On arbitrary-level IIR and FIR filters

A recently published method for designing IIR (infinite-impulse-response) digital filters with multilevel magnitude responses is reinterpreted from a different viewpoint. On the basis of this interpretation, techniques for extending these results to the case of finite-impulse-response (FIR) filters are developed. An advantage of the authors' method is that, when the arbitrary-level filter is implemented, its power-complementary filter, which may be required in specific applications, is obtained simultaneously. Also, by means of a tuning factor (a parameter of the scaling matrix), it is possible to generate a whole family of arbitrary-level filters

Theory and design of perfect reconstruction transmultiplexers and their relation to perfect reconstruction QMF banks

The theory of transmultiplexers involves the design of filters for interconversion between Time Domain Multiplexing (TDM) and Frequency Division Multiplexing (FDM), such that the undesirable Crosstalk is minimized. In TDM → FDM → TDM conversion, the perfect reconstruction trans-multiplexer (PR-TMUX) achieves complete Crosstalk Cancellation (CC) and is distortion-free. In this paper, we present an analysis of the PR-TMUX based on the polyphase component matrices of the filter banks used in TDM → FDM and FDM → TDM conversion respectively. Using that, a necessary and sufficient condition for complete CC is obtained. The close relation between PR-TMUX filters and PR-QMF banks is used to obtain a direct design procedure for PR-TMUX filters

Set-partitioning based forward/backward soft decision algorithms for MIMO detection

A near maximum a posteriori (MAP)-optimal soft detector that outputs a posteriori probabilities (APP's) for multiple-input multiple-output (MIMO) systems in flat fading channels is proposed. This is referred to as 'reduced state maximum a posteriori (RSMAP)' algorithm. This detection algorithm is based on BCJR algorithm and also uses ideas from reduced state sequence estimation (RSSE) and set partitioning. This algorithm is shown to be near optimal and the computational complexity to implement it is estimated. Finally we also show that applying the well known max-log approximation on this algorithm results in nearly same performance at much lower complexity

Generalized reduced-state vector sequence detection

A multi-dimensional set-partitioning scheme is proposed for joint reduced-state sequence detection (JRSSD) of vector sequences corrupted by intersymbol interference (ISI) and additive white Gaussian noise (AWGN). The existing multi-dimensional set-partitioning schemes result in complexity exponential in the dimensionality of the vectors in the vector sequence. The proposed set-partitioning scheme allows the construction of reduced-state trellises with very few states even when the vectors are of high dimensionality. One of the key requirements of the JRSSD algorithm is an efficient algorithm for spatial multi-symbol detection, for which we propose the reduced-state tree (RST) detection algorithm. In addition to performance improvement, the inclusion of RST algorithm for spatial multi-symbol detection provides a common framework for designing receivers for both flat-fading and frequency-selective fading MIMO channels