3118 IEEE TRANSACTIONS ON WIRELESS COMMUNICA TIONS, VOL. 7, NO. 8, AUGUST 2008 Joint Tx-Rx MMSE Design for MIMO Multicarrier Systems with Tomlinson-Harashima Precoding Antonio A. D’Amico and Michele Morelli, Senior Member, IEEE Abstract —This paper investigates the joint Tx-Rx design of a multicarrier multiple-input multiple-output (MIMO) system em- ploying Tomlinson-Harashima precoding (THP). The optimality criterion is the minimization of the mean-square-error (MSE) at the receiv er side under a const raint on the overal l trans mitte d power. Theoretical analysis and computer simulations are used to ass ess the per formance of the pr opo sed scheme in ter ms of bit-error-rate (BER) and minimum achievable MSE. It is shown that non-linear precoding may provide much better results than linear pre-filtering, especially when the number of parallel data str eams is close to the number of tra nsmitti ng and receiving antennas. Compared with other existing methods based on THP, our scheme is different in that the precode d symbols are linear ly prefiltered bef ore bei ng lau nch ed ov er the MIMO cha nne l. This re sult s into a power loa ding ope rat ion over the channel eigen mode s, which leads to a remarka ble improv ement of the error-rate performanc e. Index Terms—MIMO multicarrier , T omlinson-Harashima pre- coding, MMSE prefiltering. I. I NTRODUCTION T HE multiple -inpu t multip le-output (MIMO ) technology is a promising solution for spectrally ef ficient wireless communi cati ons. MIMO sys tems are cha ract eriz ed by the deployment of multiple antennas at both the transmitter and receiver ends, which can be exploited to improve reliability and coverage by means of space-time coding techniques [1], [2] and/or to increase the data rate through spatial multiplexing [3], [4]. The main impairment of a MI MO syst em wi th spati al multiplexing is represented by the multi-stream interference (MSI) arising from simulta neous transmis sion of paralle l data streams over the same frequency band. Traditional approaches to mitigate MSI only exploit channel state information (CSI) at the recei ve r [5]. Ho we ve r , if CSI is avail able at both ends of the wireless link, appropriate precoding and decoding techniques can be used to fully exploit the potential bene fits promised by the MIMO channel. The assumption of CSI at the tra nsmitter sid e is rea sonable in low mobilit y applic a- tions such as time-division-duplex (TDD) communications via IEEE 802.11 or Hip erLA N/I I wir eles s loca l area netw orks (WLANs ). Than ks to the inhere nt reci procity princi ple of TDD systems, channel estimate s deri ved during a time-s lot can be reused for pre filtering in the subsequent slots as long Manuscri pt rece ived Febr uary 16, 2007 ; re vise d July 9, 2007; acc epte d Sept ember 19, 2007. The associa te editor coor dina ting the revie w of this paper and approving it for publication was R. Mallik. The autho rs are with the De pa rtment of Inf ormation Eng ine er ing , Via Caruso 16, 56100 Pisa, Italy (e-mail: {antonio.damico, michele.morelli }@iet.unipi.it). Digital Object Identifier 10.1109/TWC. 2008.070195. as the environment vari es slo wly over time. In contras t, in freque ncy-d ivis ion-d uplex (FDD) netwo rks CSI must be fed back from the receiver to the transmitter using a dedicated contro l channe l. Linear transceiv ers design for transmission s over MIMO multipath fading channels is addressed in [6], [7] under several constr aint s and opt imal ity crit eri a. The resulti ng scheme s operate in both the space and time domains, and require the singu lar value decomp osition (SVD ) of the channe l matrix. In practice, they convert the MIMO channel into a set of paral- lel flat-fading single-input single-output (SISO) subchannels, where different solutions are only distinguished by how the power is loaded on each subchannel. A unifying framework for the design of linear transceivers in the frequency domain is presented in [8] using convex optimization theory. As an alternative to linear transceiver design, non-linear pre- filtering of MIMO channels based on Tomlinson-Harashima preco ding (THP) has recently receiv ed some attention [9]– [13]. Thi s tech nique employ s modulo arit hme tic and was originally proposed to combat intersymbol interference (ISI) in highly dispersive channels [14], [15]. In MIMO applications, THP can be viewed as the transmit counterpart of the Vertical Bell-Labs Layered Space-Time (V-BLAST) architecture [16]. The main difference is that the latter operates at the receiver side and can only rely on detected symbols to sepa rate interfering signals, while the true data symbols are available for THP due to the fact that signal precoding is accomplished at the transmitter side. This means that THP is not affected by error propagatio n and, accordingly , is expect ed to outper form V-BLAST. So far, the use of THP in MIMO systems has mainly been devoted to the suppression of multi-user interference (MUI) arisin g in down link multiple-acc ess trans missio ns. In these app lications, join t pro ces sin g of the rece ived sig nals is not pos sible due to lack of coordi nat ion among spatia lly dis- tributed users. Accordingly, only the transmitter is optimally designed while a conv entional single-user receiver is employed at each mobile terminal. In particular, the scheme discussed in [9] is based on a Zero-Forcing (ZF) approach and exploits the QR decomposition of the channel matrix, while in [10] and [11] the pro ces sing matr ices are des igned acco rdi ng to a minimum mean-square-error (MMSE) optimality criterion. A THP transcei ver for tra nsmiss ions over a freq uency flat MIMO channel is derived in [12] using an MMSE approach and assuming perfect CSI at the transmitter side. An alter- native scheme is proposed in [13], where only the channel statist ics (namely, the channel and noise covariance matrices) are exploited for the system design. 1536-1276/08$25.00 © 2008 IEEE Authorized licensed use limited to: VELLORE INSTITUTE OF TECHN OLOGY. Downloaded on August 4, 2009 at 10:31 from IEEE Xplore. Restrictions apply.
