| << Chapter < Page | Chapter >> Page > |
Exercise [link] asked the following question:
TRUE or FALSE: The flatter the top of the pulse shape, the less sensitive the receiver is to small timing offsets.
In the absence of noise and without matched filtering, this is TRUE. Describe a noisy situation and a matched filtering that mightcause the answer to be FALSE.
Consider the baseband communication system in [link] . The difference equation relating the symbols to the -spaced equalizer input for the chosen baud-timing factor is
where is a nonnegative integer. The finite-impulse-response equalizer (filter) is described by thedifference equation
It is now easy to experiment with various pulse shapes.
pulseshape2.m applies a
sinc shaped pulse to a random binary sequence.Since the sinc pulse extends infinitely
in time (both backward and forward), it cannot berepresented exactly in the computer (or in a real communication
system) and the parameter
L specifies the duration of
the sinc, in terms of the number of symbol periods.
N=2000; m=pam(N,2,1); % 2-PAM signal of length N
M=10; mup=zeros(1,N*M); mup(1:M:N*M)=m; % oversample by ML=10; ps=srrc(L,0,M); % sinc pulse shape 2L symbols wide
sc=sum(ps)/M; x=filter(ps/sc,1,mup); % convolve pulse shape with data
pulseshape2.m pulse shape a (random) sequence
(download file)
[link] plots the output of
pulseshape2.m .
The top figure shows the pulse shape while the bottom plotshows the “analog” pulse-shaped signal
over a
duration of about 25 symbols. The function
srrc.m first appeared in the discussion of interpolation in
[link] (and again in
Exercise
[link] ),
and is used here to generate the sinc pulse shape.The sinc function that
srrc.m produces is actually
scaled, and this effect is removed bynormalizing with the variable
sc .
Changing the second input argument from
beta=0 to other
small positive numbers changes the shape of the curve,each with a “sinc-like” shape called a square root raised cosine. This will be discussed in
greater detail in Sections
"Nyquist Pulses" and
"Matched Transmit and Receive Filters" .
Typing
help srrc in M
atlab gives useful information
on using the function.
Observe that, though the signal oscillates above and below the lines, there is no intersymbol interference. When using the Hamming pulseas in [link] , each binary value was clearly delineated. With the sinc pulse of [link] , the analog waveform is more complicated. But at the correctsampling instances, it always returns to (the horizontal lines at are drawn to help focus the eye on the crossing times).Unlike the -wide Hamming shape, the signal need not return near zero with each symbol.
Notification Switch
Would you like to follow the 'Software receiver design' conversation and receive update notifications?
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|