reducing noise Techniques

1. Spread-Spectrum
Techniques

2. DIRECT-SEQUENCE SPREAD-SPECTRUM
The message x(t) is multiplied by a wideband PN
waveform c(t) prior to modulation
The PN generator produces a pseudorandom
binary wave c(t) consisting of rectangular pulses
called chips. Each chip has a duration of Tc and an
amplitude of ±1 so that c²(t) = 1 ( an essential
condition for message recovery)

3. DSS transmitter system and spectra

4. Pseudrandom binary wave: (a) waveform; (b) autocorrelation and
power spectrum.

5. If we assume that c(t) has the same properties as
the random digital wave with ak=±1, then the
autocorrelation and power spectral density of c(t)
are
PN bandwidth

6. Chipped message
Independent of c(t) ( Sx is message power or energy)
G = Power
spectral density

7. x~(t) has a spread spectrum whose bandwidth
essentially equals the PN bandwidth Wc.
Bandwidth expansion factor = Wc / Wx

8. This wideband, noise-like signal would be
hard to distinguish from background noise at an
unauthorized receiver; accordingly, we say that
spread-spectrum transmission has a low
probability of intercept.
An authorized receiver will recover the
message without increased output noise, despite
the increased bandwidth. Moreover, the receiver
structure suppresses stray interference or hostile
jamming.

9. DSS receiver system and the effects of a single-
tone jammer.

10. additive noise or interference
Synchronous detection after bandpass filtering yields
Notice that this multiplication spreads the
spectrum of zi(t) but de-spreads and recovers x(t),
assuming near perfect synchronization of the local
PN generator.

11. If the message is digital and sent via BPSK one
can use the correlation detector. In the presence
of white noise, the probability of error
Eb= Energy per bit No= Noise power spectral density
Note: When z(t) stands for white noise n(t)

12. DSSS correlation receiver for BPSK.

13. DSSS Performance in Presence of Interference
Let z(t) stand for an interfering sinusoid or CW jamming
signal
In-phase component is

15. Signal-to-jamming ratio
The single-tone jammers spectrum has been
spread and thus, relative to the output signal
power, has been reduced by a factor
Wx/Wc˂˂1
Process gain (Pg) = bandwidth expansion ratio

16. One can treat the jammer as just another source of
noise
BPSK
If the channel is corrupted by both broadband
white noise and a CW jammer

17. Received power
Jammer power
When rb = Wx

18. The jamming margin is used as a measure of a
system’s ability to operate in the presence of
interference. If, in a given system, we specify a
minimum Pe or minimum Eb>NJ ratio and a
relatively large Pg, then the system will exhibit
rejection of interference.

19. Let the channel is shared with M-1 other spread-
spectrum users—as is the case with code division
multiple access (CDMA) — each one would have their
own unique spreading code and arrival times at the
receiver
Multiple Access
where Am, cm(t), tm, and Ѳm denote the signal
amplitude, spreading code, time delay, and phase,
respectively, of the mth user

20. In the case of BPSK, the output of the correlation receiver
z(tk)=cumulative interference of the additional M-1
CDMA users
If for simplicity Am is set to 1, then after despreading

21. Notice that since xm(t) = ± 1, the integration term
becomes the crosscorrelation between the
desired and the interferer’s PN codes. Therefore,
minimizing the cross-correlation between
spreading codes minimizes the interference
between CDMA users. Ideally, each PN code
would be chosen to be orthogonal to the other,
thereby making z(tk) = 0. Unfortunately, with
practical systems this is not completely possible.

22. All interfering signals appear to the system as
broadband noise. Therefore, unlike TDMA and
FDMA, in which additional users manifest
themselves as crosstalk, each CDMA user merely
adds to the ambient noise floor.
Multipath and the Rake Receiver
M - 1 users sharing the channel + delayed or
multipath versions of the desired signal

24. Model of multipath channel whereby the transmitted
signal travels on three distinct paths
Each path introduces a delay ti and attenuation factor Ai.

