lab2 coaxial

1

RMIT

SCHOOL OF ELECTRICAL & COMPUTER ENGINEERING

EEET2115 Communication Engineering 3

Laboratory No. 2

BASEBAND DATA TRANSMISSION

SYSTEM

EYE PATTERNS AND DATA ERROR

RATE MEASUREMENTS

2

OBJECTIVES

1. To explore a mathematical model of a baseband data transmission system by:

(a) Calculating and measuring the eye pattern to help assess its usefulness in illuminating the data

transmission - reception problem.

(b) Calculating and measuring the system’s received data error rate for the signal corrupted by

Additive White Gaussian Noise (AWGN) in the channel.

(c) Calculating and measuring the impact of the receiver filter bandwidth on the pre-decision

Signal to Noise ratio and consequentially on the error rate.

2. To explore the Matched Filter concept by:

(a) Calculating and measuring the eye pattern of a baseband data transmission system employing

a receive filter “matched” to the transmitted signal.

(b) Calculating and measuring the data error rate of a baseband data transmission system

employing a receive filter “matched” to the transmitted signal. The signal is corrupted in the

channel by AWGN as required to minimise Pe with a Matched Filter (see mathematical

derivation).

(c) Comparing the measured Matched Filter Pe with Pe’s measured using non matched filters

under the same input signal and noise conditions and pondering why the matched filter is

superior.

3. To further develop personal and group skills by participating in the group activities necessary to

complete the calculations, measurements, and report writing.

4. To improve professional thinking ability using a Predict, Observe, Explain learning process.

REFERENCES

“Digital Communications”, Ian A. Glover and Peter M. Grant, Third Edition, Prentice Hall, 2010.

Eye Diagrams 26.

Probability of Error Page 206 – 209.

Matched filtering Page 272 - 288.

PN sequence Page 628

EQUIPMENT

RMIT Baseband Data System Box. See schematic circuit diagram Appendix 2.

HP 1645A Data Error Analyser.

Dual Channel Oscilloscope Agilent DSO - X 3024A.

3

INTRODUCTION

The Baseband Data Communication Transmission – Reception Problem is defined and discussed in Lectures.

The eye pattern is introduced as a way of modelling the problem. This model displays the eye pattern's

dependence on the system rise time (related to time constant in simple circuits).

The system transmission bandwidth is the frequency domain description of the rise time and the two parameters

are related by the Fourier Transform. This relationship between system rise time (measurable), system time

constant (mathematical result), and system bandwidth (measurable and mathematical result) has been studied

previously in your program and will be applied during this laboratory.

The noise model chosen for the corrupting signal in the transmission channel in EEET2115 is Additive White

Gaussian Noise (AWGN). A Gaussian Probability Density Function (pdf) is completely specified by two

parameters, the mean value, m, and the variance, σ2. AWGN has zero mean and so is completely specified by its variance (mean square value). You are required to measure the variance of the noise during this laboratory or

the related standard deviation (root mean square, rms).

A method for calculating the Probability of Error (Pe ) in a Baseband Data Transmission System was described

in Lectures.

The signal voltage level at the comparator input at the decision time and the rms voltage (standard deviation) of

the AWGN are required to be measured. From these measurements the Pe can be calculated, as outlined in

Lectures, using the Q function of statistics given in Appendix 1.

The number of errors that occur during a test measurement can be measured using a Data Error Analyser such as

the HP 1645A. Using the number of errors counted and the total number of data bits transmitted, the probability

of error Pe can be calculated. Thus you can use this instrument to check whether the Baseband Data

Communication model and the calculation procedure used, accurately predict the Pe for the real world system of

Fig. 1.

Fig. 1A. Real World Experimental System in Laboratory for Procedures 1 and 2.

Y1

Decision

Circuit

Analog Data Digital Data

+

RMIT Baseband Data System Box

Polar NRZ

(RS232) Data

Out

HP 1645A

Data Error

Analyser

WNG

Generator

Receiver

LPF

Time

Adjuster

CRO

Tx Clock

Out CRO

ext sync

RMIT Box

Clock input

Threshold

Adjuster

TP D TP E

TP H TP F

4

Fig. 1B. Real World Experimental System in Laboratory for Procedure 3.

TP H

TTL NRZ

Data Out

HP 1645A

Data Error

Analyser

Y1

CRO

Y2

Decision

Circuit

Analog Data

Digital Data

+


WNG

Generator

Rx

Filter

Time

Adjuster

Tx Clock

Out

CRO

ext sync RMIT Box

Clock input

Threshold

Adjuster

TP D TP E

TP F

Tx

Filter

Line

Coder

Unipolar RZ

Line Code

TP D

TP E

Or various other test

points as required

TP B

TP A TP I

5

PRELIMINARY

1

(a) Draw accurately the step response of the RC Low Pass Circuit shown in Fig. 2.

