ECE 5233 Satellite Communications
Prepared by:
Dr. Ivica Kostanic
Lecture 19: Multiple Access Schemes (4)
(Section 6.8)
Spring 2011
Outline
CDMA principles
CDMA transmission and reception
DS-SS CDMA capacity
Examples
Important note: Slides present summary of the results. Detailed
derivations are given in notes.
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CDMA – basic principle
 Code Division Multiple Access (CDMA)
 Users are transmitting co-time and co-frequency
 The signals from different users are separated by codes
well, see you
tomorrow
hello, how
are you
doing?
well, see you
tomorrow
hello, how
are you
doing?
my salary,
sir...
my salary,
sir...
what?!...raise
again?
bye!
what?!...raise
again?
bye!
FDMA
3
Hello, how
are you
doing?
PABO
JA !!
TDMA
! j
ObAP AH
MAJA!
.
j
Common analogies used for the
access schemes
CDMA
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CDMA TXC and RX (single link)
 At the TX - signal multiplied by a spreading sequence
 Spreading sequence – code with higher data rate and god autocorrelation properties
 Spread signal send to satellite and received by all earth stations
 Received signal correlated with the same spreading code
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CDMA example – 2
Two signals coexist in
time and frequency
X x C1
0+0+2+2 = 4 > 0
0 0 2 2
S1 = 1
S1 x C1
x
1
1 1
1
X
C1
S
1 1
1 was
sent
X= S1C1+S2C2
C1
1
Integrate
0 0
1
2 2
1 1
1
X x C2
1
0
0 -2 -2
0+0-2-2 = -4 < 0
X
S2 = -1
X
-1 -1
Integrate
-1 was
sent
1 1
S2 x C2
C2
C2
1 1
Rc
PG
Rb
1 1
-1 -1
-1 -1
Processing gain (PG) is the ratio of chip and bit rates
Note: codes in this example are synchronized in
time
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CDMA access
 Signals from different earth stations are
co-spectrum and co time
 Signals are spread using codes that are
orthogonal even when not
synchronized
 All signals are amplified by the
transponder and send towards the
ground
 Transmission from the earth stations
must me power managed so that the
product of processing gain and power
is constant – for all earth stations
CDMA scheme
 If the earth stations have same
processing gain – they should be
received at the same power
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PN sequences (AKA M-sequences)
 Have “noise like” auto-correlation properties
 Generated as output of shift registers that have taps indicated by primitive polynomials
o Taps need to be in “special places”
o Location of taps for different code lengths:
http://www.newwaveinstruments.com/resources/articles/m_sequence_linear_feedba
ck_shift_register_lfsr.htm
Remember:
1 maps into -1
0 maps into 1
Shift register for generation of binary sequence
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M sequences - properties
1. An m-bit register produces an m-sequence of period 2m-1.
2. An m-sequence contains exactly 2(m-1) ones and 2(m-1)-1 zeros.
3. The modulo-2 sum of an m-sequence and another phase (i.e. time-delayed version) of the same
sequence yields yet a third phase of the sequence.
3a. (A corollary of 3.) Each stage of an m-sequence generator runs through some phase of the sequence.
(While this is obvious with a Fibonacci LFSR, it may not be with a Galois LFSR.)
4. A sliding window of length m, passed along an m-sequence for 2m-1 positions, will span every possible mbit number, except all zeros, once and only once. That is, every state of an m-bit state register will be
encountered, with the exception of all zeros.
5. Define a run of length r to be a sequence of r consecutive identical numbers, bracketed by non-equal
numbers. Then in any m-sequence there are:
1 run of ones of length m.
1 run of zeros of length m-1.
1 run of ones and 1 run of zeros, each of length m-2.
2 runs of ones and 2 runs of zeros, each of length m-3.
4 runs of ones and 4 runs of zeros, each of length m-4.
…
2m-3 runs of ones and 2m-3 runs of zeros, each of length 1.
6. If an m-sequence is mapped to an analog time-varying waveform, by mapping each binary zero to 1 and
each binary one to -1, then the autocorrelation function for the resulting waveform will be unity for zero
delay, and -1/(2m-1) for any delay greater that one bit, either positive or negative in time. The shape of
the autocorrelation function between -1 bit and +1 bit will be triangular, centered around time 0. That is,
the function will rise linearly from time = -(one-bit) to time 0, and then decline linearly from time 0 to time
= +(one-bit).
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Circular autocorrelation of PN sequence
PN sequence of length N:
xn 
Circular autocorrelation:
1
R p v  
N
N
 xnxmod( n  v, N )
n 1
For PN sequences
 1
R p v    1

 N
Note: PN sequences are
practically orthogonal to their
delayed versions
,v  0
,v  0
Consider N=15 sequence in the attached spreadsheet
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CDMA capacity
On the ground S/N ratio for a given link (in dB)


S / N out  C / N SS  10 log  Rc 
 Rb 
Consider Q identical earth stations using a transponder in a CDMA mode
R 

C
  10 log  c 
 NT  Q  1C 
 Rb 

S / N i  10 log 
For large Q


 C 
C
  10 log 
  10 log Q  1
10 log 




N

Q

1
C
Q

1
C


 T

Therefore
S / N i  10 log 
M 

Q

1


Solving for Q
Q
Rc 0.1 S / N ou t Max number of earth
10
stations
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Example
1.Consider DS-CDMA system with processing gain of 1023.
Required S/N at the output of the earth station receive is 12dB.
Estimate the number of the earth stations that can be
supported in the system
Q  1023 1012 /10  64.54  64
2. Example 6.8.1
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Homework
Problems 6.5, 6.6 and 6.7
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