EEC 450 Communications

Final Project – Fall 2010

By

Bansri Patel

December 3rd 2010

Objectives:

The purpose of this project was to get familiar with the use of System View

System Simulator software and to get good understanding of simple communication

system, Amplitude Modulation Double Sideband - Transmitted Carrier (AMDSB – TC)

and Binary Phase Shit Keying (BPSK) using the given parameters.

Introduction + Data & Simulation:

AMDSB – TC: In amplitude modulation the modulated wave is composed of a

carrier, in which the upper sideband’s frequency is the sum of the carrier and modulated

frequencies while the lower sideband frequency is the difference between the carrier

and modulated frequencies. Abbreviated DSB - TC is known as double – sideband

transmitted carrier modulation.

sAM ( t )= [A+a Acm ( t ) ] cos(ω¿¿c t)¿

sAM (t )=A [1+amn (t ) ] cos (ωc t )

where, mn ( t )= m (t )|m ( t )|max

=m (t )Am

is a normalized version of m(t),

A = Ac* Am and 0 ≤ a ≤ 1 is called the modulation index.

We require that A>a Ac|m (t )|max=a Ac Am because it is to guarantee that the

positive envelope never goes negative, and hence that the positive envelope has the

exact shape of m(t). The purpose of the extra carrier term in sAM(t) is to preserve the

positive envelope of the transmitted signal in the shape of m(t). The advantage of this

term is to use an envelope detector at the receiver. During a positive cycle of the AM

wave, the diode is forward biased and the capacitor charges up to the peak value,

which is the envelope. During a negative cycle of sAM(t), the diode is back biased and

the capacitor discharges through the resistor.

Part A (AMDSB – TC)

Parameters:

Carrier Frequency fc = 50 kHz

Sawtooth Signal = 1000 Hz

Offset = 0 dc

Simulation Run Time = 5 mS

SNRi = ∞ and SNRi = 15 dB

When a = 0.75

sAM (t )= [A+a Acm (t ) ] cos(ω¿¿c t)¿

Knowing the form above allowed the beginning setup of the System View model shown

in Figure 1.

Figure 1: System View Setup (a = 0.75)

Looking at Figure 1, it is shown that the transmitted signal follows the equation

for the AMDSB – TC identically. For the m(t) a sawtooth was used and then multiplied

with a as well as Ac cosωc (t ), which the product was then added to A cosωc ( t ) .

Figure 1(a) shows the input sawtooth signal when a = 0.75.

Figure 1 (a) Input Sawtooth Signal (a=0.75)

Looking at Figure 1(a) it is shown that the amplitude of the signal is 1, but with a 0.3

offset with a frequency of 1000 Hz.

The calculation of the noise is shown below,

Message signal is 1 V peak for a = 0.75. carrier signal is 1 V peak. So A will also be 1 V.

15 dB SNR in a linear number is 10( 1520 ) = 5.623413

So, SNR=A

5.623413=0.177828

Ac will be 1.

Now the noise has been found it was then added to the input signal before the signal

was recovery processs of the signal.

When a = 0.75,

Using 0.75 for peak value of m(t),

mn (t )= m ( t )|m ( t )max|

0.751

=1

Am=m (t )mn ( t )

= 10.75

=1.33333

A=Ac Am=1 (1.33333 )=1.33333

1.333333 [1+0.75mn (t ) ] cos (2π∗1000 t )

Figure 2 Modulated signal with a = 0.75

Zoomed in version of Modulated Signal with a = 0.75

Comparing this signal to the modulated signal found in Figure 7 it is shown that

this signal’s amplitude is slightly larger in the beginning and smaller at the end, due to

the change in the modulation index.

The signal was then added to the noise just solved for and Figure 3 shows the

modulated signal with the noise added.

Figure 3 Modulated Signal with Noise a = 0.75

Zoomed in version of Modulated Signal with Noise a = 0.75

Sink – 21 Sinusoidal Block Output (a=0.75)

Sink – 21 Zoomed in Sinisoidal Block Output (a = 0.75)

Lastly the signal was multiplied by another Ac cosωc (t ) passed through a rectifier,

and lastly filtered by a low filter and Figure 4 shows the corresponding output of the

system (recovered signal).

Figure 4 Output of System with Noise with a = 0.75

Zoomed in version of Output System with Noise with a = 0.75

Looking at Figure 4 it is shown that sawtooth signal was recovered, but distorted

slightly by the noise that was added to the system.

When a = 1,sAM ( t )= [A+a Acm ( t ) ] cos(ω¿¿c t)¿

Knowing the form above allowed the beginning setup of the System View model shown

in Figure 5.

