Robust Detection Algorithm for Future 4G Wireless ...

XIV INTERNATIONAL CONFERENCE ON MICRO/NANOTECHNOLOGIES AND ELECTRON DEVICES EDM 2013

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Robust Detection Algorithm for Future 4G Wireless Communication Systems A. G. Vostretsov 1, V. A. Bogdanovich2, Mohamed H. Essai3 state technical university, Novosibirsk, Russia, [email protected] 2 Novosibirsk state technical university, Novosibirsk, Russia, [email protected] 3 Al-Azhar University, Qena, Egypt, [email protected]

1Novosibirsk

Abstract - We consider the multiuser adaptive asymptotically robust invariant demodulation algorithm for future 4G communication systems that intended to use CDMA as multiple access technique. Considered algorithm provides multiple access interference suppression and does not require controlling of power of mobile transmitters. In addition, the algorithm provides high quality demodulation under the conditions of non-Gaussian noise. The algorithm characteristics were obtained by computer simulation for the case of BPSK modulation.

bustness principle. On the basis of the principle of invariance suppression of MAI with a priori uncertain parameters is provided. Asymptotic (the size of the observed sample) approach to the construction of algorithms due to a large base of signatures.

Index terms - 4G; multiaple access interference; CDMA; suboptimal multiuser algorithms; asynchronous transmission; adaptive asympotitacally robust invariant algorithm

A. Observed Signal

I. INTRODUCTION Various multiple access techniques have been proposed for 4G systems, such as DS-CDMA (Direct Spread-Code Division Multiple Access), MC-CDMA (Multicarrier-CDMA), OFDMA (Orthogonal FDMA), IDMA (Interleave Division Multiple Access) [9]. CDMA has a huge impact on wireless communication progress. It offers many features such as dynamic channel sharing, soft capacity, reuse factor of one, low dropout rate and large coverage (due to soft handoff), ease of cellular planning, robustness to channel impairments and immunity against interference. Multiple access interference (MAI) limits the performance of CDMA systems [1, 2, and 3]. The in use CDMA techniques mitigate the MAI by multiuser detection (MUD) techniques. Suboptimal MUD were constructed to reduce the negative influence of MAI. The known suboptimal MUD are designed for systems with AWGN. In this regard, the question about the possibility and efficiency of their use in systems with non-Gaussian noise, especially in the case of a priori unknown distribution of noise, remains an open question. In addition, these algorithms require knowledge of the noise and energy levels of signals received from each user [1]. Therefore the construction of multiuser detection techniques in condition of a priori uncertainty distribution of noise and energy parameters of noise and signals gains a great interest [4]. In our paper we suggest multiuser demodulation algorithms that are based on statistical principles of asymptotic robustness and invariance. A priori uncertainty distribution of noise is overcome by means of the use of asymptotic ro-

II. MODELS OF THE SIGNAL – INTERFERENCE ENVIRONMENT

λ     An observed sample is of the form = x θ S + η +ξ , N  complex envelope of the obwhere S is a sample of the   served user signature, η , ξ are the samples of disturbing signal and noise respectively. From now N ≥ B – the sample size, λ ∈ ( 0, ∞ ) – received signal a priori uncertain energy parameter, θ – modulation parameter, Θ – is a set of possible values of parameter θ , θ ∈ Θ . In the case of coherent reception and phase modulation (PM) signatures, which are

often implemented in CDMA systems, set    2π ( m − 1)  exp  j m 1, M  , where M - mod= Θ θ=  ,= m M     ulation multiplicity . Further for signatures of all users, in cluding a dedicated user, accepted ratio 1 N Sk = 1 ,  the quantity λ N Sk = λ < ∞ , for any sample size, where ⋅ is the L2 vector norm [4].

