CCN - Unit 3 - 7th ECE - VTU - Multiple Access - ramisuniverse
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UNIT 3: Multiple accesses: Random access, Controlled access, Channelisation 6 Hours
Random access
Random access or contention methods:
No station: superior to other station
None of the station: assigned the control over the other station
No station permits, or not permits: other station to send
Each instance in: station uses the procedure defined by the protocol - to decide - to send or not send the data - if it has
the data to send
Decision of the station: depends on the status of the link (idle or busy) - it connected of
Each station: can transmit when it desires - on the condition that - it follows the procedure defined by the protocol -
including the testing of the state of the medium
Features that give its name:
There is no scheduled time, for a station to transmit - transmission is random among the stations - so, these
methods are - random methods
No rules specify, which station to send next - stations complete with one another, to transmit to the medium -
so, these methods are - contention methods
Random access method: each station has the right to the medium without being controlled by any other station
Collision (access conflict): which occurs when more than one station tries to send the data - if occurs, frames will be
either destroyed or modified
Collision to avoid or to resolve collision:
Each station follows the procedure - that answers the following questions:
When can the station access the medium?
What can the station do if the medium is busy?
How can the station determine the success or failure of the transmission?
What can the station do if there is an access conflict?
Random access methods evolution
came from ALOHA
ALOHA: simple procedure of multiple access (MA)
Carrier sense multiple access (CSMA): ALOHA been - improved by the addition of a procedure - that forces the station
to sense the medium before transmitting
CSMA two methods:
CSMA/CD: Carrier Sense Multiple Access/Collision Detection: tells the station - what to do when the
collision is detected
CSMA/CA: Carrier sense Multiple Access/Collision Avoidance: tries to avoid the collision
ALOHA
ALOHA: Earliest random access method - developed at the University of Hawaii - in early 1970
Designed for the radio (wireless) LAN - can be used on any shared medium
There are potential collisions: in this arrangement – medium, is shared between the stations
Station when sends the data - another station may attempt to do so at the same time - data from the 2 stations: collide
and garbled become
Types of ALOHA: pure ALOHA and slotted ALOHA
pure ALOHA
Original ALOHA - simple, elegant protocol
Idea: Each station sends a frame whenever it has a frame to send
Channel: since, only one - possibility of collision between frames from different stations - present
Fig. shows: ex. of frame collisions in pure ALOHA
Unrealistic assumption: 4 stations that contend with one another for access to the shared channel - Fig. shows: each
station sends 2 frames - total of 8 frames on the shared medium
Some frames collide because: multiple frames are in contention for the shared channel
Fig. shows: only 2 frames survive (frame 1.1 of station 1 and frame 3.2 of station 3) - if one bit of the frames coexists
on the channel with one bit of another frame: collision will and frames will destroy - Frame resending: of the destroyed
frames to be
pure ALOHA: relies on the acks from the receiver - Station when sends the frame, it expects the ack from the receiver
Methods to prevent congestion in pure ALOHA:
Ack if not arrived after a time-out period: each station waits for a random period - before resending its frame
Back-off period, TB: max. time within which ack had to back from receiver to transmitter - for the sent frame
Randomness: helps avoid more collisions
Prevent the congestion of the channel - with retransmitted frames
Max. no. of retransmission attempts, Kmax: max.: time up to which frame resending can be - to got ack of receipt of
that frame from the receiver - Kmax time: after station can give up resending of a frame, and try to later
Fig. shows: procedure for pure ALOHA - based on the above strategy
Max. round-trip propagation delay, 2Tp: amount of time required to send a frame - between the 2 most widely
separated stations
Time-out period: equal to max. no. of possible round-trip propagation delay
K: number of attempted unsuccessful transmissions
Back-off period, TB: is a random value - normally, depends on K - formula for TB - depends on implementation
Tp: max. propagation time
Tfr: avg. time required to send out a frame
Common formula for TB: Binary exponential back-off
