Rayleigh Fading Channels in Mobile Digital Communication Systems Part II: Mitigation

A BSTRACT

In Part I of this tutorial, the m ajor elem ents that contrib ute to fad ing and their effects in a com m unication channel were characterized . Here, in Part II, these p henom ena are b riefly sum m arized , and em p hasis is then p laced on m ethod s to cop e with these

d egrad ation effects. Two p articular m itigation techniq ues are exam ined : the Viterb i eq ualizer im p lem ented in the Glob al System for

Mob ile Com m unication (GSM), and the Rake receiver used in CDMA system s b uilt to m eet Interim Stand ard 95 (IS-95).

Rayleigh Fading Channels in M obile Digital Communication Systems Part II: M itigation

Bernard Sklar, Communications Engineering Services

W manifestations. In Part I, two types of fading, large-scale and to a bandwidth interval having a correlation of at least 0.5 is

e repeat Fig. 1, from Part I of the article, where it characterized in terms of the root mean squared (rms) delay served as a table of contents for fading channel

spread, σ τ [1]. A popular approximation of f 0 corresponding

small-scale, were described. Figure 1 emphasizes the small-

(2) sca le fa d in g p h e n o me n a a n d it s t wo ma n ife st a t io n s, t ime

f 0 ≈ 1/5 σ τ

spreading of the signal or signal dispersion, and time variance Figure 2c shows the function R( ∆ t ), designated the spaced- of the channel or fading rapidity due to motion between the

tim e correlation function; it is the autocorrelation function of transmitter and receiver. These are listed in blocks 4, 5, and 6.

the channel’s response to a sinusoid. This function specifies to Examining these manifestations involved two views, time and

wh a t e xt e n t t h e r e is co r r e la t io n b e t we e n t h e ch a n n e l’s frequency, as indicated in blocks 7, 10, 13, and 16. Two degra-

response to a sinusoid sent at time t 1 and the response to a dation categories were defined for dispersion, frequency-selec-

similar sinusoid sent at time t 2 , where ∆ t = t 2 –t 1 . The coher- tive fading and flat- fading, as listed in blocks 8, 9, 11, and 12.

ence tim e ,T 0 , is a measure of the expected time duration over Two degradation categories were defined for fading rapidity,

which the channel’s response is essentially invariant. fast-fading and slow-fading, as listed in blocks 14, 15, 17, and 18.

Figure 2d shows a Doppler power spectral density, S(v), plot- In Part I, a model of the fading channel consisting of four

ted as a function of Doppler-frequency shift, v; it is the Fouri- functions was described. These functions are shown in Fig. 2

er transform of R ( ∆ t ). The sharpness and steepness of the (which appeared in Part I as Fig. 7). A m ultipath-intensity pro-

boundar ie s of the D opple r spe ctr um ar e due to the shar p file , S( τ ), is plotted in Fig. 2a versus time delay τ . Knowledge

u p p e r limit on t h e D op p le r sh ift p r od u ce d by a ve h icu la r of S( τ ) helps answer the question “For a transmitted impulse,

antenna traveling among a dense population of stationary how does the average received power vary as a function of

scatterers. The largest magnitude of S(v) occurs when the time delay, τ ?” For a single transmitted impulse, the time, T m ,

scatterer is directly ahead of or directly behind the moving between the first and last received components represents the

antenna platform. The width of the Doppler power spectrum m axim u m excess d elay d u r in g wh ich t h e m u lt ip a t h sign a l

is referred to as the spectral broadening or Doppler spread, power falls to some threshold level below that of the strongest

denoted f d and sometimes called the fading bandwidth of the

component. Figure 2b shows the function  R ( ∆ f )  , designated

channel. Note that the Doppler spread, f d , and the coherence

a spaced-frequency correlation function; it is the Fourier trans- time, T 0 , are reciprocally related (within a multiplicative con- form of S( τ ). R( ∆ f ) represents the correlation between the

stant). In Part I of this tutorial, it was shown that the time channel’s response to two signals as a function of the frequen-

(approximately the coherence time) required to traverse a dis-

tance λ /2 when traveling at a constant velocity, V, is helps answer the question “What is the correlation between

cy difference between the two signals. Knowledge of R( ∆ f )

received signals that are spaced in frequency ∆ f = f 1 –f 2 ?”

The coherence bandwidth, f 0 , is a statistical measure of the

range of frequencies over which the channel passes all spec- tral components with approximately equal gain and linear phase. Thus, the coherence bandwidth represents a frequency

D EGRADATION C ATEGORIES IN B RIEF

range over which frequency components have a strong poten-

T here in the context of Fig. 3, which summarizes small-scale fad-

he degradation categories described in Part I are reviewed

tial for amplitude correlation. Note that f 0 and T m are recipro-

ca lly r e la t e d ( wit h in a m u lt ip lica t ive co n st a n t ) . A s a n ing mechanisms, degradation categories, and their effects. (This fig- approximation, it is possible to say that

ure appeared in Part I as Fig. 6.) When viewed in the time-delay

f 0 ≈ 1/Tm

domain, a channel is said to exhibit frequency-selective fading if T m > T s (the delay time is greater than the symbol time). This

A more useful measurement of delay spread is most often condition occurs whenever the received multipath components

0163-6804/97/$10.00 © 1997 IEEE

IEEE Communications Magazine • July 1997

Fad ing channel m anifestations

Large-scale fad ing d ue to

Sm all-scale fad ing d ue to

m otion over large areas

sm all changes in p osition

Mean signal

sp read ing of

variance of

vs. d istance

m ean

the signal

the channel

Tim e-d elay

Fourier

Freq uency

Tim e

Fourier

Dop p ler-shift

d escrip tion

transform s

d escrip tion

d escrip tion

transform s

d escrip tion

17 18 Freq uency-

Duals

selective Flat Fast Slow fad ing

Freq uency-

■ Figure 1. Fading channel m anifestations.

of a symbol extend beyond the symbol’s time duration, thus causing channel-induced intersymbol interference

(ISI). S ( τ ) S ( υ ) Viewed in the time-delay domain, a channel is said

to exhibit frequency-nonselective or flat fading if T m < T s . In this case, all of the received multipath compo-

nents of a symbol arrive within the symbol time dura- tion; hence, the components are not resolvable. H ere,

