Robust Filter Design for Multicarrier Communication over Doubly Dispersive Channels

Although orthogonal frequency division multiplexing (OFDM) has been the dominant technology for broadband communications in the past, a number of researchers have noted the shortcomings of OFDM in timevarying channels. Hence, alternative systems that use filte r banks for multicarrier modulation have been proposed. Filter bank multicarrier (FBMC) systems use offset quadrature amplitude modulation (OQAM) or cosine modulated filter bank (CMFB) to maximize the transmission efficiency by maximizing the number of subcarriers in the available band. Moreover, the use of isotropic pulses for prototype filters will allow one to strike a balance between the time and frequency dispersion of the channel. However, unfortunately, such systems are not extendable to transmission over multipleinput multiple-output (MIMO) channels. The emphasis of this paper is on a class of FBMC systems in which data symbols are conventional QAM and, thus, support MIMO channels. Unlike OQAM/CMFB-based systems, the FBMC systems considered in this paper suffer some bandwidth loss. We develop a novel filter design that minimizes this bandwidth loss. I. I NTRODUCTION While orthogonal frequency division multiplexing (OFDM) has been the dominant technology for broadband communications in the past [1], [2], [3], it has a number of limitations that makes it a rather poor choice for some applications. For instance, [4] noted that the relatively large side-lobes of the spectra of the individual subcarrie rs in an OFDM signal limits its applicability to cognitive radios. On the other hand, a number of researchers have noted the limitation of OFDM in dealing with time-varying channels and have suggested the use of an alternative method that uses filter banks for multicarrier modulation, [5]-[14]. Although different names have been used in the litrature, for similar or various implementations of filter bank based multicarrier systems, in this paper we use the generic terminology of filter bank multicarrier (FBMC). The pioneering works on the FBMC techniques date back to the published works by Chang [15] and Saltzberg [16] in the 1960s. However, the first work that discusses the potential problems of OFDM in dealing with doubly dispersive channels and proposes FBMC as a solution is due to Floch et al. [5]. It is argued, an FBMC system that addresses both time and frequency dispersions should be constructed using a prototype filter p(t) whose time and frequency dispersions matches those of the channel. For this purpose, one may define the dispersion of p(t) and P (f), respectively, as