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Block-Based Transceivers With Minimum Redundancy

Block-Based Transceivers With Minimum Redundancy
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  IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 58, NO. 3, MARCH 2010 1321 Block-Based Transceivers WithMinimum Redundancy Wallace Alves Martins  , Member, IEEE  , and Paulo Sergio Ramirez Diniz  , Fellow, IEEE   Abstract— The standard design of multicarrier and single-car-rier employing frequency-domain equalization transceiversrequires, at least, elements of redundancy, where standsfor the channel order. The redundancy eliminates the inherentinterblock interference (IBI), which is part of all block-basedtransceivers, and turns the channel matrix circulant. The spec-tral decomposition of the circulant channel matrix through thediscrete Fourier transform (DFT) allows the use of superfastalgorithms for both the design of zero-forcing (ZF) and minimummean squared error (MMSE) equalizers, and the equalizationof received signals. However, it is well known that the minimumredundancy for IBI-free designs of block-based transceivers is   . This paper proposes practical ZF and MMSE solutionsby using DFT, inverse DFT, and diagonal matrices. In particular,it is shown that, for some particular mild constraints on thechannel model, the new designs may have similar bit error rateperformance when compared to the standard ones, while keepingthe same asymptotic complexity for the equalization process, thatis,        numerical operations. The key feature of theproposed transceivers is their higher throughput.  Index Terms— Bezoutian, block transmission, communications,discrete Fourier transform (DFT), frequency-domain (FD) equal-ization, frequency-selective channel, interblock interference (IBI),intersymbol interference (ISI), minimum redundancy, orthogonalfrequency-division multiplex (OFDM), single-carrier (SC), super-fast algorithms, Toeplitz matrix. I. I NTRODUCTION T HE orthogonal frequency-division multiplex (OFDM) isthe simplest and most widely used implementation of amemoryless transmultiplexer (TMUX) [1]. Transmultiplexersarekeybuildingblocksinmulticarriercommunicationssystemsas they are efficient for data transmission through channelswith moderate to severe intersymbol interference (ISI) [1], [5],[24], [25]. The main desirable features of the OFDM systemare the elimination of ISI and its inherent low computationalcomplexity. An OFDM system utilizes inverse discrete Fouriertransform (IDFT) at the transmitter and a DFT at the receiver,enabling the use of computationally efficient fast Fouriertransform algorithms. In order to avoid ISI in transmissions Manuscript received March 13, 2009; accepted August 23, 2009. First pub-lished September 25, 2009; current version published February 10, 2010. Theassociate editor coordinating the review of this manuscript and approving itfor publication was Dr. Shengli Zhou. The authors acknowledge the financialsupport provided by CNPq and FAPERJ, national and state research councils,respectively.The authors are with the Electrical Engineering Program, COPPE/Poli/Fed-eral University of Rio de Janeiro, Rio de Janeiro, RJ 21941-972, Brazil (; versions of one or more of the figures in this paper are available onlineat Object Identifier 10.1109/TSP.2009.2033000 through frequency-selective channels some redundancy mustbe included at the transmitter, reducing the data rate [22].In recent years, single-carrier (SC) digital modulation thatemploys frequency-domain (FD) equalization has also emergedas an alternative solution to overcome some drawbacks inherentto multicarrier modulation based on OFDM, such as highpeak-to-average power ratio (PAPR) and carrier-frequencyoffset (CFO) [16], [28]. In addition, for some frequency-selec-tive channels, the bit error rate (BER) of an SC-FD system canbe lower than that of OFDM, especially if some subchannelshave high attenuation [28]. The higher BER for the OFDMstems from the fact that the information of a given subchannelis usually spread over time but concentrated in frequency. If the channel behaves poorly over a given frequency range, thensome subchannel information may be lost.The role of redundancy in filter-bank transceivers was exten-sively studied in [11], [19], [22], and [20]. When dealing withblock-based or memoryless systems, it was shown in [9]–[11]that theminimum required redundancy is , where isthe length of the finite impulse response (FIR) channel model.In the open literature, improved memoryless transceivers havebeen reported that use redundant transmitters [9], [11], [21],[22], but very few works had proposed decreasing the redun-dancy while constraining the transceiver to employ fast algo-rithms [3], [26].The strategy in [26] is to transmit redundant information inthe unused subcarriers, that is, the subcarriers that will be dis-carded in the case of channel loading. By exploiting these un-used subcarriers it is possible to achieve zero-forcing equaliza-tion without sending redundant information in useful subcar-riers. Usually, the number of unused subcarriers should be atleast , restricting its application. On the other hand, the ap-proach adopted in [3] is similar to the ours, since it relies on thesame system model employed here, in which zero-padding (ZP)andzero-jamming(ZJ)techniquesareusedtoeliminateIBIwithreducedredundancy.However,theresultingdesignsdonothavewell defined structure, implying that their computational com-plexity is dependent on the channel order (in addition to the de-pendency on the transmitted block length). For long channels,the transceivers in [3] require more computations than the pro-posed transceivers, as will be clearer later on. Besides, the ca-pacity-approaching transceivers with reduced redundancy pro-posed in [27] entail high computational burden, since they arebased on singular-value decomposition (SVD) of the involvedmatrices.This paper proposes four fixed and memoryless transceiverswith minimum redundancy for frequency-selective channels,utilizing DFTs and diagonal matrices. The new transceiversmay be multicarrier or single-carrier, where for each type we 1053-587X/$26.00 © 2010 IEEE Authorized licensed use limited to: Paulo Diniz. Downloaded on February 10, 2010 at 20:15 from IEEE Xplore. Restrictions apply.
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