FUTURE generations of broadband wireless systems are

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1 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 60, NO 4, MAY Transmit Processing Techniques Based on Switched Intereaving and Limited Feedback for Interference Mitigation in Mutiantenna MC-CDMA Systems Yunong Cai, Member, IEEE, Rodrigo C de Lamare, Senior Member, IEEE, and Didier Le Ruyet Abstract In this paper, we propose transmit processing techniques based on nove switched intereaving, chipwise inear precoding, and imited feedback for both downink and upink muticarrier code-division mutipe access (MC-CDMA) mutipe-antenna systems We deveop transceiver structures with switched intereaving, inear precoding, and detectors for both upink and downink using imited-feedback techniques In the proposed schemes, a set of possibe chip intereavers is constructed and prestored at both the base station (BS) and mobie stations (MSs) For the downink, a new hybrid transmit processing technique based on switched intereaving and chipwise precoding is proposed to suppress the mutiuser interference The BS and MSs are aso equipped with another codebook of quantized downink channe-state information (CSI) Each MS quantizes its own downink CSI and feeds the index back to the BS through a ow-rate feedback channe Then, the seection function at the BS determines the optimum intereaver based on the CSI of a users Moreover, a transmit processing technique for the upink of mutipe-antenna MC-CDMA systems, which requires a very ow rate of feedback information, is aso proposed Codebook design methods for both intereavers and quantized CSI are aso proposed Simuation resuts show that the performance of the proposed techniques is significanty better than prior art Index Terms Chip intereaving, interference suppression, imited feedback, muticarrier code-division mutipe access (MC-CDMA), mutipe-antenna systems, precoding I INTRODUCTION FUTURE generations of broadband wireess systems are expected to support a wide range of services and bit rates by empoying a variety of techniques that can achieve the highest possibe spectrum efficiency [1] Muticarrier code-division mutipe access (MC-CDMA), which is a combination of orthogona frequency-division mutipexing (OFDM) and code- Manuscript received February 22, 2010; accepted January 10, 2011 Date of pubication January 31, 2011; date of current version May 16, 2011 The review of this paper was coordinated by Prof R C Qiu Y Cai is with Department of Information Science and Eectronic Engineering, Zhejiang University, Hangzhou , China (e-mai: ycai@ zjueducn) R C de Lamare is with the Communications Research Group, Department of Eectronics, University of York, YO10 5DD York, UK (e-mai: rcd500@ohmyorkacuk) D Le Ruyet was with the Eectronics and Communications Laboratory and is now with the Centre d Etudes et De Recherche en Informatique du Conservatoire Nationa des Arts et Métiers Research Laboratory, Paris, France (e-mai: eruyet@cnamfr) Coor versions of one or more of the figures in this paper are avaiabe onine at Digita Object Identifier /TVT division mutipe access (CDMA), has been attracting much attention [2] The benefits of MC-CDMA incude high spectra efficiency, easy adaptation to severe channe conditions without compex detection, and robustness to intersymbo interference (ISI) and fading caused by mutipath propagation [3] There are severa variations of MC-CDMA, eg, muticarrier directsequence CDMA (MC-DS-CDMA) proposed by DaSiva and Sousa [4] and mutitone CDMA proposed by Vandendorpe [5] These signas can easiy be transmitted and received using the fast Fourier transform (FFT) without increasing the transmitter and receiver compexities and have the attractive feature of high spectra efficiency Giannakis et a proposed the generaized muticarrier (GMC) CDMA system and afforded an a-digita unifying framework, which encompasses singe-carrier (SC) and severa MC-CDMA systems [6] Moreover, transmit processing techniques that are impemented at the base station (BS) with mutipe antennas have received wide attention, because they require a simpe receiver at the mobie station (MS) This condition eaves the BS with the task of precoding the signas in view of suppressing the mutiuser interference (MUI) and adapting to the propagation channes The essentia premise of using transmit processing techniques is the knowedge of the channe-state information (CSI) at the transmitter In time-division dupexing (TDD) systems, CSI can be obtained at the BS by expoiting reciprocity between the forward and reverse inks In frequency-division dupexing (FDD) systems, reciprocity is usuay not avaiabe, but the BS can obtain knowedge of the downink user channes by aowing the users to send a sma number of feedback bits on the upink The imited-feedback approach has widey been investigated in mutiuser mutipe-input mutipe-output (MIMO) systems [7] [12] In particuar, [8], [9], and [12] aow users to quantize some function of downink CSI and send this information to the BS When the channe is quantized, the user signas cannot perfecty be orthogonaized due to inherent quantization errors, the residua interference affects the system performance consideraby, and it aso requires a significant amount of bits for satisfactory performance Thus, nove schemes that require a ow rate of feedback bits, which can give better performance, are needed To the best of our knowedge, in the iterature, no preprocessing works have considered the signa intereaving in the time domain, together with spatia processing for MC-CDMA systems In this paper, we propose, for the first time, nove transmit processing techniques based on a /$ IEEE

