A New Filter-Bank Multicarrier System: The Linearly Processed FBMC System

Transcription

1 1 A New Filter-Bank ulticarrier Syste: The Linearly Processed FBC Syste Jintae Ki, Student eber, IEEE, Yosub Park, eber, IEEE, Sungwoo Weon, Jinkyo Jeong, Student eber, IEEE, Sooyong Choi, eber, IEEE, and Daesik Hong, Senior eber, IEEE Abstract In this paper, we propose a linearly processed filterbank ulticarrier (LP-FBC syste which eploys a faster than Nyquist signaling to reove residual intrinsic interferences. We represent the FBC transceiver in a atrix for and then apply singular value decoposition (SVD-based linear transforation in order to convert the overlapped FBC data into parallel independent interference-free data. This interferencefree characteristic of the proposed LP-FBC syste enables the use of conventional ultiple antenna configurations. Perforance evaluations show that out-of-band eission (OOBE perforance of the proposed LP-FBC syste is superior to those of conventional quadrature aplitude-based FBC (FBC-QA and orthogonal frequency division ultiplexing (OFD systes. Furtherore, the proposed LP-FBC syste outperfors the conventional FBC-QA in ters of bit error rate ( perforance when high order odulation is eployed under tie-varying channel and ultiuser uplink environent. Index Ters FBC, IO, singular value decoposition, faster than Nyquist. I. INTRODUCTION The filter-bank ulticarrier (FBC syste has been investigated as one of the alternative wavefors to orthogonal frequency division ultiplexing (OFD for future wireless counication systes 1]. There are three advantages typically associated with the FBC syste: i low out-of-band eission (OOBE, ii CP-free transission, and iii robustness to the asynchronous environent. Aong the various FBC systes, the ost thoroughly studied is the offset quadrature aplitude odulation-based FBC (FBC-OQA syste, which transits real and iaginary saples with a shift of half a sybol duration. OQA transission satisfies orthogonality conditions in the real field, since the intrinsic interference ters are iaginary-valued ]. However, these iaginary-valued intrinsic interferences represent a ajor obstacle, preventing the FBC-OQA syste fro using conventional ultiple-input ultiple-output (IO techniques. This work was supported by the National Research Foundation of Korea (NRF grant funded by the Korea governent (SIT (No. 018R1AA1A and by Institute for Inforation & counications Technology Prootion (IITP grant funded by the Korea governent (SIP (No , Developent on the core technologies of transission, odulation and coding with low-power and low-coplexity for assive connectivity in the IoT environent J. Ki, S. Weon, J. Jeong, S. Choi, and D. Hong are with the School of Electrical and Electronic Engineering, Yonsei University, Seoul , South Korea (e-ail: in3614@yonsei.ac.kr, again@yonsei.ac.kr, uranus0917@yonsei.ac.kr, csyong@yonsei.ac.kr, daesikh@yonsei.ac.kr. Y. Park is with Autonoous achine Lab., AI Center, Sasung Research, Sasung Electronics Co., Korea (e-ail: yosub.park@sasung.co. The authors of 3] 5] have proposed a nuber of approaches to enable FBC systes to use IO techniques. Zakaria et al. proposed an interference cancellation ethod which is a cobination of the iniu ean square error (SE and axiu likelihood (L techniques in 3]. Zakaria et al. again proposed a new interference-free FBC syste, called FFT-FBC in 4]. Renfors et al. proposed a block-wise Alaouti schee to obtain transit antenna diversity in 5]. However, the bit error rate ( perforance of conventional interference cancellation ethod in 3] is degraded due to the residual interferences. In addition, spectral efficiency (SE of the FFT-FBC and block-wise Alaouti schees in 4] and 5] is decreased due to the use of guard intervals. In suary, these approaches result in perforance degradation in ters of and SE, even though they enable the application of the IO schee. Recently, quadrature aplitude odulation (QA-based FBC (FBC-QA systes were proposed in 6], 7] and 8], which support QA sybol transission and enable IO transission. These systes utilize two different filters for the even- and odd-nubered subcarriers, respectively, in order to avoid intrinsic interferences caused by iaginary ters. However, due to the poor spectru confineent of the filters, these ethods show degraded OOBE perforance copared to the FBC-OQA syste. Since an essential advantage of FBC systes is excellent OOBE perforance copared with other ulticarrier systes, the result is the loss of one of the inherent strengths of the FBC syste. Furtherore, the FBC-QA systes eploy artificially designed filters, where the filters are not perfectly orthogonal to other filters. Therefore, they show inferior perforance copared to FBC-OQA systes, especially in cases where high order odulation is supported. Therefore, in this paper, we propose a new interferencefree FBC syste, called linearly processed FBC (LP- FBC syste, which retains the typical advantages of the FBC syste. The key contributions of this paper are as follows: i we represent the FBC transceiver in a atrix for, which steers us toward a breakthrough in handling intrinsic interference, ii we propose a novel FBC syste by using a singular value decoposition (SVD-based linear transforation that transfors the overlapped FBC data into the interference-free doain, and iii the proposed syste eventually akes it possible to exploit IO techniques without residual intrinsic interference. The rest of this paper is organized as follows: In Section II, the FBC syste being addressed is introduced. Section

