Trade-off between complexity and BER performance of a polynomial SVD-based broadband MIMO transceiver

In this paper we investigate non-linear precoding solutions for the problem of broadband multiple-input multiple output(MIMO) systems. Based on a polynomial singular value decomposition (PSVD) we can decouple a broadband MIMO channel into independent dispersive spectrally majorised single-input single-output (SISO) subchannels. In this contribution, the focus of our work is to explore the influence of approximations on the PSVD, and the performance degradation that can be expected as a result

Polynomial matrix decomposition techniques for frequency selective MIMO channels

For a narrowband, instantaneous mixing multi-input, multi-output (MIMO) communications system, the channel is represented as a scalar matrix. In this scenario, singular value decomposition (SVD) provides a number of independent spatial subchannels which can be used to enhance data rates or to increase diversity. Alternatively, a QR decomposition can be used to reduce the MIMO channel equalization problem to a set of single channel equalization problems. In the case of a frequency selective MIMO system, the multipath channel is represented as a polynomial matrix. Thus conventional matrix decomposition techniques can no longer be applied. The traditional solution to this broadband problem is to reduce it to narrowband form by using a discrete Fourier transform (DFT) to split the broadband channel into N narrow uniformly spaced frequency bands and applying scalar decomposition techniques within each band. This describes an orthogonal frequency division multiplexing (OFDM) based system. However, a novel algorithm has been developed for calculating the eigenvalue decomposition of a para-Hermitian polynomial matrix, known as the sequential best rotation (SBR2) algorithm. SBR2 and its QR based derivatives allow a true polynomial singular value and QR decomposition to be formulated. The application of these algorithms within frequency selective MIMO systems results in a fundamentally new approach to exploiting spatial diversity. Polynomial matrix decomposition and OFDM based solutions are compared for a wide variety of broadband MIMO communication systems. SVD is used to create a robust, high gain communications channel for ultra low signal-to-noise ratio (SNR) environments. Due to the frequency selective nature of the channels produced by polynomial matrix decomposition, additional processing is required at the receiver resulting in two distinct equalization techniques based around turbo and Viterbi equalization. The proposed approach is found to provide identical performance to that of an existing OFDM scheme while supporting a wider range of access schemes. This work is then extended to QR decomposition based communications systems, where the proposed polynomial approach is found to not only provide superior bit-error-rate (BER) performance but significantly reduce the complexity of transmitter design. Finally both techniques are combined to create a nulti-user MIMO system that provides superior BER performance over an OFDM based scheme. Throughout the work the robustness of the proposed scheme to channel state information (CSI) error is considered, resulting in a rigorous demonstration of the capabilities of the polynomial approach

A block Krylov subspace time-exact solution method for linear ODE systems

We propose a time-exact Krylov-subspace-based method for solving linear ODE (ordinary differential equation) systems of the form $y'=-Ay + g(t)$ and $y''=-Ay + g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of the source term $g(t)$, constructed with the help of the truncated SVD (singular value decomposition). The second stage is a special residual-based block Krylov subspace method. The accuracy of the method is only restricted by the accuracy of the piecewise polynomial approximation and by the error of the block Krylov process. Since both errors can, in principle, be made arbitrarily small, this yields, at some costs, a time-exact method. Numerical experiments are presented to demonstrate efficiency of the new method, as compared to an exponential time integrator with Krylov subspace matrix function evaluations

Broadband MIMO Beamforming for Frequency Selective Channels using the Sequential Best Rotation Algorithm

For a narrowband multi-input multi-output (MIMO) system the singular value decomposition has the ability to provide multiple spatial channels for data transmission. We extend this work to obtain spatial diversity techniques for frequency selective MIMO systems using a polynomial matrix decomposition known as the sequential best rotation using second order statistics (SBR2) method. This algorithm diagonalizes a MIMO frequency selective channel yielding various spatial modes for data transmission. We evaluate the diversity performance of the dominant channel provided by the SBR2 based broadband decomposition and compare it with a transmit antenna selection method (TAS) and a MIMO orthogonal frequency-division multiplexing (OFDM) singular value decomposition (SVD) based approach. Simulation results show SBR2 significantly outperforms the average bit error rate (BER) of TAS, making it very suitable for time division multiple access (TDMA) and code division multiple access (CDMA) systems. SBR2 and MIMO-OFDM systems are shown to have identical BER performance, confirming the efficiency of the proposed low delay spatial-temporal scheme

MIMO precoding for filter bank modulation systems based on PSVD

In this paper we consider the design of a linearly precoded MIMO transceiver based on filter bank (FB) modulation for transmission over broadband frequency selective fading channels. The modulation FB is capable of lowering the channel dispersion at sub-channel level. Nevertheless, the sub-channels experience some level of inter-symbol interference. Therefore, the pre-coder and the equalizer are designed exploiting the polynomial singular value decomposition (PSVD). In particular, we consider two types of FB system. The first system deploys maximal frequency confined pulses and it is referred to as filtered multitone (FMT) modulation, while the second uses maximal time confined pulses with rectangular impulse response, i.e., it corresponds to the conventional orthogonal frequency division multiplexing (OFDM) system. We compare the performance of the considered systems in terms of capacity over typical WLAN channels, showing that PSVD precoding with FMT can outperform the performance of precoded OFDM in the two-bytwo antenna case especially for moderate to low SNRs

Decomposition of optical MIMO systems using polynomial matrix factorization

Within the last years the multiple-input multiple-output (MIMO) technology has revolutionized the optical fiber community. Theoretically, the concept of MIMO is well understood and shows some similarities to wireless MIMO systems. The interference in broadband MIMO systems can be removed by applying a spatio-temporal vector coding (STVC) channel description and using singular value decomposition (SVD) in combination with signal pre- and post-processing. In this contribution a newly developed SVD algorithm for polynomial matrices (PMSVD) is analyzed and compared to the commonly used SVD-based STVC. The PMSVD is implemented by an iterative polynomial matrix eigenvalue decomposition (PEVD) algorithm, namely the second order sequential best rotation algorithm (SBR2). The bit-error rate (BER) performance is evaluated and optimized by applying bit and power allocation schemes. For our simulations, the specific impulse responses of the (2 × 2) MIMO channel, including a 1.4 km multi-mode fiber and optical couplers at both ends, are measured for the operating wavelength of 1576 nm. The computer simulation results show that the PMSVD could be an alternative signal processing approach compared to conventional SVD-based MIMO approaches in frequency-selective MIMO channels

Novel Attitude Estimation Of Strapdown Inertial Navigation Systems With Singular Value Decomposition Technique

Davenport’s q method & the Singular Value Decomposition (SVD) method are the two vigorous estimators that reduces Wahba’s loss function. In these, the q method is slightly quicker due to its computation of optimum quaternion as an eigenvector of a symmetric 4x4 matrix through the prevalent eigenvalue. The ESOQ and ESOQ2 (EStimators of the Optimal Quaternion) and the QUEST (QUaternion ESTimator) algorithms are less determined as the extreme eigenvalue’s distinguishing polynomial equation is solved by them. These estimators are apt to track the undulations of the sea with equivalent precision and accurateness. The SVD method is chosen and shown to be the most robust of all the hostile methods for the orientation of SDINS (Strap-Down Inertial Navigation Systems) using rate matching observations at sea in this paper. SVD is known most robust decomposition of all the decompositions of a matrix. SVD based attitude estimation being a batch technique would suffer from much less computational issues