Title: DIGITAL SPREAD SPECTRUM SYSTEMS
1DIGITAL SPREAD SPECTRUM SYSTEMS
ENG-737 Lecture 5
- Wright State University
- James P. Stephens
2GOLD CODE IMPLEMENTATION
- Gold Codes are used by GPS and are constructed by
the linear combination of two m-sequences of
length n10 - There are 1023 possible codes possible for n10
- Each different code is generated by inputting a
different initial fill into the G2 Coder - Each GPS satellite is assigned a different Gold
code
3GPS C/A CODER
4KASAMI CODES
- Kasami sequences are one of the most important
types of binary sequence sets because of their
very low cross-correlation and their large number
of available sets - There are two different sets of Kasami sequences,
Kasami sequences of the small set and sequences
of the large set - A procedure similar to that used for generating
Gold sequences will generate the small set of
Kasami sequences with M 2n/2 binary sequences
of period N 2n/2 1 - In this procedure, we begin with an m-sequence
a and we form the sequence a by decimating a
by 2n/2 1 - It can be verified that the resulting sequence a
is an m-sequence with period 2n/2 - 1
5KASAMI CODE IMPLEMENTATION
X4 X 1 q 2n/2 1 5 m 2n/2 - 1
3 Where, q decimation value m period of a
a
a 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0
a 1 1 0
- a xor b 0 0 1 0 1 1 1 0 1 1 1 1
1 1 0
- Kasami codes are generated by cyclically
shifting a 2n/2 -2 2 times - Including a and b there are 2n/2 4 sequences
6KASAMI CODE IMPLEMENTATION
- Example
- Let n10, therefore, N2n - 1 1023 (length of
a) - The decimation value is 2n/2 1 33 which is
used to create a - 1023/33 31 which will be the length of a
- If we observe 1023 bits of sequence a, we will
see 33 repetitions of the 31-bit sequence which
we will call sequence b - Now taking 1023 bits of sequence a and b we
form a new set of sequences by adding (modulo-2
addition) the bits from a and the bits from b
and all 2n/2 2 cyclic shifts of the bits from
b - By including a in the set, we obtain a set of
2n/2 32 binary sequences of length 1023 - All the elements of a small set of Kasami
sequences can be generated in this manner -
7KASAMI CODE IMPLEMENTATION
- The autocorrelation and cross-correlation
functions provide excellent properties, as good
or better, than Gold Codes - The large set of Kasami sequences is generated
in a similar manner with the addition of another
register - The two registers are a preferred pair as in Gold
Code and therefore when combined with the
decimated sequence, produce all the associated
Gold Codes and the Kasami sequences for an even
larger let of sequences
8FACTORS FOR DETERMINING SIGNALING FORMAT
- Signal spectrum
- Synchronization
- Interference and noise immunity
- Error detection capability
- Cost and complexity
Before we begin a more in-depth discussion of
direct sequence spread spectrum, it will be
helpful to compare various encoding and / or
signaling techniques used in digital
communications
9DIGITAL SIGNAL ENCODING FORMATS
- Biphase-Space
- Always a transition at beginning of interval
- 1 no transition in middle of interval
- 0 transition in middle of interval
- Differential Manchester
- Always a transition at middle of interval
- 1 no transition at beginning of interval
- 0 transition at beginning of interval
- Delay Modulation (Miller)
- 1 transition in middle of interval
- 0 no transition if followed by 1, transition at
end of interval if followed by 1 - Bipolar
- 1 pulse in first half of bit interval,
alternating polarity from pulse to pulse - 0 no pulse
- Nonreturn to zero-level (NRZ-L)
- 1 high level
- 0 low level
- Nonreturn to zero-mark (NRZ-M)
- 1 transition at beginning of interval
- 0 no transition
- Nonreturn to zero-space (NRZ-S)
- 1 no transition
- 0 transition at beginning of interval
- Return to zero (RZ)
- 1 pulse in first half of bit interval
