bo thu bao hieu lua chon theo thoi gian nhieu nguoi dung trong moi truong fading nhanh da duong

7/29/2019 Bo Thu Bao Hieu Lua Chon Theo Thoi Gian Nhieu Nguoi Dung Trong Moi Truong Fading Nhanh Da Duong

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Multiuser Detection of Time-Selective Signaling in Fast-Fading

Multipath EnvironmentsBộ thu báo hiệu lự a chọn theo thờ i gian nhiều ngườ i dùng

trong môi trườ ng fading nhanh đa đườ ng

Nguyễn Nguyên Minh

Tãm t¾t: Kü thuËt ph©n tËp ® − îc sö dông ®Ó chèng l¹i fading. Qu¸ tr×nh thu RAKE th«ng dông cña çc hÖ thèng CDMA (§a truy nhËp ph©n chia m·) chØ khai th¸c sù ph©n tËp vÒ thêigian vµ chÞu sù suy gi¶m n¨ng lùc ®¸ng kÓ trong tr− êng hîp cã fading nhanh. Ph− ¬ng ph¸p ph©n tËp kÕt hîp Doppler ®a ® − êng ® − îc ¸p dông nh»m t¨ng c− êng hiÖu n¨ng cho qu¸ tr×nhthu RAKE . Kü thuËt b¸o hiÖu lùa chän theo thêi gian (Time-selective Signaling) ®· ® − îc sö dông ®Ó c¶i thiÖn sù ph©n tËp theo tÇn sè. Trong çc c«ng tr×nh ®· xuÊt b¶n cña çc t¸c gi¶nh− A. M. Sayeed, S. Bhashyam, G. W. Wornell vµ P.B. Rapajic, B. S. Vucetic, kü thuËt trªn®· ® − îc ph©n tÝch trong tr− êng hîp mét ng − êi dïng. Bµi viÕt nµy sÏ ph©n tÝch hÖ thèng ® − îcnªu trong bèi c¶nh ®a ng − êi dïng nh»m kh¼ng ®Þnh hiÖu qu¶ cña kü thuËt ®ã.

I. INTRODUCTION

Code Division Multiple Access (CDMA) has emerged as one of the most promising systems for wirelesscommunication recently and in the future, due to its capability of multiuser channel exploitation and its spread-spectrum virtue for channel diversity to combat fading. Both the European Telecommunications standardsInstitute (ETSI) and the International Telecommunication Union, while defining a framework for future mobilenetworks (3-Generation), known as Universal Mobile Telecommunications System (UMTS) and InternationalMobile Telecommunications 2000 (IMT-2000), respectively, have the common preference of CDMAapplication. IMT-2000 in the Asia Pacific Region, including Vietnam, is developing, and study for itstechnologies is going on [1], [2].

The recent practical RAKE receiver of CDMA system (such as IS-95 in USA) utilizes the large signalbandwidth to exploit multipath diversity (i.e.time-diversity), but only is optimal for slow fading scenarios. In

mobile scenarios, we may encounter the fast-fading environment, in which rapid temporal channel variationscause channel estimation errors and therefore degrade the RAKE performances significantly. Temporal channelvariations, in fact, provide another form of diversity – Doppler diversity (i.e. frequency diversity) – that can beexploited in conjunction with multipath to attain joint multipath-Doppler diversity. The concept of jointmultipath-Doppler diversity is based on a canonical channel representation that decomposes the channel into aseries of independent flat fading channels corresponding to different (orthogonal) multipath-Doppler-shiftedsignal components. Diversity reception is achieved by a generalization of the RAKE receiver that performs jointmultipath-Doppler processing.

Furthermore, for maximal frequency-diversity exploitation of the channel, a new signaling technique thatspreads symbol waveform beyond the intersymbol duration to make channel time-selective, is employed.Analytical and simulation results based on realistic fast-fading assumptions demonstrate that the proposedmultiuser detectors of the system promise substantially improved performance compared to existing systems dueto the inherently higher level of diversity afforded by multipath-Doppler processing.

