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U N I V E R S I T Y O F B A L A M A N D ELEN 443

PROJECT 2

BPSK, FSK, AND ASK COMMUNICATION SYSTEMS

DIGITAL COMMINCATIOM

SUBMITTED BY RAYANE KHODOR, REWA SHOUJAA,

HAROUT GHAZARIAN & JAD ARAYJI

SUBMITTED TO DR. JIHAD DABA

PART I - PBSK SIMULATOR

THEORRETICAL APPROACHES AND MODELING

In phase shift keying (PSK), the phase of a carrier is changed according to the

modulating waveform which is a digital signal. Binary Phase Shift Keying (BPSK) is

a type of phase modulation using 2 distinct carrier phases to signal ones and zeros.

BPSK is the simplest form of PSK. This modulation is the most robust of all the PSKs

since it takes serious distortion to make the demodulator reach an incorrect decision

In BPSK, the transmitted signal is a sinusoid of fixed amplitude. It has one fixed

phase when the data is at one level and when the data is at the other level, phase is

different by 180 degree. A Binary Phase Shift Keying (BPSK) signal can be defined

as

Si(t) = (-1)i+1

Ac cos(2πfct)

Where Ac represents the peak value of sinusoidal carrier, b(t) = +1 or -1, fc is the

carrier frequency, and T is the bit duration.

The Generator Structure:

The Receiver Structure:

We generated a random unipolar signal with equally probable binary symbols. Then

we converted it into a bipolar digital waveform and finally we generated the

modulated signal si(t) using BPSK. At the receiver, we received a noisy signal with a

white Gaussian noise so a match filter is used for maximizing the signal to noise

ratio (SNR) in the presence of additive stochastic noise. Finally the signal is sampled

at the bit period Tb and a decision is made on whether a bit is 1 or 0 depending if the

signal is more or less than the computed threshold.

Summary of the system operation:

A communication system sends binary messages from the transmitter to the

receiver across a noisy channel; a matched filter can be used to detect the

transmitted pulses in the noisy received signal.

Thus, the signal to be sent by the transmitter is

A model of a noisy channel as an AWGN channel, white Gaussian noise is

added to the signal.

This is the signal after filtering with a matched filter.

It can now be safely sampled by the receiver at the correct sampling instants,

and compared to an appropriate threshold, resulting in a correct interpretation

of the binary message.

SIMULATION PROGRAMING

In our project we took Ac =1V, and the bit rate Rb=100 Kbits/s. the period Tb should

be a multiple of Tc (fc = k * Rb). In our project we took k=2. The noise for the

AWGN has a power spectral density N0/2= -10-3

W/Hz.The reference signal of the

matched filter rf= √(2/Tb) *cos(2πfct).

a1 is computed by integrating the signal s1* rf over the pit period tb; a2 is computed

similarly with signal s1. Accordingly the threshold λ is calculated by λ=(a1+a2)/2; thus

the threshold is equal to zero since a1 is equal to -a2.

The number of bits n is equal to 500 and the number of loops m is 100 times. In

addition the signal to noise ratio is computed with the given formulas.

First we generate a bit stream of equal number of 1s and 0s and then randomize this

sequence using MATLAB function ‘randperm’. The number of bits n = 100 is

chosen large in order to have a very small BER (bit error rate). A unipolar waveform

of amplitude Ac is plotted resembling the generated sequence.

We should first convert the unipolar waveform into bipolar digital waveform and the

modulate it.

The signal received is made noisy by adding additive white Gaussian noise to it.

Then use a Matched filter in order to filter the noise of the signal and reconstruct the

signal. The matched filter multiplies the received noisy signal with the reference

signal.

Finally decision is made by comparing the signal value at each interval to a threshold

λ and accordingly the signal is reconstructed.

The signal to noise ratio per sample and the probability of error is calculated. A

comparison between the theoretical and the experimental BER is made. The value of

n should be chosen so that the ration should be small typically 1 %. The BER is

plotted against the signal to noise ration Eb/n0 and N the number of bits.