2 TABLE I DEFINITION OF AIN PARAETERS Paraeters Vector for Definition s i] Transission signal of the i-th saple index. g i] Prototype filter of the i-th saple index. x,n Input data of the -th subcarrier at the n-th sybol. x even,n x even Input data of even-nubered subcarrier. x pre,n x pre Pre-processed data of the n-th sybol. x IF l,n F T x IF l F T IFFT processed data of the n-th sybol. x P l,n P N x P l P N Filtered and oversapled data of the n-th sybol. yl,n P P N yl P P N atched-filtered and downsapled data of the n-th sybol. y,n even y even Output data of even-nubered subcarrier. y,n post y post Post-processed data of even-nubered subcarrier. G l Poly-phase network (PPN atrix. F FBC transceiver atrix whose SVD is UΛV H. V, U H Pre-processing and post-processing atrices, respectively. III presents the proposed LP-FBC syste. The perforance evaluations are presented in Section IV, and the conclusion of the paper is provided in Section V. To enhance the readability, definition of paraeters is organized in TABLE I. Notation: a denotes coplex conjugate of scalar a, A] ij denotes an entry of atrix A in the i-th row and the j-th colun, A T denotes a transpose atrix whose entry in the i-th row and j-th colun is A] ji, A H denotes a coplex conjugate atrix whose entry in the i-th row and j-th colun is A] ji. II. THE FBC-QA SYSTE 9] The transitted signal of the discrete tie FBC syste was expressed in 9] as s i] = 1 =0 n=0 x,n g i n/] e j π i, (1 where i is the tie saple index, is the nuber of subcarriers, N is the nuber of transitted FBC sybols, g i] is prototype filter with K length, K is the overlapping factor of the prototype filter g i], and x,n is the data at the -th subcarrier of the n-th sybol. When we consider an ideal channel without noise, the received data for the -th subcarrier at the n-th sybol is given in 9] as y,n = 1 i= =0 n =0 x,n g i n /] g i n/], ( where { } denotes a coplex conjugation. Furtherore, the received signal can be rewritten in a sipler anner, represented by y,n = x,n + I,n, (3 where I,n is the intrinsic interference at the -th subcarrier of the n-th sybol fro the other overlapped sybols, given by I,n = 1 =0 n =0 n n x,n i= g i n /] g i n/]. (4 Real Iag (a Data of the FBC-OQA syste in the frequency doain. QA subcarrier index subcarrier index (b Data of horizontal FBC-QA syste in the frequency doain. Fig. 1. Coparison of the FBC-OQA and the horizontal FBC systes in the frequency doain. In this paper, we consider the horizontal FBC-QA syste described in 9] with a transceiver architecture that is the sae as for the FBC-OQA syste, but then insert null data on odd-nubered subcarriers, given by x,n = 0, {1, 3,, 1}. (5 If {0,,, }, which are the even-nubered subcarriers, the data x,n are QA data so as to aintain the sae data rate. Since null data has been inserted on the oddnubered subcarriers, there is no interference coing fro the odd-nubered subcarriers. Furtherore, since the filters g i] used in FBC systes are well-localized prototype filters in the frequency doain ], the QA data in the evennubered subcarriers do not interfere with the other evennubered subcarriers, shown in Fig. 1, which is expressed by g i n /] g i n/] = 0, if = l, i= (6 where l is a natural nuber. Therefore, the intrinsic interference I,n can be rewritten as I,n = n =0 n n x,n i= g i n /] g i n/], (7 where there is no effect fro the other subcarriers (. Therefore, the intrinsic interferences have an effect on the

3 3,, /, IFFT,, /,,,, Channel PPN + P/S S/P + PPN FFT Noise,, /,,, /,, 1 Fig.. Horizontal FBC-QA syste 9]. horizontal FBC syste only in the tie doain, not in the frequency doain. In (7, contrary to the FBC-OQA syste, the intercarrier interferences (ICIs fro the adjacent subcarriers are eliinated by eploying the horizontal FBC-QA syste. However, as with the FBC-OQA syste, inter-sybol interferences (ISIs are still present due to the sybol overlapping. In addition, while the ISIs of the FBC-OQA syste are iaginary-valued, the ISIs of the horizontal FBC-QA syste are coplex-valued, since the coplex-valued data x,n is being used. In order to overcoe this coplex-valued ISI, we will propose a new approach which transfors the data into the interference-free doain. III. PROPOSED LINEARLY PROCESSED FBC SYSTE In this section, we propose a transceiver for the linearly processed FBC (LP-FBC syste that transfors the received data into ISI-free data by using an SVD-based linear process. We represent the FBC-QA syste explained in Section II in a atrix for. The SVD-based linear transforation is then applied to this syste to eliinate the intrinsic interferences caused by the overlapped sybols. Furtherore, we describe a power allocation strategy across sybols which axiizes the capacity of the LP-FBC syste. A. Linear Forulation of the Intrinsic Interference We forulate the input and output data of each block in Fig. as a vector for. As addressed in (5, since input data x,n is null data for odd, we will consider only the data x,n of the even-nubered subcarriers fro this point on. The output of the /-point IFFT of x,n for even-nubered subcarriers can be obtained by x IF F T l,n = =0 x even,n e j πl /, (8 where x even,n = x,n for {0, 1,, / 1}. Since the data actually used is data of the even-nubered subcarriers x even,n, the forula expansion is perfored using only x even,n fro now on. In addition, we can also obtain the vector for of the x IF l,n F T for l {0, 1,, / 1} as x IF F T l = X even w l, (9 T where x IF l F T = l,] is a vector for of the IFFT output data, X even is a atrix for of the input data x IF F T l,0,..., x IF F T whose entry in the i-th row and j-th colun is x even j,i, and w l Fig. 3. Poly-phase network