- Definitions:
- Pseudo Noise (PN) code =
a random sequence of
N bits
Example:
01001011( The number of 0's and 1's in the PN code should be approximately equal)
- Chip =
a popular name for the
PN code
- Chip length = the number of bits in the chip (PN code)
- Pseudo Noise (PN) code =
a random sequence of
N bits
- The Direct Sequence Spread Spectrum
(DSSS)
transmission technique:
- The sender and the
receiver select a common
Pseudo Noise (PN) code:
- Sender:
- Code for
transmitting 1:
- the chip (PN code)
- Code for
transmitting 0:
- the inverse of the chip (PN code)
Example:
- Code for
transmitting 1:
- Receiver: (decoding
algorithm):
- Receive N bits
(N = the chip length)
- If a majority of the
received N bits
matches the
PN code:
- The receiver decodes to a "1" bit
- If a majority of the
received N bits
fails to match the
PN code:
- The receiver decodes to a "0" bit
- Receive N bits
(N = the chip length)
- The sender and the
receiver select a common
Pseudo Noise (PN) code:
- Suppose the nodes A and B uses
the following PN code:
PN code = 0011011
- If the node B receives:
B: 1011011
then node B will decode as follows:
received: 1011011 PN code: 0011011 XOR ------------------ 1000000 NOT ------------------ 0111111 Majority = 1 ===> 1(You can compare the received data with the PN code using an Exclusive OR operation)
- The interference of
radio transmission is
very complex
- I will present a simplified explanation on how the PN code can overcome collisions (= multiple simultaneous transmissions)
- Simplification:
- I will use Amplitude Modulation
to show you the
effect
of a collision
- In a later section, I will sketch what is really going on; but not very in depth --- this is a Electrical Engineering subject...
- I will use Amplitude Modulation
to show you the
effect
of a collision
- Suppose the
PN code used is:
PN code = 0011011
- The PN code
transmitted using
Amplitude Modulation
will look like this:
(Low amplitude = 0, and high amplitude = 1)
- Effect of collision (jamming):
- Suppose there are
2 pairs of
senders/receivers:
- A/B uses PN code = 0011011
- C/D uses PN code = 1011010
- Suppose the following
transmissions happen
simulataneously:
- A sends "1" to B (i.e.: A will send 0011011 --- because its PN code "0011011")
- C sends "1" to D (i.e.: C will send 1011010 --- because its PN code "1011010")
Graphically: (using Amplitude Modulation)
- Physics:
- Simultaneous waves result in
super-imposition
(I.e.: the amplitudes are added together)
The super-imposed wave is as follows:
The receivers will both "hear" (receive) the above pattern !!!!
When both receiver try to decode the reception (using Amplitude Modulation), they will obtain this (corrupted) pattern:
- 1011011
Because:
- A large amplitude signal will be decoded as 1
- A low amplitude signal will be decoded as 0
- Simultaneous waves result in
super-imposition
- Suppose there are
2 pairs of
senders/receivers:
- Observation:
- Using amplitude modulation
(= my simplified explanation),
a collision will result in:
- or-ing the transmitted data bits
In reality, the receivers will use frequency filters to perform the decoding....
- The simplified explanation will
still be helpful
in understanding
how the
protection is provided:
- Through the redundancy (of data) in the PN code
- Using amplitude modulation
(= my simplified explanation),
a collision will result in:
- Consider
all possible scenarios
that the transmissions
A ⇒ B and
C ⇒ D
can interact
with each other:
- At the bit level, the senders A and C can transmit either a "1" bit or a "0" bit
- There are then
4 possible
interference patterns:
Namely:
- A transmits 0 to B and C transmits 0 to D at the same time
- A transmits 0 to B and C transmits 1 to D at the same time
- And so on...
Let's consider for each case whether the receivers B and D can decode the transmission correctly....
- The following figure consider these
interferences:
- A
sends "1"
and
C
sends "1"
(at the same time)
- A sends "0" and C sends "0" (at the same time)
What the receivers B and D will decode:
Result:
- Both receivers B and D will decode correctly despite the interference
- A
sends "1"
and
C
sends "1"
(at the same time)
- The following figure consider these
interferences:
- A
sends "1"
and
C
sends "0"
(at the same time)
- A sends "1" and C sends "0" (at the same time)
What the receivers B and D will decode:
Result:
- Again, both receivers B and D will decode correctly despite the interference
- A
sends "1"
and
C
sends "0"
(at the same time)
- Conclusion:
- Using these
specific chips,
each
sender/receiver pair
is able to
decode the transmitted bit correctly.
- Therefore,
the transmitting nodes
are able to
share
the transmission medium
(The direct-sequence spread spectrum has the "anti-jamming" property !!!).
- Using these
specific chips,
each
sender/receiver pair
is able to
decode the transmitted bit correctly.
- The real explanation is
much more complex...
- Direct Sequence Spread Spectrum
trasnmission:
- A digital signal
(e.g.: 10101010...) is
composed of
many different frequencies
(see:
click here)
(This decomposition is called the Fourier transform)
- The result of using the
Psuedo Noise (PN) code
to transmit
the data is:
- Transmit the data using a spectrum of frequencies
The signal strength used in DSSS transmissions look like this:
- A sender and reeiver will use filters to target the spectrum of frequencies contained in the PN code to extract the transmitted bits
- A digital signal
(e.g.: 10101010...) is
composed of
many different frequencies
(see:
click here)
- Receiver:
- The receiver will tune in to the same set of frequencies defined by the Pseudo Noise (PN) code to pickup the data
- Different PN codes
can be alike or
different
- The measure of
"likeness" is
the correlation,
defined as:
∞ 1 / Rcorr(τ) = --- | pi(t) pj(t+τ) dt (See: click here) T / 0The function pi(t) and pj(t) are the wave forms of the two PN codes.
(Don't worry, you don't need to know the details of correlation - it's there for completeness sake....)
- The correlation function
has the following properties:
- 0 ≤ Rcorr ≤ 1
- Rcorr = 1 if the PN codes ate identical
- Rcorr = 0 if the PN codes ate uncorrelated
Intermediate values (between 0 and 1) indicate how much the codes have in common.
- Property:
- If 2 PN codes are highly correlated, their collisions will be more likely to cause decoding errors