(

)

(

)

B. Noise Model The noise  sampling is represented by stationary random sequence ξ = (ξ1 , , ξ N ) . The components of this sequence are assumed to be statistically independent, quadrature components Re ξ n and Imξ n are assumed to be mutually independent at coinciding instants and to have similar marginal probability distribution density functions (PDFs) for any n = 1, N . In the case of an external noise, there are no serious reasons for accurately determining its probability distributions. In connection with this, the concept of a priori uncertain noise distributions is accepted. Therefore, a noise PDF can take any value from some fixed set P . The extended model of approximately finite probability distribution densities is chosen for representation of the a priori uncertainty of

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XIV INTERNATIONAL CONFERENCE ON MICRO/NANOTECHNOLOGIES AND ELECTRON DEVICES EDM 2013

noise distributions [5]. In this model, in contrast to common models of this type, a priori uncertain scale parameter σ is introduced which substantially extends the set of probability distribution densities of this model. The extended model of approximately finite PDFs is represented by the set  1  t P =  p ( t= w ) σ  σ 

   , w ∈ W , σ ∈ ( 0, ∞ )  ,  

(1)

1   = where W  w : ∫ w= ( t ) dt q, I ( w ) < ∞  is the class of -1   PDFs with zero mean and fixed probability q of the interval

[−1,1] , I ( w) is the Fisher information. Probability q serves

as a parameter of model (1). Many PDFs p ( t ) belong to the set (1) due to the possibility of their representation in the form 1 t  of p ( t ) = w   , where the density is w ( t ) = σ p (σ t ) , σ σ  and scale parameter σ is calculated according to the model (1) from the equation

1

∫ σ p (σ t ) dt = q .

 

η (= υ)

−1

C. Multible Access Interference Model CDMA systems are characterized by two modes of signal transmission: synchronous and asynchronous. Synchronous transmission characterizes transmission lines from a base station to a user, while asynchronous transmission characterizes transmission lines from a user to a base station. For the synchronous transmission, just one packet of each external of a particular user is present in chosen signal interval user. For the asynchronous transmission, two neighboring packets of each external user are generally present in the interval. In this paper we consider only the case of asynchronous transmission. In the case of the asynchronous transmission MAI has the form = η (t )

K −1

∑ υk( ) Sk ( t + T − τk ) + υk( ) Sk ( t − τk )Π ( t ) , t ∈ TS , 1

2

k =1



2( K −1)

∑

{

{

T − τ k , τ k < 0,

}

 

( )

P



η ϑ = ∑ ϑk Ek ,

(4)

k =1

where the vector parameter is  ϑk : Re ϑk ∈ ( −∞, ∞ ) , Im ϑk ∈ ( −∞, ∞ )  ϑ ∈Ξ =  1, P ∀k =

, τ k ≥ 0,

(3)

}

i

τ k τk = 



υk Sk , υk ∈ M = ∀k 1, 2 ( K − 1) ,

k =1  where Sk are the vectors formed from the values of signals Π (t ) Sk (t + T − τk ) for indices k ≤ K − 1 and the values of signals Π (t ) Sk − K +1 (t − τk − K +1 ) for indices k ≥ K . In the  case of linearly independent signatures, signal vectors Sk in representation (3) are also linearly independent. In this case, they form the basis of subspace L to which  vectors η belong. In the case of linearly independent signatures, subspace L has the dimensionality= P 2 ( K − 1) for the asynchronous transmission. In order to simplify calculations, it is reason able to use orthonormal basis Ek , k = 1, P of subspace L 1  with the norms Ek = 1 ∀k = 1, P instead of the initial N  basis Sk , k = 1, P . This basis is unambiguously calculated from the initial basis using the known Gram–Schmidt procedure. In terms of the orthonormal basis, expression (3) is transformed to the form

(2)

where = υk( ) λkθ k( ) ∈= W, i 1, 2, λk ∈ ( 0, ∞ ) , and (i ) θ k ∈ Θ are the a priori uncertain energy and modulation parameters in neighboring packets of external users; = W {υ : υ ∈ ( 0, ∞ ) , exp ( j arg υ ) ∈ Θ} . The time delays are determined as follows: i

where τ k are the actual delays of signals from external users relative to the time location of signal interval Ts . Delays τ k are assumed to be a priori known due to the presence of the corresponding information at the receiving end of the system. Π ( t ) is a synchronized with the signal packet of the considered user strobe with duration T for separating of the interval TS. The action of the MAI is equivalent to the transformation of process x ( t ) by shift operators g : x(t ) → x ( t ) + η ( t ) . If these operators form an algebraic group of transformations [6], [7], the invariance principle can be used for construction of demodulation algorithms. However, this condition is not i satisfied for parameters υk( ) ∈ W, i =1, 2 . Therefore, set W is extended to the set = M {υ : υ ∈ ( 0, ∞ ) , arg υ ∈ [ 0, 2π )} . Since W ⊂ M invariant algorithms obtained in this situation provide for supi pression of the MAI with parameters υk( ) ∈ W, i =1, 2 with certain excessive stability under the action of additive MAI. A discrete-time representation of MAI based on model (2) and in conditions of asynchronous transmission can be expressed in a vector form

 .

