Each station 204 can communicate directly with an AP 202
through an air link, such as by sending a radio or infrared signal
between WLAN transmitters and receivers. Each AP 202 can support
station services, as described above, and can additionally support
distribution services, such as association, disassociation,
distribution, integration, and the like. Accordingly, an AP 202 can
communicate with stations 204 within its BSS 206, 208, and 210, and
with other APs 202 through medium 212, called a distribution
system, which forms the backbone of the WLAN. This distribution
system 212 can include both wireless and wired connections.
[0025] With reference to FIGS. 2 and 3, under the current IEEE
802.11 standard, each station 204 must be authenticated to and
associated with an AP 202 in order to become a part of a BSS 206,
208, or 210. Accordingly, with reference to FIG. 3, a station 204
begins in State 1 (300), where station 204 is unauthenticated to
and unassociated with an AP 202. In State 1 (300), station 204 can
only use a limited number of frame types, such as frame types that
can allow station 204 to locate and authenticate to an AP 202, and
the like.
[0026] If station 204 successfully authenticates 306 to an AP 202,
then station 204 can be elevated to State 2 (302), where station
204 is authenticated to and unassociated with the AP 202. In State
2 (302), station 204 can use a limited number of frame types, such
as frame types that can allow station 204 to associate with an AP
202, and the like.
[0027] If station 204 then successfully associates or reassociates
308 with AP 202, then station 204 can be elevated to State 3 (304),
where station 204 is authenticated to and associated with AP 202.
In State 3 (304), station 204 can use any frame types to
communicate with AP 202 and other stations 204 in the WLAN. If
station 204 receives a disassociation notification 310, then
station 204 can be transitioned to State 2. Furthermore, if station
204 then receives deauthentication notification 312, then station
204 can be transitioned to State 1. Under the IEEE 802.11 standard,
a station 204 can be authenticated to different APs 202
simultaneously, but can only be associated with one AP 202 at any
time.
[0028] With reference again to FIG. 2, once a station 204 is
authenticated to and associated with an AP 202, the station 204 can
communicate with another station 204 in the WLAN. In particular, a
station 204 can send a message having a source address, a basic
service set identification address ("BSSID"), and a destination
address, to its associated AP 202. The AP 202 can then distribute
the message to the station 204 specified as the destination address
in the message. This destination address can specify a station 204
in the same BSS 206, 208, or 210, or in another BSS 206, 208, or
210 that is linked to the AP 202 through distribution system
212.
[0029] Although FIG. 2 depicts an extended service set 200 having
three BSSs 206, 208, and 210, each of which include three stations
204, it should be recognized that an extended service set 200 can
include any number of BSSs 206, 208, and 210, which can include any
number of stations 204.
[0030] As noted earlier, WLANs can provide users with increased
mobility, in comparison to wired LANs, but the quality of
communications over a WLAN can vary for reasons that are not
present in wired LANs. For example, as described above with regard
to FIG. 2, stations 204 can communicate with other stations 204
through an AP 202. More particularly, each station 204 can have a
transmission range within which station 204 can transmit signals to
an AP 202 within the WLAN. Different stations 204 within a WLAN can
have different transmission ranges, depending on the
characteristics of the devices used as stations 204. For example, a
handheld device used as station 204 can have a different
transmission range than a laptop used as station 204.
[0031] When a station 204 transmits a signal to an AP 202, other
stations 204 can be located within the transmission range of the
station 204 transmitting the signal. These other stations 204 can
detect the transmitted signal and can wait to send their own
signals until the wireless medium is free from traffic associated
with the transmitted signal. However, as described above, because a
station can have a limited transmission range, other stations
located outside of this transmission range, typically called
"hidden nodes," can exist in a WLAN. These "hidden nodes" can send
signals across the WLAN that can collide with signals sent by the
station. This type of collision arising from the presence of
"hidden nodes" is typically called the "hidden node problem."
[0032] More particularly, FIG. 4 depicts an exemplary embodiment of
the "hidden node problem." With reference to FIG. 4, stations 204a
and 204b are both authenticated to and associated with AP 202.
Furthermore, station 204a has a transmission range 400 and station
204b has a transmission range 402. Because station 204a is not
located within the transmission range 402 for station 204b and
because station 204b is not located within the transmission range
400 for station 204a, stations 204a and 204b can both send messages
to AP 202 during the same time period without being aware that the
other station has sent a message to AP 202. Specifically, station
204a can send message 404, which can be detected by stations 204
(FIG. 2) within transmission range 400. Because station 204b is
located outside of transmission range 400, station 204b cannot
detect message 404. During the same time period, station 204b can
send message 406 to AP 202, without being aware that message 404 is
also being sent over the WLAN. Message 406 can be detected by
stations 204 (FIG. 2) within transmission range 402. Because
station 204a is located outside of transmission range 402, station
204a cannot detect message 406. Stations 204a and 204b are
typically considered "hidden nodes" of one another because they are
located outside of each other's transmission range.
