Errata
Introduction to Wireless Systems
P. Mohana Shankar
• Page numbers are shown in blue
• Corrections are shown in red
October 2011
Page 11 below Figure 2.4
The power detected by a typical receiver is shown in Figure 2.5.
Page 13
Page 14
Pr  d   Pr  dref 
 ,
dref
d
2
d  dref , (2.4)
Example 2.1; Answer The wavelength at 900 MHz is 3.10 8/9.108 = (1/3)m.
Expressing the frequency in MHz, eqn. (2.6) can now be expressed as
Lfree  32.44  20log10  f   20log10  d  ,
(2.7)
where d must be larger than 1 km. The unit of f is in MHz and d is in kilometers.
Page 17 top of the page
to account for the terrain. Additional correction factors can be included to account for other
factors such as street orientation. These correction factors They take into account the
following:
Page 15 Figure 2.7
Transmitted power = 100 mW instead of 100 dBm
Page 19 Example 2. 3
Find approximate values of the loss parameter, n, using Hata model for the four geographical
regions, namely large city, small-medium city, suburb, and rural area.
Answer:
Using Figure 2.12, the loss values at a distance of 3 km are 131.36 dB, 131.34 dB, 121.40 dB,
and 102.8 dB, respectively, for large city, small-medium city, suburb, and rural area.
Page 27
Page 28
Figure 2.18 X axis label…, Envelope a or Power p
Sentence below eqn. (2.40)
Eqn. (2.40)
Page 34
………where p0 is the average power
 p 
pout  1  exp   thr 
 p0 
2.3.3 Frequency-dispersive Behavior of the Channel
Page 39
2.3.5 Frequency dispersion vs Time dispersion
We have seen that fading can be in the frequency domain or in the time domain. It is possible to treat the
fading in wireless communications systems as constituted by independent effects. The channel shows
time dispersive behavior when multipath phenomena are present. At the same time, independent of this
effect, the channel will also exhibit frequency dispersion if the mobile unit is moving.
Page 39
Signal bandwidth
Figure 2.31
Time dispersive/
frequency selective
Slow and Frequency Selective
Fast and Frequency Selective
Bc
Time selective/
frequency dispersive
Slow and Flat
Fast and Flat
Tc
Bit duration
Page 40
Top of the page
Page 41
The Rician probability density function is shown in Figure 2.33 for different values of the parameter K.
The transition from Rayleigh to Gaussian (or Rician to Gaussian) can be seen clearly in
Figure 2.33 as the value of K continues to increase.
Page 41 Figure 2.33
0.7
0.6
K=
-
dB
0.5
K=6 dB
K=14 dB
K=18 dB
A
f (a)
0.4
0.3
0.2
0.1
0
0
2
4
6
envelope a
8
10
12
Page 42
Eqn. 2. 66
f  pdB  
p p
exp    dB2 2 av  


dB
2
1
2
2 dB
Page 46
2.4.5 Summary of Fading
The various fading mechanisms and the attenuation described can be summarized in a diagram
shown in Fig. 2.38. Note that Rician and Rayleigh arise out of multipath effects and Nakagami
can represent them both. This is not shown in the figure. For most of the cases, analyses based
on Rayleigh or Rician fading are sufficient to understand the nature of the mobile channel. A
number of recent publications (Alhu 1985, Anna 1998, 1999) have suggested the use of
Nakagami fading models to provide a generalized view of fading in wireless systems.
Page 53
Exercise 2.1
Using MATLAB, generate plots similar to the ones shown in Figure 2.7 to
demonstrate the path loss as a function of the loss parameter for distances ranging from 2 Km to 40 Km.
Calculate the excess loss (for values of n >2.0) in dB.
Page 54
Exercise 2.18. Generate a plot similar to the lognormal fading shown in Figure 2.36.
Page 55
Exercise 2.17 Compare the maximum data transmission capabilities of the two channels characterized
by the impulse responses shown below.
dBm
0
dBm
0
-10
-10
-20
-20
-30
-30
60
85
(a)
110
ns (delay)
0
4
8
(b)
microsec (delay)
FIGURE P2.17
Page 62
Line below equation (3-21)
where W ( = 2fm) is the maximum frequency of the modulating signal and Df is the peak
frequency deviation.
Page 75
P(f)
Figure 3.18
f0
frequency
f0+R
|M(f)I2
f 0- R
0
R
2R
frequency
Page 79 (below eqn. 3.45)
The output noise, n(T), has a spectral density, Gout(f), given by (See Appendix A.6)
Page 80
Eqn. (3.51) Use Min in place of Mout
H  f   KMin  f  exp   j 2 fT 
Page 84
(3.51)
Equation (3-70)
s1  t  
2E
T
cos  2 f 0t   E
2
T
cos  2 f 0t   E  1  t 
s0  t  
2E
T
sin  2 f 0t   E
2
T
sin  2 f 0t   E  0  t 
(3-70)
Page 87
The probability of error can be expressed (Taub 1986) as (Exercise 3.21)
p  e   12 erfc
Page 90
E
2 N0
pBPSK  e   12 erfc
(3.79)
 
