Polynomial matrix QR decomposition and iterative decoding of frequency selective MIMO channels

For a frequency flat multi-input multi-output (MIMO) system the QR decomposition can be applied to reduce the MIMO channel equalization problem to a set of decision feedback based single channel problems. Using a novel technique for polynomial matrix QR decomposition (PMQRD) based on Givens rotations, we show the PMQRD can do likewise for a frequency selective MIMO system. Two types of transmitter design, based on Horizontal and Vertical Bell Laboratories Layered Space Time (H-BLAST, V-BLAST) encoding have been implemented. Receiver processing utilizes Turbo equalization to exploit multipath delay spread and to facilitate multi-stream data feedback. Average bit error rate simulations show a considerable improvement over a benchmark orthogonal frequency division multiplexing (OFDM) technique. The proposed scheme thereby has potential applicability in MIMO communication applications, particularly for a TDMA system with frequency selective channels

Polynomial matrix QR decomposition and iterative decoding of frequency selective MIMO channels

For a frequency flat multi-input multi-output (MIMO) system the QR decomposition can be applied to reduce the MIMO channel equalization problem to a set of decision feedback based single channel problems. Using a novel technique for polynomial matrix QR decomposition (PMQRD) based on Givens rotations, we show the PMQRD can do likewise for a frequency selective MIMO system. Two types of transmitter design, based on Horizontal and Vertical Bell Laboratories Layered Space Time (H-BLAST, V-BLAST) encoding have been implemented. Receiver processing utilizes Turbo equalization to exploit multipath delay spread and to facilitate multi-stream data feedback. Average bit error rate simulations show a considerable improvement over a benchmark orthogonal frequency division multiplexing (OFDM) technique. The proposed scheme thereby has potential applicability in MIMO communication applications, particularly for a TDMA system with frequency selective channels

A polynomial QR decomposition based turbo equalization technique for frequency selective MIMO channels.

In the case of a frequency flat multiple-input multiple-output (MIMO) system, QR decomposition can be applied to reduce the MIMO channel equalization problem to a set of decision feedback based single channel equalization problems. Using a novel technique for polynomial matrix QR decomposition (PMQRD) based on Givens rotations, we extend this work to frequency selective MIMO systems. A transmitter design based on Diagonal Bell Laboratories Layered Space Time (D-BLAST) encoding has been implemented. Turbo equalization is utilized at the receiver to overcome the multipath delay spread and to facilitate multi-stream data feedback. The effect of channel estimation error on system performance has also been considered to demonstrate the robustness of the proposed PMQRD scheme. Average bit error rate simulations show a considerable improvement over a benchmark orthogonal frequency division multiplexing (OFDM) technique. The proposed scheme thereby has potential applicability in MIMO communication applications, particularly for TDMA systems with frequency selective channels

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

An algorithm for calculating the QR and singular value decompositions of polynomial matrices

In this paper, a new algorithm for calculating the QR decomposition (QRD) of a polynomial matrix is introduced. This algorithm amounts to transforming a polynomial matrix to upper triangular form by application of a series of paraunitary matrices such as elementary delay and rotation matrices. It is shown that this algorithm can also be used to formulate the singular value decomposition (SVD) of a polynomial matrix, which essentially amounts to diagonalizing a polynomial matrix again by application of a series of paraunitary matrices. Example matrices are used to demonstrate both types of decomposition. Mathematical proofs of convergence of both decompositions are also outlined. Finally, a possible application of such decompositions in multichannel signal processing is discussed

Estimation and detection techniques for doubly-selective channels in wireless communications

A fundamental problem in communications is the estimation of the channel. The signal transmitted through a communications channel undergoes distortions so that it is often received in an unrecognizable form at the receiver. The receiver must expend significant signal processing effort in order to be able to decode the transmit signal from this received signal. This signal processing requires knowledge of how the channel distorts the transmit signal, i.e. channel knowledge. To maintain a reliable link, the channel must be estimated and tracked by the receiver. The estimation of the channel at the receiver often proceeds by transmission of a signal called the 'pilot' which is known a priori to the receiver. The receiver forms its estimate of the transmitted signal based on how this known signal is distorted by the channel, i.e. it estimates the channel from the received signal and the pilot. This design of the pilot is a function of the modulation, the type of training and the channel. [Continues.

