**Direct Sequence Spread Spectrum Block Diagram**

The SS modulation techniques may be divided into two groups:
averaging type systems and avoidance type systems. By averaging the
interference over a long period, averaging systems reduce it. The DS-SS (Direct
Sequence Spread Spectrum) system is an example of an averaging
system.

By making the signal avoid interference over a large fraction
of time, the avoidance type systems reduce the interference. Frequency Hopping
(FH) systems, Time Hopping (TH) systems, Chirp systems, and hybrid modulation
systems are examples of avoidance systems.

**DIRECT SEQUENCE SPREAD SPECTRUM SYSTEMS**

The most significant advantage of spread spectrum modulation
is that it protects against interfering signals created outside, such as
jamming signals. In practice, interference suppression may be achieved using
the Direct Sequence Spread Spectrum (DS-SS) approach. A bandpass channel is
used for the transmission of the information signal (eg. Satellite channel). In
this case, the communication system employs coherent Binary Phase Shift Keying
(BPSK).

When a PN sequence is used to modulate a phase shift keyed
signal in a Direct Sequence Broadened Spectrum (DS-SS) system, the transmission
bandwidth is spread instantly.

**DS-BPSK Transmitter**

The transmitter component of the Direct Sequence Spread
Spectrum with coherent BPSK is shown in the figure. Two stages of modulation are used in the
transmitter component. The NRZ encoder converts the incoming data sequence into
an NRZ sequence b(t) at the first step. By applying these two sequences to the
product modulator or multiplier, this sequence b(t) is utilized to modulate a
broadband pseudo-noise sequence c(t). Both sequences are polar. m(t) = b(t) .
c(t) is the product sequence. The spectrum of c(t) will be identical
to that of c(t). At the second step, the modulated signal m(t) is utilized to
modulate the local carrier for BPSK modulation. QPSK modulation can also be
used.

Hence, the second stage modulated output s(t) is a binary
phase shift keyed Direct Sequence Spread (DS | BPSK) signal. Depending on the
polarity of the data and PN sequences, the phase modulation ฯด(t) of the
signal S(t) has one of the two values, 0 and ฯ as shown in
Table.

**Table -
Truth table for phase modulation ****ฯด(t), Radians**

**Waveforms**

The figure illustrates the
waveforms for the first stage of modulation.

**Figure: Waveforms for the first stage of modulation**

The waveforms for the second stage of modulation for one
period of the PN sequence are shown in Figure.

** Figure: Waveforms for the second stage of modulation**** **

**DS-BPSK Receiver**

The receiver component of the DS-BPSK is shown in the
figure.

**Figure: DS-BPSK Receiver**

Demodulation takes place in two stages in the receiver
section. The received signal r(t) is initially subjected to coherent detection
utilizing the locally produced carrier signal in the first step. This carrier
signal is timed and frequency synchronized with the transmitter's carrier.

The output of the coherent detector is then de-spread in the
second stage. It is multiplied by a locally produced PN sequence that is
synchronized with the transmitter sequence. After despreading, the observed
random signal v is integrated over a bit of time. This is utilized in
decision-making since it gives an estimate of the original data sequence.

**Important Observation**

• In practice, the above-mentioned transmitter and receiver
(DS-BPSK Transmitter and DS-BPSK Receiver) are used. Before phase modulation,
spectrum spreading is conducted in the transmitter. In the receiver, phase
demodulation is also done first, followed by despreading; however, the sequence
of these two processes is reversed in the DS spread spectrum BPSK system model
used for analysis.

• BPSK is performed first in the transmitter, followed by
spectrum spreading. Similarly, at the receiver, spectrum despreading is
performed first, followed by phase demodulation.

• Since spectrum spreading and BPSK are both linear processes,
this is possible.

**Advantages of DS-SS System**

1. This system is the most effective at detecting and
preventing deliberate interference (jamming).

2. For multipath signals, this system has a very high level
of discrimination. As a result, the multipath interference is successfully
reduced.

3. When compared to other systems, the DS-SS system
outperforms them in the presence of noise.

**Disadvantages of DS-SS system**

1. The output rate of the PN code generator must be high. The
length of such a series must be sufficient to ensure that it is genuinely
random.

