Performance evaluation of IB-DFE-based strategies for SC-FDMA systems

Transcription

1 Siva et a EURASIP Journa on Wireess Communications and Networking 013, 013:9 RESEARCH Performance evauation of IB-DFE-based strategies for SC-FDMA systems Adão Siva 1*, José Assunção 1, Rui Dinis and Atíio Gameiro 1 Open Access Abstract The aim of this paper is to propose and evauate muti-user iterative bock decision feedback equaization (IB-DFE) schemes for the upink of singe-carrier frequency-division mutipe access (SC-FDMA)-based systems It is assumed that a set of singe antenna users share the same physica channe to transmit its own information to the base station, which is equipped with an antenna array Two space-frequency muti-user IB-DFE-based processing are considered: iterative successive interference canceation and parae interference canceation In the first approach, the equaizer vectors are computed by minimizing the mean square error (MSE) of each individua user, at each subcarrier In the second one, the equaizer matrices are obtained by minimizing the overa MSE of a users at each subcarrier For both cases, we propose a simpe yet accurate anaytica approach for obtaining the performance of the discussed receivers The proposed schemes aow an efficient user separation, with a performance cose to the one given by the matched fiter bound for severey time-dispersive channes, with ony a few iterations Keywords: SC-FDMA; IB-DFE; Muti-user separation; PIC; SIC; Ceuar systems 1 Introduction Singe-carrier frequency-division mutipe access (SC- FDMA), a modified form of orthogona frequency-division mutipe access (OFDMA), is a promising soution technique for high data rate upink communications in future ceuar systems When compared with OFDMA, SC-FDMA has simiar throughput and essentiay the same overa compexity A principa advantage of SC-FDMA is the peak-toaverage power ratio (PAPR), which is ower than that of OFDMA [1,] SC-FDMA was adopted for the upink, as a mutipe access scheme, of the current ong-term evoution (TE) ceuar system [3] Singe-carrier frequency domain equaization (SC-FDE) is widey recognized as an exceent aternative to OFDM, especiay for the upink of broadband wireess systems [4,5] As other bock transmission techniques, SC-FDE is suitabe for high data rate transmission over severey time-dispersive channes due to the frequency domain impementation of the receivers Conventiona SC-FDE * Correspondence: asiva@avitpt 1 DETI, Instituto de Teecomunicações, University of Aveiro, Aveiro , Portuga Fu ist of author information is avaiabe at the end of the artice schemes empoy a inear FDE optimized under the minimum mean square error (MMSE) criterion However, the residua interference eves might sti be too high, eading to performance that is sti severa decibes from the matched fiter bound (MFB) Noninear time domain equaizers are known to outperform inear equaizers and DFE are known to have good performance-compexity tradeoffs [6] For this reason, there has been significant interest in the design of noninear FDE in genera and decision feedback FDE in particuar, with the IB-DFE being the most promising noninear FDE [7,8] IB-DFE was originay proposed in [9] and was extended for a wide range of scenarios in the ast 10 years, ranging from diversity scenarios [10,11], MIMO systems [1], CDMA systems [13,14], and muti-access scenarios [15,16], among many other Essentiay, the IB-DFE can be regarded as a ow compexity turbo equaizer [17-0] impemented in the frequency domain that do not require the channe decoder output in the feedback oop, athough true turbo equaizers based on the IB-DFE concept can aso be designed [1-3] An IB-DFE-based scheme speciay designed for offset consteations (eg, OQPK and OQAM) was aso proposed in [4] In the context of cooperative systems, an IB-DFE approach was derived to separate the quantized received signas from the different base stations (BSs) [5] 013 Siva et a; icensee Springer This is an open access artice distributed under the terms of the Creative Commons Attribution icense ( which permits unrestricted use, distribution, and reproduction in any medium, provided the origina work is propery cited