In this paper, first, in Section II, some background conceptions are introduced for easier understanding of theproblems provided in the next Sections. Section III describes the joint multipath -Doppler concept and time-signaling technique applied for the RAKE reception. Section IV discusses the proposed system performances inmultiuser scenario. This work is based on the publications of professor Akbar M.Sayeed [3], [4], [5], [6] andsome other similar published ideas [7], [8].According to those preceding works, a model of mobile wireless

channel-linear time-varying system was built with the joint multipath-Doppler diversity concept to

enhance the performance of the RAKE receiver. In [3],a time-selective signaling system for single usercase was discussed . My try is to confirm the extension of the system for the multiuser scenario. Toevaluate the system, the comparison with other schemes dealing the same problem but using different techniqueswould be interesting and will be a part of my future research.



(Because the length of this paper is limited, it only develops the main concepts, more details can be found in

indicated references).

II. PRELIMIARIES

A. Diversity techniques.Diversity techniques are employed in practice to combat the effects of fading. The basic idea is to transmit

the signal over multiple independent fading channels, while keeping the total power constant by transmitting ata lower power in each channel. Common diversity techniques include antenna diversity, time diversity,frequency diversity, and polarization diversity [9].

B. Conventional RAKE receiver.In CDMA transmission system, the signal bandwidth is significantly spread, i.e. the chip-rate of the

pseudorandom codes is so big that the transmitted signal gets to the receiver in many paths with different delays,phase-shifts and attenuations. This phenomenon can be used positively by employing a special time-set receiver– the RAKE receiver, which has the time-delay line to correlate those signal paths individually beforecombining (by Maximum Ratio Combining - MRC method) to detect the transmitted information [10].

C. Channel representation The determination of optimal modulation and demodulation techniques critically depends on accurate

channel characterization. A mobile wireless channel can be generally described as a time-varying linear system:

Fig. 1 Mobile wireless channel: linear time-varying system

As illustrated in Fig.1, the signal r(t) at the receiver is given by

where x(t) is the transmitted signal, h(t,τ ) is time-varying channel impulse response[9] and n(t) is zero-mean,complex, circular AWGN with power spectral density N o.An equivalent representation of the channel, in terms of the spreading function defined as:

with the corresponding representation of s(t) given by

The spreading function H( θ ,τ ) quantifies the time-frequency spreading produced by the channel - θ correspondsto the Doppler shifts introduced by the channel (temporal variation) andτ corresponds to the multipath delays.

The second-order statistics characterizing the channel are:

whereδ (.) denotes the Dirac delta function. The (essential) support of Ψ(θ ,τ ) over τ is called themultipath spread of the channel, denoted byTm. Similarly,the Doppler spread is the (one-sided) θ -support of Ψ(θ ,τ ), denoted by Bd . So, s(t) can be expressed as :

∫∞

+−=+=0

)()(),()()()( t nd t xt ht nt st r τ τ τ

h t τx(t) s(t)

n(t)

r(t)

dt et h H t jdef

∫−= πθ

τ τ θ 2),(),(

∫∫ −= τ θ τ τ θ πθ d d et x H t s t j2)(),()(

}|),({|),(

)()(),()},(),({

2

21211122*

11

τ θ τ θ

τ τ δ θ θ δ τ θ τ θ τ θ

H E

H H E

def

=Ψ

−−Ψ=

(1)

(2)

(3)

(4)

(5)



III. JOINT MULTIPATH-DOPPLER AND TIME-SELECTIVE SIGNALING

A. Joint Multipath-Doppler.As evident from (6), the received signal consists of a linear combination of time-shifted and frequency-shifted(Doppler) copies of the transmitted signal, and its finite-dimensional representation is:

where N =[Tm/T c] ≈ [TmB] (T c is chip interval of spreading codes, B is signal bandwidth), K =[ BdT ] (T issymbol duration) andĤ ( θ ,τ ) is a smoothed version of H( θ ,τ ).

The basis waveforms xk,n(t)’s are defined as (for a single transmitted symbol):

and are approximately orthogonal to each other< xk,n , xk’,n’ >≈ T δ k-k’ δ n-n’ =0 (10)where < ⋅, ⋅>denotes the inner product and δ k denotes the Kronecker delta function [4]. q(t) is the signalingwaveform..

Fig. 2. Sampling of the time-frequency plane to create multipath-Doppler diversity channels.

By virtue of the orthogonality of the xk,n(t)’s , and the statistical independence of the channel coefficientsĤ ( θ ,τ ), the representation (7) effectively decomposes the channel into ( N +1) × (2 K +1) independent, flat-fading(diversity) channels by appropriately sampling the multipath-Doppler plane.