structure 1]. is the l-th colun of the /-point IDFT atrix W whose entry in the i-th row and j-th colun is πij ej /. The data x IF l,n F T is then inserted into the poly-phase network (PPN which is presented in ] as depicted in Fig. 3 for overlapping and filtering. After the PPN processing, the transitted data x P l,n P N can be obtained by K 1 x P l,n P N = g k/ + l] x IF l,n k F T, (10 k=0 where K is the overlapping factor of the prototype filter g i]. The transitted data can also be forulated in a vector for as follows: x P P N l = G l x IF F T l = G l X even w l, (11 T where x P l P N = x P l,0 P N,, xl,] P P N is the vector for of the transitted data x P l,n P N for n {0, 1,, N 1}. In (11, G l is a PPN atrix whose entry in the i-th row and j-th colun can be expressed by { g (i j / + l], for 0 i j < K G l ] ij = 0, otherwise (1 where A] ij denotes an entry of atrix A in the i-th row and the j-th colun. At the FBC receiver, we eploy the receiver using PPN structure presented in ]. The received data which is processed by PPN for downsapling and atched-filtering can be expressed as K 1 yl,n P P N = g k/ + ] x P l,n+k, P N (13 k=0 when an ideal channel without noise is considered. Furtherore, its vector for can be obtained by yl P P N = G H l x P l P N = G H l G l X even w l, (14 T where yl P P N = yl,0 P P N,, yl,] P P N is a vector for of the output data fro the PPN at the receiver part, and A H is denoted as a coplex conjugate atrix whose entry in the i-th row and j-th colun is A] ji. Lastly, the output data of the /-point FFT can be obtained as y even,n = yl,n P P N πl j e /. (15

4 4 The vector for of the output data y even,n can be obtained as Tx Rx Tx Rx y even = = yl P P N πl j e / (16 G H l G l X even πl j w l e /. Since the odd-nubered subcarriers are not used, there is no interference caused by the other subcarriers, i.e., no ICI. Therefore, the output vector y even can be represented by Antenna Index (a IO channel odel. Sybol Index (b FBC transceiver odel. y even = = = Fx even, G H l G l x even e j πl / e j πl / G H l G l x even (17 where y even = y,0 even,, y,] even T is a vector for of the output data at the even-nubered subcarriers and F = G H l G l is an FBC transceiver atrix. Note that the FBC transceiver atrix F is coposed of the arithetic operations of the prototype filter g i]. Therefore, this atrix depends only on the prototype filter and does not change unless the syste changes the prototype filter. When a tie-invariant channel and coplex Gaussian noise (z,n CN (0, N 0 are considered, the equation (17 can be rewritten as y even = h Fx even + = h x even }{{} Desired Data + h (F I x even }{{} Inter-sybol Interferences G H πl j l z l e / + z, (18 where h is a sall-scale channel coefficient of the -th subcarrier, z l = z l,0,, z l, ] T is a vector for of the coplex Gaussian noise, z = z,0,, z, ] T is a vector for of the noise processed by receiver using PPN, and I is an identity atrix. Fro (18, the second ter on the right-hand side stands for the inter-sybol interference, which coes fro the other sybols of the even-nubered subcarriers. As shown in Fig. 4, there is an analogy between the transceiver odel of the FBC syste in (17 and the IO channel odel 10]. By regarding the sybol indices of the FBC transceiver odel as antenna indices of the IO channel odel, we can treat the FBC transceiver atrix F as the IO channel coefficient atrix H. Therefore, various techniques, such as a precoding ethod for the IO channel odel, can be used in the FBC syste. Aong the various IO techniques, we will apply the concepts of spatial ultiplexing techniques in the proposed LP-FBC syste in this paper in order to eliinate the effect of intrinsic interference. Fig. 4. Coparison of the IO channel odel and the FBC transceiver odel. B. Linear Transforation into the Interference-Free Doain Based on the linear forulation in (17 and the siilarity of the FBC transceiver odel with the IO channel odel, we will apply an SVD-based ultiplexing technique. By applying the ultiplexing technique, overlapped FBC data with intrinsic interference can be converted into parallel independent interference-free data. Let us apply an SVD to the FBC transceiver atrix (17. The SVD result of the FBC transceiver atrix is expressed as F = UΛV H, (19 where U and V are N N unitary atrices whose coluns are left and right singular vectors of F, respectively, and Λ is an N N non-negative and diagonal atrix whose ain diagonal entries are the ordered singular values of F, {λ n } N n=1. Note that the atrix F is a Heritian atrix which is the sae as its coplex conjugate atrix. Therefore, V and U are the sae. Also, all the singular values λ n are real values. Fig. 5 shows the block diagra of the proposed linear processing. To convert the FBC data into parallel independent interference-free data, we exploit V and U H for pre-processing and post-processing, respectively. In the preprocessing, the N 1 input data vector x even, which is the /-th colun of the N / data atrix X even, is ultiplied by the pre-processing atrix V, expressed by x pre = Vx even, {0, 1,, / 1}, (0 where x pre T = x pre,0,],..., xpre represents pre-processed data. The pre-processed data is then converted by parallel-toserial conversion which converts the N 1 colun vector into the 1 N row vector. The / row vectors are stacked by / N atrix fro top to botto. Then, the n-th colun vector of the stacked atrix is a data vector which is inserted into the FBC transceiver, and can be expressed as t n = x pre 0,n x pre 1,n x pre,n ] T, (1 where t n is a / 1 colun vector which is coposed of input data fro the even-nubered subcarriers at the n-th sybol. As shown in Fig. 5, the vector t n is then inserted into the FBC transceiver which is forulated as F. After the data

5 5 Sybol index,,, Subcarrier index,,,,,»,,,, Pre- Processing,,, P/S, Sybol index,,,»,»,,,», Subcarrier index,, /, FBC Transceiver, FBC Transitter Channel, Sybol index, Subcarrier index,,,,, /, /,» /,,,, Post- Processing,,, S/P, Sybol index,,,»,»,,,», Subcarrier index,, /, FBC Receiver Noise, Fig. 5. Block diagra of the proposed LP-FBC syste. vector t n passes the FBC transceiver F, the received data can be obtained as r n = y even 0,n y even 1,n y even,n ] T, ( where y,n even is the output data of the FBC transceiver at the -th subcarrier of the n-th sybol. The N colun vectors coposed of y,n even are also stacked fro left to right as shown in Fig. 5. The -th 1 N row vector of the stacked atrix is converted to an N 1 colun vector, which is defined as y even = y,0 even,..., y,] even T, by serial-toparallel conversion. Then, the N 1 colun vector y even is ultiplied by the post-processing atrix U H, expressed as y post where y post = U H y even {0, 1,, / 1}, (3 = y post,0,..., ypost,] T is the post-processed data vector. After the pre-processing V and post-processing U H based on the SVD of the FBC transceiver odel in (19, the received data vector in (17 can be equivalently converted into y post = U H y even = U H (h Fx pre + z = h U H ( UΛV H (Vx even + U H z = h Λx even + U H z. (4 Since the atrix Λ is a diagonal atrix, we can say that the FBC transceiver atrix F is diagonalized by the pre-/postprocessing. Coparing (18 and (4, we can see that the data y which had intrinsic interference caused by the overlapped data is converted into parallel independent data. Therefore, the proposed syste enables QA data to be eployed without any effect fro residual intrinsic interferences being caused by the data at the other subcarriers or at the other sybols. C. Effective SNR and Power Allocation Strategy As shown in (4, the transitted signal power, effective signal power, and effective noise power are not the sae as other systes due to the pre-/post-processing. Therefore, in this subsection, we will show the effective signal-to-noise ratio (SNR of the LP-FBC syste. Furtherore, fro the effective SNR, we will describe a power allocation strategy which axiizes the capacity of the LP-FBC syste. Let us calculate the effective SNR which is a ratio of the effective signal power and effective noise power. The postprocessed noise can be obtained by U H z = U H G H πl j l z l e /, (5 where the su of the coplex Gaussian noise is ultiplied by the PPN atrix at the receiver G H l and post-processing atrix U H. Therefore, the power of the post-processed noise can be calculated as E U H z z H U ] = = N 0 = N 0 UH E U H G H l z l w H l w l z H l G l U ] ( U H G H l G l U = N 0 U H FU = N 0 Λ, G H l G l U (6 since the unitary atrices U and V are the sae. The equation (6 stands for that the post-processed noise is N 0 Λ (i.e., CN (0, N 0 λ n for post-processed noise of the n-th sybol. Therefore, fro (4 and (6, we can forulate the equivalent

6 6 Pre-processing Proposed LP-FBC Syste,, Post-processing TABLE II SIULATION PARAETERS Paraeters Values Filter PHYDYAS prototype filter 1] Overlapping factor (K 4 The nuber of subcarriers ( 104 odulation order QPSK, 16 QA, 64 QA Channel odel AWGN, 3GPP EPA, 3GPP EVA axiu doppler frequency 5 Hz for EPA, 70 Hz for EVA 11] Fig. 6. Equivalent interference-free parallel odel of the proposed LP-FBC syste. representation of the post-processed data y,n as y post,n = h λ n x even,n + λ n z,n, (7 where λ n is the n-th diagonal eleent of the coefficient atrix Λ. The effective SNR of the proposed LP-FBC syste at the n-th sybol of the -th subcarrier can be obtained as SNR n = h p nλ n N 0, (8 where p n is the allocated power for the n-th sybol. Fro the (8, we can calculate the capacity of the LP- FBC as C = 1 N n=0 log ( 1 + h p nλ n N 0, (9 which is an average of the capacity at the n-th sybol, since the SNRs for the different sybols are different fro each other. Furtherore, since the transitted power ust be noralized to 1, there is a constraint given by 1 p N nλ n = 1, (30 n=0 which is proved in Appendix A. By the theore of inequality of arithetic and geoetric eans, all capacities of the different sybols need to be the sae. Therefore, in order to axiize the capacity, the allocated power at the n-th sybol ust be obtained by p n = 1 λ n. (31 By applying the power allocation to the input data, the equivalent representation of the proposed LP-FBC syste at the n-th sybol of the -th subcarrier in (7 can be rewritten as y post,n = h λ n p n x even,n + λ n z,n, = h λn x even,n + λ n z,n, (3 when power of the input data x even,n is noralized as 1. As a result, by allocating power as (30, the SNR of the proposed LP-FBC syste at the n-th sybol of the -th subcarrier becoes SNR n = h p nλ n N 0 = h λ n N 0 λ n = h N 0, (33 and the total transission power becoes 1, which is the sae as with other interference-free systes. Fig. 6 shows the equivalent parallelized odel of the proposed LP-FBC syste, where the vector x P A = x P A,0,, x,] P A is a input vector applying power allocation, and atrix P is a power allocation atrix whose n- th diagonal entry is p n. By using pre-/post-processing and power allocation, the LP-FBC syste can eploy QA data without interference and noise enhanceent. In suary, the proposed LP-FBC syste exploits a half of the available spectru in order to avoid ICI which results in a half of the total data rate copared to OFD and FBC-OQA systes. To copensate the reduced data rate, transission rate in tie