(b) Draw accurately the amplitude frequency response of the RC Low Pass Circuit shown in

Fig. 2.

(c) Calculate the time constant, τ, and rise time, tr, (10% to 90%) of the RC Low Pass Circuit shown in Fig. 2.

(d) Show that = . for this low pass R C circuit?

Fig. 2

(e) Sketch the output voltage )(tvout of the circuit in Fig. 2 for the input voltage )(tvin shown

in Fig. 3 supplied from an ideal voltage source.

Fig. 3

(f) Sketch, on the same axes as used for (e), the output voltage )(tvout of the circuit in Fig. 2 for

the input voltage )(tvin shown in Fig. 4 supplied from an ideal voltage source.

Fig. 4

(g) Sketch a polar NRZ waveform for the data signal 1 0 1 1 0 1 with a data rate of 2.5 kbps,

logic level “1” being represented by -12 volt and logic level “0” being represented by +12 volt

as in the RS232 interface.

5 Kohm

C=10 nF )(tvin

)(tvout

)(tvin

t

t

+12V

-12V

0

0

()

-12V

-12V

6

(h)(i) Using the template provided in Fig. 4a draw a 2.5 kbps RS232 random data input signal over 3

bit times (1.2 ms). Superimpose all 8 possible data combinations (1, 1, 1: 1, 1, 0: 1, 0, 1: 1, 0,

0 and so on) onto the one diagram.

Fig. 4a Eye Diagram Template

(h)(ii) The diagram in (h)(i) above represents the input signal to the circuit of Fig. 2. Sketch the

output of the circuit in Fig. 2 for this input by superimposing the 8 possible responses to the

complete input data set. Input transitions from -12 volts to +12 volts will result in an

exponential rise in the output from -12 volts to +12 volts with a time constant RC as in (e)

above. Input transitions from +12 volts to -12 volts will result in an exponential fall in the

output from +12 volts to -12 volts with a time constant RC as in (f) above.

You have just constructed your first Eye Diagram. Later we call this diagram the Eye Pattern.

2. A White Gaussian Noise voltage )(tvn is described by a Gaussian Probability Density Function p(v)

with zero mean and variance 4. Calculate the probability that at a particular time, 0t , the noise voltage

will be greater than 6 volts.

3(a) Sketch the impulse response h(t) of a filter matched to the signal waveform, )(ts , shown in Fig. 5.

=1

()

= = 1

Fig. 5.

(b) Sketch the magnitude frequency response H(f) of this filter.

() = Ϝℎ() = Ϝ( −

Look up the Fourier Transform of a pulse amplitude 1 and pulse width τ in a table of transforms.

1 volt

time (ms) 0

+12V

t ms

-12V

0 0.4 0.8 1.2

()

= 1

7

ϜΠ() = . "#$(. )

(c) Calculate the noise equivalent bandwidth, NB , of this filter given that by definition

2. &' . |)(0)| = + |)()|. ,

-

.-

and + "#$)(/). ,/ = 1-

.- where "#$(/) =

0(12)

(12)

4

(a) Draw accurately the impulse response of the RC Low Pass Circuit shown in Fig. 2.

(b) What is the mathematical relationship between this impulse response and the step response in

Preliminary Question 1(a)?

(c) Sketch the output voltage )(tvout for the input voltage )(tvin shown in Fig. 6.

Fig. 6

(d) Sketch the TTL RZ waveform for the data signal 1 0 1 1 0 1 with a data rate of 2.5 kbps.

Logic level “1” is 5 volts and logic level “0” is 0 volts and the RZ pulse width is sµ10 .

(e) s1(t) is the signal transmitted to represent logic “1” and s0(t) is the signal transmitted to

represent logic “0”. Sketch s1(t) and s0(t) in 4(d) above.

(f) Construct an Eye Diagram at the output of the circuit in Fig.2 for the TTL RZ data signal of

4(d) above. Use the same technique as outlined in 1(h) previously but this time superimpose

the impulse responses for all 8 possible data transitions. Use the template below.

0

)(tvinVin(t)

t sµ10

5 v

+5 V

t ms

0 V

0 0.4 0.8 1.2

8

SPECIFIC TASKS

1. EYE PATTERNS

Fig. 1A. Real World Experimental System in Laboratory for Procedures 1 and 2.