2 Siva et a EURASIP Journa on Wireess Communications and Networking 013, 013:9 Page of 10 Works reated to IB-DFE specificay designed for SC- FDMA-based systems are scarce in the iterature In [6], the authors proposed an IB-DFE structure consisting of a frequency domain feedforward fiter and a time domain feedback fiter for singe-user SC-FDMA systems An iterative frequency domain mutiuser detection for spectray efficient reaying protocos was proposed in [7], and a frequency domain soft-decision feedback equaization scheme for singe user SISO SC-FDMA systems with insufficient cycic prefix was proposed in [8] In this paper, we consider a broadband wireess transmission over severey time-dispersive channes, and we design and evauate muti-user receiver structures for the upink singe-input mutipe-output (SIMO) SC- FDMA systems that are based on the IB-DFE principe It is assumed that a set of singe antenna user equipment (UE) share the same physica channe to transmit its own information to the base station, which is equipped with an antenna array Two muti-user IB-DFE-based processing schemes are considered, both with the feedforward and feedback fiters designed in space frequency domain: iterative successive interference canceation (SIC) and parae interference canceation (PIC) In the first approach, the equaizer vectors are computed by minimizing the mean square error (MSE) of each individua user at each subcarrier In the second one, the equaizer matrices are obtained by minimizing the overa MSE of a users at each subcarrier For both cases, we propose a quite accurate anaytica approach for obtaining the performance of the proposed receivers The remainder of the paper is organized as foows: Section presents the muti-user SIMO SC-FDMA system mode Section 3 presents in detai the considered muti-user IB-DFE-based receiver structures The feedforward and feedback fiters are derived for both cases and anaytica approach for obtaining the performance is discussed Section 4 presents the main performance resuts, both numerica and anaytica The concusions wi be drawn in Section 5 Notation: Throughout this paper, we wi use the foowing notations owercase etters, uppercase etters, are used for scaars in time and frequency, respectivey Bodface uppercase etters are used for both vectors and matrices in frequency domain The index (n) is used in time whie the index () is for frequency () H, () T, and () * represent the compex conjugate transpose, transpose, and compex conjugate operators, respectivey, E[] represents the expectation operator, I N is the identity matrix of size N N, CN(,) denotes a circuar symmetric compex Gaussian vector, tr(a) is the trace of matrix A, and e k is an appropriate coumn vector with 0 in a positions except the kth position that is 1 System mode Figure 1 shows the considered upink SC-FDMA-based transmitter of the kth user equipment We consider a BS equipped with M antennas and K singe antenna UEs share the same physica channe, ie, the information from a UEs is transmitted at the same frequency band A SC- FDMA scheme is empoyed by each UE and the data bock associated to the kth UE (k =1,,K) is{s k,n ;n =0,, n o 1}, where consteation symbo S k,n (with E S k;n ¼ σ S ) is seected from the data according to a given mapping rue Then, the -ength data bock symbos are moved to frequency domain obtaining {S k, ; =0,, 1} = DFT{s k, ; =0,, 1} After that, the frequency domain signas are intereaved so that they are widey separated in the OFDM symbo, therefore increasing the frequency diversity order Finay, an OFDM moduation is performed and a cycic prefix is inserted to avoid inter-symbo interference (ISI) Without oss of generaity, we concentrate on a singe -ength data bock, athough in practica system severa data bocks are mapped into the OFDM symbo The received signa in frequency domain (ie, after cycic prefix remova, N-FFT, and chip demapping operations), at the mth BS antenna and on subcarrier can be expressed as Y ðmþ ¼ XK H ðmþ k¼1 k; S k; þ N ðmþ ; ð1þ assuming that the cycic prefix is ong enough to account for channe impuse responses between the UEs and the BS In (1), H ðmþ k; ¼ α k H cfrðmþ k; represents the channe between user k and the mth antenna of the BS on subcarrier, whereh cfrðmþ k; denotes the normaized channe frequency response, ie, E H cfrðmþ k; ¼ 1, whie the coefficient α k is a weighting factor that accounts for the combined effects of power contro and propagation osses The average received power associated to the kth UE is therefore α k and N ðmþ CN 0; σ N is the noise In matrix format, (1) can be re-written as Y ¼ H T S þ N ; ðþ h i h i with Y ¼ Y ðþ 1 Y ðmþ T, N ¼ N ðþ 1 N ðmþ T, T, S ¼ S 1; S k; and 3 H ðþ 1 H T 1; H ð1þ 6 K; 7 ¼ 4 5: ð3þ H ðmþ 1; H ðmþ K; The channe vector of the kth user is defined as h i H k; ¼ H ð1þ k; H ðmþ k;

3 s k,-1 N-1 Siva et a EURASIP Journa on Wireess Communications and Networking 013, 013:9 Page 3 of s k,0 s k,-1 s k,0 s/p -DFT Chip Mapping N-IFFT + CP Figure 1 SC-FDMA-based transmitter 3 Muti-user IB-DFE receiver strategies In this section, we present in detai the muti-user iterative frequency domain receiver design strategies based on the IB-DFE concept [6] Two iterative approaches are considered: SIC and PIC 31 IB-DFE SIC approach Figure shows the main bocks of the IB-DFE SICbased process For each iteration, we detect a K UEs on th subcarrier, in a successive way, using the most updated estimated of the transmit data symbos associated to each UE to cance the corresponding interference Thus, this receiver can be regarded as an iterative SIC scheme However, as with conventiona singe-user IB- DFE-based receivers, we take into account the reiabiity of the bock data estimates associated to UEs for each detection and interference canceation procedure From Figure, we can see that at the ith iteration, the signa received on th subcarrier associated to the kth UE, before the -IDFT operation is given by ~S ðþ i ðþt k; S ði 1Þ k; ¼ F ðþt i k; Y B i k; ; ð4þ h i with F ðþ i k; ¼ F ðþ i k; F ðmþ T h i ðþ i k; and B k; ¼ B ðþ 1 k; B ðkþ T k; denoting the feedforward and feedback vector coefficients of the kth UE appied on the th subcarrier, respectivey The vector S ði 1Þ k; is given by S ði 1Þ k; ¼ S 1; ; ; S k 1; ; S k; ; ; S K; T of size K 1,wherethe bock S k; ; ¼ 0; ; 1 is the DFT of the bock of time domain n average vaues o conditioned to the detector output S ðþ i k;n ; n ¼ 0; ; 1 for user k and iteration i Ceary, the eements of S k 0 ; are associated to the current iteration for the UEs aready detected (k ' < k) and associated to the previous iterations for the UE that is being detected, as we as the UEs sti not detected in this iteration For normaized QPSK consteations (ie, s k,n =±1±j), the average vaues are given by [13] where 8 and s k;n ¼ tanh >< >: Re k;n ¼ σ k;n! Re k;n þ j tanh Re ~s k;n Im k;n ¼ σ Im ~s k;n ; k;n σ k;n ¼ 1 X 1 n 0 ¼0 ^s k;n 0 s k;n 0 : ð6þ! Im k;n ; ð5þ ð7þ We shoud emphasize that athough we ony consider QPSK consteations, IB-DFE-based schemes in genera and our techniques in particuar can easiy be extended to other consteations For this purpose, we just need to empoy the generaized IB-DFE design of references [9,30] The hard decision associated to the symbo S k,n is ^S k;n ¼ sign Re ~s k;n þ jsign Im ~sk;n It can be shown that S k; ρ k ^S k;,with^s k; denoting the frequency domain sampes associated to the symbos' hard decision Furthermore, Figure Iterative receiver structure for UE k based on IB-DFE SIC approach

4 Siva et a EURASIP Journa on Wireess Communications and Networking 013, 013:9 Page 4 of 10 ^S k; ρ k S k; þ Δ k;, which means that S k; ρ k S k; þ ρ k Δ k;, and in matrix form, we have S P S þ PΔ Itcanbe shown that the error Δ =[Δ 1, Δ K, ] T has zero mean and P =diag(ρ 1,, ρ K ), with correation coefficients defined as h i E ^s k;n s k;n ρ k ¼ h E i ; ð8þ s k;n being a measure of the estimates reiabiity associated to the ith iteration, approximatey given by with 8 ρ k 1 >< >: ρ ðþre i k;n ρ ðþim i k;n X 1 n¼0 ρ Re k;n þ ρim k;n ; ð9þ 0 ¼ tanh@ 0 ¼ tanh@ ðþre i k;n ðþim i k;n 1 A 1 A: ð10þ For arger consteations, an estimate of the correation coefficient can be computed as in [9,30] For a given iteration and the detection of the kth UE, the iterative receiver