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Errata Introduction to Wireless Systems P. Mohana Shankar. Page numbers are shown in blue Corrections are shown in red. May 2008. Page 11 below Figure 2.4. The power detected by a typical receiver is shown in Figure 2.5. - PowerPoint PPT PresentationTRANSCRIPT
• Page numbers are shown in blue• Corrections are shown in red
Errata
Introduction to Wireless Systems
P. Mohana Shankar
May 2008
Page 11 below Figure 2.4
The power detected by a typical receiver is shown in Figure 2.5.
Page 13 2
(, , 2.4)refd
r r ref d refd dP d P d
Expressing the frequency in MHz, eqn. (2.6) can now be expressed as
10 1032.44 20log 20log , (2.7)freeL f d
where d must be larger than 1 km. The unit of f is in MHz and d is in kilometers.
Page 14
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:
Example 2.1; Answer The wavelength at 900 MHz is 3.108/9.108 = (1/3)m.
Figure 2.7 Transmitted power = 100 mW instead of 100 dBmPage 15
Example 2. 3Find approximate values of the loss parameter, , 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 19
Page 27 Figure 2.18 X axis label…, Envelope a or Power p
Page 28 Sentence below eqn. (2.40) ………where p0 is the average power
0
1 exp throut
pp
p
Eqn. (2.40)
2.3.3 Frequency-dispersive Behavior of the ChannelPage 34
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.
Bit durationTc
Bc
Time selective/frequency dispersive
Time dispersive/frequency selective
Fast and Flat
Slow and Frequency Selective Fast and Frequency Selective
Slow and Flat
Sig
nal b
andw
idth
Page 39 Figure 2.31
Page 40
0 2 4 6 8 10 120
0.1
0.2
0.3
0.4
0.5
0.6
0.7
envelope a
f A(a
)
K = - dB
K=6 dB K=14 dB K=18 dB
Page 41
Figure 2.33
222
122
exp dB av
dBdB
p pdBf p
Page 42 Eqn. 2. 66
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 >2.0) in dB.
Page 53
Page 46
2.4.5 Summary of FadingThe 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 41 First sentence on top of the page The Rician probability density function is shown in Figure 2.33 for different values of the parameter K.
(a) (b)
Exercise 2.17 Compare the maximum data transmission capabilities of the two channels characterized by the impulse responses shown below.
dBm 0
-10
-20
-30
60 85 110 ns (delay)
dBm
0
-30
4 8 microsec (delay)
-20
-10
0
FIGURE P2.17
Page 55
Exercise 2.18. Generate a plot similar to the lognormal fading shown in Figure 2.36.
Page 54
f0
|M(f
)I2
P(f
)
f0- R f
0+R
frequency
frequency R 2R 0
Page 62 Line below equation (3-21)
where W ( = 2fm) is the maximum frequency of the modulating signal and f is the peak frequency deviation.
Page 75 Figure 3.18
The output noise, n(T), has a spectral density, Gout(f), given by (See Appendix A.6)
Page 79 (below eqn. 3.45)
1kk kbd d Table 3.2 DPSK encoding:
Page 93
exp 2 (3.51)inH f KM f j fT
Page 80 Eqn. (3.51) Use Min in place of Mout
The probability of error can be expressed (Taub 1986) as (Exercise 3.21)
Page 87
0
12 2 (3.79)E
Np e erfc
Page 90
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.
0
12 (3.83)E
BPSK Np e erfc
Data n
1 1
-1 1
-1 -1 or
1 -1 or
Table 3.4 Phase encoding in QPSK
Page 98
Page 94
In Figure 3.32, use xk and yk in place of Xk and Yk.
Page 92
2
2
20 22
1
2
|
cos exp
av BPSK
EN
p e p e f d
erfc d
0 1 2 3 4 5 6 7 8-1
-0.5
0
0.5
1QPSK
0 1 2 3 4 5 6 7 8-1
-0.5
0
0.5
1QPSK (shifted by /4)
time (units of T)
ampl
itude
(a)
(b)
Page 100 Figure 3.35In Figure 3.35a, the line at 2 should be broken as shown.
0 1 2 3 4 5 6 7-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
time(units of T)
ampl
itude
Page 103 Figure 3.41In the Figure the line at 1 should be broken as shown.
{-1 –1}
Page 104 Figure 3.43
FSKdecision
(threshold = 0)
+
_
z 1 if z > 0
0 if z < 0
cos[2(f0-f)t
cos[2(f0+f)t
0
T
dt
0
T
dt
Page 116 Figure 3.57
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 124
Page 120 The relationship between and is not given (equations 3-312 and 3-133).
2
Page 129
02log 1 /R
BE
NC B bits s (3.145)
02log 1R E R
BB N (3.146)
Page 125
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.
2log (3.139)sT M T
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.
3 1 4 2 3 21RD D R R R
TABLE 4.2
i j Nc q S/I(dB)
Page 143
Page 144Figure 4.7 A three-cell pattern (Nc=3) showing six interfering cells
3 3c
Dq N
R
Page 143
Because of this, q =D/R= is also known as the frequency reuse factor3 cN
Page 143 Figure 4.6 Expanded view of the cell structure showing a seven cell reuse pattern. H is the channel reused.
Page 169 0 0
1exp , 0 (5.5)p
Page 176 Figure 5.5 The legends should read dB instead of db.
Page 189
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.
11
0
22 1 !
(5.34)MM M
MM
Mf
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 195 ( 5.47) expc jH f A f f
Once again, the approximate probability density function, f(), of the signal-to-noise ratio (energy), at the output of the equal gain combiner can be expressed as (for << 0) (Schw 1996)
Page 213 Figure 6.8
two bits
chip sequence
modulo 2 addition of chip and data sequences
a
b
c
T
K TcTc
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.
zerfc5.010BER 3
1kKz 2BER*21erfinvz
ratedataratechipK
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. where Using the MATLAB function erfinv (.), we can solve for We get z = 4.77. We are given k=24; K=23*4.77=109.82. Since
chip rate = 109.82*9600=1.05 Mchip/s.
Page 220
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 231 Eqns. 6.21 and 6.22
The radio capacity of the system, m, is defined as radio channels/cell. (6.21)
Making use of the relationship between q and Nc (Chapter 4), , (6.22)3 cq N
*
t
cc
total allocated spectrum B
channel bandwidth B number of cells Nm
Page 225 Figure 6.21 Block diagram of the transmitter associated with an AMPS system
Change to
Page 233
0
111
(6.27)cSBc
SR BE
N R NN
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 (Bc) 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 0 (6.29)cB N
0 0 min
0 0min
max 1 (6.33)E E
N Ns
E EN N s
N K
Page 234
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
0
0
1
maxmin1 cB NE
N SK N
Page 250
0exp 2 ( .1.7)nn
g t a jn f t A
Page 263
222
122
exp ,xx
xf xx
Normal or Gaussian distribution
Page 266 where is the gamma function 1
0
z wz w e dz
Page 241 Table 6.7 Comparison of Standards
Under the column for IS 95, change 1.288 kchips/s to 1.288Mchips/s