2 1560 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 60, NO 4, MAY 2011 switched-intereaving agorithm for both downink and upink MC-CDMA mutipe-antenna systems In the proposed schemes, a set of chip intereavers are constructed and prestored at both the BS and MSs During the transmission, the optimum intereaver is chosen by the seection function at the BS For the downink systems, the summary of the contributions is isted as foows A new hybrid transmit processing technique based on switched-intereaving and chipwise precoding techniques that require the feedback quantized CSI of a users is proposed to suppress the MUI The reevant inear minimum-mean-square error (MMSE) receiver is designed for symbo recovery at the MS [13] Taking into account the intereaving and transmit precoding, we compute the effective spreading codes and obtain the received signa-to-interference-pus-noise ratio (SINR) as the seection criterion for choosing the optimum intereaver We show the abiity of the proposed downink agorithm to dea with the channe estimation error at the receiver Note that preprocessing techniques for the upink transmission are reativey unheeded due to the imitation of MS To this end, we aso propose a transmit processing technique and a transceiver for the upink of mutipe-antenna MC-CDMA systems, which requires a very ow rate of feedback information In particuar, we wi show that the proposed upink scheme is very efficient and simpe to design The contributions for the upink are summarized as foows Instead of sending the quantized CSI, the BS feeds the index that corresponds to the optimum intereaver back to the MSs The users wi send data by using the intereaver that corresponds to the index that was sent from the BS in this particuar channe situation A preprocessing technique based on the proposed switched-intereaving scheme with ow-rate feedback information is deveoped We aso present a design agorithm for the seection functions and the MMSE receivers for the upink In addition, severa chip-intereaving codebook design methods and channe quantization schemes are proposed for the downink and upink Note that the codebooks are designed offine and each user appies the same optimum intereaver to process the symbos The simuations show that the performance of the proposed techniques is significanty better This paper is structured as foows Sections II and III describe the system modes, the precoders and MMSE receivers, and the seection of parameters and optimization for the proposed downink and upink schemes, respectivey Limitedfeedback timing structures and techniques for designing codebooks are described in Section IV The simuation resuts are presented in Section V Section VI draws the concusions The superscripts () T, (), () 1, (), and () H denote the transpose, eementwise conjugate, matrix inverse, Moore Penrose pseudoinverse, and Hermitian transpose, respectivey Bod symbos denote matrices or vectors The symbos, E[],,, R(), sgn{}, ()!, and I M represent the Kronecker product, expectation operator, norm of a scaar, norm of a vector, seecting the rea part, signum function, factoria operator, and M M identity matrix, respectivey The operations (:,y), (x, :), and () x denote taking the yth coumn of a matrix, the xth row of a matrix, and the xth eement of a vector, respectivey The operation (x : y) denotes generating a new vector by taking the eements from the xth to the yth entries of a vector II DOWNLINK TRANSMISSION AND RECEPTION In this paper, we assume that the systems have contro and feedback channes that can provide the required information In practice, most standards have such channes [14] [16] The proposed downink imited-feedback-based MC-CDMA mutiantenna mode is presented in Fig 1, eft-hand side, where the soid ine represents the transmission ink, and the dashed ine represents the imited-feedback ink We consider that the BS is equipped with mutipe antennas and the MS is equipped with a singe antenna, because the MSs are ess ikey to be equipped with mutipe antennas than the BS A the MSs and the BS are equipped with the codebook of quantized CSI and the same codebook of chip intereavers The proposed downink system worksasfoows Each user seects an index from the codebook of the quantized CSI based on the downink channe estimation and reays it to the BS by a imited-feedback channe The feedback quantized CSIs are empoyed to compute the chipwise transmit precoder and the seection function to cacuate and choose the index of the optimum intereaver from the codebook of intereavers at the BS The downink data is operated by the optimum intereaver, and the BS broadcasts the index of the optimum intereaver to a the MSs prior to data transmission A Proposed Downink System Mode and Chipwise Precoder The downink transceiver structure of the proposed scheme is presented on the right-hand side of Fig 1 We consider an uncoded synchronous binary phase-shift keying (BPSK) MC- CDMA system with K users, N chips per symbo, and N t transmit antennas, where the N 1 vectors s 1,,s K denote the spreading codes We assume that each bock contains M symbos and that b k (i) [b (k) 1 (i),,b(k) M (i)]t denotes the ith bock data for user k, b m (k) (i) {±1}, m 1,,M, k 1,,K Here, we drop the index i for notation simpicity For each user, the chip intereaver permutes one bock of chips per time The permutated chips of user k before the precoding procedure are given by x () k A kp S k b k (1) where the quantity A k is the ampitude that is associated with user k The matrix P denotes the th MN MN intereaving matrix that is designed by the intereaving patterns of the codebook, where 1,,2 B, B is the number of bits to represent the index of the intereaver, and 2 B is the ength of the intereaver codebook The quantity S k s k I M is the

3 CAI et a: TRANSMIT PROCESSING BASED ON INTERLEAVING AND LIMITED FEEDBACK IN MC-CDMA 1561 Fig 1 Proposed downink imited-feedback-based mutipe-antenna MC-CDMA mode and transceiver structure MN M spreading code matrix We define the K MN matrix X () [x () 1,,x() K ]T, which consists of a bock of permutated chips of a the users Through the MN-point FFT and inverse fast Fourier transform (IFFT) and a cycic prefix, the mutipath fading channe can be divided into MN narrowband channes in the frequency domain [17], where we define a K N t matrix D β as the equivaent channe matrix of the βth chip or subcarrier β 1,,MNTheK 1 received vector c β, that consists of the βth received chips of a the users before deintereaving denotes c β, D β G β X () (:,β)+ñ β (2) where ñ β denotes the K 1 noise vector, and G β is the N t K precoding matrix of the βth chip In this paper, the zeroforcing precoding is empoyed [7], which is given by G β ( Tr U G β GH β )G β (3) where G β D β, and U denotes the transmit power constraint U E[ X () (:,β) 2 ] B Effective Spreading Code and Linear MMSE Receiver We rewrite G β as G β [g (β) 1,,g(β) K ], where g(β) k is the N t 1 precoding vector for the kth user, and we define that the MN 1 vector s k is generated by stacking M