Sparse Bayesian Learning Aided Estimation of Doubly-Selective MIMO Channels for Filter Bank Multicarrier Systems

Sparse Bayesian learning (SBL)-based channel state information (CSI) estimation schemes are developed for filter bank multicarrier (FBMC) systems using offset quadrature amplitude modulation (OQAM). Initially, an SBL-based channel estimation scheme is designed for a frequency-selective quasi-static single-input single-output (SISO)-FBMC system, relying on the interference approximation method (IAM). The IAM technique, although has low complexity, is only suitable for channels exhibiting mild frequency-selectivity. Hence, an alternative time-domain (TD) model based sparse channel estimation framework is developed for highly frequency-selective channels. Subsequently, the Kalman filtering (KF)-based IAM and its TD counterpart are developed for sparse doubly-selective CSI estimation in SISO-FBMC systems. These schemes are also extended to FBMC-based multiple-input multiple-output (MIMO) systems, for both quasi-static and doubly-selective channels, after demonstrating the special block and group-sparse structures of the IAM and TD-based models respectively, which are the characteristic features of such channels. The Bayesian Cramér-Rao lower bounds (BCRLBs) and the time-recursive BCRLBs are derived for the proposed quasi-static as well as doubly-selective sparse CSI estimation models, respectively. Our numerical results closely match the analytical findings, demonstrating the enhanced performance of the proposed schemes over the existing techniques.

I. Introduction

Orthogonal frequency division multiplexing (OFDM) signaling has gained prominence for broadband transmission in both wired and wireless systems. The subcarriers in an OFDM system are modulated and demodulated using the computationally efficient IFFT and FFT operations, respectively, which leads to low complexity, thus rendering it well-suited for practical implementation [1], [2]. However, the rectangular prototype filter of the IFFT/ FFT filter bank in an OFDM system has a sinc-shaped spectrum in the frequency-domain that suffers from relatively high out-of-band (OOB) emission, which makes the performance of these systems sensitive to practical imperfections, such as timing- and carrier frequency-offset (CFO). Therefore, OFDM may not be ideally suited for all the use cases in future mobile communication systems [3], [4]. In order to address the above shortcomings of OFDM, alternative multicarrier waveforms based on filter bank processing at the transmitter and receiver relying on different prototype filters have attracted significant research interest. In particular, offset quadrature amplitude modulation (OQAM)-aided filter bank multicarrier (FBMC) transmission has emerged as one of the potential waveform candidates to replace OFDM in next generation wireless systems [2], [4], [5]. This is because of the fact that the sharp cut-off prototype filter in FBMC-OQAM can significantly lower the OOB emission, and also obviate the use of cyclic-prefix (CP). The key differences between OFDM and FBMC-OQAM systems lie i) in the fact that the latter adopts OQAM symbols rather than QAM symbols; and ii) in the specific choice of the time-domain prototype windowing. In contrast to OFDM, FBMC uses a non-rectangular pulse, e.g. the isotropic orthogonal transform algorithm (IOTA) [6], Phydyas [7], root raised cosine (RRC), whose duration is much greater than the FBMC symbol duration. Therefore, in order to attain an identical spectral efficiency as that of OFDM, the adjacent time-domain FBMC symbols overlap with each other [8]. Furthermore, it must be noted that orthogonality in an FBMC system holds only in the real field. The accuracy of channel estimate available at the receiver has a key role in the reliable detection of data in FBMC-OQAM systems and hence, channel state information (CSI) estimation for these systems has been at the center of various contributions, as described in the next subsection. In the sequel, FBMC-OQAM is referred to as FBMC, for brevity.