Dual functions

there is no channel-induced ISI distortion, since the

0 f c -f d f c signal time spreading does not result in significant f c +f d overlap among neighboring received symbols. There is still performance degradation since the unresolvable

T m Maxim um excess d elay f d Sp ectral b road ening

phasor components can add up destructively to yield a substantial reduction in signal-to-noise ratio (SNR ).

a) Multip ath intensity p rofile

d ) Dop p ler p ower sp ectrum

When viewed in the frequency domain, a channel is

referred to as frequency-selective if f 0 < 1/T s ≈ W ,

where the symbol rate, 1/T s is nominally taken to be

equal to the signal bandwidth W. Flat fading degrada- Fourier

Fourier

transform s

transform s

tion occurs whenever f 0 > W. H ere, all of the signal’s spectral components will be affected by the channel in

R ( ∆ t ) avoid ISI distortion caused by frequency-selective fad-

a similar manner (e.g., fading or no fading). In order to

| R( ∆ f )|

ing, the channel must be made to exhibit flat fading by ensuring that the coherence bandwidth exceeds the signaling rate.

∆ f ∆ t the channel coherence time and T s is the symbol time.

referred to as fast fading whenever T 0 < T s , where T 0 is

Fast fading describes a condition where the time dura- tion for which the channe l be have s in a cor r e late d

manner is short compared to the time duration of a 0 ≈ 1/T m Coherence b and wid th 0

T 0 ≈ 1/f d Coherence tim e symbol. Therefore, it can be expected that the fading

character of the channel will change several times dur -

b ) Sp aced -freq uency

c) Sp aced -tim e

ing the time a symbol is propagating. This leads to dis-

correlation function

correlation function

t o r t io n o f t h e ba se ba n d p u lse sh a p e , be ca u se t h e received signal’s components are not all highly correlat-

■ Figure 2. Relationships am ong the channel correlation functions and

ed throughout time. H ence, fast fading can cause the

power density functions.

IEEE Communications Magazine • July 1997

Tim e-sp read ing m echanism

Tim e-variant m echanism

d ue to m ultip ath

d ue to m otion

Freq uency-selective fad ing

Fast fad ing (high Dop p ler,

will generally be “bad.” In the case

(ISI d istortion, p ulse m utilation,

PLL failure, irred ucib le BER)

of R ayleigh fading, parameters with

irred ucib le BER) m ultip ath

channel fad ing rate >

o ve r ba r s a r e o ft e n in t r o d u ce d t o

d elay sp read > sym b ol tim e

sym b ol rate

indicate that a mean is being taken

Tim e-d elay

Dual

Dop p ler-shift

d om ain

m echanism s

d om ain

over the “ups” and “downs” of the

Flat fad ing (loss in SNR)

Slow fad ing (low Dop p ler,

fading experience. Therefore, one

m ultip ath d elay sp read

loss in SNR) channel fad ing

often sees such bit error probability

< sym b ol tim e

rate < sym b ol rate

plots with mean parameters denot-

ed by — P and — B E b /N 0 . The curve that

Freq uency-selective fad ing

Fast fad ing (high Dop p ler,

reaches an irreducible level, some-

(ISI d istortion, p ulse m utilation,

PLL failure, irred ucib le BER)

t ime s ca lle d a n error floor, r e p r e -

irred ucib le BER) channel

channel coherence tim e <

sents “awful” performance, where

coherence BWS < sym b ol rate

sym b ol tim e

t h e b it e r r o r p r o b a b ilit y ca n

Freq uency

m echanism s

d om ain

a p p r o a ch t h e va lu e o f 0.5. T h is

Flat fad ing (loss in SNR)

Slow fad ing (low Dop p ler,

shows the severe distorting effects

channel coherence BW

loss in SNR) channel coherence

of frequency-selective fading or fast

> sym b ol rate

tim e > sym b ol tim e

fading.

If the channel introduces signal ■ Figure 3. Sm all-scale fading: m echanism s, degradation categories, and effects.

distortion as a result of fading, the system performance can exhibit an irreducible error rate; when larger

baseband pulse to be distorted, resulting in a loss of SNR that t h a n t h e d e sir e d e r r o r r a t e , n o a m o u n t o f E b /N 0 will h e lp often yields an irreducible error rate. Such distorted pulses

achieve the desired level of performance. In such cases, the typically cause synchronization problems, such as failure of

general approach for improving performance is to use some phase-locked-loop (PLL) receivers.

form of mitigation to remove or reduce the distortion. The Viewed in the time domain, a channel is generally referred

m it iga t io n m e t h o d d e p e n d s o n wh e t h e r t h e d ist o r t io n is

caused by frequency-selective or fast fading. O nce the distor- tion for which the channel behaves in a correlated manner is

to as introducing slow fading if T 0 > T s . H ere, the time dura-

tion has been mitigated, the P B versus E b /N 0 performance long compared to the symbol time. Thus, one can expect the

shou ld ha ve tr a nsitione d fr om the “a wfu l” bottoming ou t channel state to remain virtually unchanged during the time a

curve to the merely “bad” R ayleigh limit curve. Next, we can symbol is transmitted.

further ameliorate the effects of fading and strive to approach When viewed in the D oppler shift domain, a channel is

AWGN performance by using some form of diversity to pro- referred to as fast fading if the symbol rate, 1/T s , or the signal

vide the receiver with a collection of uncorrelated samples of

the signal, and by using a powerful error correction code. versely, a channel is referred to as slow fading if the signaling

bandwidth, W, is less than the fading rate, 1/T 0 or f d . Con-

In Fig. 5, several mitigation techniques for combating the rate is greater than the fading rate. In order to avoid signal

effects of both signal distortion and loss in SNR are listed. distortion caused by fast fading, the channel must be made to

Just as Fig. 1 serves as a guide for characterizing fading phe-

e xh ibit slo w fa d in g by e n su r in g nomena and their effects, Fig. 5 that the signaling rate exceeds the

ca n sim ila r ly se r ve t o d e scr ibe channel fading rate.

