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.

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

A compressed sensing approach to block-iterative equalization: connections and applications to radar imaging reconstruction

The widespread of underdetermined systems has brought forth a variety of new algorithmic solutions, which capitalize on the Compressed Sensing (CS) of sparse data. While well known greedy or iterative threshold type of CS recursions take the form of an adaptive filter followed by a proximal operator, this is no different in spirit from the role of block iterative decision-feedback equalizers (BI-DFE), where structure is roughly exploited by the signal constellation slicer. By taking advantage of the intrinsic sparsity of signal modulations in a communications scenario, the concept of interblock interference (IBI) can be approached more cunningly in light of CS concepts, whereby the optimal feedback of detected symbols is devised adaptively. The new DFE takes the form of a more efficient re-estimation scheme, proposed under recursive-least-squares based adaptations. Whenever suitable, these recursions are derived under a reduced-complexity, widely-linear formulation, which further reduces the minimum-mean-square-error (MMSE) in comparison with traditional strictly-linear approaches. Besides maximizing system throughput, the new algorithms exhibit significantly higher performance when compared to existing methods. Our reasoning will also show that a properly formulated BI-DFE turns out to be a powerful CS algorithm itself. A new algorithm, referred to as CS-Block DFE (CS-BDFE) exhibits improved convergence and detection when compared to first order methods, thus outperforming the state-of-the-art Complex Approximate Message Passing (CAMP) recursions. The merits of the new recursions are illustrated under a novel 3D MIMO Radar formulation, where the CAMP algorithm is shown to fail with respect to important performance measures.A proliferação de sistemas sub-determinados trouxe a tona uma gama de novas soluções algorítmicas, baseadas no sensoriamento compressivo (CS) de dados esparsos. As recursões do tipo greedy e de limitação iterativa para CS se apresentam comumente como um filtro adaptativo seguido de um operador proximal, não muito diferente dos equalizadores de realimentação de decisão iterativos em blocos (BI-DFE), em que um decisor explora a estrutura do sinal de constelação. A partir da esparsidade intrínseca presente na modulação de sinais no contexto de comunicações, a interferência entre blocos (IBI) pode ser abordada utilizando-se o conceito de CS, onde a realimentação ótima de símbolos detectados é realizada de forma adaptativa. O novo DFE se apresenta como um esquema mais eficiente de reestimação, baseado na atualização por mínimos quadrados recursivos (RLS). Sempre que possível estas recursões são propostas via formulação linear no sentido amplo, o que reduz ainda mais o erro médio quadrático mínimo (MMSE) em comparação com abordagens tradicionais. Além de maximizar a taxa de transferência de informação, o novo algoritmo exibe um desempenho significativamente superior quando comparado aos métodos existentes. Também mostraremos que um equalizador BI-DFE formulado adequadamente se torna um poderoso algoritmo de CS. O novo algoritmo CS-BDFE apresenta convergência e detecção aprimoradas, quando comparado a métodos de primeira ordem, superando as recursões de Passagem de Mensagem Aproximada para Complexos (CAMP). Os méritos das novas recursões são ilustrados através de um modelo tridimensional para radares MIMO recentemente proposto, onde o algoritmo CAMP falha em aspectos importantes de medidas de desempenho

Joint transceiver design for MIMO channel shortening.

Channel shortening equalizers can be employed to shorten the effective impulse response of a long intersymbol interference (ISI) channel in order, for example, to decrease the computational complexity of a maximum-likelihood sequence estimator (MLSE) or to increase the throughput efficiency of an orthogonal frequency-division multiplexing (OFDM) transmission scheme. In this paper, the issue of joint transmitter–receiver filter design is addressed for shortening multiple-input multiple-output (MIMO) ISI channels. A frequency-domain approach is adopted for the transceiver design which is effectively equivalent to an infinite-length time-domain design. A practical space–frequency waterfilling algorithm is also provided. It is demonstrated that the channel shortening equalizer designed according to the time-domain approach suffers from an error-floor effect. However, the proposed techniques are shown to overcome this problem and outperform the time-domain channel shortening filter design. We also demonstrate that the proposed transceiver design can be considered as a MIMO broadband beamformer with constraints on the time-domain multipath length. Hence, a significant diversity gain could also be achieved by choosing strong eigenmodes of the MIMO channel. It is also found that the proposed frequency-domain methods have considerably low computational complexity as compared with their time-domain counterparts