III. ADAPTIVE ASYMPTOTICALLY ROBUST INVARIANT ALGORITHMS According to the accepted models of signal, MAI and

XIV INTERNATIONAL CONFERENCE ON MICRO/NANOTECHNOLOGIES AND ELECTRON DEVICES EDM 2013

noise, distributions of an observed sample belong to the family

(

)

 u x λ , θ , σ , ϑ , w , λ ∈ ( 0, ∞ ) , θ ∈ Θ,   N  UN =  ,  σ ∈ ( 0, ∞ ) , ϑ ∈ Ξ, w ∈ W 

(5)

where     λ    u N x λ ,θ , σ ,ϑ , w = pN  x − S (θ ) − η ϑ σ , w N  

(

)

( )

is the PDF of the observed sample in the presence of useful, N 1  Re xn   Im xn   and MAI signals, pN ( x σ , w ) = ∏ 2 w  w    σ   σ  n =1 σ is the distribution density of a noise sample. The aforementioned family of distributions (5) is symmetric [8], [5], with respect to the group of scale and shift transformations:      P  g : x → µ0 x + ∑ µk Ek , µ0 ∈ ( 0, ∞ ) , µk ∈ ( 0, ∞ ) ,  G= k =1 ;   1, P arg µk ∈ [ 0, 2π ) , k =     g * : λ ,σ ,ϑ → µ0 λ , µ0σ , µ0ϑ + µ G =  µ = ( µ1 , , µ P )

(

*

) (

) , ,

73

The method for constructing asymptotically robust invariant demodulation algorithms is given in [4, 7]. According to m  this method, decision functions ϕ N( ) ( x ) are expressed in terms of the group- G -invariant statistic      z ( x= (6) ) [ x − PrL x ] σ� N ( x ) ,  1 P    where PrL x = ∑ x , Ek Ek is the orthogonal projection   N k =1 of sampling x on subspace L , σ N ( x ) is the equivariant N – consistent estimate of scale parameter σ (esti   mate σ N ( x ) is equivariant if σ= g *σ N ( x ) ∀g ∈ G , N ( gx ) and

where g * ∈ G* is the transformation of group G* , induced

by transformation g , and N – consistent if random quan tity N σ N ( x ) − σ has in particular a finite variance for all N ), ⋅, ⋅ is the scalar product of vectors. Scale parameter estimation may be obtained by 

σ N (= x)

    1 ˆ δ  Re ( x − PrL x )  + δˆ  Im ( x − PrL x )  , 2 

{

}

  1 where δ N ( t ) = ε ( v ) ( t ) is the quantile scale estimate, u   a ε ( v ) ( t ) is v -th order statistics of vector= t ( t1 , …, t N ) ,

= v a N  + 1 , ⋅ is the integer part of a number, ua is the quantile of order a , and quantile ua = 1 for a = q . Note that statistic (6) is the maximal invariant of group G [5]. where G is the group of transformations of a sample space, Therefore, according to the general invariance theory, any and G∗ is the group of transformations induced in the para- group G invariant algorithm can be expressed in terms of metric space by group G . In accordance with the principle this statistic. of invariance and symmetry of the family (5) with respect to Using the method of synthesis of ARI algorithms develgroups G and G∗ the class of invariant with respect to group oped in [7], it can be established that, in the case of coherent     G algorithms satisfying the identity ϕ ( gx ) ≡ ϕ ( x ) ∀g ∈ G reception and M-fold phase modulation, the decision funcis separated. The main idea of these algorithms  is suppres- tions of ARI algorithm can be written as sion of MAI (4) with an arbitrary parameter ϑ ∈ Ξ .   According to the principle of asymptotic robust1, if max Re θ k S , Ψ N  z ( x )  =   ness the optimal algorithm based on minimax criterion k =1, M    is found in the class of invariant algorithms, which pro   Re θ m S , Ψ N  z ( x )  , vides for minimum maximal (on set W ) asymptotic (m)  ϕN ( x ) =      probability of erroneous demodulation. Thus construct(7) 0, if max Re θ k S , Ψ N  z ( x )  ≠  ed algorithms are called asymptotically robust invari= 1, k M   ant (ARI) algorithms. These algorithms are represented   Re θ S, Ψ m N     z ( x )  ,  by infinite sequences = φ {= ϕ N ( x ) , N 1, 2,} , where   m = 1, M , (1)  (M )  ϕ N ( x ) = ϕ N ( x ) , , ϕ N ( x ) is a vector function, com k − 1    m = where θ k exp = ponents ϕ N( ) ( x ) define the solution probabilities in favor  j 2π  , k 1, M , and S is the vector M   of the corresponding mth signal of the constellation, when  ( m)  observing the sample x . Components ϕ N ( x ) are called obtained from the signature of the user for which the dedecision functions of the algorithm. Due to the fact that the accepted decisions form a com- modulation algorithm is designated. In the decision function (7), function plete group of events, the decision functions satisfy the iden    M  m Ψ z = ψ z , … , ψ z has complex components N ( ) { 1( ) N ( )} tity ∑ ϕ N( ) ( x ) ≡ 1 .  m =1 ψn (z) = ψ w0 ( Re zn ) + jψ w0 ( Im zn ) , n = 1, N , j = −1 ,