1 mitigation me thods that can be used to ameliorate the effects of

M fading. The mitigation approach to ITIGATION M ETHODS

be used should follow two basic igu r e 4, su bt it le d “t h e good ,

F steps: first, provide distortion mit-

Freq uency-selective fad ing or

igation; next, provide diversity. lights thr e e ma jor pe r for ma nce

the bad, and the awful,” high-

fast fad ing d istortion

(PB can approach 0.5)

ca t e go r ie s in t e r m s o f bit e r r o r

probability, P B , versus E b /N 0 . The

M ITIGATION TO C OM BAT

le ft m o st e xp o n e n t ia lly sh a p e d curve represents the performance

F REQUENCY -S ELECTIVE

that can be expected when using

D ISTORTION

any nominal modulation type in

PB 10–2

• E qualization can compensate ( A W G N ) . O b se r ve t h a t wit h a

a d d it ive wh it e G a u ssia n n o ise

Flat fad ing

and slow fad ing

t h a t is se e n in fr e q u e n cy- go o d p e r fo r m a n ce r e su lt s. T h e

Rayleigh lim it

for the channel-induced ISI

r e a so n a b le a m o u n t o f E b /N 0 ,

se le ctive fa ding. Tha t is, it middle curve, referred to as the

can help move the operating R ayleigh lim it , shows the perfor-

point from the error-perfor- m a n ce d e gr a d a t io n r e su lt in g

mance curve that is “awful” from a loss in SNR that is char-

AWGN

in F ig. 4 t o t h e o n e t h a t is

a ct e r ist ic o f fla t fa d in g o r slo w “bad.” The process of equal- fading when there is no line-of-

izing the ISI involves some sight signal component present.

10–4 0 5 10 15 20 25 30 35 method of gathering the dis- T h e cu r ve is a fu n ct io n o f t h e

persed symbol energy back reciprocal of E b /N

0 (an inverse- together into its original time lin e a r fu n ct io n ) , so fo r r e a so n-

Eb/N0 (dB)

interval. In effect, equaliza- able values of SNR , performance

■ Figure 4. Error perform ance: the good, the bad, and

the awful.

tion involves insertion of a

IEEE Communications Magazine • July 1997

To com b at d istortion

To com b at loss in SNR

filter to make the combination of chan-

Freq uency-selective d istortion

Flat-fad ing and slow-fad ing

nel and filter yield a flat response with lin e a r p h a se . T h e p h a se lin e a r it y is

• Ad ap tive eq ualization

• Som e typ e of d iversity

achieved by making the equalizer filter

(e.g., d ecision feed b ack,

to get ad d itional uncorrelated

t h e co m p le x co n ju ga t e o f t h e t im e

Viterb i eq ualizer)

estim ates of signal

• Sp read sp ectrum — DS or FH

• Error-correction cod ing

r e ve r se o f t h e d isp e r se d p u lse [1].

• Orthogonal FDM (OFDM)

Because in a mobile system the channel

• Pilot signal

response varies with time, the equalizer filter must also change or adapt to the time-varying channel. Such equalizer fil-

Fast-fad ing d istortion

Diversity typ es

ters are therefore called adaptive equalizers . An equalizer accomplishes

• Rob ust m od ulation

• Tim e (e.g., interleaving)

more than distortion mitigation; it also

• Signal red und ancy to

• Freq uency (e.g., BW exp ansion, sp read

increase signaling rate

sp ectrum FH or DS with rake receiver)

provides diversity. Since distortion mitiga-

• Cod ing and interleaving

• Sp atial (e.g., sp aced receive antennas)

tion is achieved by ga t h e r in g t h e d is-

• Polarization

persed symbol’s energy back into the symbol’s original time interval so that it doesn’t hamper the detection of other

■ Figure 5. Basic m itigation types.

symbols, the equalizer is simultaneously p r ovid in g e a ch r e ce ive d symbol wit h energy that would otherwise be lost.

signal, multiplication by the code signal yields • The decision feedback equalizer (DFE) has a feedforward

Ax (t)g 2 (t)cos(2 π f c t )

section that is a linear transversal filter [1] whose length (5) and tap weights are selected to coherently combine virtual-

+ α Ax (t – τ k )g(t)g(t – τ k )cos(2 π f c t + θ ) ly all of the current symbol’s energy. The DFE also has a

where g 2 (t) = 1, and if τ k is greater than the chip duration, feedback section which removes energy that remains from

(6) the D F E is that once an information symbol has been

| ∫ g *(t)g(t – τ k previously detected symbols [1–4]. The basic idea behind )dt | << ∫ g *(t)g(t)dt

over some appropriate interval of integration (correlation), detected, the ISI it induces on future symbols can be esti-

where * indicates complex conjugate, and τ k is equal to or larg- mated and subtracted before the detection of subsequent

er than the PN chip duration. Thus, the spread-spectrum sys- symbols.

tem effectively eliminates the multipath interference by virtue • The maximum likelihood sequence estimation (MLSE )

of its code-correlation receiver. Even though channel- induced equalizer tests all possible data sequences (rather than

ISI is typically transparent to DS/SS systems, such systems suf- decoding each received symbol by itself) and chooses the

fer from the loss in energy contained in all the multipath com- data sequence that is the most probable of the candi-

ponents not seen by the receiver. The need to gather up this dates. The MLSE equalizer was first proposed by Forney

lost energy belonging to the received chip was the motivation [5] when he implemented the equalizer using the Viterbi

for developing the R ake receiver [7–9]. The R ake receiver decoding algorithm [6]. The MLSE is optimal in the sense

dedicates a separate correlator to each multipath component that it minimizes the probability of a sequence error.