- 0 no pulse
- Biphase-Level (Manchester)
- 1 transition from hi to lo in middle of
interval - 0 transition from lo to hi in middle of
interval - Biphase-Mark
- Always a transition at beginning of interval
- 1 transition in middle of interval
- 0 no transition in middle of interval
10DIGITAL SIGNAL ENCODING FORMATS
11DIFFERENTIAL ENCODING
Inversion
1 0 1 1 0 0 0 1 1 0 1
1 0 1 1 0 0 0 1 1 0 1
0 0 1 0 0 0 0 1 0 0 1
1 0 0 0 1 0 1 1 1 0 0
12DIGITAL SIGNAL ENCODING FORMATS
- Phase-encoding schemes are used in magnetic
recording systems, optical communication, and in
some satellite telemetry links - Schemes with transitions during each interval are
self-clocking - Schemes that transition in the middle are
naturally shorter pulses and require greater
bandwidth - Differential encodes provides non-coherent
detection
13DIRECT SEQUENCE SYSTEMS
- DSSS is the most common commercially
- Sometimes called PN spread spectrum
- Used in CDMA Cellular systems, GPS, some earlier
cordless telephones, and 802.11(b) - DSSS directly modulates a carrier with a high
rate code that is combined with data - DSSS usually employs PSK and the code is often
combined with data by mod-2 addition, i.e. code
inversion keying - Predominantly, in practice, a DSSS transmitted
signal is either - BPSK (Binary Phase Shift Keyed)
- QPSK (Quadrature Phase Shifted Keyed)
- MSK (Minimum Shifted Keyed)
14BINARY SHIFT KEYING
- This technique is implemented with a Balanced
Modulator - Two basic types of modulators are
- Single balanced
- Double balanced
- Three port devices in which ? 1s on the code
data input cause 180 degree phase shifts of the
carrier
15BINARY PHASE SHIFT KEYING (BPSK)
Data Code
Typically more than one cycle per chip
1800 Phase Shifts
BPSK
Carrier
16BPSK Power Spectral Density
Suppressed Carrier
Discrete spectral lines
17SUPPRESSED CARRIER
- Reasons that make suppressed carrier desirable
are - More difficult for adversary to detect signal
- Power not wasted on carrier
- Signal has constant envelop level so that power
efficiency is maximized for the bandwidth used - Bi-phase modulators are simple, stable, low cost
devices
18BPSK CIRCUIT IMPLEMENTATION
19PHASOR REPRESENTATION
- BPSK is called antipodal
- Antipodal means that two symbols that meet the
following criteria - s1 -s2
- BPSK other than 1800 is not antipodal
20QUADRATURE PSK OR QPSK
- QPSK does not degrade as seriously as BPSK when
passed through non-linearity simultaneous with
interference - Bandwidth is one-half required by BPSK at same
data rate (or twice the data rate in the same
bandwidth)
AB ?
00 0
01 90
10 180
11 270
21QPSK BLOCK DIAGRAM
m1(t)cos(2pft)
Code 1
cos(2pft)
Data 1
Carrier
SQPSK
sin(2pft)
Code 2
m2(t)sin(2pft)
m2(t)
Data 2
SQPSK(t) m1cos(2pft) m2sin(2pft)
m1(t)
Twice the data same BW
22ALTERNATIVE IMPLEMENTATION OF QPSK
2-bit serial to parallel
Code
Data
QPSK
Half the BW same data rate
23NEAR FAR PROBLEM FOR DSSS
- Major requirement for DSSS implementation is that
one must maintain power control - If one user has more power than others, at the
receiver, the capacity of the system is degraded - For maximum capacity, transmitters must maintain
equal distance and equal power, i.e. mobile
cellular must therefore maintain power control
24NEAR FAR PROBLEM ANALYSIS
- There are many ways in which the received powers
can be unequal for a DSSS CDMA system - For this analysis assume that all users transmit
with equal power, but are different distances
from the jth receiver - Then the received power from the ith transmitter
may be represented as - Pi Po / dia
- Where,
- Po received power at unit distance
- di distance from the ith transmitter to the
jth receiver - a propagation law
- The parameter a is the propagation law and
depends upon the medium in which the transmission
takes place
25NEAR FAR PROBLEM ANALYSIS (Cont.)
