ARandomAccessAlgorithmforLTEsystems

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1 EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS Eur. Trans. Teecomms. 1; :1 1 RESEARCH ARTICLE ARandomAccessAgorithmforLTEsystems L. Sanguinetti, M. Morei and L. Marchetti University of Pisa, Department of Information Engineering,ViaCaruso16,5616Pisa,Itay. ABSTRACT The random access RA) procedure is a contention-based synchronization process specified by Long-Term Evoution LTE) standards by which upin signas can arrive at the base stationsynchronousyandwithapproximateythesame power. In this wor, a nove RA agorithm for initia synchronization in LTE systems is derived on the basis of a generaized ieihood ratio test.in contrast toexisting aternatives, our approach provides better resuts by propery taing into account the frequency seectivity of the channe. This is achieved at thepriceofanincreaseofthesystemcompexity.computer simuations are empoyed to assess the effectiveness of the proposed soution and to mae comparisons with existing aternatives. Copyright c 1 John Wiey & Sons, Ltd. Correspondence Journas Production Department, John Wiey & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 SQ, UK. 1. INTRODUCTION Long-term evoution LTE) has been introduced by the Third-Generation Partnership Project 3GPP) in order to face the ever-increasing demand for pacet-based mobie broadband communications. This emerging technoogy empoys orthogona frequency-division mutipe-access OFDMA) for downin transmission and singe-carrier frequency-division mutipe-access SC-FDMA) in the upin [1]. To maintain orthogonaity among subcarriers of different users, the 3GPP-LTE specifies a networ entry procedure caed random access RA) by which upin signas can arrive at the enodeb aigned in time and with approximatey the same power eve [], [3]. In its basic form, the RA function is a contention-based procedure, which essentiay deveops through the same steps specified by the Initia Ranging IR) process of the IEEE.16 wireess metropoitan area networ [4]. Specificay, each user equipment UE) trying to enter the networ computes frequency and timing estimates on the basis of a suitaby designed downin contro channe. The estimated parameters are next used in the subsequent upin phase, during which the UE seects atime-sotandtransmitsarandomychosencodeover the Physica Random Access Channe PRACH), which is composed by a specified set of adjacent subcarriers. The codes are obtained by appying different cycic shifts to a Zadoff-Chu ZC) sequence so as to ensure their mutua orthogonaity [5]. As a consequence of the different terminas positions within the ce, upin signas are subject to users specific propagation deays and arrive at the enodeb at different time instants. After identifying which codes are actuay present in the PRACH active codes), the enodeb must extract the corresponding timing and power information. Then, it wi broadcast a response message indicating the detected codes and giving instructions for timing and power adjustment. From the above discussion, it foows that code identification as we as mutiuser timing and power estimation are the main tass of the enodeb during the RA process. These probems have received great attention in the ast few years and some soutions are currenty avaiabe [6] [14]. The methods iustrated in [6] and[7] performcodedetectionandtimingrecovery by correating the received sampes with time-shifted versions of a training sequence. The code is detected if the correation pea exceeds a specified threshod, with the pea position providing the timing information. Since these schemes operate in the time-domain, they are not suited for muticarrier systems, wherein users codes are transmitted over a subset of the avaiabe subcarriers. In such a case, the frequency-domain correation approach outperforms its time-domain counterpart as it can easiy extract the PRACH from data-bearing subcarriers []. A simpe energy detector is empoyed in [9] toreveathe presence of a networ entry request. However, since this approach requires that the user s codes are rea-vaued, it cannot be appied to the ZC sequences empoyed in the LTE. A timing recovery scheme devised for the LTE upin is discussed in [1]. Here, the PRACH is firsty Copyright c 1 John Wiey & Sons, Ltd. 1 Prepared using ettauth.cs [Version: 1/6/1 v.]