1.1 Set Up Equipment for Filter Step Response measurement

1.1.1 The RS232 output (on rear panel of the instrument) of the HP 1645A Data Error Analyser (DEA)

is used to provide an RS232 data signal for the RMIT Baseband Data System Box.

RS232 is a Polar NRZ data line code used for measurement in Procedures 1 and 2 of this

Laboratory Exercise.

1.1.2 Set the RMIT box front panel controls as follows.

Rx Filter – Filter B initially and each of the other Rx Filters subsequently.

Tx filter – bypass until Matched Filter section, Procedure 3 of this Laboratory Exercise.

Attenuator – 0 dB

Switch noise out (or off)

1.1.3 Set the DEA front panel controls as follows.

CLOCK – 600 bps for step response measurement and then 2.4 kbps for Eye Pattern

measurement.

PATTERN – 1:1, 3:1, or 7:1

EXPONENT RANGE – continuous

Lower slide switches left to right –OFF, OFF, OFF, BIT ERROR, JITTER.

Upper slide switches left to right – DTR, mid point between START and STOP.

1.1.4 It is always sensible to check the output of the DEA on a CRO before connecting this output to

the input of the test equipment to ensure that the DEA and/or the CRO is working.

1.1.5 Connect the RS232 data output (cable No 2) of the DEA to the RS232 data input of the RMIT

box (rear panel).

Y1

Decision

Circuit

Analog Data Digital Data

+


Polar NRZ

(RS232) Data

Out

HP 1645A

Data Error

Analyser

WNG

Generator

Receiver

LPF

Time

Adjuster

CRO

Tx Clock

Out CRO

ext sync

RMIT Box

Clock input

Threshold

Adjuster

TP D TP E

TP H TP F

9

1.2 Calculate and measure the Time Constant (τ)τ)τ)τ) and rise time (tr) of the Test Filter (Filter B).

1.2.1 Use the R and C values given in Appendix 3 for Filter B to calculate the time constant and rise

time of Filter B. These are your predictions for the measurements in the next section.

1.2.2 Measure the step response and rise time of Rx Filter B as selected in 1.1.2 above.

Use the Data stream from the DEA as the (repeated) input step to the Rx Filter (TP D) and the

CRO display of the Filter output (TP E) will be the step response. From this step response use the

CRO to determine the time constant and the rise time of the filter.

Rise time measurement is provided in the CRO measurement menu.

Use the cursors to measure the time constant knowing that the step response rises to 63% of its

final value in one time constant of time. In the cursor menu each cursor can be adjusted in turn.

1.3 Compare the expected and measured values of time constant and rise time.

1.3.1 Compare the measured rise time and time constant to those predicted by your calculations from

the circuit given in Appendix 3.

If the comparison is satisfactory record the measured results. A photograph of the screen may be

pasted directly into your report. If you opt for this method of recording ensure that you correctly

identify which photo goes with this measurement for inclusion in your report.

1.3.2 If the comparison with your expected result is not satisfactory find out what is causing the

difference. If necessary seek help from the Laboratory Supervisor.

1.4 Construct Eye Pattern.

1.4.1 Use the step response measurement made in Procedure 1.2.2 above to construct an Eye Diagram

for Rx Filter B if the input data rate is 2400 bps. Take the data streams 1, 1, 1: 1, 1, 0: 1, 0, 1: 1,

0, 0: and so on and superimpose the step responses across 2 to 3 bit times as you did for

Preliminary 1(h).

Note there will be quite a similarity between the step up response and the step down response.

1.5 Measure Eye Pattern of Rx Filter B.

1.5.1 Set the data rate to 2400 bps on the DEA and set up an eye pattern on the CRO.

An eye pattern is obtained by applying pseudo random data to the system under test and setting

the time base of the CRO to display 2 or 3 bit times (about 100µs/div on CRO timebase for this data rate). The CRO is connected to the Rx Filter output /Decision Circuit input, TP E, on the

RMIT box.

1.5.2 Select a PN data sequence using the PATTERN slide switch on the DEA. Sequence lengths of

63, 511, and 2047 are available. Any length PN sequence can be used. (Remember to externally

synchronise the CRO to the transmit clock of the DEA to obtain a stable eye pattern. Use the sync

output on the rear panel of the RMIT box and change trigger to External in CRO trigger menu.)

You should now have a real eye pattern on the CRO screen. The eye pattern may be centred

horizontally using the horizontal shift control of the CRO. (Nicer photos.)

