Lab 3: PRBS generation, Noisy Channel Model and Eye Diagrams
This lab covers three subjects that are used in several subsequent labs. Pseudorandom Bit Streams (PRBS) are used to represent message data as well as for orthogonal spreading codes in the CDMA experiments. In addition, they are used to represent a "typical" data stream in Bit Error Rate measurements. The noisy channel model is a series of modules that allow us to apply noise, DC signals and bandwidth limiting to a data stream simulating what happens when it is transmitted through a real system. Eye diagrams are useful for visually seeing the quality of the data transmission and for setting the timing for gating operations to evaluate the value (one or zero) of a data bit. We will start with the PBRS generation, add the noisy channel model (evaluating some properties of noise) and finish by looking at the effects of noise and band limiting on the eye diagrams.
PRELAB
Familiarize yourself with the operation of the Sequence Generator and Error Counting Utilities, WIDEBAND TRUE RMS METER, NOISE GENERATOR, BASEBAND CHANNEL FILTERS module; 100 kHz CHANNEL FILTERS module optional.
Review Pseudo Random Bit Streams, noise and eye diagrams.
Answer the following questions:
- PL How are PRBS generated?
- PL What information does the height of the opening of the eye provide?
- PL What is timing jitter and how does it manifest itself in the eye diagram?
- What rms voltage reading would result from adding a 2 volt rms sine wave and 1 V rms AWG noise signal?
Extra Modules:
A second SEQUENCE GENERATOR, ERROR COUNTING UTILITIES. WIDEBAND TRUE RMS METER, NOISE GENERATOR, BASEBAND CHANNEL FILTERS, AUDIO OSCILLATOR module; 100 kHz CHANNEL FILTERS module optional.
Reference Material:
- “Contemporary Communication Systems” by M F Mesiya.
Achievements:
Introduction to the pseudo random binary sequence (PRBS) generator; time domain viewing: snap shot and eye patterns; two generator synchronization and alignment with the ‘sliding window correlator’.
Definition of the macro CHANNEL MODEL module. Ability to set up a noisy bandlimited channel for subsequent experiments; measurement of filter characteristics; measurement of signal-to-noise ratio with the WIDEBAND TRUE RMS METER. Observation of different levels of signal-to-noise ratio with speech.
Understanding the Nyquist I criterion; transmission rates via bandlimited channels; comparison of the ‘snap shot’ display with the ‘eye patterns‘.
LAB
PRSB GENERATION
PREPARATION
Digital Messsages
In analog work the standard test message is the sine wave, followed by the twotone signal for more rigorous tests. The property being optimized is generally signal-to-noise ratio (SNR). Speech is interesting, but does not lend itself easily to mathematical analysis, or measurement.
In digital work a binary sequence, with a known pattern of '1' and '0', is common. It is more common to measure bit error rates (BER) than SNR, and this is simplified by the fact that known binary sequences are easy to generate and reproduce.
A common sequence is the pseudo random binary sequence.
Random Binary Sequences
The output from a pseudo random binary sequence generator is a bit stream of binary pulses; ie., a sequence of 1`s (HI) or 0`s (LO), of a known and reproducible pattern.
The bit rate, or number of bits per second, is determined by the frequency of an external clock, which is used to drive the generator. For each clock period a single bit is emitted from the generator; either at the '1' or '0' level, and of a width equal to the clock period. For this reason the external clock is referred to as a bit clock.
For a long sequence the 1`s and 0`s are distributed in a (pseudo) random manner.
The sequence pattern repeats after a defined number of clock periods. In a typical generator the length of the sequence may be set to 2n clock periods, where n is an integer. In the TIMS SEQUENCE GENERATOR the value of n may be switched to one of three values, namely 5, 8, or 11. There are two switch positions for the case n = 8, giving different independent patterns. The SYNCH output provides a reference pulse generated once per sequence repetition period.
This is the start-of-sequence pulse. It is invaluable as a trigger source for an oscilloscope.
Viewing
There are two important methods of viewing a sequence in the time domain.
The Snapshot
A short section, about 16 clock periods of a TTL sequence, is illustrated in Figure 1 below.
Suppose the output of the generator which produced the TTL sequence, of which this is a part, was viewed with an oscilloscope, with the horizontal sweep triggered by the display itself.
The display will not be that of Figure 1 above ! Of course not, for how would the oscilloscope know which section of the display was wanted?
Consider just what the oscilloscope might show!
Specific sections of a sequence can be displayed on a general purpose oscilloscope, but the sequence generator needs to provide some help to do this.
As stated above, it gives a start-of-sequence pulse at the beginning of the sequence. This can be used to start (trigger) the oscilloscope sweep. At the end of the sweep the oscilloscope will wait until the next start-of-sequence is received before being triggered to give the next sweep.
Thus the beginning 'n' bits of the sequence are displayed, where 'n' is determined by the sweep speed.
