Indoor Models

Saleh and Valenzuela [SV87] consider a ncatenation of two Poisson point processes for describing the indoor propagation channel. One process defines the positions of clusters of paths and the second the positions of the paths within clusters. The modified Poisson process models described in section 2.4.1 were extended for typical indoor channels by Ganesh and Pahlavan in [GP89].

Rural Area (RU6) Hilly Terrain (HT6) Typical Urban (TU6)

d i ( s )

^j

A i

^j

2

_(dB)

d i ( s )

^j

A i

^j

2

_(dB)

d i ( s )

^j

A i

^j

2

_(dB)

0 0 0 0 0 -3

.1 -4 .1 -1.5 .2 0

.2 -8 .3 -4.5 .5 -2

.3 -12 .5 -7.5 1.6 -6

.4 -16 15 -8 2.3 -8

.5 -20 17.2 -17.7 5.0 -10

Typical Urban (TU12) Hilly Terrain (HT12)

d i ( s )

^j

A i

^j

2

_(dB)

d i ( s )

^j

A i

^j

2

_(dB)

0 -4 0 -10.01

.1 -3.01 .1 -8.01

.3 0 .3 -6

.5 -2.6 .5 -4.01

.8 -3 .7 .01

1.1 -5 1 0

1.3 -7 1.3 -4

1.7 -5 15 -8

2.3 -6.5 15.2 -9

3.1 -8.6 15.7 -10

3.2 -11 17.2 -12

5.0 -10 20 -14

Table 2.2: ETSI-COST 207 Channel Models

Signaling over Fading Channels

Signal fading is arguably the most difficult phenomenon that radio communication system designers have to cope with. As we saw in Chapter 2, the average received signal strength can drop tens of decibels due to the destructive interference of delayed reflections of the transmitted signal [Jak74]. This is especially the case in non line–of–sight communications. Moreover, for slowly moving mobile transceivers, such

“deep fades” result in unacceptably long periods of time where reliable communication is impossible.

In wide-band systems the receivers are sensitive enough to distinguish (or resolve) different faded replica of the transmitted signal, or paths, which can be used jointly to improve performance. In spread–

spectrum based systems, such as IS–95 [IS992], where the signal bandwidth is much larger than the symbol rate, some paths can be combined by what is commonly referred to as a RAKE receiver [Pro95]

to improve performance. Medium–band systems are subject to intersymbol interference (ISI) due to time dispersion so that the use of an equalizer also benefits from frequency–diversity. This is actually a situation where ISI is desirable.

In order to operate efficiently in such a hazardous environment, the system designer often opts to use so-called diversity methods. Simply put, the diversity is the number of independent replica of the transmitted signal that are made available to the receiver. In the absence of multiple antennas, this calls for the exploitation of either the frequency or the time-variation properties of the fading signal or both.

The former can be called frequency diversity, and makes use of the amplitude of the transfer function of the channel in different parts of the spectrum. Frequency–diversity schemes are quite popular in multiuser systems due to the large amount of bandwidth that is available, and can be achieved in different ways.

Another way of exploiting frequency–diversity is to use coded narrow or medium–band signals

with slow frequency–hopping. This technique is used in the GSM system and its derivatives DCS 1800 and PCS 1900 [GSM90]. Here, the information is coded and interleaved over

F = 4

(half–rate) or

F = 8

(full–rate) blocks of length

N = 208

^or

N = 378

symbols, and each block modulates a different carrier (ideally) according to some predefined hopping pattern. This is achieved by altering the FDMA allocation of users every block. It has the effect of ensuring that after deinterleaving any

F

^adjacent

received symbols modulated a different carrier. If the carriers are sufficiently separated, the resulting received symbols have uncorrelated strengths. It is well known that error–control coding can yield a significant diversity effect in such cases [Pro95].

Time diversity can also be exploited to some extent using interleaving even without frequency–

hopping. Assuming that the receiver/transmitter is in motion, interleaving spreads the information across different channel strengths whose correlation depends on the mobile speed and interleaving delay. For example, the IS54 system [IS592] encodes the information and interleaves it over

F = 2

blocks of length

N = 178

separated by 20ms. For low mobile speeds this can result in highly correlated symbols after deinterleaving. For this reason, systems exploiting frequency diversity are more desirable when reliable performance is desired at low mobile speeds.

In this chapter we will consider the different ways signaling is performed over the various types of fading channels. There is nothing really new, but much of the material is presented in a way that is not found in most classic textbooks on digital communications. More precisely we look at the different diversity methods and show that performance criteria are computed in essentially the same way in each case. Once the signal has been characterized statistically, the computation of performance criteria is a question of performing an eigenvalue analysis of a kernel or quadratic form representing the energy of the received signal in some observation interval/bandwidth. The number of significant eigenvalues or degrees of freedom of the channel process in a given frequency band or time interval will play an important role.

We end with a generic model which is useful for describing many systems which operate with a small number of degrees of freedom or eigenvalues, which we call the block–fading model. In practice, this model is applicable to systems where processing is performed over a few different channel realiza-tions which can result for instance from a frequency–hopping mechanism. Chapters 4 and 5 will treat the fundamental aspects of this model in more detail.

3.1 Performance Measures

Imagine a communication system where signal blocks or messages of duration

T

seconds are used to convey information from the sender to the receiver. We assume that a finite number,

M

, of message waveforms exist, which we denote by the set^f

x m ( t ) ;m = 0 ;

;M

^,

1

^g. The amount of information per message is

log ₂ M

bits so that the bit rate is

R = 1 T ^{log 2} M bits = s

^(3.1)

For simplicity, we will assume that the receiver requires the entire message in order to make a decision about which message was sent, so that the processing or decoding delay is

T

seconds. In many systems, there is a limit to the tolerable decoding delay. A long decoding delay for voice telephony results in an unacceptable audible delay. Some data transmission protocols also have stringent decoding delay constraints due to some quality of service requirement or limited buffer size.

The message or codeword error–rate is a critical measure of the robustness of a coding scheme in noise. Under the assumption that messages are transmitted with equal probability it can be bounded from above using the union bound [Pro95]

P e = 1 M

M

X^,

1 m=0

M

X^,

1

n=0 Prob( m

^!

n )

^(3.2)

where

Prob( m

^!

n )

is the called the pairwise error probability (PEP) between messages

m

^and

n

^and

indicates the probability of decoding

n

^{given that}

m

is transmitted if they were the only two possible messages.

The analysis of the PEP for systems working in a fading environment is usually based on charac-terizing the statistics of the total received energy in the interval

[

^,

T= 2 ;T= 2]

. It is therefore not surprising that most formulations yield very similar forms for the PEP. The goal of this chapter is to describe differ-ent narrow and wide-band systems which we will refer to in the remainder of this thesis by defining the basic receiver structures and their performance measures. We begin by defining the notion of diversity using a simple two–channel receiver which can be seen as a dual–antenna receiver.

Throughout this chapter we express all transmitted and received messages as complex baseband signals representing the complex envelope of real signals centered at a certain carrier frequency.

Dans le document Coding and multiple-access over fading channels (Page 31-36)