RESULTS

At the Transmitter

Generated Unipolar Signal

Unipolar Signal converted to Bipolar Signal

Figure 1 - Unipolar Signal

Figure 2 - Bipolar Signal

PBSK Modulated Signal

At the Receiver

Received Noisy Signal with AWGN

Figure 4 - Noisy Signal Received

Figure 3 – Modulated Signal

Filtered Signal with a Matched Filter

Reconstructed Signal

Figure 6 – Reconstructed Signal

Figure 5 – Filtered Signal

Knowing the optimal number of bits for the experiment

The goal is to have Δpe/pe very small (less than 1%).

We simulated the problems many times for different numbers of samples (different values of

N), where each time we compute the ratio Δpe/pe and see if it has a value less than 1%.

For N = 25000 samples,

Pe = Errors / ( N * 100) = 0.2398

DeltaPe = 200 * sqrt(Errors) / (N * 100 * 100) = 0.0071

DeltaPe / Pe = 0.0295 = 2.95% > 1

BER=0.023134

For N = 50000 samples,

Pe = Errors / ( N * 100) = 0.2398

DeltaPe = 200 * sqrt(Errors) / (N * 100 * 100) = 0.0025

DeltaPe / Pe = 0.0105 = 1.05% > 1% So we decided to take 100000 samples.

BER=0.0789

Checking for N = 100000,

Then, Pe = Errors / ( N * 100) = 0.2398

DeltaPe = 200 * sqrt(Errors) / (N * 100 * 100) = 0.0018

DeltaPe / Pe = 0.0074 = 0.73% < 1% So we stick to this number of samples.

BER=0.0074

Plotting BER in Function of Bit Rate

Plotting BER in function of SNR

DISCUSSION

Figure 7 plots the probability of error versus the Bit Rate in BPSK system.

The estimated probability is the total number of inversed bits over the total

number of bits and the theoretical probability is found by calculation

Pe = Q(1/2*sqrt(SNR0)).

This graph indicates that when the bit rate increases the probability of error

increases. This result illustrates a limitation of the bit rate.

Figure 7 – Rb vs. Pe

Figure 8 – SNR vs. Pe

In addition, we can notice the resemblance between the theoretical and the

estimated values of the probability of error in the case of BPSK

communication system. Thus the theoretical value of Pe in this system is

enormously close to the real value of Pe, therefore it gives a real idea on the

system we are dealing with.

In Figure 8 the probability of error (estimated and theoretical) is plotted in

function of Eb/N0 ( Eb/N0 = 10log(Ac2/2N0Rb) ). We can note that in this plot

when Eb/N0 increases the probability of error decreases. It is opposed to the

previous plot because when Rb increases Eb/N0 decreases.

We can see also that when Eb/N0 increases which is proportional to

SNR=2Eb/N0 the probability of error decreases which should be the normal

case.

PART II – COMAPRITIVE ANALYSIS PERFORMANCE

BETWEEN PSK, ASK, and FSK

The bit erroro rate BER is computed using the formulas below.

ASK PSK FSK

Ed

Pe

√

√

√

The following is a Matlab code to generate the curves for the three modulation

techniques representing the BER (Bit Error Rate) in function of SNR (Eb/N0):

All the curve plots have the water-fall shape. We can notice that PSK modulation

achieves the best error rate among the three. It has less bit error rates. FSK comes in

the second place and then comes ASK. This classification depends on the distance

between the two vectors in each modulation.

Figure 9 –Comparison of Probability of Error Among ASK, BSK, FSK

DISCUSSION AND CONCLUSION

Constellation diagram of ASK

Symbols are not equal not opposite to

each other

Constellation diagram of PSK

Symbols are equal and opposite to each

other unlike ASK

Constellation diagram of FSK Symbols are equal but not opposite to each other

As we can see that the distance between the 2 symols in PSK is greater than in FSK and

ASK. The smaller the distance between the two vectors, the higher the error. That’s why

ASK have the worst bit error rate among these three. This validates the result we got in

figure 9. It is noted that at high signal to noise ratio the difference is small, and as it SNR

increases the difference in BER becomes clearer.