Problem Set VII: Digital Baseband Processing

ECE300 Communication Theory
Problem Set VII: Digital Baseband Processing

1. Consider a digital communication scheme using 8-PSK, a bit rate of 6M bps, digital
processing with 16 samples per symbol, and employing p
RC pulses with 20% rollo§.
(a) Compute the symbol rate.
(b) Compute the sampling rate for the digital processor.
(c) Compute the bandwidth of the pulses.
2. Here you will use MATLAB to explore pulse design. Take BPSK (symbols 1) with
symbol rate Rs = 1M bps, L = 16 samples per symbol. We want an FIR approximation
to a p
RC Ölter with rollo§ 30%, that spans 4 symbols.
In MATLAB, the following will generate the coe¢ cient vector of the FIR Ölter (i.e.,
the underlying pulse shape):
p = r cos design(beta; span; L;0
sqrt0
);
where here span = 4. Let g [n] denote the pulse shape at the output of the matched
Ölter, which is obtained by convolving p [n] with its áip.
(a) Generate the p vector as above. Let N denote its length. Obtain a stem plot of
p (horizontal axis from 0 to N  1). Find the index where the peak occurs, say
kp_peak. You will note the pulse extends out so that interference comes from
indices kp_peak  L and 2L.
(b) Obtain a stem plot of the g vector, as you did for the p vector (careful: it is
longer than p!). Let kg_peak denote the index where the peak occurs. The
ISI at the output of the matched Ölter is determined by indices that are o§set
by L; 2L; 3L; 4L from this peak index. Observe the peak value of g is 1;
determine the maximum (magnitude) of any single interferer; and compute the
signal-to-interference ratio (SIR) in decibels for this case.
(c) Use freqz to compute jP (f)j and jG (f)j, the magnitude spectra of p [n] and g [n],
respectively, at 1000 frequency points from 0 to Rs. Plot jP (f)j on a linear scale
(horizontal axis in Hertz). Obtain a separate plot in which you show jG (f)j,
jG (Rs  f)j, and jG (f)j + jG (Rs  f)j superimposed (di§erent colors). Then
repeat this plot (of the jGj spectra) with the magnitude on a decibel scale; for
the case of the decibel scale, set the vertical axis limits so the maximum versus
minimum is no more than 30dB.