UNIVERSITY OF WINDSOR

ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT

WINTER 2014 SEMESTER

Lab 4 – Performance of 16QAM and NC-FSK Transmission Systems

Date: April 3, 2014

Student Name: Renan Ferreira Santa Rosa

Introduction

First, the objective of this laboratory is to generate and investigate 16QAM

and Non-Coherent FSK systems. Before start, we have to know some concepts

such:

- QAM (quadrature amplitude modulation) is a method of combining two

amplitude-modulated (AM) signals into a single channel, thereby doubling the

effective bandwidth. QAM is used with pulse amplitude modulation (PAM) in

digital systems, especially in wireless applications.

- Root-raised-cosine: In signal processing, a root-raised-cosine filter (RRC),

sometimes known as square-root-raised-cosine filter (SRRC), is frequently

used as the transmit and receive filter in a digital communication system to

perform matched filtering. This helps in minimizing intersymbol interference

(ISI). The combined response of two such filters is that of the raised-cosine filter.

It obtains its name from the fact that its frequency response is the square root

of the frequency response of the raised-cosine filter.

Figure 1: Root-raise-cosine filter

- SER (symbol error rate) is the number of symbol changes (waveform

changes or signalling events) made to the transmission medium per second

using a digitally modulated signal or a line code. The symbol rate is measured

in baud (Bd) or symbols/second.

- ISI (intersymbol interference) is a form of distortion of a signal in which one

symbol interferes with subsequent symbols. This is an unwanted phenomenon

as the previous symbols have similar effect as noise, thus making the

communication less reliable.

- Matched Filter is obtained by correlating a known signal, or template, with an

unknown signal to detect the presence of the template in the unknown signal.

This is equivalent to convolving the unknown signal with a conjugated time-

reversed version of the template. The matched filter is the optimal linear filter

for maximizing the signal to noise ratio (SNR) in the presence of additive

stochastic noise.

- FSK (Frequency-shift keying) is a frequency modulation scheme in which

digital information is transmitted through discrete frequency changes of a carrier

wave.

- BER (Bit Error Rate) is the number of received bits of a data stream over a

communication channel that have been altered due to noise, interference,

distortion or bit synchronization errors. The bit error rate (BER) is the number

of bit errors divided by the total number of transferred bits during a studied time

interval.

Procedure

In this laboratory, we used the MatLab to analyze the signals. The GA gave

us the line code and we have two programs to evaluate, ncfsk_ex.m and

QAM16_ex.m. The ncfsk_ex.m is a program to simulate noncoherent FSK

receiver. First, we stipulate the length of data symbols that is 1000000 and we

generate he random phases on the two frequencies after we introduce the logic

to the code, we plot the figure that represents the BER (Bit Error Rate).

The second program, which is QAM16_ex.m, is a program that simulate 16

QAM baseband polar transmission over AWGN channel using a root raised

cosine pulse of rolloff factor alfa and matched filter receiver. First, we stipulate

the length of data symbol that is 1000000 and the roll of factor that is 1. To

display the pulse shape, the signal is oversampled by a factor of f_oversamp

and after, we generate root raised cosine pulseshape with rolloff factor alfa.

Finally, after introduce the logic to the code we plot the two figures, one

represents the symbol error probability of 16-QAM and the other one represents

the scatter plot of the matched filter output for the 16-QAM.

Results

1) In QAM16_ex.m, we control the transmission bandwidth by applying the

root-raised cosine pulse of roll of factor 0.5 as the baseband pulse shape.

Figure 1: symbol error probability of 16-QAM

Figure 2: scatter plot of the matched filter output for the 16-QAM

- Explain the effect of increasing or decreasing the roll-off factor on the

two figures.

The effect of increasing or decreasing the roll-off factor on the two figure is

that just go down.

For each sample period T, eight uniform samples are used to approximate

and emulate the continuous time samples.

Figure 2 illustrate the signal constellation diagram of the in-phase (real) put

of the method filter output prior to begin sampled.

Very little ISI is observed at the point of sampling, validating the use of the root-

raised cosine pulse shape in conjunction with the matched filter detector for ISI

- free transmission.

- Explain Figure 1 and 2.

Figure 1 shows the symbol error probability of 16-QAM using root-raised

cosine pulse in comparison to the analytical result.

Figure 2 shows a scatter plot of the matched filter output for the 16-QAM

signaling with root-raised cosine pulse when Eb/N = 18dB.

- Is QAM successful in figure 2? Explain.

Yes. The success of QAM is shown via the real and imaginary PAM’s of the

samples factor at the matched filter output. Each dot represents a measured

sample, which clearly demonstrates the reliability of the decision that follows.

The fits are scattered (clustesed) closely around the original constellation point,

which makes the decision will be reliable.

- What does close clustering of measured sample points mean with

respect to SER?

The close-clustering of the measured sample points is a strong indication

that the SER will be very low.

2) In NCFSK_ex.m, we test the results of a no coherent binary receiver. We

assume the orthogonality of the two frequencies used.

Figure 3: BER

- Explain figure 1. (of Exll_4)

Figure 1 shows the BER from non-coherent detection of binary FSK.

- Does the measure BER match the analytical BER?

Yes, as we can see from the figure 3 the measure BER maches very well

the analytical BER.

Conclusion

We conclude that in this first laboratory of the course Digital

Communications we learned how to generate and investigate 16QAM and Non-

Coherent FSK systems. We also learned what is QAM (quadrature amplitude

modulation), Root-raised-cosine, SER (symbol error rate), ISI (intersymbol

interference), Matched Filter, FSK (Frequency-shift keying), and BER (Bit Error

Rate).