2 extracted from the upin mutiuser signa by means of adiscretefouriertransformdft)operation.then,the corresponding frequency-domain sampes are mutipied by the root ZC sequence and converted in the time-domain using an inverse DFT IDFT) device. The code detection process searches for the pea of the resuting timing metric within an observation window that is univocay specified by the cycic shift associated to the tested code. If the pea exceeds a suitaby designed threshod, the code is decared to be active and the corresponding timing estimate is obtained as the difference between the pea ocation and the beginning of the observation window. This method is expected to wor propery as ong as the received codes maintain their orthogonaity after passing thorugh the propagation channe. In the presence of mutipath distortions, however, the PRACH subcarriers may experience different attenuations and phase shifts, thereby eading to a oss of code orthogonaity. This gives rise to mutipe-access interference MAI), which may severey degrade the code detection capabiity. Possibe approaches to mitigate the MAI are proposed in [11]-[14]. More precisey, in [11] the users codes are divided into severa groups which are mapped over excusive sets of subcarrier in order to mae them perfecty separabe in the frequency domain. In the signa design iustrated in [1], the codes are transmitted in the time direction over a specified number of OFDMA bocs. This way, the code orthogonaity is maintained as ong as the channe response eeps constant over the entire transmission sot. However, using a reativey arge number of OFDMA bocs increases the sensitivity to residua carrier frequency offsets CFOs), which may compromise the orthogonaity of the received codes. Ranging schemes that are robust to frequency errors are presented in [13] and [14], where users CFOs are estimated by resorting to subspace-based methods. In spite of their resiience to MAI, the schemes discussed in [11]-[14] are based on signa designs that cannot be supported by the PRACH structure and, accordingy, they are not suited for LTE systems. In the present wor, we derive a nove RA method which is specificay taiored for LTE appications with singe or mutipe receive antennas and maes use of the generaized ieihood ratio test GLRT) to decide whether a given code is present or not in the PRACH. In formuating our testing probem, the PRACH is divided into subbands referred to as ties, eachcomposedbya certain number of adjacent subcarriers over which the channe is assumed to be constant. The timing error and the channe frequency response of the hypothesized codes are assumed to be unnown and are jointy estimated using the maximum-ieihood ML) criterion. The power eve of the detected codes is eventuay retrieved from the estimated channe frequency response. Compared to [1], our approach provides the system with improved resiience against mutipath distortions. However, this advantage is achieved at the price of an increase of the system compexity. The rest of the paper is organized as foows. Section iustratesthesystemunderinvestigationandintroduces the signa mode. In Section 3 we formuate the detection probem, whie the proposed RA scheme is derived in Section 4. Simuation resuts are presented in Section 5 and some concusions are drawn in Section 6.. SYSTEM DESCRIPTION AND SIGNAL MODEL Our system is compiant with the LTE-3GPP standard for wireess data communications. We denote by B the avaiabe bandwidth and assume that K UEs are simutaneousy trying to enter the networ. As mentioned previousy, each UE notifies its entry request by transmitting a randomy chosen code over the PRACH. According to the standard, a set C of 64 different RA codes are avaiabe in each ce. These codes are generated by cycicay shifting one or more ZC root sequences of prime-ength N ZC =39.Specificay,denotingby ξ un) =e jπunn+1)/n ZC n =, 1,...,N ZC 1 1) the eements of the uth ZC root sequence, the νth RA code obtained from ξ un) has entries x u,νn) =ξ un + C ν)mod