1.6 Compare expected and measured eye patterns.

1.6.1 Compare the measured eye pattern to that predicted by the step response measurement and if the

comparison is satisfactory record the measured eye pattern. Again a photograph of the screen

may be pasted directly into your report but ensure that you correctly identify this photo with this

measurement for inclusion in your report.

10



1.7 Repeat procedure 1.2 to 1.6 using Filter A.

Perhaps another group member can take the lead role for this calculation and measurement.

The different delay through each filter makes it necessary to centre the eye pattern for each filter.

1.8 Repeat procedure 1.2 to 1.6 using Filters 1.2k, 2.4k, and 4.8k

For these three Bessel Response Filters time constant is no longer meaningful, as it cannot be

calculated, so rise time is the only useful measurement. The rise time may be estimated from the

3 dB Bandwidth given in Appendix 3.

Further group members are encouraged to take the lead role in each measurement to ensure that

each group member is capable in all aspects of the exercise.

1.9 Noisy Eye Patterns

1.9.1 With the data rate set to 2400 bps and no Rx Filter (use “bypass” ) switched into the system add

noise to the data (by switching the noise in with the front panel switch on the RMIT box) and

observe the effect on the eye pattern. The level of noise may be varied with the Noise control

knob.

1.9.2 Change the Rx Filter bandwidth from no Rx Filter (using “bypass” - large bandwidth), to 4.8k Rx

Filter (4.8 kHz bandwidth) and note the effect on the noise as well as on the eye pattern. Put TP

D (Rx Filter input) on channel 1 of CRO and TP E (Rx Filter output) on channel 2 to see the

effect.

1.9.3 Change the Rx Filter to 2.4 k Rx Filter (2.4 kHz bandwidth) and note the effect on the noise as

well as on the eye pattern.

1.9.4 Change the Rx Filter to each of the remaining Rx Filters and note their effect on the noise as well

as on the signal (eye pattern).

1.9.5 If the results are as you expected record them for your report.

1.10 Draw conclusions from what you have just done.

Using group discussions and other research seek conclusions about the impact of the Rx Filter on

the Eye Pattern and Noise Power being studied in this work here.

Try to learn (or get a feel for) how the Rx Filter Rise Time and Bandwidth are related and how the

Filter impacts on the Signal Shape (Eye Pattern) and Noise Level.

2. PROBABILITY OF ERROR MEASUREMENTS

2.1 Setup Equipment for Error Rate Measurements with 2.4 kHz Rx Filter.

2.1.2 Connect the RS232 data output of the DEA to the RS232 data input of the RMIT box (rear panel)

as in Procedure 1.1.1 above. Connect the Data Out (TTL levels) from the RMIT box (rear panel)

to the Data Input (TTL levels) on the front panel of the DEA.


Rx Filter – 2.4 kHz initially and the other filters subsequently.

Tx filter – bypass

11

Attenuator – (-10 dB)

Switch noise in

Noise control fully clockwise

Threshold control fully anti clockwise

Delay control fully anti clockwise

2.1.3 Set the DEA front panel controls as follows.

CLOCK – 2.4 kbps

PATTERN – PN sequence and INVERTED DATA

EXPONENT RANGE – 4 and SINGLE

Upper slide switches left to right – DTR, mid-point between START and STOP.

Lower slide switches left to right –OFF, OFF, OFF, BIT ERROR, JITTER.

The OUT OF LOCK light (in top left corner of DEA) should now be off. If the RCV DATA INV

light is still on move the DATA slide switch to the inverted data position (or vice versa) to turn

the light off.

If these lights are not off the system is not working properly and must be corrected before

proceeding.

2.2 Observe a Real Noisy Eye Pattern

2.2.1 CRO setup for observing eye pattern on the CRO as in Procedure 1.5 previously.

2.2.2 Set Noise Level to about 300 mv (so that a “nice” z factor is achieved later).

The signal level must be set to zero (turn attenuator to "term" position as this will remove the data

signal) while setting the noise level.

Use the noise level control knob on the RMIT box to adjust the noise level at the Rx Filter

output/Decision Circuit (comparator) input (TP E on top panel of RMIT box) to a value in the

region of 300 mv rms (or more if possible). Use the rms signal measuring facility on the CRO.

You will need to reset the statistical measurement when you change the noise level for faster

stabilisation of the rms noise voltage reading.

2.2.3 Set Signal Level to about 2 vp-p (again so that a “nice” z factor is achieved later).

The noise level must be set to zero (turn the noise off with the noise switch to “out”) while setting

the signal level.