(finger). It is able to coherently add the energy from each fin- Because the Viterbi decoding algorithm is the way in

ger by selectively delaying them (the earliest component gets which the MLSE equalizer is typically implemented, the

the longest delay) so that they can all be coherently combined. equalizer is often referred to as the Viterbi equalizer. Later

• I n P a r t I o f t h is a r t icle , we d e scr ibe d a ch a n n e l t h a t in this article we illustrate the adaptive equalization per-

could be classified as flat fading, but occasionally exhibits formed in the Global System for Mobile Communications

frequency-selective distortion when the null of the chan- (GSM) using the Viterbi equalizer.

nel’s frequency transfer function occurs at the center of • Spread-spectrum techniques can be used to mitigate fre-

the signal band. The use of DS/SS is a good way to miti- quency-selective ISI distortion because the hallmark of any

ga t e su ch d ist o r t io n be ca u se t h e wid e ba n d SS sign a l spread-spectrum system is its capability to reject interfer-

would span many lobes of the selectively faded frequency ence, and ISI is a type of interference. Consider a direct-

response. Hence, a great deal of pulse energy would then sequence spread-spectrum (D S/SS) binary phase shift

be passed by the scatterer medium, in contrast to the keying (PSK) communication channel comprising one

nulling effect on a relatively narrowband signal (see Part

d ir e ct p a t h a n d o n e r e fle ct e d p a t h . A ssu m e t h a t t h e

I, Fig. 8c) [10].

propagation from transmitter to receiver results in a mul- • F r e qu e ncy-hopping spr e a d spe ctr u m ( F H /SS) ca n be tipath wave that is delayed by τ k compared to the direct

used to mitigate the distortion due to frequency-selective wave. If the receiver is synchronized to the waveform

fading, provided the hopping rate is at least equal to the

a r r ivin g via t h e d ir e ct p a t h , t h e r e ce ive d sign a l, r( t) , symbol rate. Compared to DS/SS, mitigation takes place neglecting noise, can be expressed as

through a different mechanism. FH receivers avoid multi-

r (t) = Ax(t)g(t)cos(2 π f c t )

path losses by rapid changes in the transmitter frequency

+ α Ax (t – τ k )g(t – τ k )cos(2 π f c t+ θ ),

band, thus avoiding the inte r fe r e nce by changing the

receiver band position before the arrival of the multipath here x(t) is the data signal, g(t) is the pseudonoise (PN)

w signal.

sp r e a d in g co d e , a n d τ k is t h e d iffe r e n t ia l t im e d e la y • O rthogonal frequency-division multiplexing (O F D M)

b e t we e n t h e t wo p a t h s. T h e a n gle θ is a r a n d o m p h a se , can be used in frequency-selective fading channels to assumed to be uniformly distributed in the range (0, 2 π ), and

avoid the use of an equalizer by lengthening the symbol α is the attenuation of the multipath signal relative to the

duration. The signal band is partitioned into multiple sub- direct path signal. The receiver multiplies the incoming r(t) by

bands, each exhibiting a lower symbol rate than the origi- the code g(t). If the receiver is synchronized to the direct path

nal band. The subbands are then transmitted on multiple

IEEE Communications Magazine • July 1997

there is the potential for frequency-selective distortion

unless we further provide some mitigation such as equal- originally referred to as Kineplex. The technique has been

than the channel’s coherence bandwidth f 0 . O FD M was

ization. Thus, an expanded bandwidth can improve system implemented in the U nited States in mobile radio sys-

performance (via diversity) only if the frequency-selective tems [11], and has been chosen by the European commu-

distortion the diversity may have introduced is mitigated. n it y u n d e r t h e n a m e co d e d O F D M ( C O F D M ) , fo r

• Spread spectrum is a form of bandwidth expansion that high-definition television (HDTV) broadcasting [12].

excels at rejecting interfering signals. In the case of direct- • Pilot signal is the name given to a signal intended to facil-

sequence spread spectrum (D S/SS), it was shown earlier itate the coherent detection of waveforms. Pilot signals

that multipath components are rejected if they are delayed can be implemented in the frequency domain as an in-

by more than one chip duration. H owever, in order to band tone [13], or in the time domain as a pilot sequence

approach AWG N performance, it is necessary to com- which can also provide information about the channel

pensate for the loss in energy contained in those rejected state and thus improve performance in fading [14].

components. The R ake receiver (described later) makes it possible to coherently combine the energy from each of the multipath components arriving along different

M ITIGATION TO C OM BAT

paths. Thus, used with a R ake receiver, D S/SS modula-

F t io n ca n be sa id t o a ch ie ve p a t h d ive r sit y. T h e R a ke AST -F ADING D ISTORTION

receiver is needed in phase-coherent reception, but in • For fast fading distortion, use a robust modulation (non-

differentially coherent bit detection a simple delay line coherent or differentially coherent) that does not require

(one bit long) with complex conjugation will do the trick phase tracking, and reduce the detector integration time [15].

• Increase the symbol rate, W ≈ 1/T s , to be greater than • FH /SS is sometimes used as a diversity mechanism. The

G SM system uses slow FH (217 hops/s) to compensate • Error-correction coding and interleaving can provide mit-

the fading rate, f d ≈ 1/T 0 , by adding signal redundancy.

for those ca se s whe r e the mobile u se r is moving ve r y igation, because instead of providing more signal energy,

slowly (or not at all) and happens to be in a spectral null.

• Spatial diversity is usually accomplished through the use with coding present, the error floor will be lowered com-

a code reduces the required E b /N 0 . F or a given E b /N 0 ,

of multiple receive antennas separated by a distance of at pared to the uncoded case.

least 10 wavelengths for a base station (much less for a • An interesting filtering technique can provide mitigation

mobile station). Signal processing must be employed to in the event of fast-fading distortion and frequency-selec-

choose the best antenna output or to coherently combine tive distortion occurring simultaneously. The frequency-

all the outputs. Systems have also been implemented selective distortion can be mitigated by the use of an

wit h mu lt ip le sp a ce d t r a n smit t e r s; a n e xa mp le is t h e O FD M signal set. F ast fading, however, will typically

Global Positioning System (GPS).

d e gr a d e co n ve n t io n a l O F D M be ca u se t h e D o p p le r • Polarization diversity [19] is yet another way to achieve spreading corrupts the orthogonality of the O FD M sub-

additional uncorrelated samples of the signal. carriers. A polyphase filtering technique [16] is used to

• Any diversity scheme may be viewed as a trivial form of provide time-domain shaping and duration extension to

repetition coding in space or time. H owever, there exist reduce the spectral sidelobes of the signal set, and thus

techniques for improving the loss in SNR in a fading chan- help preserve its orthogonality. The process introduces

nel that are more efficient and more powerful than repe- kn own I SI a n d a d ja ce n t ch a n n e l in t e r fe r e n ce ( A CI ) ,

t it io n co d in g. E r r o r co r r e ct io n co d in g r e p r e se n t s a which are then removed by a post-processing equalizer

unique mitigation technique, because instead of provid- and canceling filter [17].

ing more signal energy it reduces the required E b /N 0 in o r d e r t o a cco m p lish t h e d e sir e d e r r o r p e r fo r m a n ce .

