Spread Spectrum – Class Exercise
1) (Link Budget – CDMA)
A hand-held direct sequence spread spectrum (DS/SS) radio is part of cellular CDMA
system. The system specifications are as follows: data and SS-code modulation is
BPSK, data rate is 8,000 bits/sec, carrier frequency is 1GHz, chip rate is 25
Mchip/sec, worst case path loss is 138.6dB, gain of transmitting antenna id 5dBI,
receiver figure-of-merit G/T is -18dB/K, occasional deep small-scale fading loss is
30dB, other losses are 4dB, required Eb/N0 is 4dB. The factors Ga, Gv, H0 and  are
2.5,2.5,1.6 and 1, respectively
Sectorizing or Antenna Gain (GA): Dividing the Cell into 3 section of 1200, provides a
Gain of 4dB in the Number of users that can be accommodate.
Voice Activity Factor (GV): The Average Speaker pauses about 60% of the time
between words and sentences and for listening. For voice channels this contribute an
improvement of about 4dB in the Number of users that can be accommodate.
Outer Cell interference (H0): for 100% frequency reuse, all neighboring cells can use
the same spectrum. Therefore , for a given level of interference IX originating from
the same Cell, the additional is about 0.55Ix, resulting in a user capacity degradation
factor H0 of about 1.55 (or 1.9dB)
Nonsynchronous Interference Factor (  ): The worst case interference comes about if
all the interference are chip and phase synchronized with the desire signal. For a
nonsynchronous links interference will not always be a worst case, This lesser
interference can be described by factor  .
(a)
(b)
(c)
(d)
(e)
find the requires transmitter power Pt during deep small-scale fading.
To what level can Pt be powered down when there is no small-scale fading?
What is the minimum required Ech/N0 to meet the specifications?
What is the processing gain?
What is the Maximum number of users per call?
2) A synchronous DS-CDMA system with a total of M-users utilizes coherent
BPSK modulation and single user detection on an AWGN channel. The correlator
output for user 1 at a given bit interval is given by:
M
r1  Eb S1    Eb Si  n1
i 2
Where si  1 with equal probability of transmission is the information bit of user
i, Eb is the average energy per bit for any user, n1 is a zero-mean Gaussian random
variable with variance N0/2, and  is the cross-correlation of the spreading
waveforms of the users with 0    1/ M .
Spread Spectrum
Erez Simony
Class Exercise
a) Derive the exact bit error probability of user 1 as a function of M, 
and Eb N 0
M
b) Modeling the multiuser interference

i2
Eb Si as Gaussian random
variable independent from n1, derive a new expression for the bit error
probability of user 1 as a function of M,  and Eb N 0
c) Determine the asymptotic efficiency of the detector considering the
results of a) and then the results of b). compare the 2 results when
 2 Eb 
M=64,   1/128 and Eb N0  25dB (The reference is to Q 

 N0 
)
Spread Spectrum
Erez Simony
Class Exercise