- In free space, a is the propagation law and
depends upon the medium in which the transmission
takes place - In free space, a 2
- At UHF over an ideal earth, a tends to change to
between 3 and 4 (determined experimentally) - The above make it possible to represent the ratio
of the power received from the ith transmitter to
that received from the jth transmitter, which is
the desired signal
26NEAR FAR PROBLEM ANALYSIS (Cont.)
- This is shown by
- Pi dj / dia Pj
- Pi / Pj (Po / dja) / (Po / dja) (dj / di)a
- The SNR at the output of the jth receiver may now
be written as - 2
tm Beff Pj
2Eb / No (SNR)j
(SNR)o
27NEAR FAR PROBLEM ANALYSIS (Cont.)
- Solving for the term that is related to the
distances gives - The term (1/(SNR)j) subtracts off for the
intended signal
28NEAR FAR PROBLEM ANALYSIS (Cont.)
- To find the capacity of a CDMA system where all
powers are equal and the distances are the same,
let - Beff 20 x 106
- Tm 1/ 30,000
- SNRo 14
- SNRj 25
- Therefore, for all users U,
- U 2(20x106) / 30000(1/14) (1/25) 42
- Now if one user is 2.5 times closer than all
other users but still with equal power,
Subtracts off closer user and intended user
29NEAR FAR PROBLEM ANALYSIS (Cont.)
- For a 3.68
- U 1 1 - (2.5)3.68 2 tm Beff (1/(SNR)o)
(1/(SNR)j) - U 1 1 - (2.5)3.68 2 x 20 x 106 /
30000)(1/14 1/25) - U 14
- The number of users has been reduced by a factor
of 3 simply by one transmitter being 2.5 times
closer than all of the others - The system would completely fail as a multiple
access system if dj / di gt 2.78, since only one
user could be supported and none of the others
would be received with the desired SNRo - This is the Near Far Problem !
30PROCESSING GAIN PG
Processing gain is the improvement seen by a
spread spectrum system in SNR, within the
systems information bandwidth, over the SNR in
the transmission channel.
Typically Bi baud rate
PG BS / Bi BS / Ri PG(dB) 10 log (Bs / Ri)
Typical PG 20 to 60 dB
Bs
Typically Bs null-to-null
0
1/T
-4/T
-3/T
-2/T
-1/T
4/T
3/T
2/T
31JAMMING MARGIN
- In a general system with both noise and
interference present, the receiver output SNR can
be expressed as - (SNR)o PG (SNR)i
- Where,
- PG processing gain
- (SNR)o Output SNR
- (SNR)I Input SNR
- The ability of a communication system to reduce
the effects of jamming is called Jamming Margin
32JAMMING MARGIN MG
Jamming margin takes into account the requirement
for a useful system output SNR and allow for
internal losses.
MG GP Lsys (S/N)out , dB
Where, Lsys system implementation
losses (S/N)out SNR at information, despread,
output
33JAMMING MARGIN EXAMPLE
- Given,
- Chip rate 107 chips / sec
- Message bit rate 100 bits / sec
- Desired SNRo 25 14 dB
- System losses 2 dB
- Find MJ(dB)
- PG Bs / Ri 2 rc / Ri 2 x 107 / 100 2 x
105 - PG (dB) 10 log (2 x 105) 53 dB
- MJ(dB) 53 dB 2 dB 14 dB 37 dB
- The required output SNR will be obtained if the
jamming signal is less than 37 dB greater than
the desired signal