(

)

 

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XIV INTERNATIONAL CONFERENCE ON MICRO/NANOTECHNOLOGIES AND ELECTRON DEVICES EDM 2013

where zn are the components of vector

 z = ( z1 , , z N )

,

1 0.9

ψ w0 ( ⋅) is the logarithmic derivative of density w0 with

0.7

qopt

minimal Fisher information I ( w0 ) in class W of family (5). For the model (1) the density and logarithmic derivative have the following forms respectively:

0.8

0.6 0.5 0.4 0.3 0.2 0.1 1.2

C  2  cos 2 A 2 cos ( At 2 ) , t ≤ 1; ( ) w0 ( t ) =  , C exp  − B t − 1  , t > 1, )  ( 

ψ w0

1

B, ∫ w0 ( t ) dt , A ⋅ tg ( A 2 ) =

−1

= C cos 2 ( A 2 ) 1 + ( 2 B )  . Upper boundaries of a probability of erroneous demodulation of the algorithm (7) depends on parameter q of model (1) monotonically through the value V (q ) = I (q ) / σ (q ) , where I ( q ) is known minimal Fisher’s information in the class W [6]. Therefore the function V (q ) may be used for parametric optimization of the algorithm by maximizing of V ( q) . The dependence of optimal value qopt on parameter a of generalized Gaussian distribution (GGD) which is used as a noise distribution, is shown in the Fig. 1. GGD has the form

a 2 Γ(1/ a )Γ(3 / a )Γ(1/ a )

a     t  × exp −      Γ(1/ a )Γ(3 / a )  

× ,

(8)

where Γ(⋅) is the gamma function, a is the variable parameter which characterizes the distribution waveform. Assuming a consistent estimate zˆ ( q ) = I ( q ) σˆ ( q )

1.8

2

a

2.2

2.4

2.6

2.8

3

of the quantity V (q ) as an objective, we could adapt the algorithm to the actual noise distribution. An estimate of an optimal value qˆopt of the parameter q can be calculated as  qˆopt (vn ) = arg max zˆ ( q ) end substituted into decision function (7), and the qalgorithm becomes adaptive asymptotically robust invariant (AARI) algorithm.

where constants A , B and C depend on q and are determined from the equations

= p (t , a )

1.6

Fig. 1. Dependence of optimal q value on the variable parameter α of GGD. .

, t ∈ ( −∞, −1) ; − B  ( t )=  A ⋅ tg ( At 2 ) , t ∈ [ −1,1] ;  , t ∈ (1, ∞ ) , B

q=

1.4

(9)