NZC ) ) where C ν denotes the νth cycic shift. The atter is given by C ν = νn CS,whereN CS is a system parameter reated to the ce radius the arger the radius, the greater N CS) and ν is an integer beonging to the set {, 1,...,N U 1}, withn U = N ZC/N CS and x rounding x to the smaest integer. Bearing in mind that 64 different codes must be avaiabe in C and observing that a tota of N U codes are generated from a singe ZC root sequence, it foows that two or more root sequences are necessary whenever N U < 64. Forsimpicity,inthisworweset N CS =13,whichamountstoassumingaceradiusof approximatey 1.5 m. In these circumstances we have N U =64 and, accordingy, one singe root sequence is sufficient for the generation of the 64 codes in C. For this reason, in the seque we omit the root index u. Aso, without oss of generaity, we assume that different UEs seect different codes with indices {1,,...,K}. As specified in [], the PRACH occupies a bandwidth B RA =1. MHz with subcarrier spacing f RA = The foowing notation is used throughout the paper. Matrices and vectors are denoted by bodface etters. A =diag{an); n =1,,...,N} denotes an N N diagona matrix with entries an) aong its main diagona. We use E{ }, ), ) T and ) H for expectation, compex conjugation, transposition and Hermitian transposition, respectivey. The notation represents the Eucidean norm of the encosed vector. A the provided resuts can be easiy extended to different vaues of N CS. This vaue corresponds to the smaest upin bandwidth of six resource bocs in which LTE may operate. Eur. Trans. Teecomms. 1; :1 1 c 1 John Wiey & Sons, Ltd. Prepared using ettauth.cs

3 1.5 Hz. Vector x =[x ),x 1),...,x N ZC 1)] T is transmitted over the PRACH subcarriers using an OFDM moduator, which comprises an IDFT unit of size N = B/ f RA aong with the insertion of a cycic prefix and a guard time of N CP and N GT sampes, respectivey. This produces the N B = N + N CP + N GT time-domain sampes given by b ) N + N CP 1 s ) = N + N CP N B 1 3) where b )= 1 N ZC 1 x n)e jπin/n 4) N n= with i n being the frequency index of the nth PRACH subcarrier. Sampes s ) are eventuay fed to a digita to anaog converter DAC) with impuse response gt) and signaing interva T =1/B or, equivaenty, T =1/N f RA). Thecompexenveopofthesigna transmitted by the th UE taes the form z t) = N B 1 = s )gt T ) 5) where gt) is the DAC impuse response. This signa propagates through a mutipath channe and arrives at the enodeb, which is assumed to be equipped with R antennas. At each antenna, the received signa is down-converted to baseband and samped at a rate 1/T. The resuting time domain sampes are next passed to an N point DFT unit to extract the PRACH. Due to the different positions occupied by the users within the ce, the upin signas are received at the enodeb with specific timing offsets. We denote by θ the timing error of the th UE expressed in samping intervas. As mentioned previousy, each UE performs its upin transmission by using the frequency estimates obtained during the downin phase. Accordingy, the received signas are aso affected by the CFOs induced by downin estimation errors and/or Dopper effects. The presence of uncompensated CFOs destroys orthogonaity among PRACH subcarriers and gives rise to interchanne interference. In this wor, we assume that downin estimation errors are within a few percents of the subcarrier spacing and consider ow mobiity appications characterized by negigibe Dopper shifts so as to reasonaby negect any residua CFO. Moreover, we assume that users other than those performing RA have been successfuy synchronized to the enodeb so that they do not generate significant interference over the PRACH [1]. In these hypotheses, the DFT output over the i nth subcarrier at the rth antenna can be approximated as foows Z r) i n)= K =1 x n)h r) in)e jπinθ /N + w r) i n) 6) where H r) in) is the th channe frequency response over the i nth subcarrier at the rth antenna, whie w r) i n) accounts for bacground noise and is modeed as a