S-72.227 Digital Communication Systems
Overview into spread spectrum and CDMA
communication
Overview into spread spectrum communication





Basic principles of spread spectrum communication
Types of DS modulation: principles and circuits
– direct sequence (DS)
– frequency hopping (FH)
Spreading code sequences
– maximal length
– Gold
– Walsh
Asynchronous multiple access systems
CDMA diversity techniques
Timo O. Korhonen, HUT Communication Laboratory
How the tele-operators* market CDMA:
Capacity
Coverage
Cost
$
For Coverage, CDMA saves
wireless carriers from deploying
the 400% more cell site that
are required by GSM
Clarity
CDMA with PureVoice
provides wireline clarity
Timo O. Korhonen, HUT Communication Laboratory
CDMA’s capacity supports at
least 400% more revenue-producing
subscribers in the same spectum
when compared to GSM
Choice
CDMA offers the choice of simultaneous
voice, async and packet data, FAX, and
SMS.
$
A carrier who deploys CDMA
instead of GSM will have
a lower capital cost
Customer satisfaction
The Most solid foundation for
attracting and retaining subscriber
is based on CDMA
*This example is from Samsumg’s narrowband CDMA (CDMAOne®) marketing
Spread spectrum (SS) characteristics





The bandwidth of the transmitted signal is much greater than the original
message bandwidth
Transmitted signal bandwidth is determined by a spreading function
(code), independent of the message, and known to the transmitter and
receiver
Narrow band signal Wideband signal
Interference and noise immunity tolerance of a SS system is a function
of the processing gain G p  BT / BM
Multiple SS system often co-exist in the same band. Users independent
if they have (1) high code gain and/or (2) more orthogonal codes
Spreading sequences can be very long -> enable low PSD-> low
probability of interception (especially in military communications)
Timo O. Korhonen, HUT Communication Laboratory
Characterizing SS systems


Code gain, for BPSK
G p  BT / BM  (2 / TC ) /(1/ TB )  2TB / TC
– Larger Gp improves noise immunity, but more transmission BW is
required
– For multiple access selection of appropriate code family is important
Jamming margin
M J  G p  [ Lsys  ( SNR) desp ]
– Tells the magnitude of additional interference and noise that can be
injected to the channel without hazarding system operation.
Example:
G p  30dB,available code gain
Lsys  2dB, margin for system losses
SNRdesp  10dB, required SNR after despreading
 M j  18dB,limit for additional interference and noise
Timo O. Korhonen, HUT Communication Laboratory
Characterizing SS systems (cont.)

Spectral efficiency Eeff: describes how compactly message is fitted into
the transmission band:
Eeff  Rb / BT
BRF 
Gp
BRF ,2lev
2 / Tc


(M : number of levels)
k
log 2 M Tb log 2 M
 Eeff 

G p  2TB / TC
log 2 M
Gp
M  2
k
 k  log 2 M 
Energy efficiency: The value of received SNR   S R /( BT ) to
obtain a specified error rate (often 10-9). For BPSK the error rate is

1
exp( 2 / 2)d 
pe  Q( 2 ) Q(k ) 
2 k

QPSK-modulation can fit twice the data rate of BPSK in the same
bandwidth. Therefore it is more energy efficient than BPSK.
Timo O. Korhonen, HUT Communication Laboratory
Spread spectrum flavors: Frequency hopping (FH)

In FH basic hopping pattern is determined by the code and it is deviated
by the message:
BW  Wd
BW  Ws
BW  Ws

This method is applied in BlueTooth®
Timo O. Korhonen, HUT Communication Laboratory
BW  Wd
Slow (TC >> Tb) frequency hopping
L
2 pcs
2k pcs
Wd  fd 2L  2L / LT (  data modulator BW)
Ws  2k Wd ( total FH spectral width)
Timo O. Korhonen, HUT Communication Laboratory
TC : chip duration
T : bit duration
fd  1/ LT (difference of hopping frequencies)
Spread spectrum flavors: Direct Sequence (DS)

This figure shows a BPSK-DS transmitter and receiver (multiplication
can be realized by RF-mixers)
- DS-CDMA is used in WCDMA and IS-95 systems
Timo O. Korhonen, HUT Communication Laboratory
DS-CDMA spectra in tone jamming