equaizer is composed by coefficients F ðþ i k; and B ðþ i k; These coefficients are computed to maximize the overa signa-to-interference pus noise ratio (SINR) at the FDE output and, therefore, minimize the bit error rate (BER) h i If we consider a normaized FDE (ie, E ~S ðþ i k; ¼ S ðþ i k; ), this is formay equivaent to minimize the MSE For a QPSK consteation with Gray mapping, the BER can be approximatey given 0 1 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 BER k Q Bu t 1 C ; ð11þ 1 A MSE k; ¼0 where Q(x) denotes the we-known Gaussian function and MSE k, is the mean square error on the frequency domain sampes given by h i MSE k; ¼ E ~S k; S k; ¼ E F T k; Y B T k;s k; S k; : ð1þ For the sake of simpicity, the dependence on the iteration index is dropped in (1) and in the foowing equations After some mathematica manipuations, it can be shown that (1) is reduced as n MSE k; ¼ F H k; RY F k; þ B H k; R S;S B k; þ σ s Re FH k; RY;Sk; n o n þre B H k; R S;S k; Re B H k; R S;Y F k; o : o ð13þ The different correation matrices of (13) are given by 8 >< >: R Y ¼ E Y YT ¼ H H R s H þ R h i N R S;S ¼ E S S T ¼ P R s R Y;Sk; R S;S k; R S;Y h i ¼ E Y S k; k;k; ¼ H H R s e k h i ¼ E S k;k; S k; ¼ P R s e k ¼ E S Y ¼ P R s H ð14þ with R s ¼ σ S I K and R N ¼ σ N I M, being the correation matrices of data symbos and noise on each carrier From (11), we can see that to minimize the BER of each UE, we need to minimize the MSE of each UE on each subcarrier However, ony considering the MSE minimization may ead to biased estimates and thus to avoid it, we force the received ampitude of each user to one, ie, 1 X 1 F T k; HT k; ¼0 probem can be formuated as min MSE k; s:t 1 X 1 F T k; F k; ;B k; HT k; ¼ 1: ¼0 ¼ 1 The constrained optimization ð15þ We use the Karush-Kuhn-Tucker (KKT) [31] conditions to sove the optimization at each step with a but one variabe fixed The agrangian associated with this probem can be written by X 1 1 F k; ; B k; ; μ k ¼ MSEk; μ k F T k; HT k;!; 1 ¼0 ð16þ where μ k is the agrangian mutipier [3] The KKT conditions are 8 Fk; F k; ; B k; ; μ k ¼ 0 >< Bk; F k; ; B k; ; μ k ¼ 0 : ð17þ 1 X 1 >: F T k; HT k; 1 ¼ 0 ¼0 After straightforward but engthy mathematica manipuation, we obtain the feedforward and feedback vector coefficients with the iterative index dependence, k; ¼ HH I K P ði 1 F ðþ i Þ 1 H þ σ NI σ M H H S Ω ðþ i k ; ð18þ

5 Siva et a EURASIP Journa on Wireess Communications and Networking 013, 013:9 Page 5 of 10 and with B ðþ i k; ¼ H F ðþ i k; e k; k ¼ I K P e ði 1Þ k μ i Ω ðþ i ðþ k σ S e k: ð19þ ð0þ The agrangian mutipier is seected, at each iteration X 1 F ðþt i i, to ensure the constraint 1 k; H T k; ¼ 1 It shoud ¼0 be emphasizes that for the first iteration (i = 1), and for the first UE to be detected, P (0) is a nu matrix and S ð0þ k; ; k ¼ 1 is a nu vector 3 IB-DFE PIC approach Figure 3 shows the main bocks of the IB-DFE PICbased process For each iteration, we detect a K UE on the th subcarrier, in a parae way, using the most updated estimated of the transmit data symbos to cance the residua interference, which it coud not be canceed in the first equaizer bock Thus, this receiver can be regarded as an iterative PIC scheme [0] However, as with conventiona IB-DFE-based receivers and the above SIC approach, we take into account the reiabiity of the bock data estimates for each detection procedure From Figure 3, the received signa on th subcarrier of a UEs, before the -IDFT operation is given by ~S ðþ i S ði 1Þ ¼ F ðþt i Y B ðþt i ; ð1þ h i where F ðþ i ¼ F ðþ i 1; F ðþ i is a matrix of size MxK with K; h a UEs' feedforward vector coefficients, B ðþ i ¼ B ðþ i 1; B ðþ i K; T is a matrix of sizehkxk with a UEs' i feedback vector T coefficients, and ~S ðþ i ¼ ~S ðþ i 1; ~S ðþ i K; For this approach, the matrices F ðþ i and B ðþ i are computed to minimize the average bit error rate (BER) of a UEs, and for a QPSK consteation, the average BER can be approximatey given by 0 1 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K BER Q Bu t1 1 C MSE A : ðþ ¼0 Here, the MSE is the overa mean square error on the frequency domain sampes given by MSE ¼ E ~S ðþ i S ð3þ ¼ E tr ~S ðþ i S S ~ i H S Repacing (1) in (3) and after some mathematica manipuations, it can be shown that (3) is reduced to MSE ¼ tr F H R Y F þ tr B H R S;S B n o þkσ s tr Re FH R Y;S n o n o þtr Re B H S;S R tr Re B H S;Y R F ð4þ ðþ with the correation matrices R Y;S ( R Y;S ¼ E Y S ¼ H H R s ¼ H H R s R S;S ¼ E S S and R S;S defined as ð5þ Note that the correation matrices R Y, R S;S, and R S;Y were aready defined in (14) Contrariy to the SIC approach, to minimize the average BER, we need to minimize the overa MSE at each subcarrier Here, to avoid the bias, we force the received Figure 3 Iterative receiver structure based on IB-DFE PIC approach

6 Siva et a EURASIP Journa on Wireess Communications and Networking 013, 013:9 Page 6 of 10 ampitude to K, ie, 1 X 1 tr F T HT ¼ K The constrained ¼0 optimization probem can be formuated as min MSE s:t 1 X 1 tr F T F ;B HT ¼ K: ð6þ ¼0 We aso use the KKT conditions to sove the optimization probem The agrangian associated with this probem is now given by! ðf ; B ; μþ ¼ MSE μ 1 X 1 tr F T HT K ; ð7þ ¼0 where μ is the agrangian mutipier The KKT conditions are 8 F ðf ; B ; μþ ¼ 0 >< B ðf ; B ; μþ ¼ 0 : 1 X 1 tr F T >: HT K ¼ 0 ¼0 ð8þ After engthy mathematica manipuation, we finay obtain the feedforward and feedback matrices with the iterative index dependence, and with ¼ H H I K P ði 1 F ðþ i B ðþ i Ω ðþ i ¼ Þ 1 H þ σ NI σ M H H Ω ðþ i ; S ð9þ ¼ H F ðþ i I K ; ð30þ I K P ði 1 μðþ i Þ σ S I K : ð31þ In this approach, the agrangian mutipier is seected, at each iteration i, to ensure the constraint 1 X 1 tr F T HT ¼ ¼0 K Since a users are detected in parae, for the first iteration (i =1),P (0) is a nu matrix and S ðþ 0 is a nu vector The compexity of the SIC approach is sighty higher than the PIC one For the SIC, we need to invert a matrix of size MxM for each user on each iteration, whie for the PIC one, we need to invert a matrix of size MxM for a users on each iteration, ie, the SIC approach requires K 1 more matrix inversions per iteration Since in the receiver SIC structure, each user is detected individuay and sequentiay, the deay is aso higher 4 Performance resuts In this section, we present a set of performance resuts, anaytica and numerica, for the proposed IB-DFE-based PIC and SIC receiver schemes Two different scenarios are considered: Scenario 1, we assume two UEs (K = ) and a BS equipped with two antennas (M = ) Scenario, we assume four UEs (K = 4) and a BS equipped with four antennas (M = 4) For both scenarios, the main parameters used in the simuations are N-FFT size of 1,04; -DFT size set to 18 (this represents the data symbos bock associated to each UE); samping frequency set to 1536 MHz; usefu symbo duration is 666 μs, cycic prefix duration is 51 μs; overa OFDM symbo duration is 7186 μs; subcarrier separation is 15 khz, and a QPSK consteation under Gray mapping rue, uness otherwise stated Most of the parameters are based on TE system [33] The channe between each UE and the BS is uncorreated and severey time dispersive, each one with rich mutipath propagation and uncorreated Rayeigh fading for different mutipath components Specificay, we assume a p = 3-path frequency-seective bock Rayeigh fading channe with uniform power deay profie (ie, each path with average power of 1/ p ) The same concusions coud be drawn for other mutipath fading channes, provided that the number of separabe mutipath components is high Aso, we assume perfect channe state information, synchronization and α k =1, k The resuts are presented in terms of the average bit error rate (BER) as a function of E b /N 0, with E b denoting the average bit energy and N 0 denoting the one-sided noise power spectra density In a scenarios, we present the theoretica and simuation average BER performances for both proposed receiver structures: IB-DFE PIC and SIC For the sake of comparisons, we aso incude the matched fiter bound (MFB) performance Figures 4 and 5 show the performance resuts for the first scenario, considering IB-DFE PIC and IB-DFE SIC, respectivey Starting by anaysing the resuts presented in Figure 4, it is cear that the proposed anaytica approach is very precise, especiay regarding the first iteration Note that for this iteration, the IB-DFE PIC reduces to the conventiona MMSE frequency domain muti-user equaizer, since P (0) is a nu matrix and α k = 1, k is a nu vector Athough there is a sma difference between theoretica and simuated resuts when we have iterations, mainy due to errors in the estimation of variance of the overa error at the FDE output (see (7)) and the non-gaussian nature of the overa error, our anaytica approach is sti very accurate, with differences of just a few tenths of decibes As expected, the BER performance