Adjust the signal level at the Rx Filter output/Decision Circuit (comparator) input (TP E on top

panel of RMIT box) at the clocking instant (decision time) using the attenuation control on the

RMIT box and observing the noise free eye on the CRO. It is suggested that the attenuator be set

to about -10 dB giving a signal voltage level of a little less than 2 volt p-p at the decision time.

(You will subsequently need to vary this attenuator setting to achieve alternative values for z.)

2.2.4 Adjust the decision time to the appropriate place on the eye pattern using the delay control knob

on the RMIT box and TP H connected to the CRO. (Monitoring TP D is no longer required.)

2.2.5 Set the Threshold Voltage to 0 volts by turning the threshold control knob fully anticlockwise.

Leave the threshold set to zero for all of Procedure 2 of the experiment. (TP F monitors threshold

voltage.)

2.3 Calculate the expected value for Pe and the Error Count.

12

2.3.1 Using the measured values for signal voltage level at the decision time (will be about 2 volts p-p)

and the rms noise voltage (will be about 300 mV rms), calculate the Pe using the method described

in lectures.

3 =456.6

.47(85)

9: = ;(3)

2.3.2 Use graph in Appendix 1 (or Equation) to get Pe from z. Calculate the number of errors expected

in a 104 bits length test for this Pe.

2.4 Measure Error Count and calculate a measured Pe

2.4.1 Switch the noise back in and count the errors in a 104 bits test using the DEA. Calculate Pe from

this error count.

<= =>>?>$?#

#@>?@""#

2.4.2 Press and release the START STOP switch to START to begin the test. 104 bits will take 24

seconds at 2.4 kbps. (How did I know this?)

Always check that the threshold voltage and decision time are correct before counting the errors.

Check signal and noise levels after the test to make sure they are still the same as before the test.

The EXPONENT RANGE slide switch controls the number of bits in the test and was set to 4

indicating a 104 bits test in Procedure 2.1.3. The number to the right of the error count on the

DEA read out, top right of the front panel, gives the exponent value for the test just completed.

Remember that for a statistically significant result it is necessary to run the test for long enough to

obtain at least 30 or so errors.

You should calculate how long the test will take before commencing such a measurement

(otherwise you may be waiting for a rather long time before enough errors occur).

You should be able to calculate that values of z between 2.5 and 3.5 are suitable for this setup as

30 or so errors will occur in a test lasting less than a minute with 10,000 test bits at 2.4 kbps.)

2.4.3 Run the test a few times. The error count will vary as this is the nature of noise. The error count

however should remain substantially the same.

2.5 Comparison of Expected and Measured Results.

2.5.1 Plot the measured Pe on the predicted curve of Appendix 1. You can obtain your own curve by

using the equations given in Appendix 1 as erf and erfc are functions generally available in math

packages such as Matlab and Excel.

2.5.2. Change the value of z (by either changing the noise level or changing the signal level) to around

2.5 and again measure the Pe. (Try an attenuator setting of -12 dB.)

A different group member should take the lead role for each different z calculation and

measurement.

2.5.3 Change the value of z (by either changing the noise level or changing the signal level) to around

3.5 and again measure the Pe. (Try an attenuator setting of -8 dB.)

You will now have 3 measured points on the curve of Appendix 1 with z values of about 2.5, 3.0

and 3.5.

13

2.5.4 Compare your results with other student groups. You should aim for your points to be no more

than 5 mm from the theoretical curve.

2.6 Examine the relationship between the Rx Filter bandwidth and Pe.

2.6.1 Leave the Signal and Noise levels fixed at a value that makes z about 3 for the 2.4 kHz Rx Filter

then measure Pe for each of the other two Bessel Rx Filters in turn.

Remember to adjust the decision time to the optimum time for each filter and check that the

threshold voltage is set to zero before you count the errors.

2.6.2 From the measurements of each of the 3 Bessel Rx Filters determine which one performs best (the

one that minimises Pe) for this data rate of 2.4 kbps.

To enable a fair comparison the signal and noise levels before the Rx LPF filter (TP D on top

panel of RMIT box) should be kept the same for each Rx Filter measurement. The signal and

noise levels after the filter will depend on the filter used.


Using group discussions and other research seek conclusions about the impact of the Rx Filter on

the Data Reception problem (Pe minimisation) being studied in this work.

Try to see from your measured results how a smaller bandwidth reduces the noise but the

consequential longer rise time at some point will effect the signal too much.

3. MATCHED FILTER MEASUREMENTS.

3.1 System Model.

Fig. 7 Experimental setup for Matched Filter Measurements.