For a sequence length of many-times-n bits, there would be a long delay between sweeps. The persistence of the screen of a general purpose oscilloscope would be too short to show a steady display, so it may blink. Alternately, the oscilloscope may decide that it has waited too long and automatically triggers resulting in an unstable display.
The Eye Pattern
A long sequence is useful for examining 'eye patterns'. These are defined and examined in the part of this experiment entitled Eye patterns.
Applications
One important application of the PRBS is for supplying a known binary sequence. This is used as a test signal (message) when making bit error rate (BER) measurements.
For this purpose a perfect copy of the transmitted sequence is required at the receiver, for direct comparison with the received sequence. This perfect copy is obtained from a second, identical, PRBS generator.
The second generator requires:
- Bbit clock information, so that it runs at the same rate as the first
- A method of aligning its output sequence with the received sequence. Due to transmission through a bandlimited channel, it will be delayed in time with respect to the sequence at the transmitter.
Bit clock acquisition
In a laboratory environment it is a simple matter to use a 'stolen carrier' for bit clock synchronization purposes, and this will be done in most TIMS experiments. In commercial practice this bit clock must be regenerated from the received signal.
EXPERIMENT
The 'Snapshot' Display
Examine a SEQUENCE GENERATOR module, and read about it in the TIMS User Manual.
A suitable arrangement for the examination of a SEQUENCE GENERATOR is illustrated in Figure 2.
Notice that the length of the sequence is controlled by the settings of a DIP switch, SW2, located on the circuit board. See the Appendix to this experiment for details.
T1 Before inserting the SEQUENCE GENERATOR set the on-board DIP switch SW2 to generate a short sequence. Then patch up the model of Figure 2 above. Set the AUDIO OSCILLATOR, acting as the bit clock, to about 2 kHz. Set the oscilloscope sweep speed to suit; say about 1 ms/cm.
T2 Observe the TTL sequence on CH1-A. Try triggering the oscilloscope to the
sequence itself (CH1-A). You probably want to be able to obtain a
stable picture, but it may change when the reset button is pressed
(this re-starts the sequence each time from the same point, referred
to as the 'start of sequence').
T3 Try triggering off the bit clock. Notice that it is difficult (impossible?) to obtain a stable display of the sequence.
T4 Change the mode of oscilloscope triggering. Instead of using the signal itself, use the start-of-sequence SYNC signal from the SEQUENCE GENERATOR, connected to 'ext. trig' of the oscilloscope. Reproduce the type of display of Figure 1 (CH1-A ).
T5 Increase the sequence length by re-setting the on-board switch SW2. Reestablish synchronization using the start-of-sequence SYNC signal connected to the 'ext. trig' of the oscilloscope. Notice the effect upon the display. See Tutorial Question Q8.
T6 Have a look with your oscilloscope at a yellow analog output from the SEQUENCE GENERATOR. The DC offset has been removed, and the amplitude is now suitable for processing by analog modules (eg., by a filter representing an analog channel - which we will do later in this lab). Observe also that the polarity has been reversed with respect to the TTL version. This is just a consequence of the internal circuitry; if not noticed it can cause misunderstandings!
Band limiting
The displays you have seen on the oscilloscope are probably as you would have expected them to be ! That is, either 'HI' or 'LO' with sharp, almost invisible, transitions between them. This implies that there was no band limiting between the signal and the viewing instrument.
If transmitted via a lowpass filter, which could represent a bandlimited (baseband) channel, then there will be some modification of the shape, as viewed in the time domain.
For this part of the experiment you will use a TUNEABLE LPF to limit, and vary, the bandwidth. Because the sequence will be going to an analog module it will be necessary to select an 'analog' output from the SEQUENCE GENERATOR.
T7 select a short sequence from the SEQUENCE GENERATOR.
T8 connect an analog version of the sequence (YELLOW) to the input of a TUNEABLE LPF.
T9 on the front panel of the TUNEABLE LPF set the toggle switch to the WIDE position. Obtain the widest bandwidth by rotating the TUNE control fully clockwise.
T10 with the oscilloscope still triggered by the 'start-of-sequence' SYNC signal, observe both the filter input and output on separate oscilloscope channels. Adjust the gain control on the TUNEABLE LPF so the amplitudes are approximately equal.
T11 monitor the filter corner frequency, by measuring the CLK signal from the TUNEABLE LPF with the FREQUENCY COUNTER(divide by 880 (normal) or 360 (wide). For detail see the TIMS User Manual.) Slowly reduce the bandwidth, and compare the difference between the two displays. Notice that, with reducing bandwidth:
- Identification of individual bits becomes more difficult
- There is an increasing delay between input and output
Remember that the characteristics of the filter will influence the results of the last Task.