circuary-symmetric compex Gaussian random variabe with zero mean and variance σw. 3. PROBLEM FORMULATION The enodeb expoits the quantities {Z r) i n)} to detect the active codes and for extracting the associated timing and power information. Since it has no nowedge as to which codes are actuay present in the PRACH, the summation in 6)mustbeextendedovertheentirecode set C, withtheassumptionthath r) in) =if the th code is not active. Then, we have Z r) i n)= x n)h r) in)e jπinθ /N +w r) i n). C 7) As mentioned previousy, we divide the RA subcarriers into M ties, each composed by V = N ZC/M adjacent subcarriers. We denote by i m + v the index of the vth subcarrier within the mth tie. Moreover, we assume that the channe response is neary fat over a tie and repace the quantities {H r) 1 im + v)}vv= with an average frequency response given by mθ /N S r) m) = e jπi V 1 H r) im + v). ) V v= In such a case, we may rewrite 7)as Z r) i m + v) = C x mv + v)s r) m)e jπvθ /N + + w r) i m + v) 9) whie the power that the enodeb receives from the th UE is found to be p = 1 MR R 1 M 1 r= m= S r) m). 1) To proceed further, we coect the DFT outputs corresponding to the mth tie into a singe vector Z r) m) =[Z r) i m),z r) i m +1),...,Z r) i m + V 1)] T.Then,wehave Z r) m) = C X m)aθ )S r) m)+wr) m) 11) where w r) m) =[w r) i m),w r) i m +1),..., w r) i m + V 1)] T is the noise vector, X m) is a V V diagona matrix with eements {x mv + v)} V 1 v= aong its main diagona and aθ ) is expressed by aθ )= [ 1,e jπθ /N,...,e jπv 1)θ /N ] T. 1) Eur. Trans. Teecomms. 1; :1 1 c 1 John Wiey & Sons, Ltd. 3 Prepared using ettauth.cs

4 Code detection is now accompished by resorting to asinge-userstrategythatoperatesindividuay for any x C.Moreprecisey,foreach =1,,..., C where denotes the cardinaity of the encosed set) the enodeb decides in favour of one of the foowing two hypotheses: H ) the code x is not present in the observation vector Z =[Z )T, Z 1)T,...,Z R 1)T ] T,withZ r) = [Z r)t ), Z r)t 1),...,Z r)t M 1)] T ; H 1) x is present in Z. Indoingso,thecontributionoftheactive codes x with indices is treated as a disturbance term which inevitaby degrades the system performance. Athough suboptima, this approach has the advantage of aowing a simpe formuation of the detection probem as acompositebinaryhypothesistest: H : Y r) m) =n r) m) 13) H 1 : Y r) m) =aθ )S r) m)+n r) m) 14) where n r) m) accounts for the contribution of MAI pus therma noise, whie Y r) m) is defined as Y r) m) =X H m)z r) m). 15) In a subsequent derivations, the entries of n r) m) are modeed as statisticay independent Gaussian random variabes with zero mean and unnown power σ. Y r) Vector =[Y r)t Y =[Y )T ), Y r)t, Y 1)T,...,Y R 1)T ] T, with 1),...,Y r)t M 1)] T, is eventuay expoited to mae a decision between the two hypotheses H and H 1. From 13) and 14), it is seen that this tas is compicated by the presence of the unnown parameters S,θ,σ ), where S =[S )T, S 1)T,...,S R 1)T ] T and S r) =[S r) ),S r) 1),...,S r) M 1)] T. To overcome this probem, the GLRT criterion is appied in the seque. 4. RA ALGORITHM BASED ON THE GLRT CRITERION Let pdf Hi be the probabiity density function pdf) of Y under the hypothesis H i for i =, 1. Then,from13) and 14), we have pdf H Y ; σ ) = and 1 πσ ) MV Re 1 pdf H1 Y ; S,θ,σ ) 1 = πσ ) R 1 σ r= MV R M 1 Y r) m) m= e 1 R 1 M 1 σ Y r) m) aθ )S r) m) r= m= 16) 17) The GLRT is mathematicay formuated as pdf H1 Y ; Ŝ, ˆθ ), ˆσ H 1 pdf H Y ;ˆσ H ) H 1 H λ 1) where λ is a suitabe threshod, Ŝ, ˆθ ) is the ML estimate of S,θ ) and ˆσ H i is the ML estimate of σ conditioned on H i for i =, Code detection and timing estimation Maximizing pdf H Y ; σ ) in 16) withrespecttoσ produces ˆσ H = Y 19) from which it foows that ) ) MV R pdf H Y ;ˆσ H = πe Y. ) We now oo for the maximum of pdf H1 Y ; S, θ, σ ) where S, θ, σ ) is a tria set of S,θ,σ ).Maximizing with respect to S,whieeeping σ and θ fixed, eads to Ŝ r) m) = 1 V ah θ )Y r) m) 1) with m =, 1,...,M 1. Pugging this resut into pdf H1 Y ; S, θ, σ ) and maximizing with respect to θ yieds ˆθ =arg max Λ θ ) ) θ θ max where θ max is the maximum round trip deay and Λ θ ) taes the form Λ θ )= 1 R 1 M 1 r= m= a H θ )Y r) m). 3) Finay, maximising pdf H1 Y ; Ŝ, ˆθ, σ ) with respect to σ eads to ˆσ H 1 = 1 [ ] Y MRΛ ˆθ ) 4) from which we get pdf H1 Y ; Ŝ, ˆθ ), ˆσ H 1 = ) πe Y MRΛ ˆθ ) MV R. 5) From the above resuts, the GLRT is eventuay found to be [ ] MV R Y H1 λ 6) Y MRΛ ˆθ ) H or, equivaenty, with η =[1 λ 1/MV R) ]/MR). Λ ˆθ ) H 1 η 7) Y H 4 Eur. Trans. Teecomms. 1; :1 1 c 1 John Wiey & Sons, Ltd. Prepared using ettauth.cs

