# Chapter 21: Wireless Local Area Networks¶

## Example 21.1, Page 727¶

In [7]:
import math

#Variable declaration
Fl=902; #lower limit frequency MHz
Fh=928; #higher limit frequency in MHz
Rt=0.5; #symbol transmission rate in Mega symbols per sec
S=16; #No of symbols
BER=10**-5;#Bir error rate
SG=2.6;#sector gain
B=0.5; #Interference factor
a=0.9; #power control efficiency

#Calculations&Results
BW=Fh-Fl;
Rb=Rt*math.log(S,2);
Gp=BW/Rb;
Eb_by_No=10  #dB
M = (Gp*a*SG)/(Eb_by_No*(1+B))
print 'Number of users that can be supported by the WLAN are %d'%M
eff=Rb*int(M)/BW;
print 'The bandwidth efficiency is %.2f bps/Hz'%eff

Number of users that can be supported by the WLAN are 2
The bandwidth efficiency is 0.15 bps/Hz


## Example 21.2, Page 733¶

In [2]:
#Variable declaration
Stepsize=200.; #in Hz
Chipsmin=20.;#length of linear feedback shift register
Datarate=1.2*10**3;  #bps

#Calculations
No_of_tones=2**Chipsmin;
Bss=No_of_tones*Stepsize;
Chiprate=Datarate*Chipsmin;
Gp=Bss/Datarate;#processing gain
Symbolrate=Datarate/3;  #8-ary FSK is used
Chips_symbol=Chiprate/Symbolrate;

#Results
print 'The Hopping Bandwidth is %.3f MHz'%(Bss/10**6);
print 'The chiprate is %d kchip/sec'%(Chiprate/10**3);
print 'Chips per symbol are %d'%(Chips_symbol);
print 'The processing gain is %.1f'%Gp

The Hopping Bandwidth is 209.715 MHz
The chiprate is 24 kchip/sec
Chips per symbol are 60
The processing gain is 174762.7


## Example 21.3, Page 734¶

In [3]:
#Variable declaration
InfoSc=48.;#Information subcarriers
SyncSc=4.;#synchronization subcarriers
ReservedSc=12.;#Reserved subcarriers
Symrate=250.;  #ksps(kilosymbols per second)
BW=20.;  #/in MHz
Grdt=800.; #Guard time in nsec

#Calculations
TotalSc=InfoSc+SyncSc+ReservedSc;#Total subcarriers
BW_Sch=BW*10**6/TotalSc;#BW of subchannel
Mod_eff=Symrate*10**3/(BW_Sch);#Modulation efficiency
User_txrate=InfoSc*Symrate*10**3;
User_bitsymbol=4;  #16-QPSK is used
User_DR=36; #Mbps
Sym_Dur=1./(Symrate*10**3);
TimeUti=Sym_Dur/(Sym_Dur+(Grdt/10**9));

#Results
print 'The bandwidth of subchannel is %.1f kHz'%(BW_Sch/10**3);
print 'Modulation efficiency is %.1f symbols/sec/Hz'%Mod_eff
print 'User symbol rate is %d Msps'%(User_txrate/10**6);
print 'Time Utilization efficiency is %.2f'%TimeUti

The bandwidth of subchannel is 312.5 kHz
Modulation efficiency is 0.8 symbols/sec/Hz
User symbol rate is 12 Msps
Time Utilization efficiency is 0.83


## Example 21.4, Page 735¶

In [4]:
import math

#Variable declaration
Eb_No=10;  #in dB
Noise=-120; #in dBm
Pt=20; #in mwatt
R=1; #Data rate in Mbps
CHBW=0.5; #BW in MHz
A=37.7;  #path loss at the ﬁrst meter in dB
Y=3.3; #path loss exponent
Lf=19; #function relating power loss with number of ﬂoors n        (in dB)
Ls=10;  # lognormally distributed random variable representing the shadow effect in dB

#Calculations
S2Nreqd=Eb_No*R/CHBW;
Rx_sensi=Noise+S2Nreqd;
Lp=10*math.log10(20)-Rx_sensi;
#Lp=A+10Ylod(d)+Lf+Ls;therefore
d=10**((Lp-A-Lf-Ls)/(10*Y));

#Result
print 'The coverage of AP is %.1f metres'%d;

The coverage of AP is 25.3 metres


## Example 21.5, Page 758¶

In [6]:
#Variable declaration
R=3./4;#code rate of convolution encoder
M1=9.; #payload transmission rate in Mbps for mode 1
M2=36.; #payload transmission rate in Mbps for mode 2

#Calculations&Results
D1=M1*10**6/48;#user data  rate in kbps for mode 1
D2=M2*10**6/48;#user data rate in kbps for mode 2
#Refering to Table 21.11
print 'Data transmission rate per carrier with 3/4 convolution encoder are %.1f Kbps and %d Kbps'%(D1/10**3,D2/10**3);
C1=D1/R;
C2=D2/R;
print 'Carrier transmission rate with R=3/4 convolutional encoder are %d Kbps and %d Kbps'%(C1/10**3,C2/10**3);
print 'Carrier symbol rate with R=3/4 convolutional encoder are %d ksps and %d Ksps'%(C1/10**3,C2/4/10**3);  #Mode1 as BPSK and MOde2 as 16-QAM