Two generator alignment
It is important to be able to align two sequences. If the sequence is the spreading code in a CDMA transmission, the receiver must apply the synchronized code to the multiplexed CDMA signal received to extract that channels information. During a bit error rate measurement, unsynchronized signals will lead to false errors and an artificially high measured Bit Error Rate.
Two SEQUENCE GENERATOR modules may be coupled so that they deliver two identical, aligned, sequences.
- that they should deliver the same sequence it is sufficient that the generator circuitry be identical
- that they be at the same rate it is necessary that they share a common bit clock
- that they be aligned requires that they start at the same time.
TIMS SEQUENCE GENERATOR modules (and those available commercially) have inbuilt facilities to simplify the alignment operation. One method will be examined with the scheme illustrated in block diagram form in Figure 3 below.
The scheme of Figure 3 is shown modelled with TIMS in Figure 4 below.
You will now investigate the scheme. Selecting short sequences will greatly assist during the setting-up procedures, by making the viewing of sequences on the oscilloscope much easier.
T12 before plugging in the SEQUENCE GENERATOR modules, set them both to the same short sequence.
T13 patch together as above, but omit the link from the 'GENERATOR #1' SYNC to 'GENERATOR #2' RESET. Do not forget to connect the 'start-of-sequence' SYNC signal of the GENERATOR #1 to the 'ext. trig' of the oscilloscope.
T14 press the 'GENERATOR #2' RESET push button several times. Observe on the oscilloscope that the two output sequences are synchronised in time but the data bits do not line-up correctly. Try to synchronise the sequences manually by repeating this exercise many times. It is a hit-and-miss operation, and is likely to be successful only irregularly.
T15 connect the SYNC of the 'GENERATOR #1' to the RESET of the 'GENERATOR #2'. Observe on the oscilloscope that the two output sequences are now synchronised in time and their data are aligned.
T16 break the synchronizing path between the two generators. What happens to the alignment?
The above scheme has demonstrated a method of aligning two generators, and was seen to perform satisfactorily. But it was in a somewhat over simplified environment.
What if the two generators had been separated some distance, with the result that there was a delay between sending the SYNC pulse from GENERATOR #1 and its reception at GENERATOR #2?
The sequences would be offset by the time delay
In other words, the sequences would not be aligned.
Two sequence alignment
In the previous section two PRBS generators were synchronized in what might be called a 'local' situation. There were two signal paths between them:
1. One connection for the bit clock
2. Another connection for the start-of-sequence command
Consider a transmitter and a receiver separated by a transmission medium. Then:
1. There would be an inevitable transmission time delay
2. The two signal paths are not conveniently available
It may be difficult (impossible ?) to align the two generators, at remote sites. But it is possible, and frequently required, that a local generator can be aligned with a received sequence (from a similar generator).
The sliding window correlator is an example of an arrangement which can achieve this end.
The sliding window correlator
Consider the arrangement shown in block diagram form in Figure 5 below.
The detector is present to re-generate TTL pulses from the bandlimited received signal. We will assume this regeneration is successful.
The regenerated received sequence (which matches, but is a delayed version of the transmitted sequence) is connected to one input of a clocked X-OR logic gate.
The receiver PRBS generator (using a stolen bit clock in the example) is set to generate the same sequence as its counterpart at the transmitter. Its output is connected to the other input of the clocked X-OR gate. The clock ensures that the comparison is made at an appropriate instant within a bit clock period.
At each bit clock period there is an output from the X-OR gate only if the bits differ. In this case the receiver generator will be RESET to the beginning of the sequence.
This resetting will take place repeatedly until there are no errors. Thus every bit must be aligned. There will then be no further output from the X-OR gate.
It is the common bit clock which maintains the alignment. Because of the nature of this X-OR comparison technique the arrangement is called a sliding window correlator.
The model
You will now model the block diagram of Figure 5. In later experiments you will meet the channel and the detector, but in this experiment we will omit them both. Thus there will in fact be no delay, but that does not in any way influence the operation of the sliding window correlator.
The patching arrangement to model Figure 5 is shown in Figure 6 below.
This model will regenerate, at the receiver, an identical sequence to that sent from the transmitter. To avoid additional complications a stolen carrier is used.
T17 Before patching up select the shortest length sequence on each SEQUENCE GENERATOR.
T18 Patch together as above. Do not close the link from the X-OR output of the ERROR COUNTING UTILITIES module to the RESET of the RECEIVER GENERATOR. (See the Appendix to this experiment for some information about the ERROR COUNTING UTILITIES module.)
T19 View CH1-A and CH2-A simultaneously. The two output sequences are synchronized in time but the data bits are probably not aligned. Press the RESET push button of the RECEIVER GENERATOR repeatedly. Notice that once in a while it is possible to achieve alignment. With a longer sequence this would be a rare event indeed.
T20 switch to CH1-B; observe the error sequence produced by the X-OR operation on the two data sequences.