5 4.. Power estimation Using the invariance property of the ML estimator, from 1) itfoowsthattheestimateofthepowerp can be obtained as or, equivaenty, ˆp = 1 MR R 1 M 1 r= m= Ŝ ˆp = Λ ˆθ ) V r) m) ) 9) having used 3) and1). It is worth noting that, if the timing offset is perfecty estimated i.e., ˆθ = θ ), then we have E {ˆp } = p + σ 3) and E {ˆσ H 1 } = MRV 1) σ 31) from which it foows that ˆp and ˆσ H 1 are biased estimates of p and σ,respectivey.fromtheaboveresuts,an unbiased estimate of p is found to be ˆp f) =ˆp which can aso be rewritten as ˆp f) = 1 V 1 ˆσ H 1 MRV 1) [Λ ˆθ ) Y 3) ]. 33) Using standard computations, it turns out that the variance of ˆp for ˆθ = θ is given by var{ˆp } = p σ 4 MV R σ + V 1). 34) Numerica resuts shown ater indicate that different vaues of M,V ) shoud be used to optimize the accuracy of the power and timing estimators. This resuts into a modified scheme in which M and V are respectivey repaced by M θ and V θ = N ZC/M θ for the evauation of the timing metric Λ θ) for θ =, 1,...,θ max. Afterobtainingthe timing estimate ˆθ, Λ ˆθ ) is recomputed from 3) after repacing M and V by M P and V P = N ZC/M P, respectivey. Finay, Λ ˆθ ) is used in 33)togetthepower estimate. In the seque, we refer to the above procedure as the GLRT-based RA scheme ) Impementation and compexity anaysis The computationa oad of is mainy invoved in the evauation of the timing metric Λ θ) for any possibe code in the set C and for θ =, 1,...,θ max.intheensuing discussion, we show how the quantities Λ θ) can be computed by expoiting the specific properties of the ZC sequences. We begin by expanding the right-hand side RHS) of 3)soastoobtain Λ θ) = 1 MV R R 1 M 1 r= m= Λ r) m, θ) 35) where we have used 1)and14)andwehavedefined Λ r) m, θ) V 1 = e jπv θ/n x mv + v)z r) i m + v). v= 36) Coecting 1)and), we get x n) =ξn)e jπunc /N ZC e jφ 37) from which it foows that the quantities {x n)} are obtained by superimposing a phase shift on the root sequence {ξn)}. Substituting37)into36)yieds Λ r) where m, θ)= V 1 v= e j π N vuc N N + θ) ZC Z r) ξ mv + v) 3) Z r) ξ mv + v) =ξ mv + v)z r) i m + v). 39) Denoting by a r) m, ) = N 1 n= the N point IDFT of the sequence A r) m, n)= A r) m, n)e jπn/n 4) { Z r) ξ mv + n) n V 1 V n N 1 41) we may rewrite the RHS of 3)asfoows Λ r) m, θ) = a r) m, uc N/N ZC + θ ). 4) From the above equation it is seen that, for any Cand θ =, 1,...,θ max,thequantitiesλ r) m, θ) are obtained from a singe N point IDFT operation appied to the sequence {A r) m, n)}, therebyeadingtothescheme depicted in Fig. 1. It is worth observing that the IDFT operation in Fig. 1 requires approximatey 5ηN og N foating-point operations fops), with η =1 og N/V )+V/N 1) og N 43) accounting for the computationa saving achievabe by sipping the operations on the zero entries of {A r) m, n)} [19]. Since the IDFT operation must be performed for any vaue of r and m, thetotaamountof fops required to evauate the timing metrics Λ θ) in 4) is 5MRηN og N.RecaingthatdifferentvauesofM and V are required for power and timing estimation, it Eur. Trans. Teecomms. 1; :1 1 c 1 John Wiey & Sons, Ltd. 5 Prepared using ettauth.cs