Assume DS - BPSK transmission, with a single tone jamming (jamming
power J [W] ). The received signal is
r (t )  2 Pc1 (t  Td )cos  0t   d (t )   2J cos  0t   ' 

The respective PSD is
1
1
Sr ( f )  PTc sinc2  f  f0  Tc   PTc sinc2  f  f0  Tc 
2
2
1
 J  ( f  f0 )   ( f  f0 )
2

At the receiver r(t) is multiplied with a local code c(t) yielding
d (t )  2Pc1 (t  Tˆd )c(t  Td )cos  0t   d (t ) 
 2 Jc1 (t  Tˆd )cos  0t   ' 

data
The transmitted signal and the local code are aligned in-phase:
c1 (t  Tˆd )c(t  Td )  1 
Timo O. Korhonen, HUT Communication Laboratory
1
1
Sd ( f )  PTb sinc2  f  f0  Tb   PTb sinc2  f  f0  Tb 
2
2
1
1
 JTc sinc2  f  f0  Tc   JTc sinc2  f  f0  Tc 
2
2
F  2 Jc1 ( t Tˆd )cos 0t  '
DS spectra in tone jamming (cont.)

Despreading distributed the jammer power in frequency:
Timo O. Korhonen, HUT Communication Laboratory
DS spectra in tone jamming (cont.)

Receiver filtering suppresses the jammer power:
Timo O. Korhonen, HUT Communication Laboratory
DS and FH compared
FH is applicable in environments where there exist tone jammers that
can be overcame by avoiding hopping on those frequencies
 For large number of users DS is applicable because resource
reallocation to other users can be easily arranged by power control
 FH applies usually noncoherent modulation due to carrier
synchronization difficulties -> modulation method degrades
performance
 Both methods can be used in military techniques
– FH can be advantageous because the hopping span can be very
large
– DS can be advantageous because spectral density can be much
smaller than background noise density
 FH is an avoidance system: does not suffer on near-far effect!
 By using hybrid systems some benefits can be combined: The system
has a low probability of interception and low near-far effect at the same
time. (Differentially coherent modulation is applicable)
Timo O. Korhonen, HUT Communication Laboratory

Example of DS multiple access waveforms
Timo O. Korhonen, HUT Communication Laboratory
FDMA, TDMA and CDMA compared
Timo O. Korhonen, HUT Communication Laboratory
• Conceptually FDMA, TDMA and CDMA
yield same capacity
• However, in wireless communications
CDMA has improved capacity
• In addition CDMA has several advantages:
- Enables easy usage of multirate
- Performance can be improved also by
adaptive antennas, multiuser detection
forward error correction (FEC)
-graceful degradation
FDMA, TDMA and CDMA compared (cont.)






TDMA and FDMA principle:
– TDMA allocates a time instant for a user
– FDMA allocates a frequency band for a user
CDMA allocates a code for user
CDMA-system can be synchronous or asynchronous
Synchronous CDMA is very rare due to (multipath) channels that tend to
destroy code orthogonality.
Wireless CDMA-systems as the IS-95 and WCDMA use asynchronous
techniques where different user codes are not synchronous, especially
after multipath
CDMA codes are by their nature
– Orthogonal, as the Walsh-codes
– Near-Orthogonal, as the Gold-codes
– Non-orthogonal as the maximal length codes
Timo O. Korhonen, HUT Communication Laboratory
Illustration of CDMA potential capacity





Consider reverse link
Each user transmits
Gaussian noise whose
deterministic characteristics
are stored in RX and TX
Reception and transmission
are simple multiplications
Perfect power control: each
user’s power at the BS the same
Each user transmits using power PS that is other user’s interference
power. Hence each user receives interference power
(1)
I k  (ku  1) Ps
where ku is the number of equal power users
Timo O. Korhonen, HUT Communication Laboratory
Illustration of CDMA potential capacity (cont.)