For each retransmission: TB is the product of - a multiplier in the range of 0 to 2 power of (K-1), which is randomly
chosen and Tp or Tfr
Note: In this method - range of the random numbers increases - after each collision
Kmax.: usual value is chosen as 15
Tfr: frame transmission time
Vulnerable time: Time in which - there is the possibility of collision
Assumption: stations send fixed length frames - with each frame taking Tfr s to send
Fig. shows - vulnerable time for station A
Station A: sends the frame at time t
Assumption: station B has already send a frame between t - Tfr and t
It leads to collision, between the station A and of B - end of B's frame collide with the
Beginning of A's frame - suppose: station C sends the frame between t and t+Tfr - there is a collision between the
frames from stations A and C - beginning of C's frame, collide with the end of A's frame
Fig. : in vulnerable time - in pure ALOHA - is 2 times the frame transmission tim
Vulnerable time of pure ALOHA: 2 * Tp
Throughput
G: average number of frames generated by the system during one frame transmission time
S: average number of successful transmissions for pure ALOHA - S= G * e(power of -2G)
Smax, max. throughput: Smax. = 0.184 for G=0.5
0.5 a frame is generated during one Tfr or 1 frame generated during 2Tfr, if generated at transmitter: then 18.4 percent
of these frames, reaches the receiver successfully - because, vulnerable time in pure ALOHA is 2Tfr
Station if generates only one frame in vulnerable time (no other stations generate their frames during this time): frame
will reach the destination successfully
For pure ALOHA: Throughput: S=G*e(power of -2G) and
Max. throughput: Smax=0.184, when G=0.5
slotted ALOHA
pure ALOHA: has the vulnerable time of 2Tfr - because no rule that when the station can send the data
Station may send the data soon after another station has started or soon before another station has finished
slotted ALOHA: invented to improve - the efficiency of pure ALOHA
Time is divided into slots of Tfr s - Forces the station to send only at the beginning of the time slot
Fig. shows - ex. of frame collisions in slotted ALOHA
Station is allowed to send only at the beginning of the synchronized time slot
If the station misses the moment: it must wait until the beginning of the next time slot - i.e., station which started at the
beginning of this time slot has already finished sending its frame
Still there is the possibility of collision: if the stations try to send at the beginning of the same time slot vulnerable time
in slotted ALOHA: reduced to half of pure ALOHA - equal to Tfr
Fig. shows - this situation
slotted ALOHA: vulnerable time= Tfr
Throughput
S: avg. no. of successful transmissions for slotted ALOHA - S=G*e (power of -G)
Smax, max. throughput of slotted ALOHA: Smax=0.368, when G=1
During Tfr - if one frame is generated in transmitted: then 36.8% of these frames reach to receiver successfully -
because vulnerable time for slotted ALOHA is Tfr
Station in generated one frame in vulnerable time (no other stations generates a frame during this vulnerable time) - the
frame generated will reaches the receiver successfully
For slotted ALOHA: Throughput: S=G*e(power of -G) and
Max. throughput: Smax=0.368, when G=1
Carrier Sense Multiple Access (CSMA)
Collision chances to minimize and to increase the performance: CSMA was developed
Collision chances can be reduced: if a station senses the medium before trying to use it
CSMA: require that each station - first listens to the medium or check the state of the medium - before sending - based
on the principle - "sense before transmit" or "listen before talk" can reduce the possibility of collision - but, it
cannot eliminate it - Fig. in space and time model of CSMA been shown - stations are connected - to a shared channel -
usually, a dedicated medium possibility of collision: still exists - because, of propagation delay - station when sends a
frame, it still takes time, although very short, for the first bit to reach every station and for every station to sense it -
station may sense the medium and find it idle, only because the first bit sent by another station has not yet been
received
At t1: station B senses the medium and finds it idle - so, it sends a frame
At t2 (t2>t21): station C senses the medium and finds it idle - because, at this time, the first bits from station B have
not reached station C and station C also sends a frame - the two frames collide and both frames are destroyed
Vulnerable time (Propagation time, Tp): it’s the propagation time, Tp in slotted ALOHA
Vulnerable time:time needed for the signal to propagate from one end of the medium to the other
