A General Framework for Designing Sparse FIR MIMO Equalizers Based on Sparse Approximation

In broadband communications, the long channel delay spread, defined as the duration in time, or samples, over which the channel impulse response (CIR) has significant energy, is too long and results in a highly-frequency-selective channel frequency response. Hence, a long CIR can spread over tens, or even hundreds, of symbol periods and causes impairments in the signals that have passed through such channels. For instance, a large delay spread causes inter-symbol interference (ISI) and inter-carrier interference (ICI) in multi-carrier modulation (MCM). Therefore, long finite impulse response (FIR) equalizers have to be implemented at high sampling rates to avoid performance degradation. However, the implementation of such equalizers is prohibitively expensive as the design complexity of FIR equalizers grows proportional to the square of the number of nonzero taps in the filter. Sparse equalization, where only few nonzero coefficients are employed, is a widely-used technique to reduce complexity at the cost of a tolerable performance loss. Nevertheless, reliably determining the locations of these nonzero coefficients is often very challenging. In this work, we first propose a general framework that transforms the problem of design of sparse single-input single-output (SISO) and multiple-input multiple-output (MIMO) linear equalizers (LEs) into the problem of sparsest-approximation of a vector in different dictionaries. In addition, we compare several choices of sparsifying dictionaries under this framework. Furthermore, the worst-case coherence of these dictionaries, which determines their sparsifying effectiveness, are analytically and/or numerically evaluated. Second, we extend our framework to accommodate SISO and MIMO non-linear decision-feedback equalizers (DFEs). Similar to the sparse FIR LEs design problem, the design of sparse FIR DFEs can be cast into one of sparse approximation of a vector by a fixed dictionary whose solution can be obtained by using either greedy algorithms, such as Orthogonal Matching Pursuit (OMP), or convex-optimization-based approaches, with the former being more desirable due to its low complexity. Third, we further generalize our sparse design framework to the channel shortening setup. Channel shortening equalizers (CSEs) are used to ensure that the cascade of a long CIR and the CSE is approximately equivalent to a target impulse response (TIR) with much shorter delay spread. Channel shortening is essential for communication systems operating over highly-dispersive broadband channels with large channel delay spread. Fourth, as an application of recent practical interest for power-line communication (PLC) community, we consider channel shortening for the impulse responses of medium-voltage power-lines (MV-PLs) with length of 10 km and 20 km to reduce the cyclic prefix (CP) overhead in orthogonal frequency-division multiplexing (OFDM) and, hence, improves the data rate accordingly. For all design problems, we propose reduced-complexity sparse FIR SISO and MIMO linear and non-linear equalizers by exploiting the asymptotic equivalence of Toeplitz and circulant matrices, where the matrix factorizations involved in our design analysis can be carried out efficiently using the fast Fourier transform (FFT) and inverse FFT with negligible performance loss as the number of filter taps increases. Finally, the simulation results show that allowing for a little performance loss yields a significant reduction in the number of active filter taps, for all proposed LEs and DFEs design filters, which in turn results in substantial complexity reductions. The simulation results also show that the CIRs of MV-PLs with length of 10 km and 20 km can be shortened to fit within the broadband PLC standards. Additionally, our simulations validate that the sparsifying dictionary with the smallest worst-case coherence results in the sparsest FIR filter design. Furthermore, the numerical results demonstrate the superiority of our proposed approach compared to conventional sparse FIR filters in terms of both performance and computational complexity.Qscienc

Sparse Equalizers for OFDM Signals with Insufficient Cyclic Prefix

The cyclic prefix (CP) is appended in orthogonal frequency division multiplexing (OFDM) signals to combat inter-symbol interference (ISI) and inter-carrier interference (ICI) induced by the communication channel, which limits its spectral efficiency. Therefore, inserting an insufficient CP and equalizing the resulting ICI and ISI is a method that has been circulating the literature for a while, aiming at increasing the efficiency of OFDM systems. In this paper, we propose a reduced-complexity sparse linear equalizer and a decision-feedback equalizer for OFDM signals with insufficient CP. A performance-complexity trade-off is highlighted, where we show that it is possible to equalize the received signal with a reduced complexity equalizer while having a limited performance loss. Our proposed equalizer designs are not only less complex to realize, but are shown to provide a higher data rate. The proposed equalizers are further evaluated in terms of the worst-case coherence, a metric determining the effectiveness of our used approach. Numerical results show that we can significantly and reliably reduce the order of the design complexity while performing very close to the conventional complex optimal equalizers. 2013 IEEE.This work was supported by GSRA from the Qatar National Research Fund (a member of Qatar Foundation) under Grant 2-1-0601-14011. The statements made herein are solely the responsibility of the authors.Scopu

Sparse Filter Design Under a Quadratic Constraint: Low-Complexity Algorithms

This paper considers three problems in sparse filter design, the first involving a weighted least-squares constraint on the frequency response, the second a constraint on mean squared error in estimation, and the third a constraint on signal-to-noise ratio in detection. The three problems are unified under a single framework based on sparsity maximization under a quadratic performance constraint. Efficient and exact solutions are developed for specific cases in which the matrix in the quadratic constraint is diagonal, block-diagonal, banded, or has low condition number. For the more difficult general case, a low-complexity algorithm based on backward greedy selection is described with emphasis on its efficient implementation. Examples in wireless channel equalization and minimum-variance distortionless-response beamforming show that the backward selection algorithm yields optimally sparse designs in many instances while also highlighting the benefits of sparse design.Texas Instruments Leadership University Consortium Progra