6 Figure 1. Boc diagram of. foows that the overa number of fops needed by GLRT- RA is eventuay given by 5M θ η θ + M P η P )RN og N where η θ and η P are obtained from 43) afterrepacingv with V θ and V P,respectivey. It is worth noting that a singe IDFT operation is required when M θ = M P =1 and in such a case the scheme depicted in Fig. 1 reduces to the one iustrated in [1]. This means that is equivaent to [1]under the assumption of a fat fading channe. Since in practica appications the received signa is typicay affected by mutipath distortions, the is expected to provide some potentia benefits with respect to [1]. As we sha see, such an advantage is achieved at the price of a higher compexity since the required IDFT operations invoved by increases with the tie number. 5. NUMERICAL RESULTS 5.1. System parameters The system parameters are chosen in compiance with the LTE standard []. The signa bandwidth is B = 7.6 MHz, so that the DFT size is N = B/ f RA = 6144 and the samping interva T is 13 ns. The cycic prefix and guard time have duration of.1 ms, which corresponds to N CP = N GT =76sampes. The carrier frequency is.6 GHz and the CFO of each UE is uniformy distributed in the interva [.1,.1]. Weuse aroot-raisedcosinefunctionwithro-offα =. and duration T g =6T as a moduation puse. The path gains are modeed as statisticay independent and circuary symmetric Gaussian random variabes with zero mean and power deay profie as specified in the ITU IMT- Vehic. A channe mode []. A new channe snapshot is generated at each simuation run. The channe impuse responses of the active UEs have a maximum order of 3 and unit average power. Recaing that we assume a ce radius of 1.5 m, the maximum propagation deay normaized by the samping period T ) θ max is equa to. The performance of is first assessed in the presence of a singe UE with a fixed timing offset θ 1 =5, whie the case of mutipe UEs is considered ater. 5.. Performance evauation We start evauating the impact of the number of ties on the timing estimation accuracy of. Fig. iustrates the variance of the timing estimate ˆθ 1,defined as varˆθ 1)=E{ˆθ 1 E{ˆθ 1}) }, vs. M θ for different vaues of SNR and with K =1 and R =1.Itisworth observing that, since θ 1 is the timing error normaized by the samping period T,itsestimateˆθ 1 is an adimensiona quantity. As it is seen, the best resuts are obtained for 4 M θ 7, whieadegradationisobservedforargervaues of M θ as the SNR decreases. As expected, some advantage is achieved with respect to M θ =1,whichcorresponds to the conventiona RA scheme CRA) iustrated in [1]. Since the number of fops required by increases with M θ,inasubsequentsimuationsm θ is fixed to 4. 6 Eur. Trans. Teecomms. 1; :1 1 c 1 John Wiey & Sons, Ltd. Prepared using ettauth.cs

7 1 =1, R =1 1-1 =1, R=1 Varianceofthetimingestimates SNR=6dB SNR=1dB SNR=1dB Normaizedvarianceofthepowerestimates Simuated Theoretica SNR=6dB SNR=1dB SNR=1dB M Figure. varˆθ 1) vs. M θ for with K =1, R =1and different SNR vaues. Figure 4. nvarˆp f) 1 ) vs. MP for with K =1, R =1 and different SNR vaues. M P 1 9 =1, R = Varianceofthetimingestimates SNR/dB 16 CRA Figure 3. varˆθ 1) vs. SNR for the investigated schemes with K =1and R =1. Normaizedvarianceofthepowerestimates CRA Theoretica 4 1 SNR/dB 16 =1, R =1 Figure 5. nvarˆp f) 1 ) vs. the SNR for the investigated schemes with K =1and R =1. 4 Fig. 3 iustrates varˆθ 1) as a function of the SNR with K =1and R =1.Athoughtheestimationaccuracyof both CRA and is ony marginay affected by the SNR, a remarabe gain is achieved by using GLRT- RA in pace of CRA. We now assess the performance of the power estimator. For this purpose, Fig. 4 iustrates the normaized variance of the power estimate, say nvarˆp f) 1 )=var{ˆpf) 1 }/ [E{p 1}],asafunctionofM P for different SNR vaues and with K =1and R =1.Thetheoreticaresutsgiven in 34) are aso shown for comparison. As is seen, the agreement between numerica resuts and theoretica anaysis is achieved ony when M P is adequatey arge. In order to achieve a good trade-off between accuracy and system compexity, the vaue of M P is chosen equa to 5. In Fig. 5 we show nvarˆp f) 1 ) as a function of the SNR with K =1and R =1.Asbefore,comparisonsare made with the CRA scheme, which corresponds to setting M P =1.Weseethatattainsthetheoretica resuts at a SNR vaues, whie the accuracy of CRA is virtuay independent of the SNR and exhibits a significant oss compared to. The code detection capabiity of the investigated schemes is assessed in terms of mis-detection probabiity P md and fase aarm probabiity P fa.forthispurpose,the Eur. Trans. Teecomms. 1; :1 1 c 1 John Wiey & Sons, Ltd. 7 Prepared using ettauth.cs