When a station sends a frame - and any other stations send the frames at this time - collision will result
If the first bit of the frame reaches the send of the medium - every station will already have heard the bit and will
refrain from sending
Leftmost station A sends a frame at time t1: it reaches the rightmost station D at time t1+Tfr
Grey area: shows the vulnerable area in time and space
Persistence methods: stations do what, if channel is busy and channel free: is answered by persistence methods
Persistence methods types: 1-persistent method, non-persistent method, p-persistent method
Fig. shows behavior of 3 persistent methods - when a station finds a channel busy
1-persistent method: simple and straightforward
After a station finds the line idle: it sends its frame immediately (with probability 1)
Has the highest chance of collision - because, 2 or more stations may find the line idle and send their frames
immediately - Ethernet: uses this method
Non-persistent method: station that has the frame to send - senses the line
If the line is idle: it sends immediately
If the line is not idle: it waits a random amount of time and then senses the line again
Reduces the chance of collision - because, it is unlikely that 2 or more stations will wait the same amount of time and
retry to send simultaneously
Reduces the efficiency of the network - because, medium remains idle when there may be stations with frames to send
p-persistent method: used if the channel has the time slots with a slot duration >= max. Tp
Combines the advantages of other 2 strategies
Reduces the chance of collision and improves the efficiency
After the station finds the line idle - it follows these steps:
1. With probability p: station sends the frame
2. With probability q=(p-1): station waits for the beginning of the next time slot and checks the line again
a. If the line is idle: it goes to step 1
b. If the line is busy: it acts as though a collision has occurred and uses the back-off procedure
CSMA: does not specify the procedure - following a collision
Types of CSMA: CSMA/CD and CSMA/CA
Carrier Sense Multiple Access/Collision Detection (CSMA/CD)
Augments the algorithm to handle the collision
Station monitors the medium after it sends a frame to see if the transmission was successful
If so - station is finished - If there is a collision, frame is sent again
Understanding of CSMA/CD: First bits transmitted by the 2 stations involved in the collision been important
Each station continues to send bits in the frame until it detects the collision if the first bits collide - shown in fig.
Stations A and C: frame been in collision
At t1: station A has executed its persistence procedure - and, starts sending the bits of its frame
At t2: station C has not yet sensed the first bit sent by A
Station C executes - its persistence procedure and starts sending the bits in its frame - which propagates both to the left
and the right
After time t2: collision also occurs - station C detects the collision at time t3, when it receives the first bit of A's frame
- station C immediately (or after a short time, but assumption we that it is immediately) aborts the transmission
Station A detects collision at time t4: when it receives the first bit of C's frame - it also immediately aborts the
transmission
A transmits for the duration: t4-t1
C transmits for the duration: t3-t2
Protocol to be operated for: length of any frame divided by the bit rate must more than t4-t1 and t3-t2 durations
At t4: transmission of A's frame - though incomplete, is aborted
At t3: transmission of B's frame - though incomplete, is aborted
Fig. shows more complete graph - for the durations for the 2 transmissions
Minimum frame size
CSMA/CD to work: restriction on frame size is needed
Before sending last bit of the frame - sending station must detect a collision, if any, and aborts the transmission -
because station once the entire frame is sent, does not keep a copy of the frame and does not monitor the lien for
collision detection- so, min. Tfr = 2 *max.Tp to understand let the worst case scenario been considered -
If the 2 stations involved in the collision are max. distances apart - signals from the first takes time Tp to reach the
second and the effect of the collision takes another time Tp to reach the first - so, requirement is that the first station
must still be transmitting after 2Tp
Procedure
Fig. shows the flow diagram for CSMA/CD - is similar to one of ALOHA protocol, but with few differences
CSMA/CD differences compared when with ALOHA
1. Addition of the persistence processes:
Needs to sense the channel before - start sending the frame - by using one of the persistent processes corresponding box
can be replaced by one of the persistent processes shown in Fig.