Precoded FIR and Redundant V-BLAST Systems for Frequency-Selective MIMO Channels

The vertical Bell labs layered space-time (V-BLAST) system is a multi-input multioutput (MIMO) system designed to achieve good multiplexing gain. In recent literature, a precoder, which exploits channel information, has been added in the V-BLAST transmitter. This precoder forces each symbol stream to have an identical mean square error (MSE). It can be viewed as an alternative to the bit-loading method. In this paper, this precoded V-BLAST system is extended to the case of frequency-selective MIMO channels. Both the FIR and redundant types of transceivers, which use cyclic-prefixing and zero-padding, are considered. A fast algorithm for computing a cyclic-prefixing-based precoded V-BLAST transceiver is developed. Experiments show that the proposed methods with redundancy have better performance than the SVD-based system with optimal powerloading and bit loading for frequency-selective MIMO channels. The gain comes from the fact that the MSE-equalizing precoder has better bit-error rate performance than the optimal bitloading method

Channel equalization to achieve high bit rates in discrete multitone systems

textMulticarrier modulation (MCM) techniques such as orthogonal frequency division multiplexing (OFDM) and discrete multi-tone (DMT) modulation are attractive for high-speed data communications due to the ease with which MCM can combat channel dispersion. With all the benefits MCM could give, DMT modulation has an extra ability to perform dynamic bit loading, which has the potential to exploit fully the available bandwidth in a slowly time-varying channel. In broadband wireline communications, DMT modulation is standardized for asymmetric digital subscribe line (ADSL) and very-high-bit-rate digital subscriber line (VDSL) modems. ADSL and VDSL standards are used by telephone companies to provide high speed data service to residences and offices. In an ADSL receiver, an equalizer is required to compensate for the channel’s dispersion in the time domain and the channel’s distortion in the frequency domain of the transmitted waveform. This dissertation proposes design methods for linear equalizers to increase the bit rate of the connection. The methods are amenable to implementation on programmable fixed-point digital signal processors, which are employed in ADSL/VDSL transceivers. A conventional ADSL equalizer consists of a time-domain equalizer, a fast Fourier transform, and a frequency domain equalizer. The time domain equalizer (TEQ) is a finite impulse response filter that when coupled with a discretized channel produces an equivalent channel whose impulse response is shorter than that of the discretized channel. This channel shortening is required by the ADSL standards. In this dissertation, I first propose a linear phase TEQ design that exploits symmetry in existing eigen-filter approaches such as minimum mean square error(MMSE), maximum shortening signal to noise ratio (MSSNR) and minimum intersymbol interference (Min-ISI) equalizers. TEQs with symmetric coefficients can reach the same performance as non-symmetric ones with much lower training complexity. Second, I improve Min-ISI design. I reformulate the cost function to make long TEQs design feasible. I remove the dependency of transmission delay in order to reduce the complexity associated with delay optimization. The quantized weighting is introduced to further lower the complexity. I also propose an iterative optimization procedure of Min-ISI that completely avoids Cholesky decomposition hence is better suited for a fixed-point implementation. Finally I propose a dual-path TEQ structure, which designs a standard singleFIR TEQ to achieve good bit rate over the entire transmission bandwidth, and designs another FIR TEQ to improve the bit rate over a subset of subcarriers. Dualpath TEQ can be viewed as a special case of a complex valued filter bank structure that delivers the best bit rate of existing DMT equalizers. However, dual-path TEQ provides a very good tradeoff between achievable bit rate vs. implementation complexity on a programmable digital signal processor.Electrical and Computer Engineerin

Physical layer network coding based communication systems in frequency selective channels