doain is doubled, which is faster than Nyquist rate. Without additional processing, the ISI causes severe perforance degradation due to the sybol overlapping in tie doain. However, since the proposed LP-FBC syste eploys SVD-based linear preand post-processing, the ISI is reoved. As a result, the proposed LP-FBC can transfor the overlapped FBC data into interference-free doain fro the SVD-based linear processing. IV. PERFORANCE EVALUATIONS In this section, we copare the perforance of the proposed LP-FBC syste with that of the CP-OFD and FBC- QA systes in 6] in ters of OOBE perforance, perforance under tie-varying channel, and perforance in an asynchronous ulti-user uplink environent. Furtherore, this section contains the coputational coplexities of the ulti-carrier systes. In the conventional FBC-OQA and proposed LP-FBC systes, a PHYDYAS prototype filter with K = 4 is used 1]. We considered an AWGN channel odel, the Extended Pedestrian-A (EPA 5 Hz and Extended Vehicular-A 70 Hz channel odels certified by the 3rd Generation Partnership Project (3GPP LTE standard in 11]. In the case of the 3GPP EPA and EVA channel odels, a tie-variant channel during transission with 5 Hz and 70 Hz axiu Doppler frequency is assued. Perfect channel estiation with SE channel equalization is also assued. The siulation paraeters are suarized in Table II. A. Out-of-band Eission Perforances One of the fundaental advantages of the FBC syste is excellent OOBE perforance copared to the other ulticarrier systes. In order to copare the OOBE perforances,

7 Conv. CP-OFD Conv. FBC-QA 8] Conv. FBC-OQA 64QA Conv. FBC-QA 8] -60 PSD (db QPSK Conv. FBC-OQA 16QA Fig Noralized frequency (Hz PSD coparison to calculate the nuber of usable subcarriers EbNo (db (a perforances of the conventional FBC-QA 8] and LP- FBC systes in the 3GPP EPA 5 Hz channel odel. CP-OFD Conv. FBC-OQA Conv. FBC-QA 8] 64QA Conv. FBC-QA 8] QPSK 16QA Eb/No (db Fig. 8. perforances of the CP-OFD, FBC-OQA, conventional FBC-QA 8] and LP-FBC systes when QPSK data are used in an AWGN channel EbNo (db (b perforances of the conventional FBC-QA 8] and LP- FBC systes in the 3GPP EVA 70 Hz channel odel. Fig. 9. perforances of the conventional FBC-QA 8] and LP- FBC systes in the tie-varying channel odel. the power spectral densities (PSDs of the CP-OFD, FBC- OQA, FBC-QA and LP-FBC systes are siulated with 104 active subcarriers out of 048 total subcarriers in Fig. 7. As shown in Fig. 7, OOBE perforance of the proposed LP-FBC is alost the sae with that of FBC- OQA. Since the proposed syste eploys pre-processing before the transitter filtering and post-processing after the receiver filtering, there is no change in the prototype filter shape and its well-localized characteristic. On the other hands, the conventional FBC-QA syste odifies the filter shape opposed to the proposed LP-FBC syste. The odified filter is not well-localized in frequency doain copared to the prototype filter of the FBC-OQA syste. As a result, the OOBE perforance of the conventional FBC-QA syste is better than CP-OFD syste but is far worse than the other FBC systes. B. Bit Error Rate Perforances Let us copare perforances of the proposed LP- FBC with other ulticarrier systes. We have assued that the total nuber of sybols is 14 which is the nuber of sybols per subfrae. Fig. 8 deonstrates the perforances of the CP-OFD, conventional FBC-QA, and proposed LP-FBC systes when quadrature phase shift keying (QPSK data is used under AWGN channel. The proposed LP-FBC syste shows the sae perforance as FBC-OQA and conventional FBC-QA, and is better than the CP-OFD. By using the pre-/post-processing, the interferences fro the other sybols are copletely reoved in the proposed LP-FBC syste. Furtherore, due to the power allocation, the effective SNR of the LP-FBC syste is the sae with the SNR of the other systes. Therefore, in the AWGN channel, the proposed LP-FBC syste can achieve

8 8 64QA Conv. FBC-QA 8] Conv. FBC-QA 8] Conv. FBC-OQA CP-OFD QPSK 16QA EbNo (db Fig ISO perforances of the conventional FBC-QA 8] and LP-FBC systes in the 3GPP EPA 5 Hz channel odel EbNo (db (a perforances of the proposed LP-FBC, the conventional FBC-QA 8], FBC-OQA, and CP-OFD systes when 64 QA data are used under 3GPP EPA 5 Hz channel odel. the sae perforance as the other FBC systes and superior perforance to CP-OFD syste. Fig. 9 shows the perforances of the conventional FBC-QA and proposed LP-FBC systes in the 3GPP EPA 5 Hz and EVA 70 Hz channel odels, respectively, when SE-based frequency doain equalization is perfored. For the high order odulation, the perforances of the LP-FBC syste are superior to the conventional FBC- QA syste. The reason for this is that the pre-/postprocessing does not change the filter configuration, while the conventional FBC-QA changes the prototype filter of the FBC-OQA syste. Specifically, the conventional FBC-QA syste utilizes an artificially designed filter to lower the OOBE. This artificially designed filter does not perfectly achieve the orthogonality condition presented in (6. Consequently, the use of this artificially designed filter renders the FBC-QA syste vulnerable to the tie-varying channel, resulting in inferior perforance with tie-varying channels. We copare the perforance with a ultiple-input single-output (ISO channel in order to verify that the proposed LP-FBC is able to eploy IO configuration, especially transit antenna diversity. Fig. 10 exhibits the perforances of the conventional FBC-QA and proposed LP-FBC systes in a 1 ultiple-input single-output EPA 5 Hz channel odel when the spatial frequency block code (SFBC is applied. The perforance