7 Siva et a EURASIP Journa on Wireess Communications and Networking 013, 013:9 Page 7 of BER Iter1 Sim Iter1 The Iter Sim Iter The Iter4 Sim Iter4 The MFB Eb/No, db Figure 4 Performance of the IB-DFE PIC structure for scenario 1 improves with the iterations, and it can be observed that for the fourth iteration, the performance is cose the one obtained by the MF, many for high SNR regime Therefore, the proposed IB-DFE PIC scheme is quite efficient to separate the users and achieve the maximum system diversity order, with ony a few iterations From Figure 5, we can aso see that the anaytica approach proposed for the IB-DFE SIC structure is very accurate The BER performance approaches, with a number of iterations as ow as 4, very cosey to the imit obtained with the MFB This means mean that this receiver structure is aso abe to efficienty separate the UEs, whie taking advantage of the space-frequency diversity inherent to the MIMO SC-FDMA-based systems Comparing the SIC and the PIC approach, it is cear that for the first iteration the SIC approach outperforms the BER Iter1 Sim Iter1 The Iter Sim Iter The Iter4 Sim Iter4 The MFB Figure 5 Performance of the IB-DFE SIC structure for scenario Eb/No, db

8 Siva et a EURASIP Journa on Wireess Communications and Networking 013, 013:9 Page 8 of 10 PIC one It can be observed a penaty of approximatey 1 db of the PIC against the SIC, for a BER = 10 3 This is because the SIC-based structure to detect a given user takes into account the previous detected ones, with the exception for the first user However, when the number of iteration increases, the performance of the PIC approach tends to the one given by the SIC approach We can observe that the BER performance of both approaches is basicay the same for four iterations Figures 6 and 7 show the performance resuts for the second scenario, considering IB-DFE PIC and SIC, respectivey From these figures, we basicay can point out the same concusions as for the resuts obtained in the previous ones We can see that simiary to the first scenario the proposed anaytica approaches for both IB- DFE SIC and PIC structure are very accurate However, comparing the resuts obtained for this scenario with the ones obtained for scenario 1, we can see that the overa performance is much better This is because our receiver structures can take benefit of the higher space-diversity order avaiabe in this scenario, since they are efficient in removing both muti-user and inter-carrier interferences The previous resuts indicate that IB-DFE receivers can have exceent performance, cose to the MFB, for MIMO systems with QPSK consteations One question that arises naturay is if this is sti vaid for arger consteations such as QAM consteations In fact, the performance of a DFE for arger consteations can be seriousy affected due to error propagation effects As an exampe, we present in Figure 8 the performance resuts for 16- QAM consteations in the second scenario, considering IB-DFE SIC approach Ceary, we are sti abe to approach the MFB, athough we need more iterations, the convergence is ess smooth and we ony approach the MFB for ower BER (and, naturay, arger SNR) Athough these good resuts might be somewhat surprising, we shoud have in mind that an IB-DFE is not a conventiona DFE due to the non-causa nature of the feedback Moreover, the error propagation effects are much ower in IB- DFE receivers due to the foowing issues: Symbo errors (which are in the time domain) are spread over a frequencies Due to the frequencydomain nature of the feedback oop input, a