copies of the kth user s spreading code vector on top of each other The intereaved spreading code vector is given by p k, P s k We obtain the MN 1 deintereaved effective spreading code vector of the kth user for the th intereaver that corresponds to the k 0 th user s channe as s k,k0, P 1 D 1 (k 0, :)g (1) k (p k,) 1 D MN (k 0, :)g (MN) k (p k, ) MN (4) where P 1 denotes the deintereaving matrix k 0 1,,K Then, we define two K MN matrices C and C r, which are given by C [c 1,,,c MN, ] and C r P 1 C T, and the received vector that corresponds to the mth symbo after deintereaving for the desired user k 0 is given by r (m) k 0, Cr ((m 1)N +1:mN),k 0 ) K k1 A k s (m) k,k 0, b(k) m + n m,k0 (5) where the N 1 vector s (m) k,k 0, s k,k 0,((m 1)N +1: mn) denotes the effective spreading code of the kth user that corresponds to the k 0 th user s channe for the mth symbo, the vector n m,k0 is the N 1 deintereaved noise vector, and E[ n m,k0 n H m,k 0 ]σ 2 I N To obtain the MMSE receiver, we minimize [ J MSE E Ak0 b(k 0) m wm,k H 0,r (m) 2] (6) k 0 We take the gradient with respect to wm,k 0, and set it to zero After further mathematica manipuations, we obtain the

4 1562 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 60, NO 4, MAY 2011 desired user s MMSE receiver of the th intereaver for the mth symbo, which is given by ( K ) 1 w m,k0, A 2 k s(m) k,k, s(m)h 0 k,k 0 + σ2 I N A 2 k 0 s (m) k 0,k 0, k1 (7) The compexity of the downink chipwise precoder and the MMSE receiver is O(Nt 3 ) and O(N 3 ), respectivey, due to the matrix inversion To reduce the compexity, we can rey on advanced ow-compexity parameter estimation agorithms [18] [21] C Seection of Parameters and Optimization By using the different intereaving patterns, we generate 2 B groups of effective spreading sequences with different cross correations, which cause different eves of MUI The BS transmitter is equipped with the seection function Through the feedback quantized CSIs of a the users, the optimum intereaver index is chosen to maximize the sum received SINR over a the users in this codebook The received SINR of the th branch for the k 0 th user is given in (8), which is computed as the ratio between the signas energy of user k 0 per bock and the energy of interference pus noise in the same bock, ie, SINR (k 0) M m1 [w E m,k H 0, A2 k 0 s (m) k 0,k, s(m)h 0 [ M m1 E k 0,k 0, w m,k 0, ] wm,k H 0, F,k 0 F H,k 0 w m,k0, ] M m1 [wm,k H 0, R() s,k 0 w m,k0, ] (8) M m1 [wm,k H 0, R() I,k 0 w m,k0, where the interference-pus-noise component F,k0 r (m) k 0, A k 0 s (m) k 0,k 0, b(k 0) m, and the matrices R () s,k 0 A 2 k 0 s (m) k 0,k, s(m)h 0 k 0,k 0,, R() I,k 0 U () I,k 0 U ()H I,k 0 + σ 2 I, and U () I,k 0 [ A 1 s (m) 1,k 0,,, A k 0 1 s (m) k 0 1,k 0,,A k 0 +1 s (m) k 0 + 1,k 0,,, A K s (m) K,k 0, ], 1,,2B, k 0 1,,K The optimum index opt for the downink system maximizes the sum received SINR, as given by opt arg max 12 B { K k 0 1 SINR (k 0) The fina output is given by ( )} ˆb(f) k 0,m {R sgn wm,k H 0, opt r (m) k 0, opt ] } (9) (10) (f) where ˆb k 0,m is the mth estimated symbo within a bock for the k 0 th user The MMSE receiver w m,k0, in (8) can be repaced by the effective spreading sequence s (m) k 0,k 0, to reduce the compexity of the seection function; thus, (8) becomes SINR (k 0) M m1 [ s (m)h k 0,k 0, R() s,k 0 s (m) k 0,k 0, M m1 [ s (m)h k 0,k 0, R() I,k 0 s (m) k 0,k 0, M m1 M m1 A2 (m) k 0 s k 0,k 0, σ 2 M k k 0 A 2 k ρ (m) k,k 0, ] ] m1 s (m) k 0,k 0, 2 (11) where the cross correation of the mth symbo is denoted by ρ (m) k,k 0, s(m)h k,k 0, s(m) k 0,k 0,, k 1,,K, k k 0Itiseasyto show that (11) can be written as SINR (k A 0) 2 k 0 s k0,k 0, 4 k k 0 A 2 k sh k 0,k, s 0 k,k 0, + σ 2 s k0,k 0, 2 (12) Note that the vaue of s k0,k 0, 2 is the same for a the intereavers Thus, the received SINR of the k 0 th user in this case changes as the cross-correation summation k k 0 s H k 0,k, s 0 k,k 0, buiding on the th intereaver within one bock The optimum intereaver is chosen from the wedesigned prestored intereaving codebook to maximize the received SINR for each fading bock III UPLINK TRANSMISSION AND RECEPTION The proposed upink scheme and transceiver structure are presented in Fig 2 Simiar to the downink, the BS with N r receive antennas, and each MS with a singe antenna is equipped with the same codebook of chip intereavers Based on the estimated upink CSI of each user, the BS feeds back an index that corresponds to the best avaiabe codebook entry to a the MSs, which seect the same chip intereaver that corresponds to the feedback index to transmit signas A Proposed Upink System Mode Spatia processing techniques can be empoyed at the BS receiver to detect users symbos [22] The MN 1 received vector of the th intereaver for the n r th receive antenna after deintereaving is given by r nr, K k1 P 1 Λ k,nr A k P S k b k + n nr (13) where n r 1,,N r, the quantity n nr is the MN 1 deintereaved compex Gaussian noise vector of the n r th receive antenna, and the matrix Λ k,nr denotes an MN MN diagona matrix, which is the equivaent frequency-domain upink channe matrix between the kth user and the n r th received antenna

5 CAI et a: TRANSMIT PROCESSING BASED ON INTERLEAVING AND LIMITED FEEDBACK IN MC-CDMA 1563 Fig 2 Proposed upink imited-feedback-based mutipe-antenna MC-CDMA mode and transceiver structure B Linear MMSE Receiver Due to the mutipe antennas at the BS, we propose an MMSE receiver based on spatia tempora processing techniques for the proposed upink scheme To reuse the space dimension, we stack the N 1 deintereaved vectors r nr,((m 1)N +1:mN) from a the receive antenna eements on top of each other; thus, we obtain an N r N 1 vector with regard to the mth symbo, ie, [ ] T r s m, r (m)t 1,, r (m)t 2,, r (m)t N r, (14) where the vector r (m) n r, r n r,((m 1)N +1:mN) The fina MN 1 effective spreading code vector of the th intereaver for the kth user with regard to the n r th receive antenna is given by p k,nr, P 1 Λ k,nr p k, (15) If we define the vector p (m) k,n r, p k,n r,((m 1)N +1: mn), then the stacked received vector with regard to the mth symbo can be written as r s m, K k1 p s m,k,a k b (k) m + n s m (16) where the N r N 1 vector p s m,k, [ p(m)t k,1,,, p(m)t k,n r, ]T, and n s m is the N r N 1 stacked noise vector E[ n s m nsh m ] σ 2 I Nr N By foowing the same approach in the previous