8 1 9 =1 SNR =1dB Varianceofthetimingestimates 6 5 R=1 R= R=4 Varianceofthetimingestimates R =1 R =4 1 1 SNR/dB Figure 6. var ˆθ 1) vs. the SNR for with K =1 and R =1, or Numberofuserequipments ) Figure. var ˆθ 1) vs. K for when SNR= 1dB and R =1or 4. 1 Normaizedvarianceofthepowerestimates Simuated Theoretica R 1 R R 4 =1 Normaizedvarianceofthepowerestimates SNR =1dB R =1 R = SNR/dB Figure 7. nvarˆp f) 1 ) vs. the SNR for with K =1and R =1, or Numberofuserequipments ) Figure 9. nvarˆp f) 1 ) vs. K of when SNR= 1dB and R =1or 4. SNR is set to 1 db and we et K = R =1.Numerica resuts averaged over 5, channe reaizations have shown that for threshod vaues centered around η =.1 both and CRA provide a P fa smaer than 1 5. On the other hand, achieves a P md in the order of 7 1 4, whie CRA provides P md = Thismeansthatexhibits improved code detection capabiity with respect to CRA. The performance of when mutipe antennas are empoyed at the enodeb is now investigated. Figs. 6 and 7 iustrate varˆθ 1) and nvarˆp f) 1 ) as a function of the SNR with K =1 and R =1, or 4. Asexpected, increasing R improves the timing and power estimation accuracy of. In particuar, for SNR vaues smaer than 16 db an array gain equa to 1 og R db is achieved in terms of nvarˆp f) 1 ) with respect to a singeantenna scenario. The performance of in the presence of K UEs is reported in Figs. and 9 for R =1or 4. Here, the timing offset of the th UE with =1,,...,K) is chosen equa to θ =5+5 1), whietheaverage signa power of a active UEs is set to unity. Without oss of generaity, the system performance is measured on the basis of the signa received from the first UE. Inspection of Fig. reveas that the accuracy of the timing estimates is virtuay independent of the number of UEs, whie the Eur. Trans. Teecomms. 1; :1 1 c 1 John Wiey & Sons, Ltd. Prepared using ettauth.cs

9 resuts in Fig. 9 indicate that the accuracy of the power estimator deteriorates as K grows from 1 to 4. Moreover, from Fig. 9 it foows that using more than one antenna has no practica benefit when K Computationa compexity It is interesting to compare the investigated schemes in terms of their computationa requirement. In doing so it is worth pointing out that, even though N = 6144 is not a power of two, the number of fops invoved in the IDFT operation in Fig. 1 is sti we approximated by 5ηN og N just because the IDFT size can be decomposed into the product of an integer number and a power of two as N =3 11. Hence, setting M θ =4, V θ =9, M P =5, V P =33 and R =1, the compexity of is approximatey 1.7 times higher than that invoved by CRA. This means that the improved performance of is achieved at the price of an increased computationa oad. However, the resuts shown in Fig. 4 indicate that, at practica SNR vaues around 1 db, parameter M P can be reduced from 5 to 11 with ony a margina oss of the estimation accuracy. The same vaue can be used for M θ without incurring any significant degradation in the timing estimation accuracy for SNR 1 db. In these circumstances, one singe IDFT operation can be used, thereby reducing the compexity of by a factor.4.theseargumentsaowthesystemdesignertoachieve the desired trade-off between computationa requirement and system performance. 