Near-Instantaneously Adaptive HSDPA-Style OFDM Versus MC-CDMA Transceivers for WIFI, WIMAX, and Next-Generation Cellular Systems

Burts-by-burst (BbB) adaptive high-speed downlink packet access (HSDPA) style multicarrier systems are reviewed, identifying their most critical design aspects. These systems exhibit numerous attractive features, rendering them eminently eligible for employment in next-generation wireless systems. It is argued that BbB-adaptive or symbol-by-symbol adaptive orthogonal frequency division multiplex (OFDM) modems counteract the near instantaneous channel quality variations and hence attain an increased throughput or robustness in comparison to their fixed-mode counterparts. Although they act quite differently, various diversity techniques, such as Rake receivers and space-time block coding (STBC) are also capable of mitigating the channel quality variations in their effort to reduce the bit error ratio (BER), provided that the individual antenna elements experience independent fading. By contrast, in the presence of correlated fading imposed by shadowing or time-variant multiuser interference, the benefits of space-time coding erode and it is unrealistic to expect that a fixed-mode space-time coded system remains capable of maintaining a near-constant BER

QR factorization equalisation scheme for mode devision multiplexing transmission in fibre optics

Optical communication systems play a major role in handling worldwide Internet traffic. Internet traffic has been increasing at a dramatic rate and the current optical network infrastructure may not be able to support the traffic growth in a few decades. Mode division multiplexing is introduced as a new emerging technique to improve the optical network capacity by the use of the light modes as individual channels. One of the main issues in MDM is mode coupling which is a physical phenomenon when light modes exchange their energy between each other during propagation through optical fiber resulting in inter-symbol interference (ISI). Many studies based on Least Mean Square (LMS) and Recursive Least Square (RLS) have taken place to mitigate the mode coupling effect. Still, most approaches have high computational complexity and hinders high-speed communication systems. Blind equalisation approach does not need training signals, thus, will reduce the overhead payload. On the other hand, QR factorization shows low computational complexity in the previous research in the radio domain. The combination of these two concepts shows significant results, as the use of low complexity algorithms reduces the processing needed to be done by the communication equipment, resulting in more cost effective and smaller equipment, while having no training signal saves the bandwidth and enhances the overall system performance. To the best knowledge of the researcher, blind equalisation based on QR factorization technique has been not used in MDM equalisation to date. The research goes through the four stages of the design research methodology (DRM) to achieve the purpose of the study. The implementation stage is taken two different simulators has been used, the first one which is the optical simulator is used to collect the initial optical data then, MATLAB is used to develop the equalisation scheme. The development starts with the derivation of the system’s transfer function (H) to be used as the input to the developed equalizer. Blind equalisation based on QR factorization is chosen as a way to introduce an efficient equalization to mitigate ISI by narrowing the pulse width. The development stages include a stage where the channel estimation is taken place. Statistical properties based on the standard deviation (STD) of the powers of the input and output signals has been used for the blind equalisation’s channel estimation part. The proposed channel estimation way has the ability in estimating the channel with an overall mean square error (MSE) of 0.176588301 from the initial transmitted signal. It is found that the worst channel has an MSE of 0.771365 from the transmitted signal, while the best channel has and MSE of 0.000185 from the transmitted signal. This is done by trying to avoid the issues accompanied with the development of the previous algorithms that have been utilized for the same goal. The algorithm mentioned in the study reduces the computational complexity problem which is one of the main issues that accompany currently used tap filter algorithms, such as (LMS) and (RLS). The results from this study show that the developed equalisation scheme has a complexity of O(N) compared with O(N2) for RLS and at the same time, it is faster than LMS as its calculation CPU time is equal to 0.005242 seconds compared with 0.0077814 seconds of LMS. The results are only valid for invertible and square channel matrices