M E rror correction coding coupled with interleaving [15, ITIGATION TO C OM BAT L OSS IN SNR

20–25] is probably the most prevalent of the mitigation fter implementing some form of mitigation to combat the

A sch e me s u se d t o p r ovid e imp r ove d p e r for ma n ce in a

possible distortion (frequency-selective or fast fading),

fading environment.

the next step is to use some form of diversity to move the ope r ating point fr om the e r r or -pe r for mance cur ve that is “bad” in F ig. 4 to a curve that approaches AWG N perfor -

S UM M ARY OF THE K EY P ARAM ETERS

mance. The term “diversity” is used to denote the various methods available for providing the receiver with uncorrelat-

C HARACTERIZING F ADING C HANNELS

e summarize the conditions that must be met so that the t u r e h e r e , sin ce it wo u ld n o t h e lp t h e r e ce ive r t o h a ve

ed renditions of the signal. U ncorrelated is the important fea-

W channel does not introduce frequency-selective and fast-

additional copies of the signal if the copies were all equally fading distortion. Combining the inequalities of Eq. 14 and 23 poor. Listed below are some of the ways in which diversity

from Part I of this article, we obtain

can be implemented: • Time diversity — Transmit the signal on L different time

f 0 > W> f d (7a)

slots with time separation of at least T 0 . Interleaving, often

or

used with error correction coding, is a form of time diversity. • Frequency diversity — Transmit the signal on L different

(7b)

In other words, we want the channel coherence bandwidth width expansion is a form of frequency diversity. The sig-

carriers with frequency separation of at least f 0 . Band-

to exceed our signaling rate, which in turn should exceed the

fading rate of the channel. R ecall from Part I that without dis- providing the receiver with several independently fading

nal bandwidth, W, is expanded to be greater than f 0 , thus

tortion mitigation, f 0 sets an upper limit on the signaling rate, signal replicas. This achieves frequency diversity of the

and f d sets a lower limit on it.

IEEE Communications Magazine • July 1997

4.615 m s

0 1 2 3 4 5 6 7 slot so that the receiver can learn the impulse response of the channel. It then uses a Viterbi equalizer (explained

later) for mitigating the frequency-selective distortion.

• Once the distortion effects have been reduced, introduce some form of diversity and error correction coding and

3 57 1 26 1 57 3 interleaving in order to approach AWG N performance.

Burst

For direct-sequence spread-spectrum (DS/SS) signaling,

148 Bits

a R ake receiver (explained later) may be used for provid-

156.25 Bits

ing diversity by coherently combining multipath compo-

nents that would otherwise be lost. ■ Figure 6. The GSM TDMA fram e and tim e slot containing a

0.577 m s

F AST -F ADING AND F REQUENCY -S ELECTIVE F ADING

norm al burst.

D ISTORTION :E XAM PLE 3

F AST -F ADING D ISTORTION :E XAM PLE 1 Consider the case where the coherence bandwidth is less than the signaling rate, which in turn is less than the fading rate.

If the inequalities of Eq. 7 are not met and distortion mitiga- The channel exhibits both fast-fading and frequency-selective tion is not provided, distortion will result. Consider the fast-

fading, which is expressed as

fading case where the signaling rate is less than the channel fading rate, that is,

f 0 < W< f d (10a)

M it iga t ion con sist s of u sin g on e or mor e of t h e followin g

(10b) methods (Fig. 5):

R ecalling from Eq. 7 that f 0 sets an upper limit on the signal- • Choose the modulation/demodulation technique that is

ing rate and f d sets a lower limit on it, this is a difficult design most robust under fast-fading conditions. This means, for

problem because, unless distortion mitigation is provided, the example, avoiding carrier recovery with PLLs since fast

maximum allowable signaling rate is (in the strict terms of the fading could keep a PLL from achieving lock conditions.

above discussion) less than the minimum allowable signaling • Incorporate sufficient redundancy that the transmission

rate. Mitigation in this case is similar to the initial approach symbol rate exceeds the channel fading rate. As long as

outlined in example 1.

the transmission symbol rate does not exceed the coher- • Choose the modulation/demodulation technique that is ence bandwidth, the channel can be classified as flat fad-

most robust under fast-fading conditions. ing. H owever, even flat-fading channels will experience

• U se transmission redundancy in order to increase the frequency-selective distortion whenever a channel null

transmitted symbol rate.

appears at the band center. Since this happens only occa- • Provide some form of frequency-selective mitigation in a sionally, mitigation might be accomplished by adequate

manner similar to that outlined in example 2. error correction coding and interleaving.

• Once the distortion effects have been reduced, introduce • The above two mitigation approaches should result in the

some form of diversity and error correction coding and demodulator operating at the R ayleigh limit [15] (Fig. 4).

interleaving in order to approach AWGN performance.

H owever, there may be an irreducible floor in the error-

performance versus E b /N 0 curve due to the frequency

m o d u la t e d ( F M ) n o ise t h a t r e su lt s fr o m t h e r a n d o m

T HE V ITERBI E QUALIZER AS A PPLIED TO GSM

D oppler spreading (see Part I). The use of an in-band pilot tone and a frequency-control loop can lower this

igu r e 6 sh o ws t h e G SM t im e -d ivisio n m u lt ip le a cce ss irreducible performance level.

F (TDMA) frame, with a duration of 4.615 ms and compris-

• T o a vo id t h is e r r o r flo o r ca u se d by r a n d o m D o p p le r ing eight slots, one assigned to each active mobile user. A nor- spreading, increase the signaling rate above the fading

mal transmission burst, occupying one slot of time, contains 57 rate still further (100–200 x fading rate) [26]. This is one

message bits on each side of a 26-bit midamble called a train- architectural motive behind time-division multiple access

ing or sounding sequence. The slot-time duration is 0.577 ms (TDMA) mobile systems.