6. CONCLUSIONS We have presented a nove RA method which is specificay devised for ow-mobiity LTE-3GPP systems characterized by negigibe Dopper shifts. The proposed scheme reies on the GLRT criterion to decide whether a given code is present or not in the PRACH and inherenty taes into account the mutipath distortions introduced by the propagation channe. After modeing the MAI as white Gaussian noise, the ML principe is empoyed to estimate the timing error and power eve of the detected codes. Computer simuations indicate that the resuting scheme ) outperforms the conventiona RA method derived under the simpifying assumption of a fatfading channe. The price for such a performance gain is a certain increase of the computationa compexity. However, a judicious design of the agorithm parameters aows one to reduce the processing oad without incurring any significant performance degradation. In order to improve the resiience to MAI, we are currenty studying a mutiuser extension of the GLRT- RA, wherein the contribution of the strongest RA signa is iterativey detected and removed from the received waveform in accordance to the successive interference canceation principe. The resuts of this research wi be the subject of a future pubication. ACKNOWLEDGEMENT This research was supported in part by the Seamess Aeronautica Networing through integration of Data ins, Radios, and Antennas SANDRA) project co-funded by the European Commission within the Cooperation Programme GA No. FP REFERENCES 1. C. Ciochina, D. Mottier and H. Sari, An anaysis of three mutipe access techniques for the upin of future ceuar mobie systems, Eur. Trans. Teecomm.,19:51 5,.. 3GPP TS Physica Channes and Moduation Reease 1). 3. R. Müüner, C. F. Ba, M. Boussif, J. Lienhart, P. Hric, H. Winer, K. Kremnitzer and R. Kronachner, Enhancing upin performance in UTRAN LTE networs by oad adaptive power contro, Eur. Trans. Teecomm.,1:45 46,1. 4. IEEE IEEE standard for oca and metropoitan area networ part 16: Air interface for broadband wireess access systems, Tech. Rep., L. Li, P. Zhou, H. Hu and X. Zhang, A robust ce search scheme for OFDMA systems, Eur. Trans. Teecomm.,19:935 94,. 6. X. Fu and H. Minn, Initia upin synchronization and power contro ranging process) for OFDMA systems, in Proc. of the IEEE Goba Commun. Conf. GLOBECOM), Daas,Texas,USA,Nov.9 -Dec.3,4,pp D. Hwan Lee, OFDMA Upin Ranging for IEEE.16e Using Modified Generaized Chirp-Lie Poyphase Sequences, in Proc. of Int. Conf. in Centra Asia on Internet, Bishe,KyrgyzRepubic, 6-9 Sept. 5, pp Y. Zhou, Z. Zhang, and X. Zhou, OFDMA Initia Ranging for IEEE.16e Based on Time-Domain and Frequency-Domain Approaches, in Proc. of Int. Conf. on Commun. Techn. ICCT),Guiin,China,7-3 Nov. 6, pp H. Mahmoud, H. Arsan, and M. Ozdemir, Initia Ranging for WiMAX.16e) OFDMA, in Proc. of the Miitary Commun. Conf.,WashingtonD.C.,3-5 Oct. 6, pp S. Sesia, I. Toufi, and M. P. J. Baer, LTE, The UMTS Long Term Evoution - From Theory to Practice,Wiey,9. Eur. Trans. Teecomms. 1; :1 1 c 1 John Wiey & Sons, Ltd. 9 Prepared using ettauth.cs

10 11. X. Zhuang, K. Baum, V. Nangia, and M. Cuda, Ranging Enhancement for.16e OFDMA PHY, IEEE C.16e-4/143, June4. 1. X. Fu, Y. Li, and H. Minn, A New Ranging Method for OFDMA Systems, IEEE Trans. Wireess Commun.,vo.6,no.,pp ,Feb M. Morei, L. Sanguinetti and H.V. Poor, A Robust Ranging Scheme for OFDMA-Based Networs, IEEE Trans. Commun., vo.57,no.,pp , Aug L. Sanguinetti, M. Morei and H. V. Poor, An ESPRIT based approach for initia ranging in OFDMA systems, IEEE Trans. Commun., vo.57, no. 11, pp , Nov D. Chu, Poyphase codes with good periodic correation properties, IEEE Trans. Inf. Theory, vo.1, no.4, pp , Ju B. M. Popovic, Efficient matched fiter for the generaized chirp-ie poyphase sequences, IEEE Trans. Aer. Eectr. Systems, vo.3,no.3,pp , Ju Panasonic, R : RACH Sequence Aocation for Efficient Matched Fiter Impementation, 3GPP TSG RAN WG1, meeting 4bis, St Juians, Mata, March Huawei, R1-7149: Efficient Matched Fiters for Paired Root Zadoff Chu Sequences, 3GPP TSG RAN WG1, meeting 4bis, St Juians, Mata, March W. W. Smith and J. M. Smith, Handboo of Rea-time Fast Fourier Transforms. New Yor: Wiey Inter- Science, ITU-R, Guideines for evauation of radio transmission technoogy for IMT-, Recommendation ITU-R M. 15, Tech. Rep., Eur. Trans. Teecomms. 1; :1 1 c 1 John Wiey & Sons, Ltd. Prepared using ettauth.cs

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