B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

Problems 665
(a) Find the probability that exactly 1 of the signal bands used by the desired user during a
signal bit is jammed by the interfering signals.
(b) Determine the probability that none of the signal bands used by the desired user during a
signal bit will be jammed by the interfering signals.
(c) Assume that when a partial signal band is jammed, we can compute the BER effect by
discarding the signal energy within the jammed band. Find the BER of a given user within
the system.
11.4-1 Let the AWGN noise n(t) have spectrum N /2. If the A WGN noise n(t) is ideally band-limited
to 1 /2Tc Hz, show that if the spreading signal c(t) has autocorrelation function
Rc(r) = L S(r - i · LTc)
then the PSD of x(t) = n(t)c(t) is approximately
l-oo 2
N
Sx(f) = S 0 (v)Sc<f - v) dv = -
11.5-1 Consider DSSS systems with interference signal i(t). At the receiver, the despread signal c(t) =
± 1 with bandwidth Be,
(a) Show that i(t) and the despread interference
have identical power.
ia (t) = i(t)c(t)
(b) If i(t) has bandwidth B s and the spreading factor is L such that Be = L • B s , show that the
power spectrum of ia (t) is L times lower but L times wider.
11.6-1 In a multiuser CDMA system of DSSS, all transmitters are at equal distance from the receivers.
In other words, g; = constant. The additive white Gaussian noise spectrum equals S 0 (!) =
5. x 10-6 . BPSK is the modulation format of all users at the rate of 16 kbit/s.
(a) If the spreading codes are all mutually orthogonal, find the desired user signal power P;
required to achieve BER of 10-5 .
(b) If the spreading codes are not orthogonal, more specifically,
R;; = 1
R;j = -1/16 i f. j
Determine the required user signal power to achieve the same BER of 1 o- 5 by applying Gaussian
approximation of the nonorthogonal MAI.
11.6-2 Repeat Prob. 11.6-1, if one of the 15 interfering transmitter is 2 times closer to the desired
receiver such that its gain ge is 4 times stronger.
11. 7-1 For the multiuser CDMA system of Prob. 11.6-3, design the corresponding decorrelator and the
MMSE detectors.