25. To overcome the effects of multiple versions of the
signal interfering with each other, and to take advantage
of path diversity for improved signal-to-noise ratio
(SNR) and signal-to-interferance ratio ( SIR), a scheme of
separate receivers for each signal path is used and
then incorporate delay and gain adjustments to each one
to enable constructive addition of the multiple
signal versions.
Input y(t) is fed to the dispreading multipliers, each
one having a PN source that is in phase with one of the
multipath components. The output of each ith
dispreading multiplier

26. Three-finger Rake receiver
Rake receiver for signals that have three multipath components

27. i = 0, 1, 2
i = 0, 1, 2
pseudonoise

28. The output of each of the i multipliers is then fed to a
diversity combiner that consists of a set of adjustable
delay and gain elements so that the outputs add
constructively, since the signal from each finger will have
identical delays. The signal from each path is scaled so as
to increase the level of signals from the fingers with high
signal-to-noise ratios and reduce the level of those with
low signal-to-noise ratios. This naturally scales the paths
according to the received-signal quantities. Both the gain
and scaling adjustments can be done dynamically
according to the path conditions. The diversity combiner
output is
i = 0, 1, 2

29. Three-finger Rake receiver that incorporates separate correlation
stages for each signal path.
HOMEWORK

30. FREQUENCY-HOPPING SPREAD-SPECTRUM
The message is spread out over numerous carrier
frequencies, the jammer has a reduced
probability of hitting any one in particular.
Otherwise the jammer has to spread its power
over a wider frequency range in order to be
effective.
Slow-hopping SS: one or more message symbols are
transmitted per hop
Fast-hopping SS : there are two or more frequency
hops per message symbol.

31. With slow-hopping SS, the receiver demodulates
the signal like any other M-ary FSK signal.
However, with fast hop SS there are several hops
per symbol, so the detector determines the value
based on either a majority vote or some decision
rule such as maximum likelihood.
The message is usually M-ary FSK modulated to some
carrier frequency fc, although some systems use BPSK.
The modulated message is then mixed with the output of
a frequency synthesizer. The frequency synthesizer’s
output is one of Y 2k values, where k equals the number
of outputs from the PN generator. The BPF selects the
sum term from the mixer for transmission on the channel.

32. FHSS transmitter

33. FHSS receiver

34. FHSS Performance in the Presence of Interference

35. Types of jamming for FHSS systems: (a) barrage; (b)
partial-band; (c) singletone; (d ) multiple-tone.

36. PN generation
In order for a receiver to properly recognize a
transmitter’s signal and, in particular, prevent
false synchronization, it is important that the PN
code’s autocorrelation function have the largest
peak possible at τ=0 and τ = kTc and as be low as
possible everywhere else. This objective is met if
the PN generator produces a maximal-length (ML)
sequence.

37. To minimize jamming and/or casual eavesdropping, the
PN sequence should be as long as possible; the longer the
sequence, the more effort it takes for an unauthorized
listener to determine the PN sequence. However, with
linear codes, an eavesdropper only requires the
knowledge of 2˄n chips to determine the shift register
connections. Therefore vulnerability to unauthorized
listening can be reduced by either making frequent
changes in the PN sequence during transmission or by
using some nonlinear scheme for the feedback
connections. PN codes that are both secure and have
desirable correlation characteristics are generally difficult
to find, and thus if the goal is secure communications,
then the message should be encrypted separately.

38. Shift register sequence generator with [5, 2] configuration
If the appropriate feedback tap connections are
made, then an n-bit register can produce a
maximal-length (ML)
second and fifth
cells are tapped

39. 1. Balance. The number of ones generated is one more
than the number of zeros generated.
2. Run. A run is a sequence of a single type of digit. An ML
sequence will have one-half of its runs of length 1, one-
quarter of its runs of length 2, one-eighth of its runs of
length 3, and so on.
3. Autocorrelation. Its autocorrelation function has
properties similar to the correlation properties of random
noise, in that there is a single autocorrelation peak.
4. The mod-2 addition of an ML sequence and any shifted
version of it results in a shifted version of the original
sequence.
5. Except for the zero state, all of the 2n possible states
will exist during the sequence generation.
ML sequence

40. Let a PN sequence sk be used to form a binary
polar NRZ signal
where p(t) is a rectangular pulse and the
amplitude of the kth pulse is

41. The signal s(t) is deterministic and periodic, with period
NTc, and has a periodic autocorrelation function
If N is very large and Tc very small
s
so the PN signal acts essentially like white noise
with a small DC component

42. Example: Autocorrelation of a [3,1] Shift Register
A 3-bit, [3, 1] shift register configuration with values of
111 produces a periodic ML sequence of 1110100 with N
=7.

44. Cross-
correlation
of [3,1] and
[3,2] PN
sequences

45. Auto- and crosscorrelation of [3, 1] and [3, 2] PN
sequences.

46. Cross-correlation ratios for various ML sequence lengths
and feedback connections (produced from a single shift
register).
Sequences generated from a single shift register do not
have good cross-correlation properties, making them
unsuitable for CDMA systems
To generate a different output sequence requires
changing the feedback connections; therefore, a given
shift register length will give us relatively few unique
output sequences.

47. Preferred pairs, Gold Codes
Gold code generator.