(or the slot rate is 1733 slots/s). The purpose of the midamble • Incorporate error correction coding and interleaving to

is to assist the receiver in estimating the impulse response of lower the floor and approach AWGN performance.

the channel in an adaptive way (during the time duration of each 0.577 ms slot). In order for the technique to be effective,

F REQUENCY -S ELECTIVE F ADING D ISTORTION :E XAM PLE 2 the fading behavior of the channel should not change appre-

C onsider the frequency-selective case where the coherence ciably during the time interval of one slot. In other words, bandwidth is less than the symbol rate; that is,

there should not be any fast-fading degradation during a slot

f < W> f .

time when the receiver is using knowledge from the midamble

to compensate for the channel’s fading behavior. Consider the M it iga t ion con sist s of u sin g on e or mor e of t h e followin g

example of a G SM receiver used aboard a high-speed train, methods (Fig. 5):

t r a ve lin g a t a co n st a n t ve lo cit y o f 200 km /h r ( 55.56 m /s) . • Since the transmission symbol rate exceeds the channel

Assume the carrier frequency to be 900 MHz, (the wavelength fading rate, there is no fast-fading distortion. Mitigation

is λ = 0.33 m). From Eq. 3, we can calculate that a half-wave- of frequency-selective effects is necessary. O ne or more

length is traversed in approximately the time (coherence time) of the following techniques may be considered. • A d a p t ive e qu a liza t ion , sp r e a d sp e ct r u m ( D S or F H ) ,

V O FD M, pilot signal. The E uropean G SM system uses a (11) midamble training sequence in each transmission time

≈ 3 ms

Therefore, the channel coherence time is over five times

IEEE Communications Magazine • July 1997

Matched

Wind ow

waveform s

r (t )

t h e su m o f t wo co n t r ib u t io n s. T h e interval of length L CISI is due to the

tr

Channel-corrected

controlled ISI caused by G aussian fil-

Extract received

reference

tering of the baseband pulses, which

training

waveform s

are then minimum shift keying (MSK)

Received seq uence

modulated. The interval of length L C

signal r tr (t )

is d u e t o t h e ch a n n e l-in d u ce d I SI

Am b iguity

ca u se d b y m u lt ip a t h p r o p a ga t io n ;

function w (t ) R (t )

Metric

Viterb i

therefore, L o can be written as

calculations

algorithm

L o + L CISI + L C . (14) The GSM system is required to pro-

vide mitigation for distortion due to sig-

Eq ualized

signal

nal dispersions of approximately 15–20 µ s. The bit duration is 3.69 µ s. Thus,

■ Figure 7. The Viterbi Equalizer as applied to GSM. the Viterbi equalizer used in GSM has

a m e m o r y o f 4–6 b it in t e r va ls. F o r each L o -bit interval in the message, greater than the slot time of 0.577 ms. The time needed for a

the function of the Viterbi equalizer is to find the most likely significant change in fading behavior is relatively long com-

L o -bit sequence out of the 2 L o possible sequences that might pared to the time duration of one slot. Note that the choices

have been transmitted. D etermining the most likely L o -bit made in the design of the GSM TDMA slot time and midamble

sequence requires that 2 L o meaningful reference waveforms were undoubtedly influenced by the need to preclude fast fad-

be created by modifying (or disturbing) the 2 L o ideal wave- ing with respect to a slot-time duration, as in this example.

forms in the same way the channel has disturbed the transmit- The GSM symbol rate (or bit rate, since the modulation is

t e d me ssa ge . T h e r e for e , t h e 2 L o r e fe r e n ce wa ve for ms a r e binary) is 271 ksymbols/s and the bandwidth is W = 200 kH z.

convolved with the windowed estimate of the channel impulse If we consider that the typical rms delay spread in an urban

response, h w (t), in order to derive the disturbed or channel- environment is in the order of σ τ = 2 µ s , then using Eq. 2 the

corrected reference waveforms. Next, the channel-corrected

r e su lt in g coh e r e n ce ba n d wid t h is f 0 ≈ 100 kH z. I t sh ou ld

reference waveforms are compared against the received data

waveforms to yield metric calculations. H owever, before the must utilize some form of mitigation to combat frequency-

therefore be apparent that since f 0 < W, the G SM receiver

comparison takes place, the received data waveforms are con- se le ct ive d ist o r t io n . T o a cco m p lish t h is go a l, t h e V it e r bi

volved with the known windowed autocorrelation function equalizer is typically implemented.

w (t)R s (t), transforming them in a manner comparable to that

F igure 7 illustrates the basic functional blocks used in a applied to the reference waveforms. This filtered message sig-

G SM receiver for estimating the channel impulse response, nal is compared to all possible 2 L o channel-corrected refer- which is then used to provide the detector with channel-correct-

ence signals, and metrics are computed as required by the

ed reference waveforms [27]. In the final step, the Viterbi algo- Viterbi decoding algorithm (VDA). The VDA yields the max- rithm is used to compute the MLSE of the message. A received

imum likelihood estimate of the transmitted sequence [6]. signal can be described in terms of the transmitted signal con- volved with the impulse response of the channel. We show this below, using the notation of a received training sequence,

T HE R AKE R ECEIVER A PPLIED TO D IRECT -

r tr (t), and the transmitted training sequence, s tr (t), as follows:

S EQUENCE S PREAD -S PECTRUM S YSTEM S

nterim Specification 95 (IS-95) describes a D S/SS cellular where * denotes convolution. At the receiver, r tr (t) is extracted

r tr (t) = s tr (t) * h c (t)

I system that uses a R ake receiver [7–9] to provide path diver-

fr om t h e n or ma l bu r st a n d se n t t o a filt e r h a vin g impu lse sity. In Fig. 8, five instances of chip transmissions correspond- response, h mf (t), that is matched to s tr (t). This matched filter yields at its

output, an estimate of h Multip ath sp read

c (t), denoted

e (t), developed from E q. 12 as fol-

Transm ission

Transm itted

tim e

= R 1 s (t) * h c (t) wh e r e R ( t) is t h e a u t o co r r e la t io n

= s tr (t) * h c (t) * h mf (t) (13)

cod e seq uence

t0 s function of s tr (t). If R s (t) is a highly

0 t –1

peaked (impulse-like) function, then

h e (t) ≈ h c (t).

t –2 1 chip tim e

Next, using a windowing function,

t –3

w (t), we truncate h e (t) to form a com- p u t a t io n a lly a ffo r d a b le fu n ct io n ,

t –4

h w ( t) . T h e win d o w le n gt h m u st be

1 τ 2 τ 3 Delay tim e τ

large enough to compensate for the

Inp ut chip s to Inp ut chip s to effect of typical channel-induced ISI. Inp ut chip s to

correlator # 1 correlator # 2 correlator # 3

The required observation interval L o for the window, can be expressed as

■ Figure 8. An exam ple of received chips seen by a three-finger Rake receiver.