with a ISO channel deonstrates that transit antenna diversity can be achieved for the proposed LP-FBC, which can be verified by coparing the gradient of the ISO channel with the gradient of single-input single-output (SISO channel. Since the proposed LP-FBC eliinates the intrinsic interferences, it can eploy QA data, and can also eploy IO configuration. In the case of the conventional FBC-QA syste, it also eploys transit antenna diversity, since its ISO channel gradient is twice the gradient of SISO channel Conv. FBC-QA 8] Conv. FBC-OQA CP-OFD EbNo (db (b perforances of the proposed LP-FBC, the conventional FBC-QA 8], FBC-OQA, and CP-OFD systes when 64 QA data are used under 3GPP EVA 70 Hz channel odel. Fig. 11. perforances of the proposed LP-FBC, the conventional FBC-QA 8], FBC-OQA, and CP-OFD systes when 64 QA data are used in tie-varying environents. However, the becoes degraded for high order odulation, due to its artificially designed filter. In particular, it is difficult to eploy transit antenna diversity with the conventional FBC-QA syste when 64 QA odulation is applied. As a result, the siulation validates the fact that the proposed LP-FBC syste can eploy IO configuration, and that its perforance is superior to that of the conventional FBC-QA syste. Fig. 11 depicts that the perforances of the proposed LP-FBC, conventional FBC-QA, FBC-OQA, and CP-OFD systes under the tie varying channels when 64 QA is eployed. Fro the results, perforances of the conventional FBC-QA systes are inferior to those of the other ulticarrier systes. The reason for the inferior

9 9 subcarrier index / 0 User 1 User tie Fig. 1. Tie and frequency alignent of two users in an asynchronous uplink environent. TABLE III COPUTATIONAL COPLEXITIES OF THE ULTICARRIER SYSTES ulticarrier Systes CP-OFD FBC-OQA Conventional FBC-QA 8] Proposed LP-FBC Coputational Coplexity ( (log ( ( 3 + 4/ log 3 + 8/ + 4K ( ( log 3 + 8/ +4K + ( / ( ( log 3 + 8/ +4K + 4N 10 - CP-OFD Conv. FBC-QA 8] Conv. FBC-OQA Eb/No (db Fig. 13. perforances of the CP-OFD, FBC-OQA, conventional FBC-QA 8] and LP-FBC systes for asynchronous two-user uplink environent. perforance is that the conventional FBC-QA eploys artificially designed filters which do not achieve perfect orthogonality condition. As a result, the artificially designed filters render the conventional FBC-QA syste vulnerable to tie-varying channel. In the cases of the proposed LP-FBC syste, perforances are also slightly lower than those of the conventional FBC-OQA and CP-OFD systes for 0 db or higher E b /N 0. The reason for this is that the ISI caused by tie-varying channel affects a perforance of SVD-based linear pre-/post-processing for high E b /N 0. Copared to the results of conventional FBC-QA syste, however, the perforance degradation caused by the tie-varying channel is extreely low. C. Perforance in Asynchronous ulti-user Environent One of the key advantages of the FBC syste is its robustness to the asynchronous ultiuser uplink environent. Let us copare the perforance of the proposed LP- FBC syste with that of conventional ulticarrier systes under this environent. As shown in Fig. 1, we consider an asynchronous uplink environent with two users. In the considered environent, we assue that both users eploy adjacent frequency bands without a guard band. Furtherore, we assue that the signals of both users arrive asynchronously with tiing offset τ and that the tiing offset τ is a unifor rando variable in the interval 0, T/], where T is the tie duration of transission sybol. Fig. 13 shows the perforances of the ulticarrier systes when the sybols of two users are received asynchronously in the tie doain. The proposed LP-FBC shows the best perforance, as does the FBC-OQA. The reason they obtain the best perforance in the asynchronous uplink environent is that their OOBE perforances are excellent copared to the CP-OFD and conventional FBC-QA. Due to the tiing isalignent between the users, the signal of the desired user (user 1 appears nonorthogonally to the signal of the interference user (user. This non-orthogonality causes out-of-band leakage and degrades the perforance. The best OOBE perforance results in the lowest out-of-band leakage for the proposed LP-FBC and FBC-OQA. Therefore, since the proposed LP-FBC has the sae OOBE as FBC-OQA, it can be utilized for the asynchronous ultiuser uplink scenario. Conversely, the perforances of the conventional FBC-QA and CP-OFD are inferior to the proposed LP- FBC and FBC-OQA. In particular, CP-OFD shows the worst perforance in the asynchronous ultiuser uplink environent. The reason for this is that their OOBE perforances, as shown in Fig. 7, are relatively lower than the those of the proposed LP-FBC and FBC-OQA. Contrary to the proposed LP-FBC, they are relatively weak to the asynchronous ultiuser uplink environent. D. Practical Ipleentations This subsection presents the coputational coplexity and syste overhead of the proposed LP-FBC syste copared with conventional CP-OFD, FBC-OQA, and FBC- QA systes. The coputational coplexity is evaluated by coputing the nuber of real ultiplications of the transitter per QA data transission. The coputational coplexities of the conventional CP-OFD, FBC-OQA, and FBC- QA systes are suarized in III fro 8], 1], 13]. The proposed LP-FBC syste possesses an on-line coputational coplexity due to the additional atrix ultiplication fro the linear processing for each subcarrier. Since the / QA data are transitted for each sybol, N nubers of ultiplications are needed in the linear processing to transit N/ QA data. In addition, instead of ultiplying the power allocation atrix P and the pre-processing atrix V separately, we can obtain the pre-processed data vector x pre n by ultiplying the atrix VP. Therefore, since the power