section, we obtain the upink MMSE receiver expression of the th intereaver for the k 0 th user that corresponds to the mth symbo as w m,k0, ( K k1 ) 1 A 2 k ps m,k, psh m,k, + σ 2 I Nr N A 2 k 0 p s m,k 0, (17) The compexity of the upink MMSE receiver is O((N r N) 3 ) Note that some other receivers aso can be empoyed, eg, adaptive inear receivers [23] and decision feedback receivers [24], [25] C Seection of Parameters and Optimization For the upink, the seection function is aso equipped at the BS, which contains a the information of chip intereavers in this codebook, the estimated MSs upink channes, as we as the MMSE receivers Simiar to the downink case, the received SINR expression for the th intereaving pattern of the kth user has the same form as (8), where the vectors w m,k0, and s (m) k,k 0, are repaced by the upink N t N 1 receiver and the stacked effective spreading code p s m,k,, respectivey The expression of the upink optimum index is the same as (9), and the fina output for the k 0 th user of the mth symbo is given by { sgn R ˆb(f) k 0 ( w H m,k0,opt r s m,opt )} (18) IV DESIGN OF LOW-RATE FEEDBACK FRAME STRUCTURES AND CODEBOOKS In this section, the frame structures of the proposed downink and upink ow-rate feedback schemes are introduced Then, the agorithms for designing codebooks for both quantized CSI and intereavers are described To use a reativey sma number of feedback bits, we focus on the time-domain CSI and separatey quantize the channe direction and the channe norm Then, we cacuate the frequency-domain CSI based on the timedomain CSI Note that the frequency-domain reduced-feedback quantization scheme in [26], [27] can aso be empoyed A Low-Rate Feedback Frame Structures For both upink and downink schemes, preambe transmission and imited feedback are prior to payoad transmission

6 1564 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 60, NO 4, MAY 2011 Fig 3 Frame structure of the proposed downink feedback scheme within each fading bock The CSI is estimated from the preambe at the receiver Fig 3 shows the frame structure of the proposed downink feedback scheme Each MS quantizes its own CSI and feeds back the index of the quantized CSI to the BS, which seects the optimum intereaver to preprocess the data Payoad transmission starts after the imited feedback, the first B bits that are broadcast are used to inform each MS the reevant optimum deintereaver, and the rest of the payoad is the preprocessed data In this paper, we assume that the deintereaver index is accuratey known by the MSs Because we consider that the channe is a bock-fading channe, ie, the channe coefficients can be treated as constants over one fading bock, the feedback rate of the optimum index is once per fading bock The proposed upink scheme has a simiar frame structure as the downink scheme However, the BS feeds back the index of the optimum intereaver to each MS Thus, the upink payoad contains the preprocessed data ony We assume that the CSI is perfecty estimated at the receiver Aternativey, we can empoy a channe estimation agorithm that is trained with the preambe [34] Furthermore, error-free transmission of feedback information is not possibe if the feedback channe is noisy In the next section, we wi show the performance of the nove feedback schemes based on feedback channes with errors B Design of Codebooks for Channe Direction and Norm Quantization Because the channe is constant during a transmission bock, to reduce the feedback bits for the downink, we consider quantizing the mutipath mutiantenna fading channe in the time domain at the receiver Let us write the channe matrix of the kth user as H (k) (1, 1) H (k) (1, 2) H (k) (1,L p ) H k H (k) (2, 1) H (k) (2, 2) H (k) (2,L p ) H (k) (N t, 1) H (k) (N t, 2) H (k) (N t,l p ) (19) where L p is the number of channe paths, and N t denotes the number of transmit antennas at the BS By using a vector quantization scheme [28], we can quantize the vectors of (19) per row or coumn, ie, quantize the vector H k (n t, :) across the channe paths for each transmit antenna or the vector H k (:,α) across the transmit antennas for each channe path, where n t 1,,N t, and α 1,,L p Define 2 δ 1 and 2 δ 2 as the direction codebook vector size and the norm codebook size, respectivey It is easy to see that the two quantization methods require (δ 1 + δ 2 )N t and (δ 1 + δ 2 )L p feedback bits, respectivey In the foowing discussion, we introduce the codebook design to quantize the vector across the transmit antennas, and the method is straightforward for the other method Note that some simiar methods in the time domain can be found in [33], [35], and [36], and some other quantization schemes can be appied in the frequency domain [26], [27] The quantization of the channe direction information has been introduced by Narua et a in [28], where the Loyd agorithm was suggested for the design of the beamforming vector codebook The authors in [29] and [30] showed that the codebook shoud be constructed by minimizing the maximum inner product between any two beamforming vectors in the codebook We define the normaized channe vector, ie, the channe direction as h h h (20) where h H k (:,α), which denotes the N t 1 channe vector across the transmit antennas per path, h is the channe norm, and h is isotropicay distributed in the N t -dimension hypersphere of a unit radius The receiver chooses the best quantized channe direction vector from a common codebook T { h q 1,, h q } in the maximum instantaneous correation 2 δ 1 sense as h q opt arg max h H h q i 2 (21) h q i T where i 1,,2 δ 1 An appropriate direction codebook is one that is designed to maximize the minimum chorda distance [29] We have T opt max T C N t 2δ 1 min d 1 i<j 2 δ 1 ( h q i, h q j ) (22)