E
N0
(3.83)
The plot of error probability for different values of E/N0 (signal-to-noise ratio) is shown in
Figure 3.28. Comparing eqn. (3.83) with the bit error rate for ASK systems (eqn. (3.79)), it
is seen that the performance of a coherent BPSK is 3dB better than that of coherent ASK.
Page 93
Table 3.2 DPSK encoding:
dk  bk  dk 1
Page 92
pav  e  

p
BPSK
 e | Df  f  Df  df



1
2 2 f2
 erfc


E
N0
 
Page 94
In Figure 3.32, use xk and yk in place of Xk and Yk.
Page 98
Data
fn
11
/4
-1 1
3/4
-1 -1
3/4
or 5/4
/4
or 7/4
1 -1
Table 3.4

cos Df exp  2Df 2 d Df
Phase encoding in QPSK
2
f
(3-86)
Page 100 Figure 3.35
In Figure 3.35a, the line at 2 should be broken as shown.
QPSK
1
(a)
0.5
0
-0.5
-1
0
1
2
3
4
5
6
7
8
QPSK (shifted by  /4)
amplitude
1
(b)
0.5
0
-0.5
-1
0
1
2
3
4
5
time (units of T)
6
7
8
Page 103 Figure 3.41
In the Figure the line at 1 should be broken as shown.
1
0.8
0.6
amplitude
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
1
2
3
4
time(units of T)
5
6
7
Page 104 Figure 3.43
{-1 –1}
Page 116
Figure 3.57
cos[2(f0+Df)t
T
 dt
0
+
S
FSK
_
z
decision
(threshold = 0)
1 if z > 0
0 if z < 0
T
 dt
0
cos[2(f0-Df)t
Page 120
The relationship between  and a is not given (equations 3-312 and 3-133).

a
 2
Page 124
Detection and Reception of MSK and GMSK Since MSK can be generated starting from OQPSK, the bit
error performance of MSK will be identical to that of BPSK, QPSK or OQPSK. However, MSK and GMSK
can also be detected using a 1-bit differential detector, 2-bit differential detector or a frequency discriminator.
The block diagrams of these receiver structures are shown respectively in Figure 3.69 a, 3.69 b, and 3.69 c.
Page 120
c t  
qg  t  
1
4T
1
4T
erf

   erf 
nT t
2

 n1T t
2

(3-133)

n 1 T t
T   n  1 T  t  erf   2    nT  t  erf  nT2t 


(3-134)
 n1T t 
 nT t 2 





2 2
2 2
e

e






2
 4T22
Page 124
Detection and Reception of MSK and GMSK Since MSK can be generated starting from OQPSK, the bit
error performance of MSK will be identical to that of BPSK, QPSK or OQPSK. However, MSK and GMSK
can also be detected using a 1-bit differential detector, 2-bit differential detector or a frequency discriminator.
The block diagrams of these receiver structures are shown respectively in Figure 3.69 a, 3.69 b, and 3.69 c.
Page 125
Ts  log2 M T
(3.139)
As the number of levels of modulation increases, the minimum power required to
maintain a fixed bit error rate decreases increases. This can be seen from the decision
boundaries shown in Figure 3.71.
Page 129
C  B log 2 1 

R
B
 
E
N0
 log 2 1 

R
B
 bits / s
 
E
N0
R
B

(3.145)
(3.146)
Page 141
Figure 4.5 Frequency reuse pattern of cells. The alphabets (except D) represent the
different channels. D is the distance between cells having the same frequency.
D  DR 3R  1  4  2 3R  21R
Page 143
Because of this, q =D/R=
3N c
is also known as the frequency reuse factor
Page 143
TABLE 4.2
i
Page 143
j
Nc
q
S/I(dB)
Figure 4.6 Expanded view of the cell structure showing a seven cell reuse pattern. H is the
channel reused.
Page 144
Figure 4.7 A three-cell pattern (Nc=3) showing six interfering cells
D


q

 3N c  3 

R


Page 155
Example 4.4 In order to keep an acceptable level of performance, a service provider is
planning to maintain an outage probability of 2%. What should be the power margin
needed to achieve this goal (assume the worst case scenario), when the standard deviation
of fading has been found to be 5 dB.
Answer:
The outage probability is given by eqn. (4.23) which can be rewritten as
and the power margin in dB is given by
Pout  R   0.5erfc