2. Frame transmission:
In ALOHA: first transmission of entire frame will be and then wait for the ack will be
In CSMA/CD: transmission and collision detection is a continuous process
Entire frame will not send and then look for the collision
Station transmits and receives continuously and simultaneously (using 2 different ports) - loop been shown to have
transmission is a continuous process
Constant monitoring will to detect one of two conditions - either transmission is finished or a collision is detected -
either event in transmission is stopped
Loop from when came out - if the collision is not been detected - then, it means that transmission is complete; the entire
frame is transmitter otherwise the collision - has occurred
3. Sending of a short jamming signal:
Enforces the collision in case other stations have not yet sensed the collision
Energy level
Level of energy in the channel: can have 3 values
1. Zero: at this level, channel is id
2. Normal: at this level, station has successfully captured the channel and is sending its frame
3. Abnormal: at this level, there is a collision and the level of the energy is 2 the normal level
Station that has a frame to send or is sending a frame: needs to monitor the energy level - to determine if channel is
idle, busy, or in collision mode
Throughput
Max. throughput: occurs at different value of G and based on the persistence method and the value of p in the p-
persistent approach
Max. throughput in 1-persistent method: is around 50% when G=1
Max. throughput in non-persistent method: can go up to 90% when G is between 3 and 8
Max. throughput in p-persistent method: depends on p value
Carrier Sense Multiple Access/Collision Avoidance (CSMA/CA)
CSMA/CD basic idea: station need to be able to receive - while transmitting to detect a collision
When no collision - station receives one signal - its own signal
When there is a collision - station receives 2 signals - its own signal and a signal transmitted by a second station
Distinguishing between above 2 cases: received signals in these 2 cases must be different
Signal from the second station can be made: needs to add a significant amount of energy to the one created by the first
station
In wired network:
Received signal: has almost the same energy as the sent signal
Because, either the length of the cable is short or there are repeaters that amplify the energy between the sender and the
receiver - it means that, in a collision detected energy almost doubles
In a wireless network:
Much of the sent energy is lost in transmission
Received signal has very little energy - so, collision may add only 5 to 10% of additional energy - this is not useful for
effective collision detection
Collisions in wireless network - need to be avoided, since, they can't be detected - CSMA/CA been invented for this
CSMA/CA: Collisions are avoided here - by 3 strategies:
1. InterFrame Space (IFS)
2. Contention window
3. Acknowledgement
Fig. shows the 3 strategies of CSMA/CA
1. IFS (InterFrame Space):
Collisions are avoided: by deferring transmission even if the channel is found idle
Channel when idle found: station does not send immediately - stations wait for a period of time called IFS
Channel even though appeared idle - when it is sensed - a distant station may have already started transmitting - distant
stations frame might not yet reached this station
If IFS time later: channel is still idle - stations can send the frame - but only after waiting a time called contention time
Priorities of stations and frame types can be made: by varying the IFS variable
Ex.: station with shorter IFS, has a higher priority
IFS can be used define the priority of a station or a frame
2. Contention window:
Amount of time divided into slots
Station that is ready to send chooses a random number of slots as its wait time
Number of slots in the window: changes according to the binary exponential back-off strategy - that is, it is set to one
slot for the first time and then doubles each time the station cannot detect an idle channel after the IFS time
Is similar to p-persistent method - except, that a random outcome defines the number f slots taken by the waiting station
needs to sense the channel after each time slot
If the station finds the channel busy - it does not restart the process - it just stops the timer and restarts it when the
channel is sensed as idle - it gives priority to the station ith the longest waiting time
Contention window: in CSMA/CA, if the station finds the channel busy, it does not restart the timer of the contention
window; it stops the timer and restarts it when the channel becomes idle
3. Acknowledgemnt:
Data may be corrupted during transmission - from that collisions still might be, which destroy the data
Positive acks and time-out timer: can help guarantee that the receiver has received the frame
Procedure: Fig. shows the procedure
Note:
Channel needs to be sensed before and after the Ifs
Channel also needs to be sensed during the contention window
For each time slot of the contention window: channel is sensed –
