IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 63, NO. 9, SEPTEMBER 2015 3299
A Multiuser Detection Algorithm for Random AccessProcedure With the Presence of Carrier
Frequency Offsets in LTE SystemsQiwei Wang, Guangliang Ren, Member, IEEE, and Jueying Wu
AbstractIn the LTE system, uplink synchronization can beestablished through the random access channel, by which timingand frequency offsets between transceivers can be estimated andadjusted. As the single carrier frequency division multiple access(SC-FDMA) structure is utilized in LTE uplink, preambles for therandom access channel should be generated and detected in thetransform-domain at user equipments and the base station, re-spectively. However, in available literature, an explicit transform-domain signal model with respect to timing and frequency offsetshas not been provided, and the impact of frequency offsets onthe transform-domain signal is not analyzed either. Therefore,suffering from unknown interference among multiple user equip-ments, existing multiuser detection algorithms provide unsatisfiedmultiuser detection and estimation performance. In this paper,an explicit transform-domain signal model is first derived withrespect to both timing and frequency offsets. The characteristic oftransform-domain frequency offsets is then analyzed, which indi-cates that transform-domain frequency offsets behave differentlywith time-domain frequency offsets. After that, a multi-steps hy-brid multiuser detection algorithm is proposed to improve themultiuser detection and estimation performance, and the Cramr-Rao bound to the accuracy of parameters estimation for therandom access procedure is finally obtained. Simulation resultsshow that the proposed algorithm is able to significantly improvethe multiuser detection and estimation performance compared toexisting ones.
Index TermsLong term evolution, random access procedure,multiuser detection and estimation, carrier frequency offset.
IN modern orthogonal frequency division multiple access(OFDMA) systems, synchronization, especially uplink syn-chronization, is the very priority in establishing stabilizedcommunication links, and enables the transceivers to eliminatetiming and frequency uncertainties between them. With accu-rate estimation of timing offsets, uplink synchronization couldalso lower the requirement for the length of the cyclic prefix
Manuscript received January 9, 2015; revised May 24, 2015; acceptedJuly 17, 2015. Date of publication July 23, 2015; date of current versionSeptember 3, 2015. This work was supported by the National Natural ScienceFoundation of China (61401321 and 61072102) and the National Key BasicResearch Program of China (973 Program, 2014CB340205, 2014CB340206).The associate editor coordinating the review of this paper and approving it forpublication was H. Steendam.
The authors are with the State Key Laboratory of ISN, Xidian University,Xian 710071, China (e-mail: firstname.lastname@example.org).
Digital Object Identifier 10.1109/TCOMM.2015.2460241
in suppressing inter-symbol interference, thus improving theefficiency of resources utilization.
As for the LTE system, a physical random access channel(PRACH) is designated for user equipments (UEs) to establishuplink synchronization . During the random access (RA)procedure, each UE should notify its network entry by sendinga preamble, which is randomly selected from a Zadoff-Chu(ZC) code set  due to the perfect orthogonality/cross-correlation property. As the single carrier frequency divisionmultiple access (SC-FDMA) is adopted in LTE uplink, thePRACH also employs the SC-FDMA structure, by which ZCcodes are actually generated in the transform-domain (TrD) and transferred into the time-domain (TD) for transmission. Atthe receiver, the received RA signal, which is the superpositionof transmission signals of all active UEs after channel propa-gation, should be transferred back into the TrD, and the basestation (BS) is required to detect active preambles and esti-mate their corresponding parameters including timing offsets,frequency offsets and power levels. After that, both the timingand frequency offsets could be eliminated such that uplinksynchronization is established. With the rapid development ofthe internet-of-things, a large amount of UEs, not only userterminals but also radio nodes, need to access into the network, , indicating that it is a challenging task to improve thecapacity and performance of the RA procedure.
In available literature , an implicit assumption hasbeen adopted that frequency uncertainties between transceiversare small enough to be neglected, and that the BS is only re-quired to detect possible preambles and estimate correspondingtiming offsets and power levels. By treating other preamblesas interference, a single user detection (SUD) algorithm isutilized in the TrD by exploiting a bank of match filters, whichcorrelate the received RA signal with local preambles , .If a peak correlation value exceeds a pre-defined threshold, thepreamble is deemed as active. It is revealed in  that the TrDcorrelation processing of the SUD can be equivalently realizedby operating one inverse discrete Fourier transform (IDFT) tolower the complexity. As the threshold for the SUD is obtainedempirically, an adaptive one is proposed in  to make theSUD a constant false-alarm rate detector.
