7/31/2019 Chap3 Sec3 1 Wireless Channels

1/5

Introduction to wireless channelsWireless channel modeling

Chapter 3: Theoretical fundamentals and practicaltechniques in 4G physical-layer transmissions

Section 3.1: Wireless channel modeling

July 21, 2010

NGN - Chapter 3: Theoretical fundamentals and practical techniques in 4G Section 3.1: Wireless channel modeling 1

http://find/

7/31/2019 Chap3 Sec3 1 Wireless Channels

2/5

Introduction to wireless channelsWireless channel modeling

Introduction to wireless channels

The characteristic of (mobile) wireless channel is the variations of thechannel strength over time and frequency. The variations can be dividedinto two types:

Large-scale fading is yielded by path loss of signal as a function ofdistance and shadowing by large objects such as buildings and hills.

Small-scale fading is yielded by the constructive and destructiveinterference of the multiple signal paths between transmitter andreceiver.

NGN - Chapter 3: Theoretical fundamentals and practical techniques in 4G Section 3.1: Wireless channel modeling 2

http://find/

7/31/2019 Chap3 Sec3 1 Wireless Channels

3/5

Introduction to wireless channelsWireless channel modeling

Wireless channel modeling

The complex transmitted signal can be expressed by

() = Re()2

. (1)

Over a multipath ( physical paths) propagation channel, thereceived signal can be obtained by

() =

1=0

()(()) + (). (2)

Substituting (1) into (2) yields the following

() = Re1

=0

()( ())2(())+ () (3)

= Re

1=0

()( ())

2

+ ()

= Re ()2+ ()NGN - Chapter 3: Theoretical fundamentals and practical techniques in 4G Section 3.1: Wireless channel modeling 3

http://find/

7/31/2019 Chap3 Sec3 1 Wireless Channels

4/5

Introduction to wireless channelsWireless channel modeling

Wireless channel modeling (cont.)

As a result, the received baseband signal can be determined by

() =

()( ()) + (). (4)

The next step in creating a useful channel model is to convert thecontinuous-time channel to a discrete-time channel. We take the

usual approach of sampling theorem. Assuming that the inputwaveform is band-limited to , the baseband equivalent can berepresented by

() =

sinc( ), (5)

where = (/) and sinc() sin()

.

This representation follows from the sampling theorem, which saysthat any waveform band-limited to /2 can be expanded in termsof the orthogonal basis functions sinc( ) with coefficients bysamples (taken uniformly at integer multiples of 1/)

NGN - Chapter 3: Theoretical fundamentals and practical techniques in 4G Section 3.1: Wireless channel modeling 4

I d i i l h l

http://find/

7/31/2019 Chap3 Sec3 1 Wireless Channels

5/5

Introduction to wireless channelsWireless channel modeling

Wireless channel modeling (cont.)

As a result, the baseband received signal can be determined by

() =

()

sinc ((())

) + () (6)

=

()sinc (( ()) ) + (). (7)

The sampled outputs at multiples of 1/ is (/) then

=

(/)sinc ( (/)) + (/).

(8)Let then one can have

=

(/)sinc ( (/)) + (/)

=

, + (/) (9)

where , =

(/)sinc ((/))

NGN - Chapter 3: Theoretical fundamentals and practical techniques in 4G Section 3.1: Wireless channel modeling 5

http://find/