2. The acquisition time using the serial search method is too
long. As a result, the DS-SS system is sluggish.

3. The varying distance between the transmitter and receiver
affects synchronization.

4. The DS-SS signal is ineffective in the case of broadband
interference.

**Applications of DS-SS system**

1. Anti-jamming application — protecting a jamming signal.

2. Signal transmission with low detectability - the signal is
intentionally delivered at a very low power level. As a result, the signal is
known as an LPI signal since it has a low probability of being intercepted
(LPI).

3. Supporting numerous simultaneous signal transmissions on
the same channel, such as with Code Division Multiple Access (CDMA) or spread
spectrum multiple access (SSMA).

**PERFORMANCE PARAMETERS OF DS-SS SYSTEM**

A direct sequence spread spectrum system's important
performance characteristics are 1) processing gain, 2) probability of error,
and 3) jamming margin.

**1) Processing Gain**

The gain achieved by processing a spread spectrum signal over
an unspread signal is referred to as the processing gain of a DS-SS system.
It's also known as the spread spectrum signal's bandwidth divided by the
unspread signal's bandwidth.

Thus,

**Processing Gain (PG) = ****๐ต๐๐๐๐ค๐๐๐กโ**** ****๐๐**** ****๐ ๐๐๐๐๐**** ****๐ ๐๐๐๐๐/๐ต๐๐๐๐ค๐๐๐กโ**** ****๐๐**** ****๐ข๐๐ ๐๐๐๐๐**** ****๐ ๐๐๐๐๐**

The bandwidth of an unspread signal is determined by the bit
rate of binary data entering the transmitter input. It is given by

R_{b} = 1/๐_{๐}
------------------- (1)

The chip rate of the PN sequence
also refers to the spread spectrum signal's bandwidth. It is given by

R_{c} = 1/๐_{๐}
------------------ (2)

Therefore, Processing gain is given
by

PG = ๐
_{๐}/๐
_{๐}
= (1/๐_{๐})/(1/๐_{๐})
= ๐_{๐}/๐_{๐}

=> PG = ๐_{๐}/๐_{๐}_{
----------------------- }(3)

Also T_{b}
= NT_{c}. This can be rewritten as

N = ๐_{๐}/๐_{๐}
------------------- (4)

N is the spread factor, which is
the number of chips per information bit.

Both PG and N are equal. Hence

PG = N = ๐_{๐}/๐_{๐}
------------------- (5)

Since it represents the advantage gained over the jammer by
increasing the bandwidth of the transmitted signal, the Processing Gain (PG) is
also known as the bandwidth expansion factor (Be).

**2) Probability of Error**

• The probability of error P_{e} for a coherent BPSK
system can be determined as:

Where E_{b} is the energy per bit and ๐_{๐}/2
is the power spectral density of white noise.

• The interference in a DS-SS BPSK system can be expressed as
a wideband noise signal with a power spectral density of No/2. For the spread
signal, we may write N_{o} as

N_{o} = JT_{c} ------------------------ (7)

where J refers to the average interference power and T_{c}
refers to chip duration or interval.

• On substituting the value of N_{o} in equation (6),
the probability of error for the DS-SS-BPSK system can be calculated as:

**3) Jamming Margin (Antijam characteristics)**

• The bit energy to noise density
ratio is represented as Eb/No. We may write N_{o} as JTC (N_{o}
= JTc) for the DS-SS-BPSK system. The bit energy E_{b} is given by

E_{b} = P_{s}T_{b}
-------------------------- (9)

Tb is the bit duration or interval,
while Ps is the average signal power.

Thus ๐ธ_{๐}/๐_{๐}
can be written as

๐ธ_{๐}/๐_{๐}
= ๐_{๐ }๐_{๐}/๐ฝ๐_{๐}
= (๐_{๐ }/๐ฝ)
(๐_{๐}/๐_{๐})
------------------- (10)

๐ฝ/๐_{๐ }
= ๐_{๐}/๐_{๐}/๐ธ_{๐}/๐_{๐}
= (๐๐บ/๐ธ_{๐}/๐_{๐})
------------- (11)

Since we know that PG=๐_{๐}/๐_{๐}

The jamming margin is defined as
the ratio J/Ps. Thus, the jamming margin is the ratio of average interference
power J to average signal power Ps.

If the jamming margin and
processing gain are both expressed in dB (decibels), the equation for the
jamming margin is:

(Jamming margin)_{dB} =
(Processing gain)_{dB} - 10log_{10}(๐ธ_{๐}/๐_{๐})_{๐๐๐}
----------------- (12)

where (Eb/No)min is the bit
energy-to-noise density ratio required to support a given average probability
of error.