Wireless receiver designs: from information theory to VLSI implementation

Receiver design, especially equalizer design, in communications is a major concern in both academia and industry. It is a problem with both theoretical challenges and severe implementation hurdles. While much research has been focused on reducing complexity for optimal or near-optimal schemes, it is still common practice in industry to use simple techniques (such as linear equalization) that are generally significantly inferior. Although digital signal processing (DSP) technologies have been applied to wireless communications to enhance the throughput, the users' demands for more data and higher rate have revealed new challenges. For example, to collect the diversity and combat fading channels, in addition to the transmitter designs that enable the diversity, we also require the receiver to be able to collect the prepared diversity. Most wireless transmissions can be modeled as a linear block transmission system. Given a linear block transmission model assumption, maximum likelihood equalizers (MLEs) or near-ML decoders have been adopted at the receiver to collect diversity which is an important metric for performance, but these decoders exhibit high complexity. To reduce the decoding complexity, low-complexity equalizers, such as linear equalizers (LEs) and decision feedback equalizers (DFEs) are often adopted. These methods, however, may not utilize the diversity enabled by the transmitter and as a result have degraded performance compared to MLEs. In this dissertation, we will present efficient receiver designs that achieve low bit-error-rate (BER), high mutual information, and low decoding complexity. Our approach is to first investigate the error performance and mutual information of existing low-complexity equalizers to reveal the fundamental condition to achieve full diversity with LEs. We show that the fundamental condition for LEs to collect the same (outage) diversity as MLE is that the channels need to be constrained within a certain distance from orthogonality. The orthogonality deficiency (od) is adopted to quantify the distance of channels to orthogonality while other existing metrics are also introduced and compared. To meet the fundamental condition and achieve full diversity, a hybrid equalizer framework is proposed. The performance-complexity trade-off of hybrid equalizers is quantified by deriving the distribution of od. Another approach is to apply lattice reduction (LR) techniques to improve the ``quality' of channel matrices. We present two widely adopted LR methods in wireless communications, the Lenstra-Lenstra-Lovasz (LLL) algorithm [51] and Seysen's algorithm (SA), by providing detailed descriptions and pseudo codes. The properties of output matrices of the LLL algorithm and SA are also quantified. Furthermore, other LR algorithms are also briefly introduced. After introducing LR algorithms, we show how to adopt them into the wireless communication decoding process by presenting LR-aided hard-output detectors and LR-aided soft-output detectors for coded systems, respectively. We also analyze the performance of proposed efficient receivers from the perspective of diversity, mutual information, and complexity. We prove that LR techniques help to restore the diversity of low-complexity equalizers without increasing the complexity significantly. When it comes to practical systems and simulation tool, e.g., MATLAB, only finite bits are adopted to represent numbers. Therefore, we revisit the diversity analysis for finite-bit represented systems. We illustrate that the diversity of MLE for systems with finite-bit representation is determined by the number of non-vanishing eigenvalues. It is also shown that although theoretically LR-aided detectors collect the same diversity as MLE in the real/complex field, it may show different diversity orders when finite-bit representation exists. Finally, the VLSI implementation of the complex LLL algorithms is provided to verify the practicality of our proposed designs.Ph.D.Committee Chair: Ma, Xiaoli; Committee Member: Anderson, David; Committee Member: Barry, John; Committee Member: Chen, Xu-Yan; Committee Member: Kornegay, Kevi

Mode division multiplexing zero forcing equalisation scheme using LU factorization

Optical networks is considered as the main backbone networks that handled the Internet traffic worldwide. Currently, the Internet traffic has had huge annual growth due to the increment in connected devices. At this rate, it is believed that the current technology in optical network will not able to handle this growth in the near future. Till recently, multiplexing techniques in the optical communication rely on modulation techniques where polarization, amplitude and frequency of the signal are used as the main data carrier. In these techniques, light modes are considered as an undesired effect causing modal dispersion. In contrast, mode division multiplexing (MDM) was introduced as a multiplexing approach which relies on the utilization of the light modes for the benefit of increasing the capacity-distance product of the optical network. As per any new technology, it is still facing a lot of problems preventing it from being commercially standardized and used. One of the main MDM issues is the mode coupling, which is an inventible phenomena occurs when the energy of one mode transfers to another mode during their propagation throughout the optical fibre causes inter-symbol interference (ISI), increasing the bit error rate (BER) and reducing the overall system performance. Different equalization schemes have been proposed so far attempting to mitigate the effect of mode coupling on the MDM optical signal. However, they suffer from high computational complexity and rely on training signals in estimating the optical channel which increases the overhead payload. These technique mainly rely on Least Mean Squared (LMS) and Recursive Least Squared (RLS) algorithms. The purpose of this study is to introduce a Zero Forcing LU-based equalization scheme for MDM. Previous research in the radio domain on multiple-input multiple output (MIMO) and orthogonal frequency division multiplexing (OFDM) demonstrated that zero forcing schemes have low computational complexity compared to current schemes as they equalize the signal without training signals, thus reducing the overhead payload. All of the previous points motivate the work of this study to adapt this approach in optical communications. The study adopts the four stages of the Design Research Methodology (DRM). The initial data was collected from the optical simulator, processed and used to derive the transfer function (H) of the system. Then it was used to develop the equalization scheme in MATLAB. The experimentation on Zero Forcing LU based equalization scheme shows O(N) complexity which is lower than RLS which has O(N2) and faster than LMS, in fact, LMS needs an average of 0.0126 seconds to process the signal while ZF LU-based needs 0.0029 seconds only. On the other hand, the proposed equalization reduces the time delay spread of the channel, resulting three times increment in the capacity of the MDM channel and even lower computational complexity. The main contribution of this study is the reduction of the computational complexity of the previous equalization schemes in MDM. Applying this scheme in real MDM systems can produce more cost effective and smaller digital signal processing (DSP) parts for MDM equipment and can accelerate the work on the standardization of MDM for being commercially used as a multiplexing technique for optical communication networks