Unfortunately, in practical LTE systems, the carrier fre-quency offset (CFO) in the PRACH is almost inevitable. Onone hand, the maximum tolerable frequency uncertainty at theUE and BS are 0.1 and 0.05 ppm, respectively, leading at2.5 GHz to at most 375 Hz cumulated error. As the PRACH
0090-6778 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
3300 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 63, NO. 9, SEPTEMBER 2015
subcarrier spacing is only 1.25 kHz for format 0 to 3, the CFOactually corresponds to 30% of the PRACH subcarrier spacing,indicating that the CFO always takes place unless oscillatorswith high-precision are employed. On the other hand, in highmobility scenarios, a Rice channel model with a large Ricefactor is always assumed so that the Doppler frequency shift onthe dominant path becomes the most challenging issue for thePRACH . Therefore, the CFO issue in the PRACH is almostinevitable and needs to be dealt with. In literature , theimpact of the CFOs on the RA procedure is studied, indicatingthat the CFO does have a profound impact on the property of ZCcodes, hence a further impact on the performance of the SUD.In  and , the impact of CFOs on ZC codes is prelimi-narily analyzed via numerical simulation, which shows that theCFO also leads to a cyclic-shift to ZC codes like timing offsets.When correlating a CFO affected ZC code with the local one,besides the main correlation peak, false correlation peaks alsotake place. In , , it is mathematically derived that thecyclic-shift of a CFO affected ZC code corresponds to its rootvalue, which facilitates the determination of locations of falsecorrelation peaks. A restricted set of ZC codes for bearing theimpact of CFOs is designed in ,  by taking into accountcyclic-shifts which result because of CFOs. Although cyclic-shifts of ZC codes are introduced by CFOs, non-overlappedZC codes could be generated. Therefore, with the aid of therestricted code set, correlation peaks of different codes aresupposed to appear at different locations without confusing, anda multiple window SUD (MW-SUD) algorithm is thus utilizedto detect possible codes and estimate corresponding timingoffsets, CFOs, and power levels according to the locations andmagnitudes of both the main correlation peak and false ones, .
However, in literature , there exist three problemsthat restrict the development of the LTE RA procedure. Firstly,analyses are only derived for simplicity on the basis of the codedivision multiple access (CDMA) structure, which is inconsis-tent with the SC-FDMA structure in LTE uplink, leading toa wide gap between analyses and practical implementations.Secondly, because of the lack of an explicit TrD RA signalmodel, the characteristic of TrD CFOs that are totally differentwith the TD CFO is not illustrated either. Finally, due to theexistence of channel impulse responses (CIRs), timing offsets,and CFOs, the correlation property of ZC codes would bedamaged, giving rise to serious interference among them. Asthe MW-SUD treats other active preambles as interference, itsmultiuser detection and estimation performance is supposed tobe highly deteriorated.
In order to solve the problems stated above, the approachesand contributions of this paper are summarised as follows.
A TrD RA signal model is derived with respect to TrDCIRs, timing offsets, and CFOs, based on which thecharacteristic of TrD CFOs is illustrated, showing thatTrD CFOs behave totally different with TD CFOs;
To improve the multiuser detection and estimation per-formance by suppressing interference among UEs, amulti-steps hybrid multiuser detection (MS-HMUD) al-gorithm is proposed by exploiting in a hybrid fashion
both the methodology of successive interference cancel-lation and the concept of iterative parameters estimationthat is within the framework of the space alter-nating generalized expectation-maximization (SAGE)algorithm ;
The Cramr-Rao bound (CRB) to the accuracy of param-eters estimation is also derived.
As both the methodology of interference cancellation and theSAGE algorithm are able to deal with complicated multiusermaximum likelihood estimation (MLE) problems, existing re-searches in  have exploited them to improve the trans-mission of multiu