3.2 Setup hardware for Matched Filter Measurements

3.2.1 Disconnect the RS232 data signal used in Procedures 1 and 2 above.

Connect the Data Output (TTL levels) of the DEA (front panel data out) to the Data Input (TTL

levels) of the RMIT box (rear panel) to provide the RZ data line code required for Procedure 3 of

the Laboratory Exercise.

If h1(t) is symmetrical in time then h1(t) = h1(-t) and the two filters h1 and h2 are the same. For

symmetrical h(t) the filter must be linear phase. Bessel Filters are linear phase.

h1(t) h2(Tb-t) +

n(t)

Matched Filter

Receiver Filter

Decision

Circuit Impulse

Input

Transmit Filter

stx(t) = h(t) srx(t) = h(t) + n(t)

14

Check that the TTL data out from the RMIT box is still connected to the TTL data input on the

front panel of the DEA.


Rx Filter – bypass initially

Tx Filter – 2.4 kHz

Attenuator – 0 dB

Switch noise out

3.2.3 Set the DEA front panel controls as in Procedure 2 above and repeated here.

CLOCK – 2.4 kbps

PATTERN – 1:3 sequence for impulse response measurement and PN sequence for eye

pattern measurement.

EXPONENT RANGE – 4 and SINGLE

Upper slide switches left to right – DTR, mid-point between START and STOP.

Lower slide switches left to right – OFF, OFF, OFF, BIT ERROR, JITTER.

3.3 Measure Impulse Response of 2.4 kHz Tx Filter.

Fig. 1B. Real World Experimental System in Laboratory for Procedure 3.

3.3.1 Connect the Data Input waveform of the DEA (TP I) to channel 1 of the CRO. Put the RZ data

waveform (TP A on RMIT box) on channel 2 of the CRO. Record the RZ signal for Logic “1”

A(), and record the RZ signal for Logic “0”, B().

TP H

TTL NRZ

Data Out

HP 1645A

Data Error

Analyser

Y1

CRO

Y2

Decision

Circuit

Analog Data

Digital Data

+


WNG

Generator

Rx

Filter

Time

Adjuster

Tx Clock

Out

CRO

ext sync RMIT Box

Clock input

Threshold

Adjuster

TP D TP E

TP F

Tx

Filter

Line

Coder

Unipolar RZ

Line Code

TP D

TP E

Or various other test

points as required

TP B

TP A TP I

15

3.3.2 Record the impulse response of the 2.4 kHz Tx Filter using the RZ data signal of part 3.3.1 above

as your approximation for an impulse to be applied to the input of the Filter, TP A. The impulse

response of the Tx Filter can be measured at TP B which is the output of the Tx Filter.

3.3.3 Identify the Rx Filter “matched” to the signal, representing logic “1” transmission, from the 2.4

kHz Tx Filter.

Remember that the impulse response of a filter “matched” to the signal A() has an impulse response

CD() = 5D(EF − )

3.3.4 What is the signal, B(), transmitted to represent the logic “0”? What is the impulse response of a Rx Filter “matched” to this signal?

Sketch the matched filter impulse response for the Rx Filter matched to signal B(), representing logic “0” transmission, delivered to the system by the 2.4 kHz Tx filter.

3.4 Construct Eye Pattern

3.4.1 Use the Rx Filter responses to A() and B() as measured to construct an Eye Pattern for the 2.4 kHz matched Rx Filter output. Use the technique developed in Preliminary 4. (Take the data

streams 1, 1, 1: 1, 1, 0: 1, 0, 1: 1, 0, 0: and so on and superimpose the Rx Filter responses to these

input signals (impulse responses of the Tx Filter) across 2 to 3 bit times as you have done

previously but with step responses.)

3.5 Measure Eye Pattern.

3.5.1 Set up an eye pattern on the CRO (at TP E) for the Rx Filter matched to the signal from the 2.4

kHz Tx Filter, in a similar way to that used in Procedure 1.3. This time the eye pattern will be

built from impulse responses rather than step responses.

3.6 Compare the measured eye diagram with that predicted by the impulse response

measurement.

3.6.1 Compare the measured eye pattern to that predicted by the impulse response measurement and if

the comparison is satisfactory record the measured eye pattern. A photograph of the screen may

be pasted directly into your report. Ensure that you correctly identify which photo goes with this

measurement for inclusion in your report.



3.7 Set up Equipment for Expected Error Rate Calculation and Measurement .

3.7.1 Set Noise Level of about 100 mv. (As done previously in 2.2.2)

The signal level must be set to zero (turn attenuator to "term" position as this will remove the data

signal) while setting the noise level.

