TD.
4 Spread
spectrum
Mobile Networks
Exercise-1
Demonstrate that the codes in an 8 X 8 Walsh matrix are orthogonal to
each other by showing that multiplying any code by any other code
produces a result of zero.
Recall that to compute the cross-correlation, we replace 1 with +1 and 0
with -1. The 8-bit Walsh codes are:
Exercise-2
The next figure depicts a simplified scheme for CDMA encoding and
decoding. There are seven logical channels, all using DSSS with a spreading
code of 7 bits. Assume that all sources are synchronized. If all seven sources
transmit a data bit, in the form of a 7-bit sequence, the signals from all
sources combine at the receiver so that two positive or two negative values
reinforce and a positive and negative value cancel. To decode a given
channel, the receiver multiplies the incoming composite signal by the
spreading code for that channel, sums the result, and assigns binary 1 for a
positive value and binary 0 for a negative value.
a. What are the spreading codes for the seven channels?
b. Determine the receiver output measurement for channel 1 and the
bit value assigned.
c. Repeat part b for channel 2.
Exercise-3
Consider an MFSK scheme with fc = 250 kHz, fd = 25 kHz, and M = 8 (L =
3 bits).
a. Make a frequency assignment for each of the eight possible 3-bit
data combinations.
b. We wish to apply FHSS to this MFSK scheme with k = 2; that is, the
system will
Hop among four different carrier frequencies. Expand the results of
part (a) to show the 4 x 8 = 32 frequency assignments.
Exercise-4
An FHSS system employs a total bandwidth of Ws = 400 MHz and an individual
channel bandwidth of 100 Hz. What is the minimum number of PN bits required
for each frequency hop?
Exercise-5
Consider a CDMA system in which users A and B have the Walsh codes A= [-1 1
-1 1 -1 1 -1 1] and B= [-1 -1 1 1 -1 -1 1 1]; respectively.
a. Show the output at the receiver if A transmits a data bit 1 and B does
not transmit. We want to receive from A.
b. Show the output at the receiver if A transmits a data bit 0 and B does
not transmit.
We want to receive from A.
c. Show the output at the receiver if A transmits a data bit 1 and B
transmits a data bit 1. Assume the received power from both A and B is
the same. We want to receive from B.
d. Show the output at the receiver if A transmits a data bit 0 and B
transmits a data bit 1. Assume the received power from both A and B is
the same. We want to receive from B.
e. Show the output at the receiver if A transmits a data bit 1 and B
transmits a data bit 0. Assume the received power from both A and B is
the same. We want to receive from A.
f. Show the output at the receiver if A transmits a data bit 0 and B
transmits a data bit 0. Assume the received power from both A and B is
the same. We want to receive from A.
g. Show the output at the receiver if A transmits a data bit 1 and B
transmits a data bit 1. Assume the received power from B is twice the
received power from A. This can be represented by showing the received
signal component from A as consisting of element of magnitude 1 (+1, -1)
and the received signal component from B as consisting of elements of
magnitude 2 (+2, -2). We want to receive from A.
h. Show the output at the receiver if A transmits a data bit 0 and B
transmits a data bit 1. Assume the received power from B is twice the
received power from A. We want to receive from A.
Exercise-6
This problem demonstrates that different LFSRs can be used to generate an m-
sequence.
Assume an initial state of 10000 in the LFSR of figure 7.19a.
In a manner similar to figure 7.13b, shows the generation of
an m-sequence.
Now assume the configuration of 7.19b, with the same initial
state, and repeat part a. Show that this configuration also
produces an m-sequence, but that it is a different sequence
from that produced by the first LFSR.
Exercise-7
An FHSS using MFSK with M=4 employs 1000 different frequencies. What is the processing
gain (Gp=Ws/Wd) in dB