Each user applies a demodulator/decoder characterized by a certain Eb/Io
ratio (3 - 9 dB depending on channel coding, channel, modulation
method etc.)
Each user is therefore exposed to an interference density
I 0  I k / BT
(2)
where BT is the spreading bandwidth.
Received energy / bit at the signaling rate R is thus
(3)
Eb  Ps / R
Combining (1)-(3) yields the number of users
I k I o BT 1/ R  BT W / R



(4)
Ps Eb R Eb 1/ I 0  Eb / I 0
This can be increased by using voice activity coefficient Gv = 2.67 (only
about 37% of speech time effectively used), directional antenna system
gain, for instance for 3-way antenna GA=2.5.
ku  1 

Timo O. Korhonen, HUT Communication Laboratory
Illustration of CDMA potential capacity (cont.)

In cellular system other cells introduce interference that decreases
capacity. It can be shown that usually this coefficient is about
1  f  1.6

Hence asynchronous CDMA system capacity can be approximated by
ku 
W / R GvGA
Eb / I o 1  f
yielding with the given values Gv=2.67, GA=2.4, 1+f = 1.6,
4W / R
ku 
Eb / I o

Assuming efficient error correction algorithms, dual diversity antennas,
and RAKE receiver, it is possible to obtain Eb/Io=6 dB=4, and then
ku 
W
R
Timo O. Korhonen, HUT Communication Laboratory
This is of order of magnitude larger value than the
one obtained with the conventional TDMA systems!
DS is based on applying code correlation properties
Timo O. Korhonen, HUT Communication Laboratory
Maximal length codes



Have very good autocorrelation but cross correlation can be very bad
Usually generated by feedback connected shift registers
Number of codes available depends on number of shift register stages:
5 stages->6 codes, 10 stages ->60 codes,
25 stages ->1.3x106 codes

Engineering code generator design by tables:
Timo O. Korhonen, HUT Communication Laboratory
Design of a maximal length generator based on a
design table entry

Feedback connections can be written directly from the table:
Timo O. Korhonen, HUT Communication Laboratory
Maximal length code autocorrelation and PSD
Timo O. Korhonen, HUT Communication Laboratory
Other spreading codes


Walsh codes: orthogonal, used in synchronous systems, also WCDMA
downlink
Hn1 
H
Generation recursively: H0  [0] Hn   n1

 Hn1
H n1 
0
0
 All rows and columns of the matrix are orthogonal: H2  
0

 (1)(1)  (1)1  1(1)  1 1  0
0


0 0 0
1 0 1

0 1 1

1 1 0
Gold codes: generated by summing preferred pairs of maximal length
codes. Have a guarantee 3-level crosscorrelation: t(n) / N ,1/ N ,(t(n)  2) / N 
For N-length code there exists N + 2 codes in a code family and
1  2( n 1) / 2 ,for n odd
N  2  1 and t (n)  
( n  2) / 2
,for n even
1  2
n

Both Walsh and Gold codes are used for multiple access systems. The
Walsh codes are used usually in synchronous communications because
their asynchronous crosscorrelations are not good
Timo O. Korhonen, HUT Communication Laboratory
Characterizing asynchronous CDMA system

Normalize power for each user:
1 t 2
0 si (t )dt  1, i  1, 2, U
tm
m
U

mij  n j
ˆ (tm )  m jj  
Integrate and dump yields at the decision time: m
i 1
i j

Intended signal for the j:th user: m jj 

1 t
User interference: mij  0
tm
Timo O. Korhonen, HUT Communication Laboratory
m
1 t
0
tm
m
Pj s j (t )v j (t )dt  Pj
Ps
(t )v j (t )dt  Pi  ij
i i
Characterizing asynchronous CDMA system (cont.)


Effect of user interference is a function of (1) applied codes
crosscorrelation, (2) modulation method, (3) user power balance, (4)
code synchronization
The background noise component is at the the decision time
1 t
n j  0 n(t )v j (t )dt
tm
m

Therefore the j:th user experiences the SNR:
( SNR) j 
( SNR) j 
Timo O. Korhonen, HUT Communication Laboratory

m 2jj
E   mij  n j 
i

2

Pj
2


 

E    mij    2 E    mij n j    E n 2j 
 

 i
 i
Asynchronous CDMA system with AWGN (cont.)