symbo error has ony a minor effect on a frequencies The FDE is designed to take into account the reiabiity of estimates empoyed in the feedback oop When we have a arge number of symbo errors, the reiabiity decreases and the weight of the feedback part decreases When we have a decision error, we usuay move to one of the coser consteation symbos, ie, the magnitude of the error is usuay the minimum Eucidean distance of the consteation, regardess of the consteation size This is especiay important for arger consteations As we pointed out, an IB-DFE can be regarded as a compexity turbo equaizer impemented in the frequencydomain which does not empoy a channe decoder in the feedback oop For this reason, it has a turbo-ike behavior with good performance provided that the BER is ow BER Iter1 Sim Iter1 The Iter Sim Iter The Iter4 Sim Iter4 The MFB Eb/No, db Figure 6 Performance of the IB-DFE PIC structure for scenario

9 Siva et a EURASIP Journa on Wireess Communications and Networking 013, 013:9 Page 9 of BER Iter1 Sim Iter1 The Iter Sim Iter The Iter4 Sim Iter4 The MF Eb/No, db Figure 7 Performance of the IB-DFE SIC structure for scenario enough That is why we can ony approach the MFB for arger SNR 5 Concusions In this paper, we designed and evauated muti-user receiver structures based on the IB-DFE principe for the upink SIMO SC-FDMA systems Two muti-user IB- DFE PIC- and SIC-based processing schemes were considered In the first approach, the equaizer vectors were computed by minimizing the mean square error (MSE) of each individua user at each subcarrier In the second one, the equaizer matrices were obtained by minimizing the overa MSE of a users at each subcarrier For both cases, we proposed a quite accurate anaytica approach for obtaining the performance of the proposed receivers The resuts have shown that the proposed receiver structures are quite efficient to separate the users, whie aowing a cose-to-optimum space-diversity gain, with Iter 1 Sim Iter Sim Iter 3 Sim Iter 4 Sim Iter 8 Sim MFB BER Eb/No (db) Figure 8 Performance of the IB-DFE SIC structure for scenario and 16-QAM

10 Siva et a EURASIP Journa on Wireess Communications and Networking 013, 013:9 Page 10 of 10 performance cose to the MFB (severey time-dispersive channes) with ony a few iterations The performance of both PIC and SIC receiver structures is basicay the same after three or four iterations However, the main drawback of the SIC approach is the deay in the detection procedure, which is arger than for the PIC, since it detects one user at each time Thus for practica systems, where the deay is a critica issue, the PIC approach can be the best choice To concude, we can ceary state that these techniques are an exceent choice for the upink SC-FDMA-based systems, aready adopted by the TE standard Competing interests The authors decare that they have no competing interests Acknowedgements This study was supported by the Portuguese Fundação para a Ciência e Tecnoogia (FCT) COPWIN (PTDC/EEI-TE/1417/01), CROWN (PTDC/EEA-TE/ 11588/009), and ADIN (PTDC/EEI-TE/990/01) projects Author detais 1 DETI, Instituto de Teecomunicações, University of Aveiro, Aveiro , Portuga Instituto de Teecomunicações, Facudade de Ciências e Tecnoogia, University Nova de isboa, isboa , Portuga Received: 15 Juy 013 Accepted: 9 December 013 Pubished: 30 December 013 References 1 HG Myung, J im, DJ Goodman, Singe carrier FDMA for upink wireess transmission IEEE Vehicuar Mag 1(1), (006) HG Myung, DJ Goodman, Singe Carrier FDMA: A New Air Interface for ong Term Evoution (John Wiey & Sons, Hoboken, 008) 3 H Homa, A Toskaa, TE for UMTS-OFDMA and SC-FDMA based radio access (John Wiey & Sons, Hoboken, 009) 4 A Gusmão, R Dinis, J Conceição, N Esteves, Comparison of Two Moduation Choices for Broadband Wireess Communication, in Proceedings of the IEEE Vehicuar Technoogy Conference (Tokyo, 000) 5 D Faconer, S Ariyavisitaku, A Benyamin-Seeyar, B Eidson, Frequency domain equaization for singe-carrier broadband wireess systems IEEE Comm Mag 4(4), (00) 6 J Proakis, Digita Communications, 3rd edn (McGrraw-Hi, New York, 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