IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 53, NO. 12, DECEMBER 2005 4691 Linear Block Precoding for OFDM Systems Based on Maximization of Mean Cutoff Rate Yue Rong, Student Member, IEEE, Sergiy A. Vorobyov, Member, IEEE, and Alex B. Gershman, Senior Member, IEEE Abstract—A new linear block precoding technique is proposed to improve the performance of orthogonal frequency division multiplexing (OFDM) communication systems. The design of our precoder is based on the maximization of the mean cutoff rate and requires only the knowledge of the average relative channel multipath powers and delays at the transmitter. Simulation results show an improved performance of the proposed precoder relative to other known linear block precoding techniques. Index Terms—Cutoff rate, linear block precoding, orthogonal frequency division multiplexing (OFDM) communications. I. INTRODUCTION O RTHOGONAL frequency division multiplexing (OFDM) is a promising multiuser communication scheme which enables to mitigate multiple-access interference (MAI) by means of providing each user with a nonintersecting fraction of subcarriers [1]. Due to the inverse fast Fourier transform (IFFT) at the transmitter and the fast Fourier transform (FFT) at the receiver, the frequency selective fading channel is converted by OFDM into parallel flat fading channels [2]. This greatly facilitates the equalizer design at the receiver. However, a well known disadvantage of the OFDM scheme is that, at each subcarrier, the channel may be subject to a deep fading. This makes a reliable detection of the informa- tion-bearing symbols at this particular subcarrier very difficult and, as a result, the overall performance of the system may degrade substantially. Thus, the transceiver optimization is required. A general transceiver optimization framework is discussed in [3]. In application to OFDM systems, a popular recent approach to improve the performance of OFDM systems in fading envi- ronments is to use linear block precoding at the transmitter [4]. For example, the minimum mean square error (MMSE) and the minimum bit error rate (MBER) precoders for zero-forcing (ZF) equalization have been proposed in [4] and [5], respectively, and the MBER precoder for MMSE equalization has been studied in Manuscript received September 14, 2004; revised February 27, 2005. The work of A. B. Gershman was supported by the Wolfgang Paul Award Program of the Alexander von Humboldt Foundation (Germany); Discovery Grants Pro- gram of the Natural Sciences and Engineering Research Council (NSERC) of Canada; Premier’s Research Excellence Award Program of the Ministry of En- ergy, Science, and Technology (MEST) of Ontario; and Research Partnerships Program of Communications and Information Technology Ontario (CITO). The results of this paper were presented in part at EUSIPCO’04, Vienna, Austria, September 2004, and ITG/IEEE WSA’05, Duisburg, Germany, April 2005. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Ioan Tabus. The authors are with the Department of Communication Systems, Darm- stadt University of Technology, Darmstadt D-64283, Germany (e-mail: yue.rong@ieee.org; svor@ieee.org; gershman@ieee.org). Digital Object Identifier 10.1109/TSP.2005.859325 [6]. Another efficient precoding technique based on the channel capacity maximization has been proposed in [7]. Unfortunately, the application of precoders [4]–[7] may be limited by the fact that they require the full channel knowledge at the transmitter. To avoid this drawback, another linear pre- coder has been designed in [8] based on maximization of the di- versity and coding gains. In contrast to the precoders of [4]–[7], the technique of [8] requires only the knowledge of the multi- path channel order at the transmitter. Another MBER based technique that does not require any channel information has been proposed in [9]. However, the class of MBER-optimal channel independent precoders devel- oped in [9] is limited by the case when the MMSE equaliza- tion and quadriphase shift keying (QPSK) modulation are used. Moreover, the performance of MBER precoder with MMSE equalization can be significantly improved by combining it with a water-filling procedure [6]. However, in the latter case the full channel knowledge at the transmitter is required. In this paper, a new linear precoder is proposed that maxi- mizes the channel mean cutoff rate and requires the knowledge of the average relative channel multipath powers and delays at the transmitter. Our simulations show that the proposed pre- coder substantially outperforms the approach of [8] and several other linear precoding techniques in terms of BER. II. SYSTEM MODEL For the sake of simplicity and following [4]–[7], let us con- sider the single-user block transmission system with subcar- riers. The extension to the multiuser case can be done straight- forwardly by allocating a different group of subcarriers to each user [8]. The frequency selective wireless channel between the transmitter and the user is characterized by the path gains ( ) and the delays ( ), where all path gains are assumed to be independent (but not necessarily iden- tically distributed) zero-mean complex Gaussian random vari- ables. Employing the cyclic prefix (CP)-based OFDM transmis- sions, we have the following relationship [4]–[7]: (1) where is the block index, is the 1 vector of the received symbols after the FFT operation, is the transmitted symbol power, is the 1 vector of the transmitted symbols without CP, is the 1 vector of white complex Gaussian noise with the covariance matrix 1053-587X/$20.00 © 2005 IEEE