Optimized Paraunitary Filter Banks for Time-Frequency Channel Diagonalization

Abstract

We adopt the concept of channel diagonalization to time-frequency signal expansions obtained by DFT filter banks. As a generalization of the frequency domain channel representation used by conventional orthogonal frequency-division multiplexing receivers, the time-frequency domain channel diagonalization can be applied to time-variant channels and aperiodic signals. An inherent error in the case of doubly dispersive channels can be limited by choosing adequate windows underlying the filter banks. We derive a formula for the mean-squared sample error in the case of wide-sense stationary uncorrelated scattering (WSSUS) channels, which serves as objective function in the window optimization. Furthermore, an enhanced scheme for the parameterization of tight Gabor frames enables us to constrain the window in order to define paraunitary filter banks. We show that the design of windows optimized for WSSUS channels with known statistical properties can be formulated as a convex optimization problem. The performance of the resulting windows is investigated under different channel conditions, for different oversampling factors, and compared against the performance of alternative windows. Finally, a generic matched filter receiver incorporating the proposed channel diagonalization is discussed which may be essential for future reconfigurable radio systems.

An Overview of FIR Filter Design in Future Multicarrier Communication Systems

“…Secondly, to ensure the minimum leakage of signal components outside the target area in TF plane, the prototype window shows the best TF localization feature. To satisfy the first property, the parametrization of paraunitary filter banks in Reference [137] is used and longer pulses are extended in Reference [138]. As for the second property, the Rihaczek distribution is used in TF region, and the objective function along with the constraints is transformed into a form which can be solved by semi-definite programming (SDP) algorithm.…”

Performance Analysis of Filter Bank Multicarrier Cognitive Radio for Physical Layer under Binary Symmetric Radio Fading Channel

“…The paper analyzes three different realization structures, presenting also numerical comparisons, and compares the best FMT approach with a cyclically prefixed OFDM system in the IEEE 802.11 wireless LAN channel [9].Ziyang Ju et al (2009), developed a method to diagonalize a doubly dispersive channel in the time-frequency domain using a filter bank approach. The related paraunitary filter bank design problem is formulated as a convex optimization problem, and the performance of the resulting window is investigated under different channel conditions [10].Jun Ma et al (2009) discussed the practical issues involved to build a CR network from perspective of signal processing. The author identified spectrum sensing and spectrum sculpting as the two fundamental capabilities for any CR network to adapt to its environment and provide resilience under adverse conditions [11].H.…”

Post detection integration in DFT modulated filter bank transceivers for cognitive radio

“…However, transmission of information over a wireless fading channel based on the found FB has not been considered. The design of paraunitary FBs in [7] aims at tight Gabor frames facilitating TF domain channel diagonalization with minimal inherent error under given channel conditions for SAC. While the found FBs can be used for SSE as well, the bit detection for SAC is carried out with complete channel knowledge in a correlation detector operating in the TF domain at the output of a FB optimized by semidefinite relaxation being used as well in [6].…”