loge ( m )
 2

and the power margin in dB is given by M  10 log10 m 
The relation ship between  and  dB is given in eqn. (2.68) as
. We, therefore, have  = 1.15.
Outage probability  0.02  0.5erfc

loge ( m )
1.6282
1 ln 10 
  10
dB

As we have done in Chapter 3, we can solve this using the MATLAB function erfinv. We get
m = 10.6 and M to be 10.3 dB.
Page 169
p   
  
exp    ,   0
0
 0 
1
(5.5)
Page 175
5.2.2 Effects of Frequency Selective Fading, Co-Channel Interference
As discussed in Chapter 2, frequency selective fading arises when the coherent bandwidth of
the channel is less than the message bandwidth. The error rates vary with the form of
modulation and demodulation used. The performances of the modems also depend on the ratio
of (d/T), where d is the r.m.s delay spread (eqn. 2.42) and T is the symbol period. The exact
equations governing the error probability, taking frequency selective fading into account, are
once again very complex, and are beyond the scope of this book. Numerical results are
available in a number of research papers (Fung 1986, Guo 1990, Liu 1991a,b).
Page 176
Page 189
Figure 5.5
f   
The legends should read dB instead of db.
M 1
2M 1 M M 
 2 M 1!  0M
(5.34)
The performances of the three signal processing schemes are shown in Figure 5.17, with av equal to the
signal-to-noise ratio after combining. They are also given in tabular form in Table 5.1.
Page 195
H c  f   A  f  exp  j  f  
Eqn. 5.47)
Page 213 Figure 6.8
two bits
a
T
chip sequence
b
K Tc
Tc
modulo 2 addition of chip and data sequences
c
Page 214 First Paragraph
The PN sequence is unique to each user and is almost orthogonal to the sequences of other
users. Thus, the interference from other users in the same band will be much less. The
number of orthogonal codes, however, is limited. As the number of users increase, the codes
become less and less orthogonal more and more correlated (orthogonality is compromised)
and the interference will increase.
Page 220
Example 6.1 In a DS-CDMA cell, there are 24 equal power channels that share a common frequency
band. The signal is being transmitted on a BPSK format. The data rate is 9600 bps. A coherent receiver is
used for recovering the data. Assuming the receiver noise to be negligible, calculate the chip rate to
maintain a bit error rate of 1e-3.
Answer:
Assuming that there is no thermal noise, the bit error rate is given by eqn. (6.15) where K is the
processing gain and k is the number of channels. BER  10 3  0.5erfc z
 
where
z  kK1 Using the MATLAB function erfinv (.), we can solve for z  erfinv1  2* BER
2
chip rate
We get z = 4.77. We are given k=24; K=23*4.77=109.82. Since K  data rate
chip rate = 109.82*9600=1.05 Mchip/s.
Page 222 Figure 6.18
Instead of BPSK, it should be BFSK
Page 223 Figure 6.20
Instead of FH/BPSK signal, it should be FH/BFSK
Page 225
Figure 6.21 Block diagram of the transmitter associated with an AMPS system
Change
Page 231
to
Eqns. 6.21 and 6.22
The radio capacity of the system, m, is defined as
m  channel bandwidth Bc  * numberoft cells Nc 
total allocated spectrum B
radio channels/cell.
(6.21)
Making use of the relationship between q and Nc (Chapter 4),
q  3Nc,
(6.22)
Page 233 3rd line from the top
Let us start by considering a single cell with N (= k of eqn (6.11)) users who share the cell.
Page 233
E
N0
S
R
  N 1 S 
Bc
Bc
R
1
 N 1
(6.27)
where R is the information bit rate and Bc is the RF bandwidth. We have divided the signal power
(S) in the numerator by the bandwidth (data rate R) of the message data, while the signal power in
the numerator has been divided by the bandwidth (B c) occupied by the interfering signal. (See
Section 3.2.7) The quantity (Bc /R) is the processing gain K of the CDMA processing, defined in
connection with Figure 6.7.
0  Bc N0
(6.29)
Page 233
 
E
N0 min
Page 234
Nmax
K
N
max
1 
  NE0 s  NE0 min 
 1 K  E
E



N0 
N0 
 min s 

Bc N0 1
S
(6.33)
Page 241
Table 6.7 Comparison of Standards
Under the column for IS 95, change 1.288 kchips/s to 1.288Mchips/s
Page 250
g t  

a
n 
n
exp  jn2 f 0t 
( A.1.7)
Page 263
Normal or Gaussian distribution
f  x 
1
2 x2
x
exp    2 2

x
2
 ,   x  


Page 266
where G is the gamma function
G  z    wz 1e wdz
0