If channel is found idle: the timer continues
If channel is found busy: timer is stopped and continues after the timer becomes idle again
CSMA/CA and wireless networks
CSMA/CA: Mostly intended for use in wireless networks
Procedure above: not enough sophisticated to handle wireless networks of hidden terminals and exposed terminals
problems - these problems can be solved by using hand-shaking features
Controlled Access
Controlled access: stations consult one another - to find which station has the right to send
Station cannot send: unless it has been authorized by other stations
Popular controlled access method:
1. Reservation
2. Polling
3. Token passing
1. Reservation
Reservation: station need to make a reservation before sending data - time is divided into intervals
Each interval in: a reservation frame precedes the data frames sent in that interval
N stations: if in the system - N minislots in the reservation frame - each minislot - belongs to a station
Station when needs to send a data frame: it makes a reservation in its own minislot
Stations made reservations: can send their data frames after the reservation frame
Fig. shows the situation with 5 stations and 5 minislot reservation frame
First interval in: only stations 1, 3, and 4 have made reservations
Second interval in: only station 1 has made a reservation
2. Polling
Polling: works with topologies in which one device is designed as a primary station and the other devices, the
secondary stations
Data exchanges: all to be from primary device - even destination when is the secondary device
Primary device: controls the link - determines which device is allowed to use the channel at a given time - is the
initiator of a session
Secondary devices: follow its instruction
Poll: Primary: if wants the data - it asks the secondary, if they have anything to send
Select: Primary if wants to send data: it tells the secondary to get ready to receive
Select:
Used whenever - primary device has something to send
Primary - controls the link
Primary if neither sending the data nor receiving the data: it knows the link is available
Primary does not know: however, whether the target device is prepared to receiver - so,
Primary alert to the secondary to the upcoming transmission - and wait for the ack of the
secondary ready status
Primary: prior to send the data - transmits a select (SEL) frame - which contains will be the address of the secondary
Poll:
Used by the primary: to solicit the transmissions from the secondary devices
Primary when ready: to receive the data - it ask (poll) each device in turn – whether they had any data for it
First secondary when approached: it responds with NAK - if no data is there for it to primary
with data frame: if it has the data for primary
Response if NAK: primary polls the next secondary - in the same manner - until it finds the secondary having data for it
Primary: reads the frame - when the response is positive (a data frame) - and returns an ACK frame - verifying its
receipt
Token Passing
Token passing: Stations in a network - are organized in a logical ring
For each station: there is a predecessor and a successor
Predecessor: station which is logically before the station in the ring
Successor: station which is logically after the station in the ring
Current station: station which the one being accessing the channel
Channel accessing right: passed from predecessor to the current station
Channel accessing right: passes from current station to the successor - when current station has no more data to send
Token: special packet circulates through the ring possession of it - gives the station - right to access the channel, and
send its data
Station: When has some data to send - it waits until it receives the token from its predecessor then holds the
token - and sends its data
When no more data to send - it releases the token - passes the token to next station
Cannot send data - until it receives the token again in the next round
When receives the token - no data to send - then, it transfers token to next station
Token management
Need for token management:
For accessing the token
Stations: must be limited in the time - they can have possession of the token
Token: must be monitored - to ensure it has not been lost or destroyed
Ex.: If a station, holding the token fails - token will disappear form the network
Priorities to be assigned - to the stations and to the type of data being transmitted
Maintenance of priorities - to make low-priority stations release the token to high-priority stations
Logical ring
Token-passing network: stations do not have to be physically connected in a ring stations can be connected in the
logical ring form
Fig. shows 4 different physical topologies - that can create a logical ring
Physical ring topology:
When the station sends the token: to its successor - token cannot be seen by other stations - successor is next one in the
line - token does not have to have the address of the next successor