T21 now close the alignment link by connecting the error signal at the X-OR output to the RESET input of the RECEIVER GENERATOR.
T22 confirm that the error sequence is now zero. Confirm that, if the RESET push button of the RECEIVER GENERATOR is repeatedly pressed, the error signal appears for a short time and then disappears.
T23 repeat the previous Task with a long sequence. Note that the system takes a longer time to acquire alignment.
T24 having achieved alignment, disconnect the error signal from the RESET input of the RECEIVER GENERATOR, and observe that the two sequences remain in alignment.
Future experiments will assume familiarity with the operation of the SEQUENCE GENERATOR, and the alignment of two sequences using the sliding window correlator. So, before you finish this experiment, make sure you have looked at as many aspects of this arrangement as you have time for.
Tutorial Questions
Q1 you have seen the first 'n' bits of a sequence, using the start-of-sequence signal to initiate the oscilloscope sweep. How could you show the next 'n' bits of the same sequence ? Can you demonstrate your method with TIMS?
Q2 estimate the bandwidth of the sequence as a function of bit rate clock frequency. Describe a method for estimating the maximum rate at which a binary sequence can be transmitted through a lowpass filter. Relate its predictions with your observations.
Q3 explain what is meant when two sequences are 'synchronized' and 'aligned'.
Q4 was there any obvious misalignment between the TTL sequence input to, and the bandlimited sequence output from, the TUNEABLE LPF? Explain.
Q5 in the last model examined, explain why the sequence alignment takes longer when the sequence length is increased.
Q6 suppose the TIMS SEQUENCE GENERATOR is driven by an 8.333 kHz TTL clock. What would the TIMS FREQUENCY COUNTER read if connected to the output sequence? Explain.
Q7 what should an rms meter read if connected to a TTL pseudo random binary sequence?
Q8 with a 2.083 kHz clock what is the delay, for a 2048 bit sequence, between consecutive displays ?
THE NOISY CHANNEL MODEL
ACHIEVEMENTS:
Definition of the macro CHANNEL MODEL module. Ability to set up a noisy bandlimited channel for subsequent experiments; measurement of filter characteristics; measurement of signal-to-noise ratio with the WIDEBAND TRUE RMS METER. Observation of different levels of signal-to-noise ratio with speech.
PREREQUISITES:
None
EXTRA MODULES:
WIDEBAND TRUE RMS METER, NOISE GENERATOR, BASEBAND CHANNEL FILTERS module; 100 kHz CHANNEL FILTERS module optional.
PREPARATION
Since TIMS is about modelling communication systems it is not surprising that it can model a communications channel.
Two types of channels are frequently required, namely lowpass and bandpass.
Lowpass (or baseband) channels
A lowpass channel by definition should have a bandwidth extending from DC to some upper frequency limit. Thus it would have the characteristics of a lowpass filter.
A speech channel is often referred to as a lowpass channel, although it does not necessarily extend down to DC. More commonly it is called a baseband channel.
Bandpass channels
A bandpass channel by definition should have a bandwidth covering a range of frequencies not including DC. Thus it would have the characteristics of a bandpass filter.
Typically its bandwidth is often much less than an octave, but this restriction is not mandatory. Such a channel has been called narrow band.
Strictly an analog voice channel is a bandpass channel, rather than lowpass, as suggested above, since it does not extend down to DC. So the distinction between baseband and bandpass channels can be blurred on occasion.
Designers of active circuits often prefer bandpass channels, since there is no need to be concerned with the minimization of DC offsets.
For more information refer to the chapter entitled Introduction to modelling with TIMS, within Volume A1 - Fundamental Analog Experiments, in the section entitled 'bandwidths and spectra'.
Over Simplification
The above description is an oversimplification of a practical system. It has concentrated all the bandlimiting in the channel, and introduced no intentional pulse shaping. In practice the bandlimiting, and pulse shaping, is distributed between filters in the transmitter and the receiver, and the channel itself. The transmitter and receiver filters are designed, knowing the characteristics of the channel. The signal reaches the detector having the desired characteristics.
Noise
Whole books have been written about the analysis, measurement, and optimization of signal-to-noise ratio (SNR).
SNR is usually quoted as a power ratio, expressed in decibels. But remember the measuring instrument in this experiment is an rms voltmeter, not a power meter. See Tutorial Question Q6.
Although, in a measurement situation, it is the magnitude of the ratio S/N which is commonly sought, it is more often the which is available. In other words, in a non-laboratory environment, if the signal is present then so is the noise; the signal is not available alone.
In this, and most other laboratory environments, the noise is under our control, and can be removed if necessary. So that , rather than , can be measured directly. For high SNRs there is little difference between the two measures.
The noisy channel mode
A representative noisy, bandlimited channel model is shown in block diagram form in Figure 1 of the following page.
Band limitation is implemented by any appropriate filter.