[0033] In the present exemplary embodiment, because messages 404
and 406 are transmitted to AP 202 during the same time period,
messages 404 and 406 can collide at AP 202. This collision can
interrupt the delivery of both messages. Typically, the collision
of messages originating from hidden nodes in this manner is called
the "hidden node problem."
[0034] The collision of messages resulting from the "hidden node
problem" can create unacceptable performance and reliability
problems in a WLAN. For instance, each message that is interrupted
by a collision can be resent according to the IEEE 802.11 standard.
However, resending the message can delay the receipt of the message
at its destination. In addition, each resent message can consume
additional bandwidth in the WLAN. Such delays and bandwidth
consumption can affect other messages being sent across the WLAN,
thereby creating performance and reliability problems in the
WLAN.
[0035] Accordingly, identifying hidden nodes in a WLAN can be
useful in determining the characteristics of a WLAN, such as the
potential for performance and reliability problems in the WLAN.
With reference to FIGS. 5 and 6, an exemplary embodiment of a
process that can be used to identify hidden nodes for a station in
a WLAN is depicted. More particularly, station 204a can obtain a
list of medium access control ("MAC") addresses for stations 204b
in a WLAN by any convenient method. For instance, station 204a can
discover stations 204b and their associated MAC addresses by
detecting signals transmitted over the WLAN for a period of time,
and from various locations. In another example, a list of MAC
addresses can be imported to station 204a. For instance, a list of
stations 204b associated with AP 202 can be imported to station
204a.
[0036] In the present embodiment, after station 204a obtains MAC
addresses for stations 204b, then station 204a can determine which
stations 204b are hidden nodes to station 204a. More particularly,
station 204a can determine if station 204b is a hidden node during
sequence of frame exchanges across the WLAN. In step 600, station
204a can send a message 500. With reference to FIG. 7, message 500
can include a header 700, having a destination address 704, a basic
service set identification ("BSSID") 706, a source address 708, and
other information 710. Specifically, header 700 in message 500 can
have a destination address 704 set to station 204b, a BSSID 706 set
to AP 202, and a source address 708 set to station 204a.
[0037] In step 602, AP 202 can receive message 500. In response to
receiving message 500, then in step 604, AP 202 can send an
acknowledgement ("ACK") 502 to station 204a. In step 606, station
204a can receive ACK 502. In some embodiments, if station 204a does
not receive ACK 502 from AP 202 within a specified period of time,
then station 204a can resend message 500, and begin again from step
600 of FIG. 6.
[0038] According to the present exemplary embodiment, in step 608,
AP 202 can send message 500 to station 204b as message 504, based
on the destination address 704 set forth in header 700 of message
500. Next, in step 610, station 204b can receive message 504 from
AP 202. In response to receiving message 504, then in step 612,
station 204b can send ACK 506 to AP 202. ACK 506, sent from station
204b, can be transmitted across the WLAN throughout a transmission
range 402 (FIG. 4). As described above, other stations 204 (FIG. 2)
that are located in this transmission range can detect ACK 506.
[0039] Next, in step 614, station 204a can monitor for ACK 506. If
station 204a can detect ACK 506, then station 204a is within
transmission range 402 (FIG. 4) of station 204b. If station 204a
cannot detect ACK 506, then station 204a is not within transmission
range 402 (FIG. 4) of station 204b. Furthermore, if station 204a is
within transmission range 402 (FIG. 4) of ACK 506, then station
204b is not a hidden node of station 204a. Alternatively, if
station 204a is not within transmission range 402 (FIG. 4) of ACK
506, then station 204b is a hidden node of station 204a.
[0040] In step 614, it should be recognized that station 204a can
fail to detect ACK 506 for various reasons. For instance, if AP 202
fails to send message 504 to station 204b, then station 204b would
not send ACK 506. In this case, there would be no ACK 506 for
station 204a to detect, and station 204a's failure to detect ACK
506 could be attributed to transmission problems between AP 202 and
station 204b. Accordingly, in some applications, if station 204a
does not detect ACK 506, station 204a can send another message 500
and monitor for another ACK 506. By repetitively sending messages
500 and monitoring for ACKs 506, station 204a can more confidently
determine whether station 204b is a hidden node of station 204a. If
station 204a receives any ACK 506 from station 204b, then station
204a can determine that station 204b is not a hidden node.