IEEE Communications Magazine • July 1997

[4 ] S. U. H. Qu re sh i, “Ad a p t ive Eq u a liza t io n ,” Proc. IEEE, vo l. 7 3 , n o . 9 ,

ing to the code sequence 1 0 1 1 1 are shown, with the trans-

Sep t. 1985, p p . 1340–87.

mission or observation times labeled t –4 for the earliest trans-

[5 ] G. D. Fo rn e y, “Th e Vit e rb i Alg o rit h m ,” Proc. IEEE, vo l. 6 1 , n o . 3 , Ma r.

m issio n a n d t fo r t h e la t e st . E a ch a b scissa sh o ws t h r e e

1978, p p . 268–78. 0 [6] B. Sklar, Digital Communications: Fundamentals and Applications, Ch. 6,

“finge r s” of a signa l tha t a r r ive a t the r e ce ive r with de la y

times τ 1 , τ 2 , and τ 3 . Assume that the intervals between the t i

Englewood Cliffs, NJ: Prentice Hall, 1988.

[7] R. Price and P. E. Green, Jr., “A Communication Technique for Multipath Chan-

t r a n smission t ime s a n d t h e in t e r va ls be t we e n t h e τ i d e la y

nels,” Proc. IRE, vol. 46, no. 3, Mar. 1958, pp. 555–70.

times are each one chip long. F rom this, one can conclude

[8] G. L. Turin, “Introd uction to Sp read -Sp ectrum Antim ultip ath Techniq ues

that the finger arriving at the receiver at time t and Their Ap p lication to Urb an Dig ital Rad io,” Proc. IEEE, vol. 68, no. 3,

τ Mar. 1980, pp. 328–53.

–4 , with delay

3 , is time-coincident with two other fingers, namely the fin-

[9] M. K. Sim on et al., Spread Spectrum Communications Handbook, McGraw

gers arriving at times t –3 and t –2 with delays τ 2 and τ 1 , respec-

Hill, 1994.

tively. Since, in this example, the delayed components are

[10] F. Am o ro so , “Use o f DS/SS Sig n a lin g t o Mit ig a t e Ra yleig h Fa d in g in a

separated by exactly one chip time, they are just resolvable. At Den se Sca t t erer En viro n m en t ,” IEEE Pers. Commun., vo l. 3, n o . 2, Ap r.

1996, p p . 52–61.

the receiver, there must be a sounding device that is dedicated

[11] M. A. Birch ler a n d S. C. Ja sp er, “A 64 kb p s Dig it a l La n d Mo b ile Ra d io

to estimating the τ i delay times. Note that for a terrestrial

System Em p loying M-16QAM,” Proc. 1992 IEEE Int’l. Conf. Sel. Topics in

mobile radio system, the fading rate is relatively slow (mil-

Wireless Commun. , Vancouver, Canad a, June 25–26, 1992, p p . 158–62.

liseconds) or the channel coherence time large compared to [12] H. Sari, G. Karam , and I. Jeanclaude, “Transm ission Techniques for Digital

the chip time (T 0 > T ch ). H ence, the changes in τ i occur slow-

Te rre st ria l TV Bro a d ca st in g ,” IEEE Commun. M ag., vo l. 3 3 , n o . 2 , Fe b .

1995, pp. 100–109.

ly enough that the receiver can readily adapt to them.

[13] J. K. Cavers, “The Performance of Phase Locked Transparent Tone-in-Band with

O nce the τ i delays are estimated, a separate correlator is

Symmetric Phase Detection,” IEEE Trans. Commun., vol. 39, no. 9, Sept. 1991,

dedicated to processing each finger. In this example, there pp. 1389–99.

[14] M. L. Moher and J. H. Lodge, “TCMP — A Modulation and Coding Strategy

would be three such dedicated correlators, each processing a

for Rician Fading Channel,” IEEE JSAC, vol. 7, no. 9, Dec. 1989, pp. 1347–55.

delayed version of the same chip sequence, 1 0 1 1 1. In Fig. 8,

[15] R. L. Bogusch, Digital Communications in Fading Channels: Modulation

each correlator receives chips with power profiles represented

and Coding , Missio n Research Co rp ., San ta Barb ara, CA, Rep . n o . MRC-

by the sequence of fingers shown along a diagonal line. Each R-1043, Mar. 11, 1987.

[16] F. Harris, “On th e Relatio n sh ip Betw een Mu ltirate Po lyp h ase FIR Filters

correlator attempts to match these arriving chips with the same

a n d Win d o w ed , Overla p p ed FFT Pro cessin g ,” Proc. 23rd Annual Asilo-

PN code, similarly delayed in time. At the end of a symbol

mar Conf . Signals, Sys., and Comp. , Pa cific Gro ve, CA, Oct . 30–No v. 1,

interval (typically there may be hundreds or thousands of chips

1989, p p . 485–88.

per symbol), the outputs of the correlators are coherently com- [1 7 ] R. W. Lo w d e rm ilk a n d F. Ha rris, “De sig n a n d Pe rfo rm a n ce o f Fa d in g

In sen sit ive Ort h o g o n a l Freq u en cy Divisio n Mu lt ip lexin g (OFDM) Usin g

bined, and a symbol detection is made. At the chip level, the

Po lyp h a se Filt erin g Tech n iq u es,” Proc. 30t h Annual Asilomar Conf . Sig-

R ake receiver resembles an equalizer, but its real function is to

nals, Sys., and Comp. , Pacific Grove, CA, Nov. 3–6, 1996.

provide diversity.