Problem: if one of the links (medium between two adjacent stations) fails - the whole system fails
Dual ring topology:
Uses a second (auxiliary) ring - which operates in the reverse direction compared with the main ring
Second ring: used in emergency
Main ring: in one of the links - failed if - system automatically combines - the two rings - to form a temporary ring
Failed link - when restored - auxiliary ring becomes idle again
Note: This topology to work - each station needs to have 2 transmitter ports and 2 receiver ports - CDDI and FDDI:
high-speed token ring networks - use this topology
Bus ring topology (Token bus):
Bus: stations are connected to single cable
Stations make: a logical ring - since, each station knows the address of its successor and also the predecessor for token
management purposes
Station when finished the data sending: it releases the token - inserts the address of its successor in the token - station:
with the address - matching with the address in the toke - gets the token - to access the shared media
Toke bus LAN: standardized by IEEE - uses this topology
Star ring topology:
Star: is the physical topology
Hub: acts as a connector - wiring inside the hub, makes the ring - stations are connected to this ring through 2 wire
connections
Advantage: less-prone to failures - if a link goes down, it will be bypassed by the hub - and the rest of the stations can
operate - adding and removing of stations - is easier
IBM Token ring LAN: uses this topology
CHANNELIZATION
Channelization: Multiple access method - in which the available bandwidth of a link is shred in time, frequency, or
through code - between different stations
Three channelization protocols:
1. FDMA
2. TDMA
3. CDMA
Frequency-Division Multiple Access (FDMA)
FDMA: Available bandwidth is divided into frequency bands
Each station is allocated a band to send its data
Each band is reserved for a specific station
Each band belongs to the station all the time
Each station also uses a band pass filter to confine the transmitter frequencies
Guard bands: used to prevent interferences - separate allocated bands from one another
Fig. shows the FDMA idea
FDMA: Available bandwidth of the common channel is divided into bands that are separated by guard bands
Specifies a predetermined frequency band for the entire period of communication
Stream data (continuous flow of data that may not be packetized): can easily be used with FDMA
FDMA Vs FDM
Both seem conceptually similar - but, they have differences between them
FDM: Physical layer technique
Combines the load from low-BW channels and transmits them by using a high-BW channel
Channels combines: are low pass
Multiplexer: modulates the signals - combines them - creates a band pass signal
BW of each channel is shifted by the multiplexer
FDMA: An access method in the data link layer
DLL in each layer: tells its physical layer - to make a band pass signal from the data passed to it
Signals must be created in the allocated band
There is no physical multiplexer at the physical layer
Signals created at each station are automatically band pass-filtered - they are mixed when they are sent to the
common channel
Time-Division Multiple Access (TDMA)
TDMA: Stations share the BW of the channel in time
Each station is allocated a time slot - during which it can send data
Each station transmits - its data in is assigned time slot
Fig. shows the idea behind TDMA
Synchronization: main problem in TDMA - between different stations
Each station: needs to know the beginning of its slot and location of its slot - is difficult because of propagation delays -
introduced in the system if the stations are spread over a large area
Guard times: can be inserted to compensate for the delays
Synchronization - normally, accomplished by having some synchronization bits
Synchronization bit: Preamble bit: is added at the beginning of each slot
TDMA: BW is just one channel - timeshared between different stations
TDMA Vs TDM
TDMA and TDM: conceptually seem the same - but, there are differences between them
TDM: Physical layer technique
Combines the data from slower channels and transmits them by using a faster channel
TDM uses: a physical multiplexer - that interleaves data units from each channel
TDMA: An access method in the DLL
DLL in each station: tells its physical layer - to use the allocated time slot
NO physical multiplexer - is present at the physical layer
Code-Division Multiple Access (CDMA)
CDMA: Was conceived several decades back
Implementation made possible: by recent advancements in electronic technology
Differs from FDMA: because only one channel occupies the entire BW of the link
Differs form TDMA: because all sections can send data simultaneously there is no time sharing
CDMA: one channel carries all transmission simultaneously
Analogy: CDMA: simply means - communication with different codes
Ex.: In a room: 2 can talk in English, if they only know English, and no others there - 2 can talk in Chinese, if they only
know Chinese, and no others there
Room: here, is common channel - can allow communication between several couples – but in different languages