Use the noise level control knob on the RMIT box to adjust the noise level at the Rx

Filter/Decision Circuit (comparator) input (TP E on top panel of RMIT box) to a value in the

region of 100 millivolt rms. Use the rms signal measuring facility on the CRO. You will need to

reset the statistical measurement when you change the noise level for quicker adjustment.

3.7.2 Measure Signal Level at the decision time for a 0 dB attenuator setting. (As done previously in

2.2.3)

16

The noise level must be set to zero (turn the noise off with the noise switch to “out”) while setting

the signal level.

Measure the signal level at the Decision Circuit (comparator) input (TP E on top panel of RMIT

box) at the clocking instant (decision time) by using the cursors on the noise free eye pattern on

the CRO.

The 0 dB position for the attenuator is best for your measurements and value of z can be set by

varying the noise level.

3.7.3 Set the decision time to the appropriate place on the eye pattern using the delay control knob on

the RMIT box and TP H connected to the second channel of the CRO.

3.7.4 Set the threshold voltage to a value mid-way between the signal voltages representing the two

logic levels at the decision time. (One level will close to 0 volt and the other will be a bit less

than 1 volt.) The threshold voltage is available at TP F.

Use channel 2 of the CRO to set the threshold and decision time in turn.

3.7.5 Calculte the value of z from your measured values of Signal Level and rms Noise Level. Adjust

the noise level to set z close to 3.

3.8 Calculate the Expected Error Rate.

3.8.1 Use the same method as in Procedure 2.8 and repeated here.

3 =456

.47(85)

9: = ;(3)

3.8.2 Use graph in Appendix 1 (or Equation) to get Pe from z.

3.9 Measure the Error Count and Calculate a Measured Pe.

3.9.1 Switch the noise back in and count the errors in a 104 bits test using the DEA. Calculate Pe from

this error count.

<= =>>?>$?#

#@>?@""#

Remember that for a statistically significant result it is necessary to run the test for long enough to

obtain at least 30 or so errors. You should calculate how long the test will take before

commencing such a measurement using the technique in Procedure 2.

Check that the signal level at the decision time, the rms noise level, the threshold voltage, and the

decision time are all correct before and after making the error count.

3.10 Compare the predicted (calculated) Pe with the measured Pe.

3.10.1 Plot the measured Pe on the predicted curve in Appendix 1. You can obtain your own curve by

using the error function erf and complementary error function erfc normally available on

calculating platforms such as Matlab and Excel.

3.10.2 Record your results if they are satisfactory.

3.11 Test Matched Rx Filter Performance against other Non-Matched Rx Filters.

17

3.11.1 Measure how well the matched filter performs compared to other receive filters by leaving the

noise and signal levels set for a value of z of about 3 for the Matched Rx Filter (at TP E) as was

done in Procedure 3.7.

3.11.2 Now switch in any of the other “non-matched” Rx Filters (all four of them in turn) and measure

the error rate for each one of these filters.

Remember to reset the decision time and threshold voltage to the best position for each filter

before counting the errors. This is just to be fair to all in that all the Rx Filters are performing as

best they can.

3.12 Compare Measured and Expected results.

3.12.1 Compare the measured Pe’s for each Rx Filter to the Matched Rx Filter result and if the

comparison is satisfactory record the results.




Using group discussions and other research draw conclusions about the performance of a Rx Filter

“matched” to the signal from the Tx Filter as studied in this work.

Build on your thoughts at Procedure 2.7 and try to understand (maths aside) how the Matched Rx

Filter effects the signal and the noise in such a way that it outperform all others by minimising Pe.

18

REPORT

1. Restate the purpose of your investigation, as you now understand it, in your own words. State what

assumptions you made and how you interpreted what you had to do. You should also state the

conclusions sought by your investigation. (Please do not restate the aim of the investigation as

presented in this guide as this will not earn you any marks.)

2. Provide a formal statement of your conclusions from the investigation together with explanations,

proofs and other evidence to justify your conclusions. An evaluation of the conclusions should be

given and, where appropriate, you are encouraged to suggest how the conclusions of your particular

investigation could be generalised to apply to other applications. For example you might suggest some

problems of measuring the error rate in low error systems. For example consider how long it would

take to for 100 errors to occur in a 10 Mbps Ethernet that has a Pe of 10-10. (Relating your investigation

to your own previous individual real life experiences is strongly encouraged and will be rewarded with

extra marks.)