7 CAI et a: TRANSMIT PROCESSING BASED ON INTERLEAVING AND LIMITED FEEDBACK IN MC-CDMA 1565 where ( d h q i, ) h q j 1 h qh h q 2 (22) and C N t 2 δ 1 denotes the N t 2 δ 1 compex matrix space The Loyd agorithm is described in the Appendix To avoid the sum-rate degradation, we propose to use different direction codebooks for each user, and each user rotates the common codebook by a random unitary matrix to generate its own codebook [12] With regard to the channe norm (scaar information), the agorithm is much simper, and we use a nonuniform scaar quantizer C Codebook of Intereavers We assume that the th intereaving order is φ (1),φ (2),,φ (MN), where φ () is defined as the order permutation function For β 1,,MN, the permutation matrix P is generated by fiing the eement of the βth row and the φ (β)th coumn of an MN MN zero matrix with 1 The βth row vector of the matrix P is given by P(β,:) [0,,0, 1, 0,,0] (24) }{{} φ (β) 1 The optimum intereaving codebook consists of (MN)! intereavers It is ceary impractica for any system when M and N are arge numbers Therefore, we need to seect a subset of entries from the optimum codebook to buid a practica suboptimum codebook that performs we The first method is to randomy permutate the chips within one bock, and we create the codebook by generating 2 B random-intereaving patterns The second method is based on a bock-intereaving method [31], where a bock of chips comes into a matrix coumnwise and goes out rowwise, and by varying the dimension of the matrix, we can obtain different intereaving patterns for the codebook entries We assume that, for the th intereaving pattern, the matrix dimension is dx () dy (), where dx () dy () MN, and the permutation matrix P is given by θ 1, I dy () θ 2, I dy () P (25) θ dx (), I dy () where θ μ, is a 1 dx () vector, μ 1,,dx (), and i θ μ, [0,,0, 1, 0,,0] (26) }{{} μ 1 We aso propose a method for the intereaving codebook design The basic principe is to buid a codebook that contains the intereaving patterns with the maximum sum SINR (MASS) To impement the method, we need to conduct an extensive set of experiments and compute the sum SINRs for the indices of the random candidate patterns The codebook is generated based on the statistics by choosing 2 B patterns with the maximum average sum SINR as the entries of the codebook We define j an N i N e matrix V SINR as the storage of the sum SINRs for N i possibe intereavers over N e testing channes, where N i shoud be a arge integer and practica for the experiment, N e is the tota number of experiments, and V 0 is the ist that contains a N i intereaving patterns The agorithm is summarized as foows Step 1 Initiaization phase Initiaize N e and 2 B and choose an appropriate vaue for N i Set v idx, V SINR, and V MASS with nu Generate N i random-intereaving patterns, given the ist of the intereavers to the matrix V 0 Step 2 Set n e 1 Step 3 Set 1 Step 4 Sum SINR cacuation Generate the th permutation matrix that corresponds to the th entry in the intereaver ist V 0 The sum SINR of the th intereaver entry is computed based on the permutation matrix P, the n e th testing channe matrix, and spreading sequences s k Giveittothe th eement of the coumn vector V SINR (:,n e ) Step 5 +1 Loop back to Step 4 unti >N i Step 6 n e n e +1 Loop back to Step 3 unti n e >N e Step 7 Compute the average sum SINR Based on the matrix V SINR, by averaging the sum SINRs over the N e testing channes, an N i 1 vector v idx is generated Step 8 Generate codebook The fina codebook V MASS is generated by seecting 2 B patterns from V 0 with the maximum average sum SINR according to v idx V S IMULATIONS In this section, we evauate the performance of the proposed inear processing schemes with switched intereaving and compare them to other existing schemes, ie, the conventiona MC-CDMA system [2] and the MC-CDMA system that uses the chip-intereaving agorithm [31] We adopt a simuation approach and conduct severa experiments to verify the effectiveness of the proposed techniques We carried out simuations to assess the average bit-error-rate (BER) performance of the intereaving agorithms for different oads, signa-tonoise ratios (SNR), the number of antennas, and the number of intereaving patterns In this paper, our simuation resuts are based on an uncoded system with perfect CSI at the receiver The ength of the data bock is set to M 8 symbos, 128 subcarriers are used for each bock, the random spreading code with a spreading gain N 16is generated for the simuations, and the ength of the CP is enough to eiminate interbock interference A channes have a profie with three taps whose powers are p 0 0dB, p 1 7 db, and p 2 10 db, respectivey, which are normaized, and the spacing between paths is 1/(MN) symbo duration The sequence of channe coefficients is given by h (i) p α (i)( 0, 1, 2), where α (i) are zero-mean circuary symmetric compex Gaussian random variabes with unit variance We have studied the proposed

8 1566 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 60, NO 4, MAY 2011 Fig 4 Average BER performance versus the number of transmit antennas for the proposed downink schemes with precoders and the conventiona MC- CDMA schemes without precoders schemes with other channe profies; however, we have opted for this approach to make the resuts easiy reproducibe Note that the three-tap channe mode has been used by previousy reported works, eg, [23] [25] Other channe modes, eg, the Universa Mobie Teecommunications System (UMTS)- Vehicuar channes, can be aso used; however, our studies indicate that the gains provided by the proposed schemes do not significanty change for the other channe modes studies Among the different schemes and quantization agorithms, we consider the foowing approaches: C-MC-CDMA: the conventiona MC-CDMA system with the MMSE detector; P-MC-CDMA-prec-SI: the proposed preprocessing MC- CDMA system with switched intereaving and chipwise precoding schemes for the downink; P-MC-CDMA-SI: the proposed preprocessing MC- CDMA system with switched-intereaving scheme for the upink; MC-CDMA-prec: the conventiona MC-CDMA system that empoys the chipwise precoding scheme for the downink; Perfect CSI: the perfect CSI at the transmitter; Quan-ant: vector quantization for the CSI across the channe paths per transmit antenna; Quan-tap: vector quantization for the CSI across the transmit antennas per channe path; B-bit: the proposed system empoying B bits for the switched-intereaving scheme Fig 4 shows the average BER performance of the proposed downink switched-intereaving schemes combined with precoders and the conventiona MC-CDMA schemes without precoders In this experiment, we consider the scenario with a SNR of 10 db and seven users The knowedge of the CSI is given for the precoders at the transmitter, and the intereav- Fig 5 Average BER performance versus SNR for the proposed downink agorithms with different CSI quantization schemes and the conventiona MC- CDMA systems Fig 6 Average BER performance versus the number of users for the proposed downink agorithms with different CSI quantization schemes and the conventiona MC-CDMA systems ing codebook is designed by using the random-intereaving method The schemes with precoders are much better than the conventiona MC-CDMA MMSE receivers As the number of transmit antennas increases, the average BER decreases, and the gap between them becomes arger Furthermore, the precoders with the proposed switched-intereaving scheme outperform the precoder without switched intereaving, and the performance improves as the number of the intereaving patterns increases The second experiment, which is shown in Figs 5 and 6, considers the comparison in terms of the average BER of the