(codes here)
Idea:
Assumption: 1 2 3 and 4 stations - connected to same channel
Station 1: d1 - data and c1 - code
Station 2: d2 - data and c2 - code
Station 3: d3 - data and c3 - code
Station 4: d4 - data and c4 - code
Assumption: Assigned codes have 2 properties
1. If we multiply each code by another: we get 0
2. If we multiply each code by itself: we get 4 (the number of stations)
Fig. shows how the 4 stations can send data using the same common channel
Station 1: multiples its data by its code to get: d1.c1
Station 2: multiples its data by its code to get: d1.c2
Station 3: multiples its data by its code to get: d1.c3
Station 4: multiples its data by its code to get: d1.c4
data on the channel: sum of the data from all the terms above calculated
Any station that wants to receive data from one of the other 3: multiples the data on the channel by the code of the
ender
Ex.: Station 1 and 2: are talking to each other
Station 2: wants to hear what station 1 is saying
Station 2: multiplies the data on the channel by c1(code of station 1)
(c1.c1) = 4, (c2.c1) = 0, (c3.c1) = 0, (c4.c1) = 0
Station 2: divides the result by 4 - to get the data of station 1
Data = (d1.c1 + d2.c2 + d3.c3 + d4.c4).c1 = d1.c1.c1+d2.c2.c1+d3.c3.c1+d4.c4.c1 = 4.d1 + 0 + 0 + 0 =4.d1 and station
2: divides result by 4: 4.d1/4 = d1 (data of station 1)
Chips
CDMA: based on coding theory
chip: each station is assigned a code - which is a sequence of numbers
Fig. shows the codes using for previous ex. - c1, c2, c3, and c4 of
Fig. chip sequences - chip sequences are carefully selected
Orthogonal sequences:
Chip sequences carefully selected - which obey the properties given below:
1. Each sequence is made of N elements - N, number of stations
2. Multiplication of a sequence by a scalar: Number with if, a sequence is multiplied - every element in the sequence is
multiplied by that element 2.[+1 +1 -1 -1]=[+2 +2 -2 -2]
3. Inner product of 2 equal sequences: 2 equal sequences: if, multiplied - element by element -and added - N is result -
N: number of elements in each sequence – [+1 +1 -1 -1].[+1 +1 -1 -1]=1+1+1+1 = 4
4. Inner product of 2 different sequences: two different sequences - if multiplied - element by element – and added -
result is 0 and [+1 +1 -1 -1].[+1 +1 +1 +1]=1+1-1-1=0
5. Two sequences of addition: adding the corresponding elements result - is another sequence
[+1 +1 -1 -1]+[+1 +1 +1 +1]=[+2 +2 0 0]
Data representation
Encoding rules: Station if sending 0: -1 is encoding
Station if sending 1: 1 is encoding
Station if not sending data: 0 is encoding
Encoding and Decoding:
Ex.: 4 stations share - the link during a 1-bit interval
Procedure: can easily be repeated for additional intervals
Assumption: Stations 1 and 2 are sending a 0 bit - channel 4 is sending a 1 bit - station 3 is silent
Data at sender site: are translated to -1, -1, 0, and 1
Each station: multiplies the corresponding number (chip: it's orthogonal sequence) - which is unique for each station -
Result: is a new sequences at the same time
Sequence on the channel: sum of all 4 sequences -as defined before
Fig. shows - the situation
Assumption: station 3 - which was silent earlier - is listening station 2
Station 3: multiplies the total data on the channel by the code for station 2
[-1 -1 -3 +1].[+1 -1 +1 -1] = -4/4 = -1 i.e., the bit 1
Signal Level
Fig. shows: Digital signal produced by each station and data recovered at the destination
Fig. also shows: corresponding signals - for each station (by NRZ-L for simplicity) and also the signal that is on the
common channel
Fig. shows: Station 3 detection of data of station 2 - using code of station 2
Station 3: Total data on the channel: multiplied (inner product operation) - by station 2 chip code
then integrates and adds the area under the signal(Here: -4 is the result) - divides the result by 4
If answer is -1: data is interpreted as 0
If answer is 1: data is interpreted as 1
If answer is 0: data being not sent
Sequence Generation
Walsh table: Used to generate the chip sequences
2-D table - with an equal number of rows and columns
Fig. : shows the Walsh table
Fig. : General rule and examples of creating Walsh tables
Walsh table: each row is a table of chips
W1: is used for - one-chip sequence - having 1 row and 1 column
Walsh: according to - if Walsh table (WN) for N sequences known - for 2N sequences table (W2N) can be created
Fig. shows this
WN bar - is the complement for WN: here, each 1 is changed to -1 and vice versa
Fig. shows: how W2 and W4 - can be created using W1
W1 and W2: can be made from 4 W1's - with the last 1 complement of W1
W4: can be generated - by 4 W2's and by complementing the last one
W8: composed of 4 W4s and can be repeated this procedure for WNs
Note: WN formed later - each station is assigned a chip - corresponding to a row
Number of sequences needs to be: power of 2 - it must obey N=2(power of m)
Number of sequences in the Walsh table: N = 2 (power of m)
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