Note that the number of diversity channels is proportional to the product TmBd (T/T c). Thus, for fixed channelparametersTm and Bd , the level of diversity is proportional to the time-bandwidth product (TBP), TB≈(T/T c), of the signaling waveform. This also illustrates the remarkable ability of CDMA systems with spread-spectrumsignals to exploit channel diversity.Base on the concept described above, the detector structure (time-frequency (TF) RAKE receiver) for jointmultipath-Doppler diversity is developed in [4], which consists of a bank of conventional RAKE receiversshifted in time and frequency to take samples. Analytical and simulated results show that even the relativelysmall Doppler spreads encountered in practice can be leveraged in to substantial gains that significantlyimprove the performances of the proposed system, specially in fast-fading environments [4].

τ θ τ τ θ πθτ d d et x H t s j

Tm Bd

Bd

2

0

)(),()( −= ∫ ∫−

∑ ∑= −=

≈ N

n

K

K k

nk cc t xnT

T

k H

T

T t s

0,

^

)(),()(

∫ ∫−

−− −−=Tm Bd

Bd

c

T j

c

d d T cT ce H T

T H

0

)'(^

'')/)'((sin))'((sin)','(),( τ θ τ τ θ θ τ θ τ θ θ θ π

)/2(, )()( T kt j

c

def

nk enT t qt x π −=

Tc

1/T

τ

N

MULTIPATH

-K

K

D OP P L E R

(7)

(8)

(9)



B. Time-selective signaling A direct way to attaint lager values of TBP (so the system can yield more diversity gains) is increasingT . Inorder to keep data rate at a prescribed value ( R=1/T ), this can be done by increasing spreading symbolwaveform duration (T s) (typically longer than prescribed intersymbol durationT ) and there by introducingoverlap between symbols. The received signal can be rewritten:

Fig.3. Time-selective signaling

As shown in Fig.3, each of the symbols is spread in frequency to bandwidth B≈1/T c to exploit multipathdiversity by making the channel frequency-selective, and in time to a durationT s to exploit Doppler diversity bymaking the channel time-selective. The reception technique is discussed in [3]. According to (11), for maximalexploitation of channel diversity, the T s should be increased as much as possible. In practice, the amount of achievable diversity is limited by intersymbol interference (ISI) introduced by symbol overlapping and by themore important reason – limited delays of T s introduced at the receiver due to the computational complexitydiscussed later.

IV. MULTIUSER DETECTOR

A. Signal model and receiver structure.As we know, the CDMA system has an advantage of bigger capacity (number of users) over the precedingsystems (Time Division Multiple Access -TDMA or Frequency Division Multiple Access FDMA), by virtue of multiuser exploitation, but in turn, it suffers from interferences of different users (i.e. near-far effect)[10]. In thissection, the time-frequency RAKE receiver with time-selective signaling is analyzed in multiuser scenario. Withthe proposed suboptimal linear detectors that are computational tractable, it is showed that the system can keepthe multiuser effect, while attain Doppler diversity gains as well.According to the discussions in [3], [5] the optimal receiver structure theoretically can be achieved, but due tothe exponential computational complexity in the number of users and number of symbols that overlap,suboptimal linear approaches are more realizable in practice. To develop suboptimal receivers, the signals arerepresented conveniently in matrix notation as described below.Consider the case with L user, signal at the input of the receiver can be written:

∑ ∑= −=

+=+= L

l

I

I i

i

l

i

l t nt sbt nt st r 1

)()()()()(

bil is the ith symbol of the l user, sl

i (t) is the unmodulated received baseband signal for the ith symbol of the l thuser, I is the size of the detection window and is determined by number of symbols that overlap, n(t) is theAWGN.In terms of the representation (11), the signal sl

i (t) can be expressed:

)()(),()(0

,

^

t nt xnT T

k H

T

T t r

N

n

K

K k

nk c

s s

c +≈ ∑ ∑= −=

)/2(, )()( sT kt j

nk enTct qt xπ −=

T

Ts

Tc

b1

b2

b3

(11)

(12)

(13)



