Abstract
In this paper, we propose a generalized singular value decomposition (GSVD) for polynomial matrices, or polynomial GSVD (PGSVD). We then consider PGSVD-based beamforming for two-user, frequency-selective, multiple-input multiple-output (MIMO) multicasting. The PGSVD can jointly factorize two frequency-selective MIMO channels, producing a set of virtual channels (VCs), split into: private channels (PCs) and common channels (CCs). An important advantage of the proposed PGSVD-based beamformer, over the application of GSVD independently to each frequency bin of the orthogonal frequency division multiplexing (OFDM) scheme, is that it can facilitate different modulation and/or access schemes to various users. Using computer simulations, we characterize the bit error rate performance of our two-user MIMO multicasting system for different PCs/CCs configurations. Here, we also propose an OFDM-GSVD benchmark system, and show that our PGSVD-based beamformer compares favorably to this benchmark under erroneous and uncertain MIMO channel conditions, in addition to its advantage of facilitating heterogeneous modulation and access for various users.
Highlights
T HE transmission of data from one point to multiple points has become important in recent times because of the increasing demand by end-users for wireless multimedia content, or multicasting
We propose a broadband beamformer based on polynomial GSVD (PGSVD) to enable multicasting over frequencyselective multiple-input multiple-output (MIMO) channels
We provide two sets of simulation studies to demonstrate the performance of the proposed PGSVD algorithm and PGSVDbased, point-to-two point MIMO-channel equalization method described in the previous sections
Summary
T HE transmission of data from one point to multiple points has become important in recent times because of the increasing demand by end-users for wireless multimedia content, or multicasting. In [3], Senaratne and Tellambura propose a beamformer based on the generalized singular value decomposition (GSVD) [4] for data transmission from a single source to two users through two MIMO channels. One possible way forward in this regard is by way of a frequency-domain scheme based on orthogonal frequencydivision multiplexing (OFDM) [9], [11], [12] Such an approach would utilize the discrete Fourier transform (DFT) over the entire data to convert the multipath-channel problem into a number of individual narrowband tones [13]. A number of time-domain, iterative algorithms for PEVD approximation have been proposed [17], [18] These algorithms broadly fall under one of two categories: the second-order sequential best rotation (SBR2) [17] and the sequential matrix diagonalisation (SMD) algorithms [18]. When the number of antennas is significantly greater than the intended number of spatial channels, it may be beneficial to consider a hybrid analogue and digital beamforming, as in [29], [30], to reduce the complexity associated with the massive number of RF chains
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