Experiment 7 – Pulse Shaping, Bandwidth Constraints and Inter-Symbol
Interference (ISI) in Baseband Signaling.
INTRODUCTION
In Experiment 3, we saw how filtering can obliterate a signal. If a rectangular pulse, binary signal is
passed through a low pass filter with Fpass set too low, the symbols literally smear into one
another. The energy in any given bit time is affected by the bit or even several bits before it.
In practical applications, more than one signal may share a channel. As we shall see in bandpass
signaling, the bandwidth of the baseband signal is translated directly to the carrier frequency.
The bandwidth of the modulated bandpass signal is the same as the baseband signal. To maximize
the number of users in a shared band, it will be necessary to use frequency multiplexing with
different users on different carrier frequencies. The bandwidth of the transmitted signal will
become critical as more users demand access to the band. It is therefore important to find a
minimum bandwidth symbol while insuring against or accounting for inter-symbol interference
(ISI). As we shall discover, this comes at a cost.
The Sinc pulse offers a possible solution to this problem. Sinc pulses have sharply defined
bandwidths, in theory. To achieve this, the pulses would have to have infinite length, violating
causality constraints. A variation of the Sinc pulse is the raised cosine pulse, which has limited
bandwidth, but is also of finite length.
PRE-LAB
MATLAB uses finite length FIR filters to generate Raised Cosine Pulses and Root Raised Cosines.
Determine the energy in a single Root Raised Cosine pulse that extends to the eighth zero crossing
in both directions from the center peak of amplitude 1, i.e. at -8T to +8T. Assume a sampling
interval of T/10. You may use a MATLAB model to make your determination empirically.
PROCEDURE
1. Use the results from Experiment 3 to review the spectrum of a bipolar rectangular pulse
signal.
2. Build the block diagram as shown below. This will implement a model which sends a single
1 ms , bipolar rectangular pulse through a low pass filter with Fpass = 500 and Fstop =
550, simulating a bandwidth limited channel Set the blocks as follows:
Discrete Impulse:
Sample time:
1/1000
Unipolar to Bipolar Converter:
M-ary number:
2
Rectangular Pulse Filter:
Pulse length:
10
Lowpass Filter:
Input processing:
Sample based
Impulse response:
Frequency units:
Input Fs:
Fpass:
Fstop:
Input processing
FIR
Hz
10000
500
550
Sample based
Use a matched digital filter designed to receive the rectangular pulse. Set the Transfer
function type to FIR (all zeros) and Input processing to Sample based. Set the numerator
coefficients to receive the rectangular pulse. Set a downsampler to sample the output of
the matched filter. Adjust the offset of the downsampler to sample the matched filter
output at its peak point. (This value should be about 0 or 1 for the filter specified above
and 10 samples per pulse.) Run the simulation for 0.01s.
3. Measure the intersymbol interference (ISI) by recording the values of the output of the
downsampler at the time of pulse and the samples either side of it. If there was no ISI,
what should the output of the downsampler be at these three points?
4. Using the Raised Cosine Transmit and Receive filters, repeat steps 2 and 3. Your model
should be similar to the one shown below.
Set the filters as follows:
Raised Cosine Transmit Filter:
Filter type:
Group delay:
Rolloff factor:
Upsampling factor:
Input processing:
Linear amplitude filter gain:
Normal
8
0
10
Sample based
.1
Raised Cosine Receive Filter:
Filter type:
Input samples per symbol:
Group delay:
Rolloff factor:
Output mode:
Downsampling factor:
Input processing:
Linear amplitude filter gain:
Normal
10
8
0
Downsampling
10
Sample based
.1
If you wish, you may set the Output Mode to None and use the external downsampler as
you did earlier. Measure the ISI as you did before, noting the values of the output of the
downsampler for the samples before and after the main pulse, and for the pulse itself.
5. Vary the Sample Offset of the downsampler through a range of 0 to 4. If you are using the
downsampling of the Raised Cosine Receive Filter you should set the offset within it. How
does this affect the ISI?
6. Using the energy per pulse you calculated in the pre-lab, set up a transmitter and receiver
using the Square Root Raised Cosine pulse through an AWGN channel. Configure the
AWGN channel Mode to Eb/No with 100 dB and symbol period of 1/1000. On the receive
filter, use User Specified Gain set to 1. Test, record and plot the BER for 0 through 8 dB.
(Remember to measure and adjust the Receive delay for the Error Rate Calculation block.
It should be the accumulated delay of the Transmitter and the Receiver). Compare this on
the same plot with the theoretical BER for a bipolar signal.
7. Observe and record the average spectrum of the transmitted spectrum (before the
AWGN). How does it compare with the spectrum for the rectangular pulse (without the
low pass filter) from Experiment 3?
THOUGHTS FOR CONCLUSION
Why can the Sinc pulse pass through a narrow bandwidth and be detected while a rectangular
pulse at the same rate cannot?
What are the ‘costs’ of using Sinc pulses? Think of how you might have to implement a system
using them in a real world application. Remember, MATLAB provides perfect synchronization
between the transmitter and receiver. This will rarely if ever exist in reality unless they system is
designed to provide it.
As always, do not limit your conclusions to these topics.