PhD ThesisThe demand for wireless communications is growing every day which requiresmore speed and bandwidth. In two way relay networks (TWRN), physical layer network coding (PLNC) was proposed to double the bandwidth. A TWRN is a system where two end users exchange data through a middle node called the relay. The two signals are allowed to be physically added before being broadcasted back to the end users. This system can work smoothly in flat fading channels, but can not be applied straightforward in frequency selective channels. In a multipath multi-tap FIR channel, the inter-symbol interference (ISI) spreads through several symbols. In this case, the symbols at the relay are not just an addition of the sent symbols but also some of the previous symbols from both sides. This not only causes a traditional PLNC to fail but also a simple one equalizer system will not solve the problem. Three main methods have been proposed by other researchers. The OFDM based PLNC is the simplest in terms of implementation and complexity but suffers from the disadvantages of the OFDMlike cyclic prefix overhead and frequency offset. The main disadvantage, however is the relatively low BER performance because it is restricted to linear equalizers in the PLNC system. Another approach is pre-filtering or pre-equalization. This method also has some disadvantages like complexity, sensitivity to channel variation and the need of a feedback channel for both end nodes. Finally, the maximum likelihood sequence detector was also proposed but is restricted to BPSK modulation and exponentially rising complexity are major drawbacks. The philosophy in this work is to avoid these disadvantages by using a time domain based system. The DFE is the equalizer of choice here because it provides a non-trivial BER performance improvement with very little increase in complexity. In this thesis, the problem of frequency selective channels in PLNC systems can be solved by properly adjusting the design of the system including the DFE. The other option is to redesign the equalizer to meet that goal. An AF DFE system is proposed in this work that provides very low complexity especially at the relay with little sensitivity to channel changes. A multi-antenna DNF DFE system is also proposed here with an improved performance. Finally, a new equalizer is designed for very low complexity and cost DNF approach with little sacrifice of BER performance. Matlab was used for the simulations with Monte Carlo method to verify the findings of this work through finding the BER performance of each system. This thesis opens the door for future improvement on the PLNC system. More research needs to be done like testing the proposed systems in real practical implementation and also the effect of adding channel coding to these systems.Iraqi Government, Ministry of Higher Educatio

Low-complexity soft-decision feedback turbo equalization for multilevel modulations

This dissertation proposes two new decision feedback equalization schemes suitable for multilevel modulation systems employing turbo equalization. One is soft-decision feedback equalization (SDFE) that takes into account the reliability of both soft a priori information and soft decisions of the data symbols. The proposed SDFE exhibits lower signal to noise ratio (SNR) threshold that is required for water fall bit error rate (BER) and much faster convergence than the near-optimal exact minimum mean square error linear equalizer (Exact-MMSE-LE) for high-order constellation modulations. The proposed SDFE also offers a low computational complexity compared to the Exact-MMSE-LE. The drawback of the SDFE is that its coefficients cannot reach the matched filter bound (MFB) and therefore after a large number of iterations (e.g. 10), its performance becomes inferior to that of the Exact-MMSE-LE. Therefore, soft feedback intersymbol interference (ISI) canceller-based (SIC) structure is investigated. The SIC structure not only exhibits the same low complexity, low SNR threshold and fast convergence as the SDFE but also reaches the MFB after a large number of iterations. Both theoretical analysis and numerical simulations demonstrate why the SIC achieves MFB while the SDFE cannot. These two turbo equalization structures are also extended from single-input single-output (SISO) systems to multiple-input multiple-output (MIMO) systems and applied in high data-rate underwater acoustic (UWA) communications --Abstract, page iv

Sparse equalizer filter design for multi-path channels

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 81-82).In this thesis, sparse Finite Impulse Response (FIR) equalizers are designed for sparse multi-path channels under a pre-defined Mean Squared Error (MSE) constraint. We start by examining the intrinsic sparsity of the Zero Forcing equalizers and the FIR Minimum MSE (MMSE) equalizers. Next the equalization MSE is formulated as a quadratic function of the equalizer coefficients. Both the Linear Equalizer (LE) and the Decision Feedback Equalizer (DFE) are analyzed. Utilizing the quadratic form, designing a sparse equalizer under a single MSE constraint becomes an 10-norm minimization problem under a quadratic constraint, as described in [2]. Three previously developed methods for solving this problem are applied, namely the successive thinning algorithm, the branch-and-bound algorithm, and the simple linear programming algorithm. Simulations under various channel specifications, equalizer specifications and algorithm specifications are conducted to show the dependency of the sparsity on these factors. The channels include the ideal discrete multipath channels and the Vehicular A multi-path channels in both the Single-Input-Single- Output (SISO) and the Multiple-Input-Multiple-Output scenarios. Additionally, the sparse FIR equalizer is designed for MIMO channels under two MSE constraints. This is formulated as an 10-norm minimization problem under two quadratic constraints. A sub-optimal solution by decoupling the two constraints is proposed.by Xue Feng.S.M