The noise is added before the filter so that it becomes bandlimited by the same filter that band limits the signal. If this is not acceptable then the adder can be moved to the output of the filter, or perhaps the noise can have its own bandlimiting filter.
Controllable amounts of random noise, from the noise source, can be inserted into the channel model, using the calibrated attenuator. This is non signal-dependent noise.
For lowpass channels lowpass filters are used.
For bandpass channels bandpass filters are used.
Signal dependent noise is typically introduced by channel non-linearities, and includes intermodulation noise between different signals sharing the channel (cross talk). Unless expressly stated otherwise, in TIMS experiments signal dependent noise is considered negligible. That is, the systems must be operated under linear conditions. An exception is examined in the experiment entitled Amplifier overload (within Volume A2 - Further & Advanced Analog Experiments).
Diagrammatic representation
In patching diagrams, if it is necessary to save space, the noisy channel will be represented by the block illustrated in Figure 2 below.
Note it is illustrated as a channel model module. Please do not look for a physical TIMS module when patching up a system with this macro module included. This macro module is modelled with five real TIMS modules, namely:
- An INPUT ADDER module.
- A NOISE GENERATOR module.
- A bandlimiting module. For example, it could be:
- Any single filter module; such as a TUNEABLE LPF (for a baseband channel).
- A BASEBAND CHANNEL FILTERS module, in which case it contains three filters, as well as a direct through connection. Any of these four paths may be selected by a front panel switch. Each path has a gain of unity. This module can be used in a baseband channel. The filters all have the same slot bandwidth (40 dB at 4 kHz), but differing passband widths and phase characteristics.
- A 100 kHz CHANNEL FILTERS module, in which case it contains two filters, as well as a direct through connection. Any of these three paths may be selected by a front panel switch. Each path has a gain of unity. This module can be used in a bandpass channel.
Definition of filter terms, and details of each filter module characteristic, are described in Appendix A to this text.
- An OUTPUT ADDER module, not shown in Figure 1, to compensate for any accumulated DC offsets, or to match the DECISION MAKER module threshold.
- A source of DC, from the VARIABLE DC module. This is a fixed module, so does not require a slot in the system frame.
Thus the CHANNEL MODEL is built according to the patching diagram illustrated in Figure 3 below, and (noting item 5 above) requires four slots in a system unit.
Channel gain
Typically, in a TIMS model, the gain through the channel would be set to unity. This requires that the upper gain control, 'G', of both ADDER modules, be set to unity. Both the BASEBAND CHANNEL FILTER module and the 100 kHz CHANNEL FILTER module have fixed gains of unity. If the TUNEABLE LPF is used, then its adjustable gain must also be set to about unity.
However, in particular instances, these gains may be set otherwise.
Noise level
The noise level is adjusted by both the lower gain control 'g' of the INPUT ADDER, and the front panel calibrated attenuator of the NOISE GENERATOR module. Typically the gain would be set to zero [g fully anti-clockwise] until noise is required. Then the general noise level is set by g, and changes of precise magnitude introduced by the calibrated attenuator.
Theory often suggests to us the means of making small improvements to SNR in a particular system. Although small, they can be of value, especially when combined with other small improvements implemented elsewhere. An improvement of 6 dB in received SNR can mean a doubling of the range for reception from a satellite, for example.
Revision
You should look now at the Tutorial Questions, as important preparation for the experiment.
Signal to noise ratio
This next part of the experiment will introduce you to some of the problems and techniques of signal-to-noise ratio measurements.
The maximum output amplitude available from the NOISE GENERATOR is about the TIMS ANALOG REFERENCE LEVEL when measured over a wide bandwidth - that is, wide in the TIMS environment, or say about 1 MHz. This means that, as soon as the noise is bandlimited, as it will be in this experiment, the rms value will drop significantly.
You will measure both , (ie, SNR) and , and compare calculations of one from a measurement of the other.
The uncalibrated gain control of the ADDER is used for the adjustment of noise level to give a specific SNR. The TIMS NOISE GENERATOR module has a calibrated attenuator which allows the noise level to be changed in small calibrated steps.
Within the test set up you will use the macro CHANNEL MODEL module already defined. It is shown embedded in the test setup in Figure 5 below.
As in the filter response measurement, the oscilloscope is not essential, but certainly good practice, in an analog environment. It is used to monitor waveforms, as a check that overload is not occurring.
The oscilloscope display will also give you an appreciation of what signals look like with random noise added.
T25 Set up the arrangement of Figure 5 above. Use the channel model of Figure 3. In this experiment use a BASEBAND CHANNEL FILTERS module. Before commencing the experiment proper have a look at the noise alone; first wideband, then filtered.
T26 Switch the BASEBAND CHANNEL FILTERS module to the straight-through connection - switch position #1. Look at the noise on the oscilloscope.