10 10 allocation and pre-processing can be perfored concurrently, the total coputational coplexity fro the power allocation and pre-processing is 4N. Therefore, the total coputational coplexity of the proposed FBC-QA for each piece fo QA data is given by c prop LP-FBC = (log ( 3 + 8/ } {{ } IFFT + }{{} 4K PPN + }{{} 4N. Pre-processing (34 Contrary to the other ulticarrier systes, the coplexity of the LP-FBC syste increases when the nuber of sybols increases. The reason for this is that size of the linear processing atrices V and U H increase as the nuber of sybols increases. The LP-FBC syste requires off-line syste overhead in order to calculate the pre-processing atrix V and postprocessing atrix U H fro SVD operation. In addition, power allocation ust be perfored for each sybol. However, the kind of syste overhead is not the sae as on-line or real-tie syste overhead, since the pre-/post-processing and power allocation do not depend on the input data but depend only on the prototype filter. Therefore, the LP-FBC syste requires off-line syste overhead only once, when the LP- FBC syste is initially set. In addition to the coputational coplexity, there is additional syste latency fro the post-processing. Postprocessing should be perfored after all the sybols are received. The reason is that such linear processing is burst level processing, while the CP-OFD and FBC-OQA systes are sybol level processing. Receiver need to wait for all the sybols in order to decode data, even if the data is involved in the first sybol. Therefore, the syste latency should be twice the total sybol length than CP-OFD and FBC-OQA systes. In the actual counication syste, however, there is an interleaving technique which also needs to wait for all the sybols in the receiver. Such interleaving technique is also perfored after all sybols are received. Therefore, since the post-processing can be siultaneously applied with an interleaving technique, syste latency fro the burst level processing is reasonable. Contrary to the coputational coplexity and syste latency, peak-to-average power ratio (PAPR of the proposed LP-FBC does not increase. The proposed LP-FBC exploits QA data which doubles the power copared to OQA data. However, the QA data are allocated only to even-nubered subcarriers, half of the total subcarriers. This iplies that LP- FBC s transission power per a sybol is the sae with that of the FBC-OQA syste. Furtherore, the transission duration of the LP-FBC is also the sae with that of the FBC-OQA. As a result, PAPR of the proposed LP-FBC is the sae with that of the FBC-OQA. V. CONCLUSION In this paper, we proposed an LP-FBC syste which can utilize conventional IO techniques by reoving the intrinsic interferences. For the first step, reoving the intrinsic interferences, we represented the intrinsic interferences fro the other sybols in a linear atrix for. The received data were transfored into the interference-free doain by eploying SVD-based linear processing. Also, we eployed power allocation across sybols to axiize the capacity of the syste. The proposed LP-FBC syste opens up new horizons for enabling conventional IO technology in the FBC systes. Nuerical results showed that the OOBE perforance is alost identical to that of the FBC-OQA syste and perforance is the sae with the FBC-QA syste. Thanks to this superior OOBE perforance, the perforance of the proposed LP-FBC syste outperfors the CP-OFD and conventional FBC-QA systes under high order odulation and asynchronous uplink ultiuser environents. Possible topics for the future include extending our work to cover reducing the coputational coplexity of the LP-FBC syste. APPENDIX A PROOF OF THE CAPACITY CONSTRAINT Fro (11, the average power of the transission signal s,n can be calculated by N E tr (X P P N ( X P P N ] H = { ( E tr x P P N ( x P P N H ]} N =0 = {Etr(G VX even w N = N = 1 N E tr =0 =0 w H (X even H V H G H ]} { E tr ((X even H V H G H G VX even]} ( (X even H ΛX even] = 1 N n=0 p nλ n. (35 Therefore, since the average power of the transission signal s,n ust be noralized to 1, the constraint of the capacity (30 is satisfied. REFERENCES 1]. Bellanger, D. Le Ruyet, D. Roviras and. Terré, J. Nossek, L. Baltar, Q. Bai and D. Waldhauser and. Renfors, T. Ihalainen and et al., FBC physical layer: a prier, PHYDYAS, January, vol. 5, no. 4, pp. 7 10, 010. ] P. Siohan and C. Siclet and N. Lacaille, Analysis and design of OFD/OQA systes based on filterbank theory, IEEE Transactions on Signal Processing, vol. 50, no. 5, pp , ay 00. 3] R. Zakaria and D. Le Ruyet and. Bellanger, axiu likelihood detection in spatial ultiplexing with FBC, in Wireless Conference (EW, 010 European, April 010, pp ] R. Zakaria and D. Le Ruyet, A Novel Filter-Bank ulticarrier Schee to itigate the Intrinsic Interference: Application to IO Systes, IEEE, vol. 11, no. 3, pp , arch 01. 5]. Renfors and T. Ihalainen and T. H. Stitz, A block-alaouti schee for filter bank based ulticarrier transission, in Wireless Conference (EW, 010 European, April 010, pp