3. Report on the mathematical knowledge, software tools, and hardware that you used in your

investigation. You should also report any techniques and tools used for group management.

4. Report on the investigation process you went through to arrive at your results. Include group

arrangements and task allocation methods used. Show how you started off, how your understanding of

the data communication problem developed, what you tried at various stages and any important insights

and breakthroughs which occurred as you sought explanations for the differences between what you

expected and what you observed. You should highlight, with hindsight, the problem-solving strategies,

other techniques, and computer assistance you tried. Any rough notes made when thinking about your

explanations may be included as an Appendix to your report.

5. Give a brief acknowledgment of the ideas or help provided by other students, specialist information

sources, and so on. Include any references actually found to be useful during your investigation.

6. Include appendices, which may help the reader of your report, understand important details of your

report. Include rough notes, any necessary calculations, raw data, or other essential resources.

Appendices should only be included if they have been specifically referred to in the text. They should

be numbered consecutively and each should bear a title.

7. Reflect on the project both individually, first, and then as a group, after the investigation has been

completed. Think about what you have learned by doing the exercise and reflect on the original

objective of the project.

The assessment break-up for your project is (13+30+10+30+2+2+13 = 100%)

One report per group is required for assessment.

The report is due 2 weeks after your final measurement session.

Revised 3/12 KG and RL

19

APPENDIX 1

Q FUNCTION OF GAUSSIAN STATISTICS

Fig. 2 Q Function Curve from Statistics

Equation for Q Function

−=

=

21

2

1

22

1)(

zerf

zerfczQ

Remember that erf and erfc are available in Matlab.

There seems little need for approximate results with today’s computational power available.

0 1 2 3 4 5 6 710

-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Q(z) Function Curve

z

Probability of Error (Pe)

20

APPENDIX 2

RMIT BASEBAND DATA SYSTEM BOX CIRCUIT DIAGRAM

22

33

44

Title

Number

Size A4

Date:

01/04/2011

Sheet of

File:

C:\Documents and Settings\..\MFILTER2.schDrawn By:

-12

-12

-12

-12

+12

+12

+12

+12

+12

1k

1k

1k1k

1k

1kR20

+5

5k

DELAY

470nF

C3

470pF

C2

82nFC1

1k2R22

1k2R21

10k

THRESHOLD

1k2R16

1k2R15

1k2R14

1k2R13

1k2R12

1k2R11

1k2R10

ATT-S2

560RR8

10kR4

10kR3

10kR2

20kR1

LM311

IC1

1 OF 6

RX FILTER

RX-FS2

RX-FS1

TX-FS2

TX-FS1

1 OF 6

TX FILTER

IC2B

LF353

IC2A

IC6B

LF353

IC6A

IC3D

IC3C

IC3B

7400

1C3A

1k2R5

1k2R6

1k2R7

+5

+5

+5

+5

10k

NOISE

1k 1k

1k1k

1k

1k

1k

+12

-12

-12

+12

1k

1k

NOISE OUT

74121

74121

74121

7475

A2

A1

43

A2

A1

B

QDo

Eo

A2

Q

- Q- Q

PLUGIN PCBrd

PLUGIN PCBrds

PLUGIN PCBrds

6

IC3C pin1

IC4 pin6

10

11

3 4

5

11

10

5

64

10

11

6

13

16

2

7

32

7

561

32

7

6 5

6

1

32

5

23

1

4

8

109

11

COMP OUT

G

SAMLPING

H

TXF OUT

RXF OUT

C

E

A

RS232

NOISE

INPUT

DATA

OUT

TX CLK

Noise

Source

Atten Network

1 of 10

DATA

-EDGE

LATCH

MONO

+EDGE

MONO

+EDGE

MONO

IC5

IC8

IC4

IC7

0 to -20dB

600 Ohm I/O

0V

NOISE SOURCE

PLUGIN

NOISE

INPUT

DATA ERROR / MATCHED

FILTER EXPERIMENT

DRXF IN

TXF IN

21

APPENDIX 3

RMIT BASEBAND DATA SYSTEM BOX Tx and Rx FILTER DETAILS

Filter A - RC Low Pass Circuit

Filter B - RC Low Pass Circuit

4.8 kHZ Filter

4 Pole Low Pass Bessel Filter with 3 dB Bandwidth of 4.8 kHz. (G ∶= 70J)

2.4 kHZ Filter


1.2 kHZ Filter


56 nF 4.7 kΩΩΩΩ

4.7 kΩΩΩΩ

27 nF 5.1 kΩΩΩΩ

4.7 kΩΩΩΩ