Yuan - Pei Lin ,

© 1997 DIGITALSTOCK Feature * This work was supported in parts by NSC 95-2221-E-009-080, NSC94-2752-E-002-006-PAE, and NSC 95-2221-E-002-197, Taiwan, R.O.C. FIRST QUARTER 2007 1531-636X/07/$25.00©2007 IEEE IEEE CIRCUITS AND SYSTEMS MAGAZINE 19 Authorized licensed use limited to: National Chiao Tung University. Downloaded on October 13, 2008 at 06:43 from IEEE Xplore. Restrictions apply. 20 IEEE CIRCUITS AND SYSTEMS MAGAZINE FIRST QUARTER 2007 Introduction T he DFT (discrete Fourier transform) based multicarrier systems have found important applications in DMT (discrete multitone) systems such as ADSL (asymmetric digital subscriber lines) [1] and VDSL (very high speed digital subscriber lines) [2], and in OFDM (orthogonal frequency division multiplexing) systems such as wireless LAN (local area network) [3] and DVB (digital video broadcasting) [4]. The transmitter and receiver perform M -point IDFT (inverse DFT) and DFT computation, respectively, where M is the number of subchannels. At the transmitter side, a cyclic prefix of length ν is inserted. The channel can usually be assumed to be an FIR (finite impulse response) filter of order L after proper time-domain equalization. When the prefix length ν ≥ L, there will be no inter-block interference. With the aid of redundant cyclic prefix, an FIR channel is converted into M zero-ISI subchannels. The subchannel gains are the M -point DFT of the FIR channel impulse response. In the conventional DFT based multicarrier system the transmitting and receiving filters come from rectangular windows. Rectangular windows are known to have large spectral sidelobes and the stopband attenuation is insufficient for many applications. At the transmitter side poor frequency separation leads to significant spectral leakage. This could pose a problem in applications where the spectrum of the transmitted signal is required to have a large roll-off in certain frequency bands. For example, in some wired transmission application, the spectrum of the transmitted signal needs to fall below a threshold in the transmission bands of the opposite direction to avoid interference [1], [2]. The transmitted spectrum should also be attenuated in amateur radio bands to reduce interference or egress emission [2]. On the other hand, poor frequency separation at the receiver side results in poor out-of-band rejection. In DMT applications such as ADSL and VDSL, some of the frequency bands are also shared by radio transmission systems, e.g., amplitude-modulation stations and amateur radio. The radio frequency signals can be coupled into the wires and this introduces radio frequency interference (RFI) or ingress [5]. Ill frequency separation means many neighboring tones can be affected. The signal-to-interference-noise ratio of these tones are reduced and the total transmission rate decreased. Many methods have been proposed to improve the frequency characteristics of the transmitter and receiver. To improve the spectral roll-off of the transmitted signal, a number of continuous-time pulse shaping filters have been proposed, [6]–[11]. Usually continuous-time pulse shapes are designed based on an analog implementation of transmitters and a digital implementation is not admitted [12]. Discrete-time windows have been considered in [13]–[15]. The design of overlapping windows for OFDM with offset QAM (quadrature amplitude modulation) over ISI free channels are studied fully in [14], [15]. More recently, transmitting windows with the cyclic-prefixed property have been considered in [16], [17] for egress control. Windows that are the inverse of a raised cosine function are optimized in [16], to minimize egress emission. To compensate for the transmitter window, the corresponding receiver requires post-processing equalization [16], [17]. A joint consideration of spectral roll-off and SNR degradation due to post-processing is given in [17]. Per-tone windows are proposed in [18] for shaping transmitted spectrum. The shaping of spectrum allows more tones to be used for transmission. Windowing is also often applied at the receiver side. In [19], Muschallik used Nyquist windows, which have the property that shifts of the window in the time domain add to a constant, to improve the reception of OFDM systems. Optimal Nyquist windows are considered in [20] to mitigate the effect of additive noise and carrier frequency offYuan-Pei Lin and Chien-Chang Li are with the Dept. Electrical and Control Engr., National Chiao Tung Univ., Hsinchu, Taiwan, R.O.C. and See-May Phoong is with the Dept. of EE & Graduate Inst. of Comm. Engr., National Taiwan Univ., Taipei, Taiwan, R.O.C., [email protected] s0(n)