IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 53, NO. 4, JULY 2004 945 Optimum Beamforming for Pre-FFT OFDM Adaptive Antenna Array Montree Budsabathon, Yoshitaka Hara, Member, IEEE, and Shinsuke Hara, Member, IEEE Abstract—It is well known that orthogonal frequency-division multiplexing (OFDM) is robust to frequency-selective fading in wireless channels due to the exploitation of a guard interval that is inserted at the beginning of each OFDM symbol. However, once delayed signals beyond the guard interval are introduced in a channel with a large delay spread, intersymbol interference causes a severe degradation in the transmission performance. In this paper, we propose a novel pre-fast Fourier transform (FFT) OFDM adaptive antenna array, which requires only one FFT processor at a receiver, for suppressing such delayed signals. We derive the optimum weight set for beamformers based on the max- imum signal-to-noise-and-interference power ratio (Max-SNIR) and the minimum mean square error (mmse) criteria, respectively. In addition, we propose a novel mmse-criterion-based commuta- tive optimization scheme, which is more robust to the estimation error of the channel state information. Furthermore, we show the equivalence between the Max-SNIR-criterion-based scheme and the proposed commutative optimization scheme. Computer simu- lation results show its good performance even in channels where directions of arrival of arriving waves are randomly determined. Index Terms—Commutative scheme, delayed signal, pre-fast Fourier transform (pre-FFT) orthogonal frequency-division multiplexing (OFDM). I. INTRODUCTION I T IS well known that orthogonal frequency division mul- tiplexing (OFDM) is an efficient technique for high-speed digital transmission over severe multipath fading channels [1], [2]. OFDM has been adopted in the physical layer of wireless local area network (LAN) systems [3] and has been recently considered to be a promising technique for next-generation mobile communications [4]. OFDM is robust to frequency-se- lective fading in wireless channels due to the exploitation of a guard interval, which is inserted at the beginning of each OFDM symbol [1], [2]. However, once delayed signals beyond the guard interval are introduced in a channel with a large delay spread, intersymbol interference (ISI) causes a severe degradation in the transmission performance. To cancel the ISI, time-domain signal-processing techniques have been proposed for wireless OFDM receivers, such as a decision feed-back equalizer (DFE) [5] and a maximum likelihood sequence esti- Manuscript received January 14, 2003; revised December 23, 2003 and March 4, 2004. This paper was presented in part at the IEEE Wireless Communications and Networking Conference (WCNC) 2003. M. Budsabathon and S. Hara are with the Department of Electronic, Informa- tion System and Energy Engineering, Graduate School of Engineering, Osaka University, Osaka 565-0871, Japan (e-mail: hara@comm.eng.osaka-u.ac.jp). Y. Hara is with the Mitsubishi Electric Information Technology Centre Eu- rope, Rennes 35708, France. Digital Object Identifier 10.1109/TVT.2004.830939 mator (MLSE) with a smoothed fast Fourier transform (FFT) window [6]. They have high interference cancellation capabil- ities; however, they have complicated structures because they need to estimate the channel impulse response, including the delayed signals beyond the guard interval. On the other hand, to maintain high-speed reliable radio transmission, a multiple antenna array has been considered as an effective tool not only for gain enhancement and increased spectral efficiency [7], but also for interference suppression [8]–[12]. In terms of cancellation capability for cochannel inter- ference including ISI, multiple antenna arrays are advantageous over time-domain signal-processing techniques, because they can cope with any interfering signals that are uncorrelated with desired signals by means of “nulling out.” Unfortunately, the signal-processing techniques mentioned above can cancel only ISI by means of “equalization.” The structure of OFDM antenna array can be classified into two types, namely, pre- and post-FFT antenna array types. In [13], a post-FFT OFDM adaptive antenna array for cochannel interference suppression has been proposed. Although the pro- posed post-FFT subcarrier-by-subcarrier combining scheme is optimum in terms of maximizing signal-to-noise-and-interfer- ence power ratio (SNIR), it requires an increased number of FFT processors, large computations that increase with the number of antennas and subcarriers, and a quite long training signal. Fur- thermore, the proposed system requires that the received signals on different antenna elements are statistically independent. To establish such a diversity system, the antenna-element spacing has to be in the order of several carrier wavelengths. Therefore, depending on the number of antenna elements, the frequency band used, and the angular spread that is the angle over which the signal arrives at the receive antennas, the antenna size might become quite large. On the other hand, a pre-FFT combining di- versity scheme proposed in [14], which requires only one FFT processor, can drastically reduce the computational complexity by tolerating a slight performance degradation, while achieving a space diversity gain. However, in [14], no interfering signal has been taken into account. In this paper, we first propose a novel pre-FFT OFDM adaptive antenna array for suppressing delayed signals beyond the guard interval (or, in short, delayed signals) [11], [12]. We derive the optimum weight set for the beamformers based on the Maximum (Max-) SNIR and the minimum mean square error (mmse) criteria, respectively. Furthermore, we propose a novel mmse-criterion-based commutative optimization scheme that is more robust to the estimation error of the channel state information (CSI) than the Max-SNIR-based scheme. Computer simulation results show its good performance even 0018-9545/04$20.00 © 2004 IEEE