Background AWGN noise is
E n

2
j
  G (f)

n
2
2
V ( f ) df
tm
N
N 1
  0  2 r 2 (t )dt  0
2tm
 2  tm 0


Cross-noise average is zero due to uncorrelated AWGN and codes, eg


2 E    mij n j    0

 i

User interference induced noise
U U

2


2



E    mij    E   mij mkj  
 

 i 1 k 1

 i j k  j

Timo O. Korhonen, HUT Communication Laboratory
Asynchronous CDMA system (cont.)

User interference is comparable to code cross-correlation and can be
expressed by
2

  U
 ij2 
E    mij     PE
i
  i 1

i j

Assuming that the all users have the same code-correlation Rs ( )
2 t 2
Rs ( )d

0
tm
E[ ij2 ] 
1
that yields for the maximal length codes
2 t
E[ ij2 ]  0
tm
1

2
 
2 t1
1

d


 t
3 tm
 1
Defining now the effective bandwidth Beff in terms of signal power
spectral density G(f) we get for BPSK
2

1 
3
1
Beff   G( f )df  /  G 2 ( f )df 
 E[ ij2 ] 

2
4t1
2tm Beff
Timo O. Korhonen, HUT Communication Laboratory
Asynchronous CDMA system: j:th user SNR

Thus the SNR for the j:th user is
( SNR ) j 
Pj
2


 

E    mij    2 E    mij n j    E n 2j 
 

 i
 i
0

Pj
 1
P

i
i 1
 2tm Beff
U
i j
 N0

 2tm

2tm Beff Pj
N 0 Beff   Pi
tm : bit duration
Beff : receiver effection bandwidth
Pj : power of the i:n user
N 0 : input noise [W/Hz]
U: number of users
Timo O. Korhonen, HUT Communication Laboratory
U
i 1
i j
Perfect power control

All users have the same power at the receiver input
U
Pi  Pr   Pi  (U  1) Pr
i 1
i j

Assuming U users we will have then for each user
2tm Beff Pr
( SNR)U 
N 0 Beff  (U  1) Pr

Yielding the maximum number of users

U  1   2tm Beff

 1
1 



(
SNR
)
(
SNR
)

U
1 
2t P 2 E
where SNR1  m r  b
N0
N0
(SNR1: a single-user system SNR)
Timo O. Korhonen, HUT Communication Laboratory
Near-far effect

Assume a single user of received power Pi exists in a wireless
communications at the distance di having the propagation exponent a
P
Pi  a0
di

For the i:th and j:th node at a power balanced network the received
power is therefore
a
d j 
P0  di Pi  d j Pj , Pi  Pj  
 di 
a
a
and the single user SNR0 is
SNR U 
a
2tm Beff Pj
a
d 
N 0 Beff    j  Pj
i 1 d
 i
i j
U
 dj 
     2tm Beff
i 1 d
 i
i j
U
SNR1 
Timo O. Korhonen, HUT Communication Laboratory
 1
1 
 ( SNR )  ( SNR ) 

U
1
2tm Pr 2 Eb

<- One-user system
N0
N0
received SNR
Example of the near-far effect

Assume a set of parameters for a asynchronous CDMA system and that
the RX-TX have equal distance except for the first transmitter
d i  d j , i  j ; d1  d j / 2.5;a  3.68

 SNR  11.46dB;Rb  30kb/s;Beff  20MHz
E / N  12.5
 b 0
a
 dj 
     2.53.68  U  2  U  14
i 1 d
 i
i j
U


For the ideal power control, eg all received powers are equal the number
of users is

 1
1 
U  1  int 2tm Beff 

  42
 (SNR)U (SNR)1 

Note that for d1<dj/2.78 only one user fits to the system!
Timo O. Korhonen, HUT Communication Laboratory
Direct Sequence Techniques: QPSK-system
d (t )
S/P
P sin ot
P cosot
c2 (t )
s (t )
q
c1 (t )
i




Serial-parallel transform moves the data stream to carriers
Orthogonal carriers convey the spreaded waveforms
Spreading codes c1 and c2 may or may not be orthogonal
What kind of circuit can make the demodulation?
Timo O. Korhonen, HUT Communication Laboratory
constellation
diagram
RAKE receiver and wideband channel model
Timo O. Korhonen, HUT Communication Laboratory
RAKE-receiver utilizes diversity gain

RAKE receiver yields
diversity gain, for large SNR
 2 L  1  1 
p ( )  


