Chapter 4
Basics of Wireless Communications
4.1 Signals
f
= v λ
) 2
sin(
)
(t At ftt t
g = π +ϕ (4.1)
) 2 . 4 (
4.1.1 Modulation
4.1.2 Representing Signals in the Frequency Domain
)]
2 sin(
) 2
cos(
2 [ )
( 0
1
0
0 A n f t B n f t
t A g
n
n
n π π
∑
∞=
+ +
=
∫
∫
∫
=
=
=
T n
T n
T
dt t f n t
T g B
dt t f n t
T g A
dt t T g
A
0 0
0 0
0 0
) 2
sin(
) 2 (
) 2
cos(
) 2 (
) 2 (
π π
) 3 . 4 (
) 4 . 4 (
4.1.3 Signal Spectrum and Bandwidth
] [
log
2B 2 M bits/s C =
) 1
(
log2 SNR B
C = +
) 5 . 4 (
) 6 . 4 (
4.2 Propagation of Radio Signals
4.2.1 The Electromagnetic Spectrum
4.2.2 Antennas
4.2.3 Speed of Electromagnetic Waves m/s 458 792 ,
0 299 ,
c =
c n = c0
) 7 . 4 (
) 8 . 4 (
2
1 81 f
n = εr ≈ − Ne (4.9)
4.2.4 Attenuation
2
)2
d 4 (
λ
= π
r t
P P
2
) 0
( )
(
=
d d d
P d
Pr r f
) 10 . 4 (
) 11 . 4 (
α
=
d d d
P d
Pr( ) r( f ) 0 (4.12)
4.2.5 Multipath Propagation
4.2.6 Doppler Effect
λ cosα
fd = v (4.13)
4.3 Multiplexing and Multiple Access
4.3.1 SDM and SDMA 4.3.2 FDM and FDMA
4.3.3 TDM and TDMA
4.3.4 CDM and CDMA
∑
=+
=
Φ N
m
i i
ii c m c m n
n N
1
] [
] 1 [
] [
∑
=+
=
Φ N
m
j i
ij c m c m n
n N
1
] [
] 1 [
] [
) 14 . 4 (
) 15 . 4 (
−
= =
Φ 1 otherwise
...
, 2 , , 0 1
] [
N
N N n
ii n
) 16 . 4 (