Figure 5: System View Setup (a = 1)

Looking at Figure 5, it is shown that the transmitted signal follows the equation

for the AMDSB – TC identically. For the m(t) a sawtooth was used and then multiplied

with a as well as Ac cosωc (t ), which the product was then added to A cosωc ( t ) .

Figure 6 shows the input sawtooth signal when a = 1.

Figure 6 Input Sawtooth Signal (a = 1)

Looking at Figure 6 it is shown that the amplitude of the signal is 1, but with a 0

offset with a frequency of 1000 Hz.

The calculation of the noise is shown below,

Message signal is 1 V peak for a = 0.75. carrier signal is 1 V peak. So A will also be 1 V.

15 dB SNR in a linear number is 10( 1520 ) = 5.623413

So, SNR=A

5.623413=0.177828

Ac will be 1.

Now the noise has been found it was then added to the input signal before the

signal was recovery processs of the signal.

When a = 1,

Using 1 for peak value of m(t),

mn (t )= m (t )|m (t )max|

11=1

Am=m (t )mn ( t )

=11=1

A=Ac Am=1 (1 )=1

1 [1+1mn ( t ) ]cos (2 π∗1000 t )

Figure 7 Modulated signal with a = 1

Zoomed in Modulated Signal with a = 1

The signal was then added to the noise just solved for and Figure 8 shows the

modulated signal with the noise added.

Figure 8 Modulated Signal with Noise a = 1

Zoomed in Modulated Signal with Noise a = 1

Sink – 21 Sinusoidal Block Output (a = 1)

Sink – 21 Zoomed in Sinusoidal Block Output (a = 1)

Lastly the signal was multiplied by another Ac cosωc (t ) passed through a rectifier,

and lastly filtered by a low filter and Figure 9 shows the corresponding output of the

system (recovered signal).

Figure 9 Output of System with Noise with a = 1

Zoomed in version of Output System with Noise with a = 1

Comparing this output to the output from Figure 4 it is observed that this ouput

has a smaller amplitude.

Overall System Outputs (a = 0.75)

Overall System Bode Plot (a = 0.75)

Overall System Outputs (a = 1)

Overall System Bode Plot (a = 1)

Part B (BPSK)

BPSK: Phase shift keying (PSK) involves transmitting digital information by shifting the

phase of a carrier among several discrete values. When a binary sequence is to be

transmitted, the phase is usually switched between 0⁰ and 180⁰, and the PSK signal is

sometimes designated as phase reversal keying (PRK).

s (t )=Ac cos(ω¿¿c t) for alogic 1¿

s ( t )=−Ac cos (ωc t ) for a logic0

The frequency content binary PSK (BPSK) waveform can be obtained using,

Sx (ω )=|P (ω)|2

T s {Ra (0 )+2∑k=1

∞

Ra (k )cos kωT s}

Parameters:

Carrier Frequency fc = 50 kHz

Data Rate = 5000 bps

Simulation Run Time = 20 mS

Eb/N0 = ∞ and Eb/N0 = 6 dB

Figure 10 System View Setup

The graph below is the input sequence of bits that were being transferred.

Figure 11 Input (PN) Sequence of Waveform

Looking at figure 11 the input sequence it is shown that the amplitude is in fact 1,

with a random sequence of positive and negative pulses.

Next the bits are separated and different frequencies are assigned to them which

is shown in figure 12 the modulated signal with a frequency of 50000 Hz.

Figure 12 Modulated Signal with Frequency 50000 Hz

Zoomed in Modulated Signal with Frequency 50000 Hz

At this point, the noise has been added to the system,

Figure 13 Waveform after adding Noise in the System

Zoomed in Waveform after adding Noise in the System

Looking at the figure 13 it is obvious that noise has affected the transmitting

signal. We no longer have a nice sinusoidal waveform that was seen in figure 12

(Zoomed in version), but we have a noisy signal with peaks spiking at various locations.

Figure 14 Multiplier of Sinusoidal Waveform after adding Noise to the System

Zoomed in Multiplier of Sinusoidal Waveform after adding Noise to the System

Next, the signal travels through the envelop detector as well as the comparator

where the demodulated signal can than be seen. Looking at the figure 15, the

demodulated signal that has been recovered can be seen.

Figure 15 Output of the System

Zoomed in Output of the System

Negative Bandpass Bode Plot

Negative Low Pass Bode Plot

Positive Band Pass Bode Plot

Positive Low Pass Bode Plot

Overall System Output Waveforms

Conclusion

This project was a great introduction to the system view software. It was little

difficult at first attempt to use this software as it was never been used before, but after a

few trial the software was easy to understand and run the simulations. This project was

very interesting in the way that one could actually see what is going on inside the

system as it is occurring with the live windows that can be place on the screen.