Alternatively, if station 204a does not receive any ACK 506 from
station 204b, then station 204a can determine that station 204b is
a hidden node with more confidence as the number of messages 500
repetitively sent from station 204a increases.
[0041] After determining whether station 204b is a hidden node of
station 204a, station 204a can repeat the above described process
for other stations 204b in the list described above. Although the
present embodiment describes obtaining a list of MAC addresses for
stations 204b in a WLAN, it should be recognized that a single MAC
address can be obtained in order to determine if a specific station
204b having the single MAC address is a hidden node of a station
204a.
[0042] With reference to FIG. 8, another exemplary process that can
be used to identify hidden nodes for a station in a WLAN is
depicted. More particularly, station 204a can be located within
transmission range 804 of AP 202. Although station 204a can be
associated with AP 202, it should be recognized that station 204a
can be unassociated with AP 202 in some applications. When AP 202
sends a message 800, which can originate from any station 204 (FIG.
2) or from any AP 202 in the WLAN, to station 204b, station 204a
can detect this message 800. In response to receiving message 800,
station 204b can send ACK 802 to AP 202. This ACK 802 can be
detected by stations 204 or APs 202 (FIG. 2) within transmission
range 806 of station 204b.
[0043] After detecting message 800, station 204a can monitor for
ACK 802, which can be sent from station 204b to AP 202. If station
204a can detect ACK 802, then station 204a is within transmission
range 806 of station 204b. If station 204a cannot detect ACK 802,
then station 204a is not within transmission range 806 of station
204b, as shown in FIG. 8. Furthermore, if station 204a is within
transmission range 806 of ACK 802, then station 204b is not a
hidden node of station 204a. Alternatively, if station 204a is not
within transmission range 806 of ACK 802, then station 204b is a
hidden node of station 204a.
[0044] One advantage of the present embodiment includes allowing
station 204a to passively monitor the WLAN for messages sent by an
AP and to passively monitor for ACKs sent to the AP from a
receiving station. By passively monitoring the WLAN in this manner,
station 204a can obtain information about hidden nodes in the WLAN
without consuming bandwidth or interfering with traffic over the
WLAN. Furthermore, station 204a can passively monitor multiple
stations in the WLAN during the same time period. Although the
exemplary embodiments described above are described separately, it
should be recognized that these exemplary embodiments can be
combined. Such a combination can allow a station to actively
monitor the WLAN according to the previously described exemplary
embodiment and passively monitor the WLAN according to the present
embodiment, during the same time period.
[0045] In each of the exemplary processes described above, station
204a can be mobile, portable, stationary, and the like. For
instance, station 204a can be a laptop computer, a personal digital
assistant, and the like. In addition, station 204a can be used by a
user as a diagnostic tool, by an administrator as an administrative
tool, and the like, to assess the quality of communications in the
WLAN.
[0046] Furthermore, the messages described above with regard to the
"hidden node problem" and exemplary embodiments are sent as data
frames according to the IEEE 802.11 standard. More particularly, in
accordance with the current IEEE 802.11 standard, data frames can
have lengths of at least 29 bytes. In contrast, the ACKs are sent
as control frames. In accordance with the current IEEE 802.11
standard, control frames can have lengths of at most 20 bytes. For
instance, a standard IEEE 802.11 ACK has a length of 14 bytes. It
should be noted that these size limitations for data frames and
control frames may change if the IEEE 802.11 standard is
revised.
[0047] In addition to being smaller in size than data frames,
control frames are solely generated at the data link layer 104
(FIG. 1) and below. For example, when a message is received, an ACK
is automatically generated at and sent out from data link layer 104
(FIG. 1) at AP 202. As such, the received message does not need to
be processed above data link layer 104 (FIG. 1) in order for the
ACK frame to be generated and sent.
[0048] As described above, the messages and ACKs described above
can be detected by stations and APs within the transmission range
of the station or AP sending the messages or ACKs. Furthermore, the
information detected can include header information, such as the
source address, destination address, BSSID, and the like.
Accordingly, this information can be used in the exemplary
embodiments described above to gather information about stations
that are hidden nodes in the system.
[0049] Although the present invention has been described with
respect to certain embodiments, examples, and applications, it will
be apparent to those skilled in the art that various modifications
and changes may be made without departing from the invention.
* * * * *