9 CAI et a: TRANSMIT PROCESSING BASED ON INTERLEAVING AND LIMITED FEEDBACK IN MC-CDMA 1567 time-domain CSI quantization scheme across the channe paths for each transmit antenna and across the transmit antennas for each channe path with the proposed downink schemes The intereaving codebook is designed by using the randomintereaving method We use δ 1 10bits to feed back the channe direction and δ 2 6bits to feed back the channe norm The Loyd agorithm is used by these two CSI quantization methods Note that, when we quantize the vector across the channe paths, a different codebook that is subject to the constraint of the normaized channe profie is designed In particuar, we show the average BER performance curves versus SNR and the number of users (K) for the anayzed schemes The resuts in Fig 5 indicate that, due to the arge quantization error, the performance of the genera precoding technique significanty decreases The quantization scheme across the transmit antennas per tap is sighty better than the scheme across the taps per transmit antenna In the case of three transmit antennas, the two quantization schemes both require 48 feedback bits for each user The proposed downink schemes outperform the genera precoding agorithm without switched intereaving and the conventiona MC-CDMA MMSE receiver with intereaving and without intereaving In particuar, the proposed downink transmission scheme with 5 bits can save up to 5 db compared with the genera precoding agorithm without switched intereaving and can save up to more than 3 db compared with the conventiona MC-CDMA MMSE receiver with intereaving, at an average BER eve of 10 2 Fig 6 indicates that the proposed scheme with 5 bits can support up to four more users at an average BER eve of 10 2 compared with the conventiona MC-CDMA MMSE receiver As we increase the number of intereaving patterns, we achieve the performance of the genera precoder with perfect CSI In the next experiment, we compare the codebooks of the intereavers that were created by the foowing three methods, as outined in Section V: 1) the random-intereaving agorithm; 2) the bock-intereaving agorithm; and 3) the MASS agorithm In particuar, we show the average BER performance curves versus the number of feedback bits for the upink scenario In this case, we consider K 5,SNR8dB, and 2 receive antennas at the BS Note that the codebooks are designed offine For the MASS agorithm, we set the number of simuations N e 1000 and the number of candidates β 100 and 1000, and one bock of symbos is transmitted per simuation The resuts for an upink system with N 16in the scenario of mutipath fading channes are iustrated in Fig 7 We can see that the best performance is achieved with the MASS agorithm, foowed by the random- and bock-intereaving methods In particuar, as we increase the number of candidates, the performance is improved for the MASS agorithm The resuts in Fig 8 show the average BER performance versus SNR for the proposed downink preprocessing scheme and the MC-CDMA system with transmit precoding using perfect and imperfect CSI at the receiver Quantization across the transmit antennas for each channe path is empoyed In the simuation, we assume that the imperfect channe coefficients are given by ĥ(α,k) v (i) h (α,k) v (i)+ε (α,k) v (i), where v 1,,N t, α 1,,L p, k 1,,K, and ε (α,k) v (i) denotes a compex Gaussian random variabe with zero mean and Fig 7 Average BER performance versus the number of feedback bits for different intereaving codebooks N e 1000 β 100 Fig 8 Average BER performance versus SNR for the proposed downink preprocessing scheme with perfect and imperfect CSI at the receiver Quantization across the transmit antennas for each channe path is empoyed, where δ 1 10,andδ 2 6 variance p 2 The imperfect channe vector of the αth path of the kth user is given by ĥ(α,k) [ĥ(α,k) 1 (i),,ĥ(α,k) N t (i)] T Thus, the variance approaches the MSE of the channe estimation error at the receiver [32] We compare the proposed downink preprocessing scheme to the conventiona MC-CDMA system with precoding based on the quantization errors with different p Here, we seect p 0, 015, 025 and empoy 10 feedback bits for the channe direction, six feedback bits for the channe norm, and four users and 16 intereavers for the proposed scheme We can see that the performance decreases as the vaue p increases In particuar, the curves with p 015 are cose to the ones with perfect CSI at the receiver The case with

10 1568 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 60, NO 4, MAY 2011 Fig 9 Average BER performance versus SNR for the proposed upink switched-intereaving preprocessing schemes and the conventiona MC-CDMA MMSE receiver p 025 has amost 15-dB degradation, compared with the perfect CSI case at a BER eve of 10 3 This case shows the abiity of our proposed downink preprocessing agorithms to dea with channe estimation errors We can reax the channe estimation agorithm at the receiver and reduce the computationa compexity to meet the associated performance Now, et us consider the experiments of our proposed upink preprocessing structure equipped with a different number of feedback bit configurations We compare the performance in terms of the average BER of the proposed imited-feedback structures with MMSE receivers, ie, 1-, 2-, 3-, 4-, and 5-bits feedback, respectivey, and the conventiona MC-CDMA system with MMSE receiver In particuar, we show the average BER performance curves versus the SNR and the number of users K for the anayzed schemes In this simuation, the intereaving codebook is designed by the MASS agorithm At the receiver, the