∑ ∑= −=

−−≈ N

n

K

K k

T

kn j

cl

ikn

l

s

ci

l senT iT t q H

T

T t s

0

2

)()(

π

where ql (t) is the spreading waveform of the l th user and H l ikn are the channel coefficients corresponding to the

ith symbol of thel th user.Let:

sT

kt j

cl

def ikn

l enT iT t qt q

π 2

)()( −−=

and letq(t) denote the L(2I+1)(2K+1)( N+1)x1 vector

T T

L

T T def

t Qt Qt Qt Q )]()...(),([)( 21= 1

where the (2 I +1)(2 K +1)( N +1)x1 vectors Ql (t) are given by

T T I

l

T

l

T I

l

T I

l

def

l t Qt Qt Qt Qt Q )](),...()...(),([)( 01+−−=

l =1,2,… L.in terms of the (2 K +1)( N +1)x1 vectors:

T T K i

l

T K i

l

T K i

l

def i

l t Qt Qt Qt Q )]()...(),([)( )()1()( +−−=

i=- I ,- I +1,…0,… I -1, I .In terms of the ( N +1)x1 vectors

T N ik

l

ik

l

ik

l

def ik

l t qt qt qt Q )]()...(),([)( )()1()0(=

n =1… N .Similarly, as with Ql (t) ,Ql

i(t) and Ql ik (t) , define the (2 I +1)(2 K +1)( N +1)x1 vectors H l in terms of the

(2 K +1)( N +1)x1 vectors H l i in terms of the ( N +1)x1 vectors H l

ik which are in turn defined in terms of H l kn.

Finally, define the L(2 I +1)(2 K +1)( N +1)x L channel matrix for the symbol as

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

L

def

H

H

H

H

0...0

...00

0...0

2

1

MOMM

and the L(2 I +1)x1 vector B:

T T

L

T T def

B B B B ],...,[ 21=

T I

l

I

l

I

l

def

l bbb B ],...,[ 1+−−=

so, r(t) can be expressed as:

)()()( t n HBt Qt r T +≈

Thus, the received signal is linear combination of the time-frequency-shifted signal ql ikn(t).

Base on that notation, the L(2 I +1)(2 K +1)( N +1) vector Z of sufficient statistics is given by:

N RHB Z += where

1 The [] T forms are indicated for matrix conversion, ‘ T‘ here is not a symbol duration.

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)



∫

∫

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

==

dt t Qt Q R

R R R

R R R

R R R

dt t Qt Q R

T

l l

def

ll

LL L L

L

L

T def

)()(

...

...

...

)()(

'*

'

21

22221

11211

*

MMMM

and ∫= dt t nt Q N def

)()(*(27) is a L(2 I +1)(2 K +1)( N +1)x1 zero-mean complex Gassian noise vector with

E [ NN H ]= N o R. (28)Recall that the l th component of Z =[ Z 1 ,Z 2….Z L]

T consists of the TF (time-frequency) correlator outputs for thel th user:

∫ ∫−−== dt enTct qt r dt t qt r z sT kt ì

l

ikn

l

ikn

l

/** )()()()( π (29)

In fact, the front-end TF correlators are a generalization of the RAKE receiver and can be efficientlyimplemented via a bank of RAKE receivers [4]. This is the reason for referring to the proposed receiverstructures for joint multipath-Doppler processing as TF RAKE receivers.

The structure of the suboptimal receivers is motivated by the optimal MRC detector. The basic idea is to obtainan estimate of the noise-free correlator outputs, H l bl and then to coherently combine them as in (11) to obtain thebit estimated for each user. Let

∫ == = HBdt t Qt r Y t st r )()(* |)()( (30)

The nature of the estimate of Y determines the structure of the receivers. Generically, the estimate of Y takesthe form: Ŷ =FZ=FRHB +FN (31)

The matrix F is chosen to yield a near-far resistant estimate of Y [5]. Since the noise in the estimate Ŷ iscorrelated (the FN part), a prewhitening operation is needed. The general form of the overall multiuser TF-RAKE receiver becomes:â=sign{Re[ H H DŶ ]} =sign{Re[ H H DFZ ]} (32)Where the block-diagonal matrix D performs the prewhitening and the matrix H H performs MRC.