11 11 6] H. Na and. Choi and S. Han and C. Ki and S. Choi and D. Hong, A New Filter-Bank ulticarrier Syste with Two Prototype Filters for QA Sybols Transission and Reception, IEEE Transactions on Wireless Counications, vol. PP, no. 99, pp. 1 1, ] C. Ki, K. Ki, Y. H. Yun, Z. Ho, B. Lee, and J. Y. Seol, QA- FBC: A New ulti-carrier Syste for Post-OFD Wireless Counications, in 015 IEEE Global Counications Conference (GLOBE- CO, Dec 015, pp ] C. Ki, Y. H. Yun, K. Ki, and J.-Y. Seol, Introduction to QA- FBC: Fro Wavefor Optiization to Syste Design, IEEE Counications agazine, vol. 54, no. 11, pp , ] R. Zakaria and D. Le Ruyet, On axiu likelihood IO detection in QA-FBC systes, in Personal Indoor and obile Radio Counications (PIRC, 010 IEEE 1st International Syposiu on. IEEE, 010, pp ] D. Tse and P. Viswanath, Fundaentals of wireless counication. Cabridge university press, ] 3GPP, TS , TSG RAN; Evolved Universal Terrestrial Radio Access (E-UTRA; User Equipent (UE radio transission and reception, Rel.15 v15.0.0, ] L.G. Baltar, F. Schaich,. Renfors and J. A. Nossek, Coputational coplexity analysis of advanced physical layers based on ulticarrier odulation, in Future Network & obile Suit (FutureNetw, 011. IEEE, 011, pp ] A. Sahin, I. Guvenc and H. Arslan, A survey on ulticarrier counications: Prototype filters, lattice structures, and ipleentation aspects, IEEE Counications Surveys & Tutorials, vol. 16, no. 3, pp , 014. Jintae Ki (S 15 received the B.S. degree in Electrical and Electronic Engineering fro Yonsei University, Seoul, South Korea, in 015. He is working toward a Ph.D. degree in Electrical and Electronic Engineering fro Yonsei University, Seoul, South Korea. His research interests are 5G and 6G wireless counications. In addition, his current research interests include the achine learning-based counication syste and design of new wavefor such as the QA-based FBC and GFD. Yosub Park (S 11, 18 received the B.S. and Ph. D. degrees in Electrical and Electronic Engineering fro Yonsei University, Seoul, Korea, in 011 and 018, respectively. Fro arch 018, he is currently an Senior Engineer with Autonoous achine Lab., AI Center, Sasung Research, Sasung Electronics, Seoul, Korea. His research interests are in 5G/6G wireless counications such as ultra-dense networks and cellular-based VX counications. In addition, his current research interests include the siulator design and developent for autonoous driving systes and new wavefor design issues such FBC, GFD, and F-OFD. Sungwoo Weon (S 1 received the B.S. degree in electrical and electronic engineering fro Yonsei University, Seoul, South Korea, in 01, where he is currently pursuing the joint.s./ph.d. degree in electrical and electronic engineering. His current research interests include 5G wireless counications. In addition, his current research interest is the perforance iproveent of filter bank ulticarrier (FBC syste and design of new wavefor for future internet of things (IoT service. Jinkyo Jeong (S 15 received his B.S. degree in Electrical and Electronic Engineering fro Yonsei University, Seoul, Korea, in 015. He is working toward a Ph.D. degree in Electrical and Electronic Engineering at Yonsei University, Seoul, Korea. His research interests are in 5G and beyond 5G wireless counications. In addition, his current research interests are in new wavefor design, full-duplex systes and achine learning. Sooyong Choi (S was born in Seoul, South Korea, in He received the B.S.E.E.,.S.E.E., and Ph.D. degrees fro Yonsei University, Seoul, in 1995, 1997, and 001, respectively. In 001, he was a Post-Doctoral Researcher with the IT Research Group, Yonsei University. His work focused on proposing and planning for the fourth generation counication syste. Fro 00 to 004, he was a Post-Doctoral Fellow with the University of California at San Diego, La Jolla, CA, USA. Fro 004 to 005, he was a Researcher with Oklahoa State University, Stillwater, OK, USA. Fro 005 to 016, he was Assistant Professor and Associate Professor with the School of Electrical and Electronic Engineering, Yonsei University. Since 016, he has been a Professor with the School of Electrical and Electronic Engineering. His research interests include adaptive signal processing techniques (equalization and detection, assive IO systes for wireless counication, and new wavefors and ulticarrier transission techniques for future wireless counication systes. Daesik Hong (S86, 90, S05 received the B.S. and.s. degrees in Electronics Engineering fro Yonsei University, Seoul, Korea, in 1983 and 1985, respectively, and the Ph.D. degree fro the School of Electronics Engineering, Purdue University, West Lafayette, IN, in He joined Yonsei University in 1991, where he is currently the Dean of the College of Engineering and a Professor with the School of Electrical and Electronic Engineering. He has been serving as Chair of Sasung-Yonsei Research Center for obile Intelligent Terinals. He also served as a Vice-President of Research Affairs and a President of Industry-Acadeic Cooperation Foundation, Yonsei University, fro 010 to 011, and served as a Chief Executive Officer (CEO for Yonsei Technology Holding Copany in 011. He also served as a President of the Institute of Electronics and Inforation Engineers (IEIE fro 016 to 017. Dr. Hong is a senior eber of the IEEE. He served as an editor of the IEEE fro 006 to 011. He also served as an editor of the IEEE Wireless Counications Letters fro 011 to 016. He was appointed as the Underwood/Avison distinguished professor at Yonsei University in 010, and received the Best Teacher Award at Yonsei University in 006, 010, and 01. He was also a recipient of the HaeDong Outstanding Research Awards of the Korean Institute of Counications and Inforation Sciences (KICS in 006 and the IEIE in 009. His current research activities are focused on future wireless counication including 5G systes, vehicle-to-everything counication systes, new wavefor, non-orthogonal ultiple access, full-duplex, and AI-based counications. ore inforation about his research is available at