BS is equipped with two antennas The resuts in Figs 9 and 10, which are based on K 12 and SNR 10dB, respectivey, indicate that the best performance is achieved with the nove switched-intereaving preprocessing scheme with five feedback bits, and we can see that the average BER decreases as the number of feedback bits increases In particuar, the proposed scheme with 5 bits can save up to 3 db and support up to eight more users, which is near an average BER eve of 10 3, compared with the conventiona MC-CDMA MMSE receiver Finay, Fig 11 iustrates the average BER performance versus the percentage of each user s feedback errors for both upink and downink scenarios Here, we use 5 bits for the proposed switched-intereaving schemes The intereaving codebooks are based on the random-intereaving method In particuar, the downink scheme quantizes the CSI across the transmit antennas per channe path We use a structure based on a frame format where the indices are converted to 0 and 1 s This frame of 1 and 0 s with the feedback information is transmitted Fig 10 Average BER performance versus the number of users for the proposed upink switched-intereaving preprocessing schemes and the conventiona MC-CDMA MMSE receiver Fig 11 Average BER performance versus the percentage of each user s feedback errors for the proposed downink and upink schemes over a binary symmetric channe with an associated probabiity of error Pe The burst errors scenario in the imitedfeedback channe can easiy be transferred to the case of the binary symmetric channe by empoying a conventiona bit intereaver As we increase the feedback errors for each user, the performance of the proposed imited-feedback schemes decreases In the case of the downink scheme, the performance decreases fast after 1%, and compared with the conventiona MC-CDMA, it starts to ose at 20% The performance of the upink decays faster than the downink scheme, because the intereaver is not in accordance with the deintereaver due to the feedback errors for the upink scenario, which creates a

11 CAI et a: TRANSMIT PROCESSING BASED ON INTERLEAVING AND LIMITED FEEDBACK IN MC-CDMA 1569 significant detection error for a fading bock To ensure that the errors are controed, channe-coding techniques shoud be empoyed for the feedback channes with errors VI CONCLUSION In this paper, we have proposed inear preprocessing schemes based on switched-intereaving techniques with imited feedback for both downink and upink MC-CDMA systems The chipwise inear precoder and reevant MMSE receivers were introduced The seection functions were aso proposed to choose the optimum intereaver from the codebook The CSI quantization scheme based on the Loyd agorithm and three methods for intereaving codebook design were described The resuts showed that the proposed intereaving and detection schemes significanty outperform existing agorithms and support systems with higher oads We remark that our proposed agorithms can aso be extended to take into account coded, distributed, and other types of communication systems APPENDIX LLOYD ALGORITHM FOR THE CHANNEL DIRECTION CODEBOOK DESIGN Step 1 Initiaization phase Generate a training sequence that consists of source vectors h with coefficients that are independent and identicay distributed (iid) with a compex Gaussian distribution with zero mean and unit variance Step 2 Set t 1 Step 3 Nearest neighbor rue A input vectors h that are coser to the codeword h q i,t 1 than any other codeword shoud be assigned to the neighborhood of h q i,t 1 or region Ω i h Ω i if and ony if d(h, h q i,t 1 ) d(h, h q j,t 1 ), i, j 1,,2 δ 1 Step 4 Centroid condition Take the ith region Ω i as an exampe, whose oca correation matrix Σ i : E[hh H h Ω i ] According to the centroid condition, the optima vector h q i,t shoud maximize ωh i Σ iω i subject to the unit norm constraint, ie, h q i,t arg max ω H ω H i ω i Σ i ω i u i (27) i1 where u i is the eigenvector that corresponds to the argest eigenvaue of Σ i Loop back to Step 3 unti convergence REFERENCES [1] L Hanzo, L-L Yang, E-L Kuan, and K Yen, Singe- and Muticarrier DS-CDMA: Mutiuser Detection, Space Time Spreading, Synchronization, Networking and Standards New York: IEEE Press-Wiey, Jun 2003 [2] S Hara and R Prasad, Overview of muticarrier CDMA, IEEE Commun Mag, vo 35, no 12, pp , Dec 1997 [3] K Faze and S Kaiser, Muticarrier and Spread Spectrum Systems Chichester, UK: Wiey, 2003 [4] V M Dasiva and E S Sousa, Performance of orthogona CDMA codes for quasisynchronous communication systems, in Proc IEEE ICUPC, Ottawa, ON, Canada, Oct 1993, pp [5] L Vandendorpe, Mutitone direct sequence CDMA system in an indoor wireess environment, in Proc IEEE 1st Symp Commun Veh Techno Beneux, Deft, The Netherands, Oct 1993, pp [6] G B Giannakis, P A Anghe, and Z Wang, Generaized muticarrier CDMA: Unification and inear equaization, EURASIP J App Signa Process, vo 2005, no 5, pp , 2005 [7] A D Dabbagh and D J Love, Mutipe-antenna MMSE-based downink precoding with quantized feedback or channe mismatch, IEEE Trans Commun, vo 56, no 11, pp , Nov 2008 [8] N Jinda, MIMO broadcast channes with finite-rate feedback, IEEE Trans Inf Theory, vo 52, no 11, pp , Nov 2006 [9] C Swannack, G W Worne, and E Uysa-Biyikogu, Efficient quantization for feedback in MIMO broadcasting systems, in Proc IEEE Asiomar Conf Signas, Syst, Comput, Oct/Nov 2006, pp [10] M Triveato, F Boccardi, and F Tosato, User seection schemes for MIMO broadcast channes with imited feedback, in Proc IEEE Veh Techno Conf, Apr 2007, pp [11] T Yoo, N Jinda, and A Godsmith, Mutiantenna downink channes with imited feedback and user seection, IEEE J Se Areas Commun, vo 25, no 7, pp , Sep 2007 [12] P Ding, D J Love, and M D Zotowski, Mutipe-antenna broadcast channes with shape feedback and imited feedback, IEEE Trans Signa Process, vo 55, no 7, pp , Ju 2007 [13] Y Cai, R C de Lamare, and D Le Ruyet, Linear precoding based on switched intereaving and imited feedback for interference suppression in downink mutiantenna MC-CDMA systems, in Proc IEEE Int Conf Acoust, Speech, Signa Process, Daas, TX, Mar 2010, pp [14] R T Derryberry, S D Gray, D M Ionescu, G Mandyam, and B Raghothaman, Transmit diversity in 3G CDMA systems, IEEE Commun Mag, vo 40, no 4, pp 68 75, Apr 2002 [15] H Homa and A Toskaa, WCDMA for UMTS: Radio Access for Third- Generation Mobie Communications Chichester, UK: Wiey, 2002 [16] C R Murthy, J Zheng, and B D Rao, Performance of quantized methods for equa gain transmission with noisy feedback channes, IEEE Trans Signa Process, vo 56, no 6, pp , Jun 2008 [17] Z Wang and G B Giannakis, Wireess muticarrier communications, IEEE Signa Process Mag, vo 17, no 3, pp 29 48, May 2000 [18] R C de Lamare and R Sampaio-Neto, Reduced-rank adaptive fitering based on joint iterative optimization of adaptive fiters, IEEE Signa Process Lett, vo 14, no 12, pp , Dec 2007 [19] R C de Lamare and R Sampaio-Neto, Adaptive reduced-rank processing based on joint and iterative interpoation, decimation and fitering, IEEE Trans Signa Process, vo 57, no 7, pp , Ju 2009 [20] R C de Lamare and R Sampaio-Neto, Reduced-rank space timeadaptive interference suppression with joint iterative east squares agorithms for spread-spectrum systems, IEEE Trans Veh Techno, vo 59, no 3, pp , Mar 2010 [21] Y Cai and R C de Lamare, Low-compexity variabe-step-size mechanism for code-constrained constant moduus stochastic gradient agorithms appied to CDMA interference suppression, IEEE Trans Signa Process, vo 57, no 1, pp , Jan 2009 [22] M Jankiraman, Space Time Codes and MIMO Systems Norwood, MA: Artech House, 2004 [23] R C de Lamare and R Sampaio-Neto, Adaptive interference suppression for DS-CDMA systems based on interpoated FIR fiters with adaptive interpoators in mutipath channes, IEEE Trans Veh Techno, vo 56, no 5, pp , Sep 2007 [24] R C de Lamare and R Sampaio-Neto, Minimum mean-square-error iterative successive parae arbitrated decision feedback detectors for DS- CDMA systems, IEEE Trans Commun, vo 56, no 5, pp , May 2008 [25] Y Cai and R C de Lamare, Space Time adaptive MMSE mutiuser decision feedback detectors with mutipe-feedback interference canceation for CDMA systems, IEEE Trans Veh Techno,vo58,no8,pp , Oct 2009 [26] T Pande, D J Love, and J V Krogmeier, Reduced feedback MIMO OFDM precoding and antenna seection, IEEE Trans Signa Process, vo 55, no 5, pp , May 2007 [27] J Choi and R W Heath, Jr, Interpoation-based transmit beamforming for MIMO OFDM with imited feedback, IEEE Trans Signa Process, vo 53, no 11, pp , Nov 2005

12 1570 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL 60, NO 4, MAY 2011 [28] A Narua, M J Lopez, M D Trott, and G W Worne, Efficient use of side information in mutipe-antenna data transmission over fading channes, IEEE J Se Areas Commun, vo 16, no 8, pp , Oct 1998 [29] D J Love, R W Heath, Jr, and T Strohmer, Grassmanian beamforming for mutipe-input mutipe-output wireess systems, IEEE Trans Inf Theory, vo 49, no 10, pp , Oct 2003 [30] K K Mukkavii, A Sabarwa, E Erkip, and B Aazhang, On beamforming with finite-rate feedback in mutipe-antenna systems, IEEE Trans Inf Theory, vo 49, no 10, pp , Oct 2003 [31] Y Na, M Saquib, and M Z Win, Piot-aided chip-intereaved DS- CDMA transmission over time-varying channes, IEEE J Se Areas Commun, vo 24, no 1, pp , Jan 2006 [32] N S Jayant and P No, Digita Coding of Waveforms: Principes and Appications to Speech and Video Engewood Ciffs, NJ: Prentice-Ha, 1984 [33] D J Love, R W Heath, Jr, W Santipach, and M L Honig, What is the vaue of imited feedback for MIMO channes? IEEE Commun Mag, vo 42, no 10, pp 54 59, Oct 2004 [34] Y Cai, R C de Lamare, and R Fa, Linear interference suppression for spread spectrum systems with switched intereaving and imited feedback, in Proc Wireess Commun Netw Conf, Budapest, Hungary, Sep 2009, pp 1 6 [35] H Shirani-Mehr and G Caire, Channe-state feedback schemes for mutiuser MIMO OFDM downink, IEEE Trans Commun, vo 57, no 9, pp , Sep 2009 [36] Y Liang, R Schober, and W Gerstacker, Time-domain transmit beamforming for MIMO OFDM systems, in Proc GLOBECOM, 2007, pp Yunong Cai (S 07 M 10) received the BS degree in computer science from Beijing Jiaotong University, Beijing, China, in 2004, the MSc degree in eectronic engineering from the University of Surrey, Guidford, UK, in 2006, and the PhD degree in eectronic engineering from the University of York, York, UK, in 2009 From January 2010 to January 2011, he was a Postdoctora Feow with the Eectronics and Communications Laboratory, Conservatoire Nationa des Arts et Métiers, Paris, France Since February 2011, he has been with the Department of Information Science and Eectronic Engineering, Zhejiang University, Hangzhou, China, where he is currenty a Lecturer His research interests incude spread spectrum communications, adaptive signa processing, mutiuser detection, and mutipeantenna systems Rodrigo C de Lamare (S 99 M 04 SM 10) received the Dipoma degree in eectronic engineering from the Federa University of Rio de Janeiro, Rio de Janeiro, Brazi, in 1998 and the MSc and PhD degrees in eectrica engineering from the Pontifica Cathoic University of Rio de Janeiro in 2001 and 2004, respectivey Since January 2006, he has been with the Communications Research Group, Department of Eectronics, University of York, York, UK, where he is currenty a Lecturer in communications engineering His research interests incude communications and signa processing, areas in which he has pubished about 200 papers in refereed journas and conference proceedings He serves as an Associate Editor for the EURASIP Journa on Wireess Communications and Networking Dr de Lamare served as the Genera Chair of the Seventh IEEE Internationa Symposium on Wireess Communications Systems, hed in York, UK, in September 2010 Didier Le Ruyet received the BEng and PhD degrees from the Conservatoire Nationa des Arts et Métiers (CNAM), Paris, France, in 1994 and 2001, respectivey From 1988 to 1996, he was a Research Engineer with the Image Processing and Teecommunication Departments, Société d Appications Généraes de ectricité et de a Mécanique (SAGEM), Paris, France In 1996, he joined the Signa and Systems Laboratory, CNAM, as a Research Assistant From 2002 to 2009, he was an Assistant Professor with the Eectronics and Communications Laboratory, CNAM Since 2010, he has been a Fu Professor with the Centre d Etudes et De Recherche en Informatique du CNAM Research Laboratory, CNAM He has pubished about 60 papers in referred journas and conference proceedings His main research interests incude digita communications and signa processing, particuary advanced channe coding, detection and estimation agorithms, and mutiantenna transmission techniques for mutiuser systems