The discussions of F and D matrix coefficient counting (for Maximum Likelihood Estimation-DecorrelatingReceiver and Minimum-Mean-Squared Error Receiver cases) is similar to those provided in [5].Fig.4 shows the receiver structure:

Fig.4. Multiuser TF RAKE receiver

B. Simulation result

As it is analyzed above, by finding the sub-optimal solutions for multiuser case while taking advantage of Doppler-diversity, the proposed multiuser receiver offers better performances in comparison with theconventional RAKE receiver, especially in fast-fading environments. A simulation result of four-user system ina practical condition is shown in Fig.5.This uses time-selective signaling system employing time frequency

Z1

Z2

ZL

H1

H2

HL

â1

â2

âL

r(t) MultiuserSeparation

(F)

Prewhitener(D )

Prewhitener(D2)

Prewhitener

(D )

MRC T-F MatchedFilter 1

T-F MatchedFilter 2

T-F Matched

Filter L

MRC

MRC

sign(Re(*))

sign(Re(*))

sign(Re(*))

(25)

(26)



RAKE receiver with overlapping codes of length L=511,with a new symbol transmitted every 31chips. The Jakes fading channel model with a carrier frequency of 1.8 GHz and mobile speed of 90 km/h is used to simulatethe channel at a data rate of 10 kHz. Single-user system performance (of multipath (conventional) RAKEreceiver and proposed multipath-Doppler) has also been shown for reference. As evident, Doppler diversitygains are attained in the multiuser system as well.

Fig.5. BER versus SNR per symbol for user 1 in a proposed four-user system (dash lines)

Of course, by employing the frequency diversity stage, the proposed receiver structure is more complex, and itsdetection counting process requests more and faster calculuses to guarantee the transmission speed. But due tothe microprocessor complexity, speed and power characteristics vs. time analyzed in [11], the computationalcomplexity of the system (is linearly proportional to the number of users and the number of symbols thatoverlap) is tractable and reasonable for the next generation CDMA system. Moreover, for most practicalscenarios, ISI is virtually negligible due to the excellent correlation properties of pseudorandom codes, so the

one-shot detector structure can be employed at the receiver to reduce the symbol detection window size [3].V. CONCLUSIONS

In this paper, the joint multipath-Doppler diversity and time-selective signaling concepts are provided todevelop the new proposed reception structure. The performances of the system in multiuser scenario areanalyzed to show its effectiveness and applicability for future mobile networks. More thorough investigation of the system and its comparison with other effective schemes are next steps of my research. Finally, I would liketo thank professor Akbar. M. Sayeed for his guidance and support of this publication.

REFERENCES[1] M. C. Chan and T. Y . C. Woo, “Next-Generation Wireless Data Services: architecture and Experience”,

IEEE Personal Commun., Feb.1999.

[2] “IMT-2000 Developments in the Asia Pacific Region” , IEEE Commun. Mag ., Sep.1998.[3] S. Bhashyam, A. M. Sayeed, B. Aazhang, “Time-Selective Signaling and Reception for Communication overMultipath Fading Channels ” , IEEE Transactions on Commun. Vol.48, No.1, Jan.2000.[4] A. M. Sayeed, B. Aazhang, “Joint multipath-Doppler Diversity in Mobile Wireless Communications”, IEEE

Transactions on Commun. Vol.47, No.1, Jan.1999.[5] A. M. Sayeed, A. Sendonaris, B. Aazhang, “.Multiuser Detection in Fast-fading Multipath Environments”

IEEE J. on Select. Areas in Commun. Vol.16, No.9, Dec.1998.[6] http://dune.ece.wisc.edu/



[7] G. W. Wornell, “Spread-response precoding for communication over fading channels”, IEEE Trans. Inform.

Theory, Vol.42, Mar.1996.[8] P.B. Rapajic and B. S. Vucetic, “adaptive receiver structures for asynchronous CDMA systems”, IEEE J. on

Select. Areas in Commun.,vol.12,May 1994.[9] J. G. Proakis , Digital Communications, 3rded. New york: McGraw Hill, 1995.[10] K.Wesolowski “Systemy radiokomunikacji ruchomej ” 2nd ed. Warszawa 1999.[11] R. D. Carsello and fellows ,”IMT-2000 Standards: Radio Aspects”, IEEE Personal Commun.,Aug.1997

------------------------------------------------------About Author:

NGUYEN NGUYEN MINH

1993-1998 Student of Warsaw University of Technology, Electronics andInformation Techniques Department, POLAND1998 received Eng.& M.Sc. degree from Institute of Radio-electronicsRecently is working toward the Ph.D. degree at the same Institute.Research interests: Digital Radio Transmission, Modulation & Demodulationtechniques, Third Generation Communication Systems.Email: [email protected]

bo thu bao hieu lua chon theo thoi gian nhieu nguoi dung trong moi truong fading nhanh da duong

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