[18] M. Kavehrad and G. E. Bod eep , “Desig n and Exp erim ental Results for a

The inte r fe r e nce -suppr e ssion natur e of D S/SS syste ms Direct -Seq u en ce Sp rea d -Sp ect ru m Ra d io Usin g Differen t ia l Ph a se-Sh ift

Ke yin g Mo d u la t io n fo r In d o o r Wire le ss Co m m u n ica t io n s,” IEEE JSAC,

st e m s fr o m t h e fa ct t h a t a co d e se q u e n ce a r r ivin g a t t h e

vol. SAC-5, no. 5, June 1987, p p . 815–23.

r e ce ive r me r e ly on e ch ip t ime la t e , will be a ppr oxima t e ly

[1 9 ] G. C. He ss, Land-M ob ile Radio Syst em Engineering, Bo st o n : Art e ch

orthogonal to the particular PN code with which the sequence

House, 1993.

is correlated. Therefore, any code chips that are delayed by [20] J. Hag enauer and E. Lutz, “Forw ard Error Correction Cod ing for Fad ing

Co m p en sa t io n in Mo b ile Sa t ellit e Ch a n n els,” IEEE JSAC, vo l. SAC-5, n o .

one or more chip times will be suppressed by the correlator.

2, Feb . 1987, p p . 215–25.

The delayed chips only contribute to raising the noise floor

[21] P. I. McLane, et. al., “PSK and DPSK Trellis Cod es for Fast Fad ing, Shad -

(correlation sidelobes). The mitigation provided by the R ake

owed Mob ile Satellite Com m unication Channels,” IEEE Trans. Commun.,

receiver can be termed path diversity, since it allows the ener- vol. 36, no. 11, Nov. 1988, p p . 1242–46.

[2 2 ] C. Sch le g e l, a n d D. J. Co st e llo , Jr., “Ba n d w id t h Efficie n t Co d in g fo r

gy of a chip that arrives via multiple paths to be combined

Fa d in g Ch a n n e ls: Co d e Co n st ru ct io n a n d Pe rfo rm a n ce An a lysis,” IEEE

coherently. Without the R ake receiver, this energy would be

JSAC , vol. 7, no. 9, Dec. 1989, p p . 1356–68.

transparent and therefore lost to the DS/SS system. In Fig. 8,

[2 3 ] F. Ed b a u er, “Perfo rm a n ce o f In t erlea ved Trellis-Co d ed Differen t ia l 8 -

looking vertically above point PSK Mo d u la t io n o ve r Fa d in g Ch a n n e ls,” IEEE JSAC, vo l. 7 , n o . 9 , De c. τ

3 , it is clear that there is inter-

1989, p p . 1340–46.

chip interference due to different fingers arriving simultane-

[24] S. So lim a n a n d K Mo kra n i, “Perfo rm a n ce o f Co d ed Syst em s o ver Fa d-

ously. The spread-spectrum processing gain allows the system

in g Disp e rsive Ch a n n e ls,” IEEE Trans. Com m un., vo l. 4 0 , n o . 1 , Ja n .

to endure such interference at the chip level. No other equal-

1992, p p . 51–59

ization is deemed necessary in IS-95. [2 5 ] D. Divsa la r a n d F. Po lla ra , “Tu rb o Co d es fo r PCS Ap p lica t io n s,” Proc.

ICC ’95 , Seattle, WA, June 18–22, 1995, p p . 54–59. [26] A. J. Batem an and J. P. McGeehan, “Data Transm ission over UHF Fad ing

S Mobile Radio Channels,” IEE Proc., vol. 131, pt. F, no. 4, July 1984, pp. 364–74. UM M ARY

[2 7 ] L. Ha n zo a n d J. St e fa n o v, “Th e Pa n -Eu ro p e a n Dig it a l Ce llu la r Mo b ile

I Ed ., Ch. 8, Lond on: Pentech Press, 1992.

n Part II of this article, the mathematical model and the Ra d io Syst e m — Kn o w n a s GSM,” M obile Radio Commun., R. St e e le ,

major elements that contribute to fading in a communica- tion channel have been briefly reviewed (from Part I of the tutorial). Next, mitigation techniques for ameliorating the

B IOGRAPHY effects of each degradation category were treated, and sum-

B ERNARD S KLAR [LSM] h a s o ve r 4 0 ye a rs o f e xp e rie n ce in t e ch n ica l d e sig n

marized in Fig. 5. Finally, mitigation methods that have been

and m anag em ent p ositions at Rep ub lic Aviation Corp ., Hug hes Aircraft, Lit -

implemented in two system types, G SM and CD MA systems t o n In d u st rie s, a n d Th e Ae ro sp a ce Co rp o ra t io n . At Ae ro sp a ce , h e h e lp e d

d evelo p t h e MILSTAR sa t ellit e syst em , a n d w a s t h e p rin cip a l a rch it ect fo r

meeting IS-95, were described.

EHF Sa t e llit e Da t a Lin k St a n d a rd s. Cu rre n t ly, h e is h e a d o f a d va n ce d sys- t e m s a t Co m m u n ica t io n s En g in e e rin g Se rvice s, a co n su lt in g co m p a n y h e found ed in 1984. He has taug ht eng ineering courses at several universities,

R EFERENCES

in clu d in g t h e Un ive rsit y o f Ca lifo rn ia , Lo s An g e le s a n d t h e Un ive rsit y o f So u t h e rn Ca lifo rn ia , a n d h a s p re se n t e d n u m e ro u s t ra in in g p ro g ra m s

[1 ] T. S. Ra p p a p o rt , Wireless Co m m u n icat io n s , Up p e r Sa d d le Rive r, NJ: t h ro u g h o u t t h e w o rld . He h a s p u b lish ed a n d p resen t ed sco res o f t ech n ica l Prentice Hall, 1996.

p a p ers. He is a p a st Ch a ir o f t h e Lo s An g eles Co u n cil IEEE Ed u ca t io n Co m - [2] J. G. Proakis, Digital Communications, Ch. 7, New York: McGraw-Hill, 1983.

m it t ee. His acad em ic cred en t ials in clu d e a B.S. d eg ree in m at h an d scien ce [3 ] R. L. Bo g u sch , F. W. Gu ig lia n o , a n d D. L. Kn ep p , “Freq u en cy- Select ive

fro m t h e Un iversit y o f Mich ig a n , a n M.S. d eg ree in elect rica l en g in eerin g Scintillation Effects and Decision Feedback Equalization in High Data-Rate

from the Polytechnic Institute of Brooklyn, New York, and a Ph.D. d egree in Satellite Links,” Proc. IEEE, vol. 71, no. 6, June 1983, pp. 754–67.

engineering from the University of California, Los Angeles.

IEEE Communications Magazine • July 1997

109