T27 Switch the BASEBAND CHANNEL FILTERS module to any or all of the lowpass characteristics. Look at the noise on the oscilloscope. Probably you saw what you expected when the channel was not bandlimiting the noise - an approximation to wideband white noise. But when the noise was severely bandlimited there is quite a large change.
For example:
- The amplitude dropped significantly. Knowing the filter bandwidth you could make an estimate of the noise bandwidth before bandlimiting?
- The appearance of the noise in the time domain changed quite significantly. You might like to repeat the last two tasks, using different sweep speeds, and having a closer look at the noise under these two different conditions.
Record your observations.
You are now going to set up independent levels of signal and noise, as recorded by the WIDEBAND TRUE RMS METER., and then predict the meter reading when they are present together. After bandlimiting there will be only a small rms noise voltage available, so this will be set up first.
T28 Reduce to zero the amplitude of the sinusoidal signal into the channel, using the 'G' gain control of the INPUT ADDER.
T29 Set the front panel attenuator of the NOISE GENERATOR to maximum output.
T30 Keep the filter in its pass through state and adjust the gain control 'g' of the INPUT ADDER to maximum. Adjust the 'G' control of the OUTPUT ADDER for about 1 volt rms. Record the reading. The level of signal into the BASEBAND CHANNEL FILTERS module may exceed the TIMS ANALOG REFERENCE LEVEL, and be close to overloading it - but we need as much noise out as possible. If you suspect overloading, then reduce the noise 2 dB with the attenuator, and check that the expected change is reflected by the rms meter reading. If not, use the INPUT ADDER to reduce the level a little, and check again.
Switch to one of the filter positions and record the rms voltage level of the noise through the filter.
T31 Reduce to zero the amplitude of the noise into the channel by removing its patch cord from the INPUT ADDER, thus not disturbing the ADDER adjustment.
T32 Set the AUDIO OSCILLATOR to any convenient frequency within the passband of the channel. Adjust the gain 'G' of the INPUT ADDER until the WIDEBAND TRUE RMS METER reads the same value as it did for the noise level in step T30.
T33 Turn to your note book, and calculate what the WIDEBAND TRUE RMS METER will read when the noise is reconnected. Show this calculation in your report.
T34 Replace the noise patch cord into the INPUT ADDER. Record what the meter reads.
T35 Calculate and record the signal-to-noise ratio in dB.
T36 Measure the signal-plus-noise, then the noise alone, and calculate the SNR in dB. Compare with the result of the previous Task.
T37 Increase the signal level, thus changing the SNR. Measure both , and , and predict each from the measurement of the other. Repeat for two additional SNR by changing the signal gain.
Group delay
How might you have measured, or estimated, or at least demonstrated the existence of, a time delay through any of the filters?
Hint: try using the SEQUENCE GENERATOR on a short sequence.
TUTORIAL QUESTIONS
Q1 When plotting filter amplitude responses it is customary to use decibel scales for the amplitude, versus a logarithmic frequency scale. Discuss some of the advantages of this form of presentation over alternatives.
Q2 An analog channel is overloaded with a single sinewave test signal. Is this always immediately obvious if examined with an oscilloscope?
Is it obvious with:
- A single measurement using a voltmeter?
- Two or more measurements with a voltmeter?
Explain you answers to (a) and (b).
Q3 Suppose an rms voltmeter reads 1 volt at the output of a noisy channel when the signal is removed from the input. What would it read if the bandwidth was halved? State any assumptions which were necessary for this answer.
Q4 A sinusoidal waveform has a peak-to-peak amplitude of 5 volts. What is its rms value?
Q5 What would an rms meter read if connected to a square wave:
- Alternating between 0 and 5 volt?
- Alternating between ± 5 volt?
Q6 The measuring instrument used in this experiment was an rms volt meter. Could you derive a conversion factor so that the instrument could be used as a direct reading (relative) power meter?
Q7 Suppose a meter is reading 1 volt rms on a pure tone. Wideband noise is now added until the meter reading increases by 10%.
- What would be the signal-to-noise ratio in dB?
- What would the rms volt meter read on noise alone?
This answer is meant to show that measuring small changes to signal-to-noise ratios is difficult unless the signal-to-noise ratio is already small. Do you agree ? How small?
Q8 wideband white noise is passed through a lowpass filter to a meter. If the filter bandwidth is decreased by one half, what would be the change of the reading of the meter if:
- It responds to power - answer in dB
- It is a true rms volt meter - give the percent change
Q9 explain how you might measure, or at least demonstrate the existence of, a time delay through any of the filters?
EYE PATTERNS
PREPARATION
Pulse Transmission
It is well known that, when a signal passes via a bandlimited channel it will suffer waveform distortion. As an example, refer to Figure 1. As the data rate increases the waveform distortion increases, until transmission becomes impossible.
In this experiment you will be introduced to some important aspects of pulse transmission which are relevant to digital and data communication applications.