Data transmission rate per carrier with 3/4 convolution encoder are 187.5 Kbps and 750 Kbps
Carrier transmission rate with R=3/4 convolutional encoder are 250 Kbps and 1000 Kbps
Carrier symbol rate with R=3/4 convolutional encoder are 250 ksps and 250 Ksps


## Example 21.6, Page 759¶

In [7]:
import math

#Variable declaration
R=3./4; #code rate for convolution encoder

#Calculations
#64-QAM modulation is used
Sc=250; #Carrier symbol rate(ksps) from Exa 21.5
Bits_sym=math.log(64,2); #64-QAM is used
User_R=Bits_sym*Sc*10**3*R*48;

#Result
print 'The user data rate is %d Mbps'%(User_R/10**6);

The user data rate is 54 Mbps


## Example 21.7, Page 762¶

In [8]:
#Variable declaration
D=1000.*8;  #packet size in bits
R=2.*10**6;  #transmission rate in bps
L=3.; #msec(Dwell time)
H=0.625; #msec(Duration of BT packet)

#Calculations
Tw=10**3*D/R;   #the packet duration of IEEE 802.11 in msec
H_L=1.;
G=(H_L)*L-Tw-H;
Gm=abs(G);
PER_FH=1-((1-Gm/L)*(78./79)**(H_L)+Gm/L*(78./79)**((H_L)-G/Gm));
PER_DS=1-((1-Gm/L)*(57./79)**(H_L)+Gm/L*(57./79)**((H_L)-G/Gm));

#Results
print 'The PER for FH packet and PER for DS packet are %d percent & %.2f percent respectively'%(round(PER_FH*100),PER_DS*100);
print "The collision probability with 802.11 DS is much higher than with 802.11 FH."

The PER for FH packet and PER for DS packet are 2 percent & 38.73 percent respectively
The collision probability with 802.11 DS is much higher than with 802.11 FH.


## Example 21.8, Page 765¶

In [9]:
import math

#Variable declaration
d=10; # distance between AP and IEEE 802.11 device in metres
Y=4; #path loss exponent
PBt=20;  #the transmitted power by the BT in dBm
PAp=40;  #the transmitted power by the AP in dBm
Pe=10**-5;#acceptable error probability

#Calculations
#Pe=0.5*e**(-0.5*Eb/No)
SIR=math.log(Pe/0.5)/(-0.5);# signal-to-interference ratio
rmax=d*(SIR*PBt/PAp)**(1./Y);# range of interference between Bluetooth and 802.11 device

#Results
print 'Minimum SIR is %.2f dB = %.1f'%(10*math.log10(SIR),SIR);
print 'Maximum coverage range is  %.2f metres'%rmax;

Minimum SIR is 13.35 dB = 21.6
Maximum coverage range is  18.14 metres


## Example 21.9, Page 765¶

In [10]:
#Variable declaration
SIRmin=21.6; #From eg 21.8 i.e(13.36 dB)
d=10; #distance between AP and IEEE 802.11 device in m
PMs=40; # transmitted power of the IEEE 802.11 device in dBm
PBt=20; #the transmitted power by the BT in dBm
Y=4 ; #path loss exponent

#Calculations
rmax=d*(SIRmin*PMs/PBt)**(1./Y);

#Result
print 'Maximum coverage range is %.1f metres'%rmax

Maximum coverage range is 25.6 metres


## Example 21.10, Page 765¶

In [11]:
import math

#Variable declaration
Gp=11;#processing gain(given)
#Defining variables from Exa 21.8 & 21.9
PBt=20; #  transmitted power by the BT in dBm
PMs=40;  # transmitted power of the IEEE 802.11 device in dBm
PAp=40;  # transmitted power by the AP in dBm
d=10;  # distance between AP and IEEE 802.11 device in m
Y=4;  #path loss exponent
Pe=10**-5;#Error probability

#Calculations&Results
#Pe=0.5*e**(-0.5*Eb/No)
SIR=math.log(Pe/0.5)/(-0.5);
r1max=d*(SIR*PBt/(PAp*Gp))**(1./Y);# range of interference between Bluetooth and 802.11 device
print 'Maximum coverage range for IEEE 802.11 DS is  %.2f metres'%r1max
r2max=d*(SIR*PMs/(PBt*Gp))**(1./Y);
print 'Maximum coverage range for IEEE 802.11 FH is %.2f metres'%r2max;
print "Thus, the interference ranges are smaller for the IEEE 802.11 DS device than the IEEE 802.11 FH device."

Maximum coverage range for IEEE 802.11 DS is  9.96 metres
Maximum coverage range for IEEE 802.11 FH is 14.08 metres
Thus, the interference ranges are smaller for the IEEE 802.11 DS device than the IEEE 802.11 FH device.