 L   4 c 

L
pb   pe   p   d  ; pe  Q ( 2 c ) (BPSK),  c  Eb / N 0
0
Timo O. Korhonen, HUT Communication Laboratory
Orthogonal Frequency Division Multiplexing
(OFDM) communications


A dense FDM methods
Independent, orthogonal carriers arranged in frequency domain by 1/D,
where D is the symbol period
Frequency

Benefits:



f D  1/ D
OFDM is an efficient way to deal with multipath. For a given delay
spread, the implementation complexity is significantly lower than that
of a single carrier system with an equalizer.
In relatively slow time-varying channels, it is possible to significantly
enhance the capacity by adapting the data rate per subcarrier according
to the signal-to-noise ratio of that particular subcarrier.
OFDM is robust against narrowband interference, because such
interference affects only a small percentage of the subcarriers.
Timo O. Korhonen, HUT Communication Laboratory
Discrete Multi-Tone (DMT) modulation





Used in Digital Subscribe Line (DSL).
Usable frequency band is separated into 256 small frequency bands (or
subchannels) of 4.3125 kHz each.
Within each subchannel, modulation uses quadrature amplitude
modulation (QAM).
By varying the number of bits per symbol within a subchannel, the
modem can be rate-adaptive.
DMT uses the fast Fourier transform (FFT) algorithm for modulation
and demodulation.
Timo O. Korhonen, HUT Communication Laboratory
OFDM spectra of individual subcarriers
OFDM system
di
S/P
IFFT
Transmitter



P/S
Channel
S/P
FFT
P /S
Receiver
Modules
– serial to parallel converter (S/P)
– IFFT (Inverse Fast Fourier Transformer)
– parallel to serial converter (P/S)
Guard interval takes care of adaptation to multipath environment
– added after each OFDM symbol
– duration comparable to RMS delay spread
– decreases transmission efficiency
Transmitted signal can have large dynamic range - linear amplifiers
required -> power dissipation problems (battery problems)
Timo O. Korhonen, HUT Communication Laboratory
di
OFDM modem
Rx chain
Binary input data
Tx chain
Binary output data
coding
decoding
RF RX
interleaving
deinterleaving
QAM
mapping
QAM
demapping
ADC
RF TX
DAC
Timing and
frequency
synchronization
Symbol timing
Add cyclic
extension and
windowing
Paralle to serial
Pilot
insertion
Channel
correction
Serial to
parallel
Paralle to serial
IFFT(TX)
FFT(RX)
Timo O. Korhonen, HUT Communication Laboratory
Contains channel
Remove cyclic
extension
Serial to parallel
Frequency
corrected
signal
Addendum: Orthogonal and Non-Orthogonal Systems
Timo O. Korhonen, HUT Communication Laboratory
Orthogonal and nonorthogonal systems

Consider the following waveforms and their presentations in frequency
domain:
They are orthogonal dispute of their waveform overlap both in time and
in frequency
 Using orthogonal signals enables signaling of several users as they
would be transmitted alone
 How many orthogonal waveforms of duration T and bandwidth BT can
be transmitted simultaneously? Based on certain bounds1 it can be stated
that about K = 2TBT polar waveforms. Therefore the respective
bandwidth is for a channel having rate R=1/T
K RK
BT 

1. M. Petrich, "On the number oforthogonal signals which
2
T
2
Timo O. Korhonen, HUT Communication Laboratory
can be placed in a WT-product, " SIAM Journal, pp. 936-940, Dec. 1963

Orthogonal and nonorthogonal systems (cont.)



In nonorthogonal systems power of all users leaks as noise background
to other users
However, using nonorthogonal systems is often appealing:
– Non need to worry about maximum number of users in terms of TB
product. Users will anyhow influence to each other that is
manifested in some deterioration in their error rates.
– No need to worry about inter-user synchronization. Thus relaxed
hardware requirements.
– Channel resource sharing becomes dynamic. Thus reception quality
can be traded to system capacity
Which factors determine the capacity (number of users with a certain
quality of service) in a nonorthogonal system?
– Dimensionality of signal space (time- bandwidth product) or
spreading signal cross correlations
– Receiver sensitivity
– Data redundancy (manifested via channel coding)
Timo O. Korhonen, HUT Communication Laboratory