Issues of interest include:
- In the 1920s Harry Nyquist proposed a clever method now known as Nyquist`s first criterion, that makes possible the transmission of telegraphic signals over channels with limited bandwidth without degrading signal quality. This idea has withstood the test of time. It is very useful for digital and data communications.
The method relies on the exploitation of pulses that look like sin(x)/x - see the Figure opposite. The trick is that zero crossings always fall at equally spaced points. Pulses of this type are known as 'Nyquist I' (there is also Nyquist II and III). - In practical communication channels distortion causes the dislocation of the zero crossings of Nyquist pulses, and results in intersymbol interference (ISI). Eye patterns provide a practical and very convenient method of assessing the extent of ISI degradation. A major advantage of eye patterns is that they can be used 'on-line' in real-time. There is no need to interrupt normal system operation.
- The effect of ISI becomes apparent at the receiver when the incoming signal has to be 'read' and decoded; ie., a detector decides whether the value at a certain time instant is, say, 'HI' or 'LO' (in a binary decision situation). A decision error may occur as a result of noise. Even though ISI may not itself cause an error in the absence of noise, it is nevertheless undesirable because it decreases the margin relative to the decision threshold, ie., a given level of noise, that may be harmless in the absence if ISI, may lead to a high error rate when ISI is present.
- Another issue of importance in the decision process is timing jitter. Even if there is no ISI at the nominal decision instant, timing jitter in the reconstituted bit clock results in decisions being made too early or too late relative to the ideal point. As you will discover in this experiment, channels that are highly bandwidth efficient are more sensitive to timing jitter.
Maximum transmission rate assessment
This is what is going to be done:
- First, set up a pseudorandom sequence. To start you will use the shortest available sequence, so that you can easily observe it with an oscilloscope. Very long sequences are not easy to observe because the time elapsed between trigger pulses is too long. The oscilloscope will be triggered to the start of sequence signal. The display has been defined as a 'snap shot' (see the experiment entitled PRBS generation).
- Next you will pass this sequence through a selection of filters. Three are available in the BASEBAND CHANNEL FILTERS module, and a fourth will be the TUNEABLE LPF module. You will observe the effect of the filters on the shape of the sequence, at various pulse rates.
- Then the above observations will be repeated, but this time the oscilloscope will be triggered by the bit clock, giving what is defined as an eye pattern.
- Finally you will compare the performance of the various cases in terms of achievable transmission rate and 'eye opening'.
EXPERIMENT
T38 Set up the model of Figure 2. The AUDIO OSCILLATOR serves as the bit clock for the SEQUENCE GENERATOR. A convenient rate to start with is 2 kHz. Select CHANNEL #1. Select a short sequence (both toggles of the on-board switch SW2 UP)
T39 Synchronize the oscilloscope to the 'start-of-sequence' synchronizing signal from the SEQUENCE GENERATOR. Set the sweep speed to display between 10 and 20 sequence pulses (say 1 ms/cm). This is the 'snap shot' mode. Both traces should be displaying the same picture, since CHANNEL #1 is a 'straight through' connection.
The remaining three channels (#2, #3, and #4) in the BASEBAND CHANNEL FILTERS module represent channels having the same slot bandwidth 3 (40 dB stopband attenuation at 4 kHz), but otherwise different transmission characteristics, and, in particular, different 3 dB frequencies. Graphs of these characteristics are shown in Appendix A. You should also prepare a TUNEABLE LPF to use as a fourth channel, giving it a 40 dB attenuation at 4 kHz. To do this:
T40 Using a sinusoidal output from an AUDIO OSCILLATOR as a test input:
- Set the TUNE and GAIN controls of the TUNEABLE LPF fully clockwise. Select the NORM bandwidth mode.
- Set the AUDIO OSCILLATOR to a frequency of, say, 1 kHz. This is well within the current filter passband.
- Note the output amplitude on the oscilloscope.
- Increase the frequency of the AUDIO OSCILLATOR to 4 kHz.
- Reduce the bandwidth of the TUNEABLE LPF (rotate the TUNE control anti-clockwise) until the output amplitude falls 100 times. This is a 40 dB reduction relative to the passband gain.
Snap-shot assessment
Now it is your task to make an assessment of the maximum rate, controlled by the frequency of the AUDIO OSCILLATOR, at which a sequence of pulses can be transmitted through each filter before they suffer unacceptable distortion. The criterion for judging the maximum possible pulse rate will be your opinion that you can recognise the output sequence as being similar to that at the input.
It is important to remember that the four filters have the same slot bandwidth (ie., 4 kHz, where the attenuation is 40 dB) but different 3 dB bandwidths.
To relate the situation to a practical communication system you should consider the filters to represent the total of all the filtering effects at various stages of the transmission chain, ie., transmitter, channel, and the receiver right up to the input of the decision device.
T41 Record your assessment of the maximum practical data rate through each of the four channels.