III. CHARCHTERSTICS OF ALGORITHM In our simulation we used GGD as a noise distribution. To evaluate the effectiveness of AARI-algorithm it was evaluated by using computer simulation in comparison with Decorrelator algorithm. The probability of demodulation error per 1 bit (BER - Bit Error Rate) was estimated at different numbers of active users in the system (multiple access interference), general Gaussian noise distribution indicated by a = 2, 1, and 0.6 , and MAI/Signal ratios Λ p = 10 . Simulations were performed by computer simulation of the AARI-algorithm, in the case of BPSK modulation, and M-sequence signatures of length 127 were used. Figure 2 shows, that at MAI/Signal ratio, Λ p = 10 , and 5 active users the performance of AARI and DEC algorithms at a = 2 approximately identical. While at a = 1, and 0.6 DEC- algorithm performance degrades compared with AARI-algorithm. For example when the BER is equal to 0.1, AARI-algorithm outperforms the DEC-algorithm in the signal/noise ratio by more than 4 dB at MAI represented by five active users. Figure 3 shows, that at MAI/Signal ratio Λ p = 10 , and 17 active users the proposed AARI-algorithm has a good performance and outperforms the DEC-algorithm at a = 2, 1, and 0.6 . Clearly Figure 3, depicts the superiority of AARI-algorithm over DEC- algorithm at the additive white Gaussian noise in the case of 17 active users. The most important notice is that our proposed AARIalgorithm, adapts successfully at various noise distributions a = 2, 1, and 0.6 . This adaptation is realized by finding the estimate of the optimal value of q parameter of the least favorable noise distribution.

XIV INTERNATIONAL CONFERENCE ON MICRO/NANOTECHNOLOGIES AND ELECTRON DEVICES EDM 2013

BER

1

DEC- alpha = 2 AARI- alpha = 2 DEC- alpha = 1 AARI- alpha = 1 DEC- alpha = 0.6 AARI- alpha = 0.6

0.1

0.01 −5

− 4.3

− 3.6

− 2.9

− 2.2

− 1.5

− 0.8

− 0.1

0.6

1.3

2

SNR, dB

Fig. 2. BER performance versus SNR comparison for AARI and Decorrelator algorithms in condition of generalized Gaussian noise distribution when (α = 2, 1, and 0.6), number of active users=5, Λp = 10, and asynchronous reception. 1

BER

DEC- alpha = 2 AARI- alpha = 2 DEC- alpha = 1 AARI- alpha = 1 DEC- alpha = 0.6 AARI- alpha = 0.6

0.1 −5

− 4.3

− 3.6

− 2.9

− 2.2

− 1.5

− 0.8

− 0.1

0.6

1.3

2

SNR, dB

Fig. 3. BER performance versus SNR comparison for AARI and Decorrelator algorithms in condition of generalized Gaussian noise distribution when (α = 2, 1, and 0.6), number of active users=17, Λp = 10, and asynchronous reception.

REFERENCES [1] J. G. Proakis, Digital communications (McGraw-Hill, New York, 1989; Radio and Communication’, Moscow, 2000). [2] Ramjee Prasad and Tero O Janepera, “A Survey on CDMA: A Evolution towards Wideband CDMA” in proc. of IEEE, 1998. [3] A. Shukla, D. Purwar, D. Kumar, “Multiple Access Scheme for Future (4G) Communication: A Comparison Survey” , International Journal of Computer Applications® (IJCA), 2011. [4] Bogdanovich V.A.  CDMA Robust Demodulation Algorithm in The Presence of Multiple Access Interference  / V.A. Bogdanovich, A.G. Vostretsov, M. H. Essai // Proceedings. The 5th International Forum on Strategic Technology. Oct. 13-15, 2010. IEEE Catalog Number: CPF10786-PRT. ISBN 978-1-4244-9035-6.Ulsan, Korea. Ulsan, 2010. - P. 100 – 104. [5] V. A. Bogdanovich and A. G. Vostretsov, Theory of stable detection, distinguishing and estimation of signals (Fizmatlit, Moscow, 2004) [in Russian]. [6] E. L. Lehmann, Testing statistical hypotheses (Wiley, New York, 1959; Nauka, Moscow, 1979). [7] P. J. Huber, Robust Statistics (Wiley, New York, 1981). [8] V. A. Bogdanovich and A. G. Vostretsov. “Application of the Invariance and Robustness Principles in the Development of Demodulation Algorithms for Wideband Communications Systems,” Journal of Communications Technology and Electronics, vol. 54, no. 11, pp. 1283–1291, Nov. 2009, © Pleiades Publishing, Inc., 2009. original Russian text ©V.A. Bogdanovich, A.G. Vostretsov, 2009, published in Radiotekhnika i Elektronika, vol. 54, no. 11, pp. 1353–1362, Nov. 2009.

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