At the very least your report will be a record of the four maximum transmission rates. But it is also interesting to compare these rates with the characteristics of the filters. Perhaps you might expect the filter with the widest passband to provide the highest acceptable transmission rate?
Eye pattern assessment
Now you will repeat the previous exercise, but, instead of observing the sequence as a single trace, you will use eye patterns. The set-up will remain the same except for the oscilloscope usage and sequence length.
So far you have used a short sequence, since this was convenient for the snapshot display. But for eye pattern displays a longer sequence is preferable, since this generates a greater number of patterns. Try it.
T42 Change the oscilloscope synchronizing signal from the start-of-sequence SYNC output of the SEQUENCE GENERATOR to the sequence bit clock. Increase the sequence length (both toggles of the on-board switch SW2 DOWN). Make sure the oscilloscope is set to pass DC. Why? Try AC coupling, and see if you notice any difference.
T43 Select CHANNEL #2. Use a data rate of about 2 kHz. You should have a display on CH2-A similar to that of Figure 3 below.
T44 Increase the data rate until the eye starts to close. Figure 4 shows an eye not nearly as clearly defined as that of Figure 3.
T45 Take some time to examine the display, and consider what it is you are looking at ! There is one 'eye' per bit period. Those shown in Figure 3 are considered to be 'wide open'. But as the data rate increases the eye begins to close.
The actual shape of an eye is determined (in a linear system) primarily by the filter (channel) amplitude and phase characteristics (for a given input waveform).
Timing jitter will have an influence too. See the experiment entitled Bit clock regeneration (within Volume D2 - Further & Advanced Digital Experiments).
The detector must make a decision, at an appropriate moment in the bit period, as to whether or not the signal is above or below a certain voltage level. If above it decides the current bit is a HI, otherwise a LO. By studying the eye you can make that decision. Should it not be made at the point where the eye is wide open, clear of any trace ? The moment when the vertical opening is largest?
You can judge, by the thickness of the bunch of traces at the top and bottom of the eye, compared with the vertical opening, the degree-of-difficulty in making this decision.
T46 determine the highest data rate for which you consider you would always be able to make the correct decision (HI or LO). Note that the actual moment to make the decision will be the same for all bits, and relatively easy to distinguish. Record this rate for each of the four filters.
You have now seen two different displays, the snapshot and the eye pattern.
It is generally accepted that the eye pattern gives a better indication of the appropriate instant the HI or LO decision should be made, and its probable success, than does the snapshot display. Do you agree?
Noise and other impairments will produce the occasional transition which will produce a trace within the apparently trace-free eye. This may not be visible on the oscilloscope, but will none-the-less cause an error. Turning up the oscilloscope brilliance may reveal some of these transitions.
Such a trace is present in the eye pattern of Figure 4.
An oscilloscope, with storage and other features (including in-built signal analysis !), will reveal even more information.
It does not follow that the degradation of the eye worsens as the clock rate is increased. Filters can be designed for optimum performance at a specific clock rate, and performance can degrade if the clock rate is increased or reduced.
The present experiment was aimed at giving you a 'feel' and appreciation of the technique in a non-quantitative manner.
In later experiments you will make quantitative measurements of error rates, as data is transmitted through these filters, with added noise.
Your conclusions
Theory predicts a maximum transmission rate of 2 pulses per Hz of baseband bandwidth available. On the basis of your results, what do you think?
TUTORIAL QUESTIONS
Q1 explain why it is important to have the oscilloscope switched to 'DC' when viewing eye patterns. Explain the meaning, and possible causes of, 'baseline wander'.
Q2 why have the filters in the BASEBAND CHANNEL FILTERS module got common slotband widths (instead, for example, of having common passband widths)?
Q3 why would a storage oscilloscope provide a more reliable eye pattern display?
Q4 why is a long sequence preferable for eye pattern displays?
Q5 how would timing jitter show up in an eye pattern?
APPENDIX
PRBS generator - sequence length
The length of the sequences from the SEQUENCE GENERATOR can be set with the DIP switch SW2 located on the circuit board. See Table A-1 below.
LH toggle | RH toggle | n | Sequence length |
UP | UP | 5 | 32 |
UP | DOWN | 8 | 256 |
DOWN | UP | 8 | 256 |
DOWN | DOWN | 11 | 2048 |
Table A-1: on-board switch SW2 settings |
There are two sequences of length 256 bits. These sequences are different.
Error counting utilities - X-OR
This is the first time the ERROR COUNTING UTILITIES module has been used. It contains two independent sub-systems, only one of which (X-OR) is required in this experiment.
A complete description of its characteristics and behaviour can be obtained from the TIMS Advanced Modules User Manual.
A condensed description of the X-OR function, suitable for this experiment, is given in the experiment entitled Digital utility sub-systems (within Volume D2 - Further & Advanced Digital Experiments), under the heading Exclusive-OR.