Design and Implementation of Belief Propagation Symbol Detectors for Wireless Intersymbol Interference Channels

In modern wireless communication systems, intersymbol interference (ISI) introduced by frequency selective fading is one of the major impairments to reliable data communication. In ISI channels, the receiver observes the superposition of multiple delayed reflections of the transmitted signal, which will result errors in the decision device. As the data rate increases, the effect of ISI becomes severe. To combat ISI, equalization is usually required for symbol detectors. The optimal maximum-likelihood sequence estimation (MLSE) based on the Viterbi algorithm (VA) may be used to estimate the transmitted sequence in the presence of the ISI. However, the computational complexity of the MLSE increases exponentially with the length of the channel impulse response (CIR). Even in channels which do not exhibit significant time dispersion, the length of the CIR will effectively increase as the sampling rate goes higher. Thus the optimal MLSE is impractical to implement in the majority of practical wireless applications. This dissertation is devoted to exploring practically implementable symbol detectors with near-optimal performance in wireless ISI channels. Particularly, we focus on the design and implementation of an iterative detector based on the belief propagation (BP) algorithm. The advantage of the BP detector is that its complexity is solely dependent on the number of nonzero coefficients in the CIR, instead of the length of the CIR. We also extend the work of BP detector design for various wireless applications. Firstly, we present a partial response BP (PRBP) symbol detector with near-optimal performance for channels which have long spanning durations but sparse multipath structure. We implement the architecture by cascading an adaptive linear equalizer (LE) with a BP detector. The channel is first partially equalized by the LE to a target impulse response (TIR) with only a few nonzero coefficients remaining. The residual ISI is then canceled by a more sophisticated BP detector. With the cascaded LE-BP structure, the symbol detector is capable to achieve a near-optimal error rate performance with acceptable implementation complexity. Moreover, we present a pipeline high-throughput implementation of the detector for channel length 30 with quadrature phase-shift keying (QPSK) modulation. The detector can achieve a maximum throughput of 206 Mb/s with an estimated core area of 3.162 mm^{2} using 90-nm technology node. At a target frequency of 515 MHz, the dynamic power is about 1.096 W. Secondly, we investigate the performance of aforementioned PRBP detector under a more generic 3G channel rather than the sparse channel. Another suboptimal partial response maximum-likelihood (PRML) detector is considered for comparison. Similar to the PRBP detector, the PRML detector also employs a hybrid two-stage scheme, in order to allow a tradeoff between performance and complexity. In simulations, we consider a slow fading environment and use the ITU-R 3G channel models. From the numerical results, it is shown that in frequency-selective fading wireless channels, the PRBP detector provides superior performance over both the traditional minimum mean squared error linear equalizer (MMSE-LE) and the PRML detector. Due to the effect of colored noise, the PRML detector in fading wireless channels is not as effective as it is in magnetic recording applications. Thirdly, we extend our work to accommodate the application of Advanced Television Systems Committee (ATSC) digital television (DTV) systems. In order to reduce error propagation caused by the traditional decision feedback equalizer (DFE) in DTV receiver, we present an adaptive decision feedback sparsening filter BP (DFSF-BP) detector, which is another form of PRBP detector. Different from the aforementioned LE-BP structure, in the DFSF-BP scheme, the BP detector is followed by a nonlinear filter called DFSF as the partial response equalizer. In the first stage, the DFSF employs a modified feedback filter which leaves the strongest post-cursor ISI taps uncorrected. As a result, a long ISI channel is equalized to a sparse channel having only a small number of nonzero taps. In the second stage, the BP detector is applied to mitigate the residual ISI. Since the channel is typically time-varying and suffers from Doppler fading, the DFSF is adapted using the least mean square (LMS) algorithm, such that the amplitude and the locations of the nonzero taps of the equalized sparse channel appear to be fixed. As such, the channel appears to be static during the second stage of equalization which consists of the BP detector. Simulation results demonstrate that the proposed scheme outperforms the traditional DFE in symbol error rate, under both static channels and dynamic ATSC channels. Finally, we study the symbol detector design for cooperative communications, which have attracted a lot of attention recently for its ability to exploit increased spatial diversity available at distributed antennas on other nodes. A system framework employing non-orthogonal amplify-and-forward half-duplex relays through ISI channels is developed. Based on the system model, we first design and implement an optimal maximum-likelihood detector based on the Viterbi algorithm. As the relay period increases, the effective CIR between the source and the destination becomes long and sparse, which makes the optimal detector impractical to implement. In order to achieve a balance between the computational complexity and performance, several sub-optimal detectors are proposed. We first present a multitrellis Viterbi algorithm (MVA) based detector which decomposes the original trellis into multiple parallel irregular sub-trellises by investigating the dependencies between the received symbols. Although MVA provides near-optimal performance, it is not straightforward to decompose the trellis for arbitrary ISI channels. Next, the decision feedback sequence estimation (DFSE) based detector and BP-based detector are proposed for cooperative ISI channels. Traditionally these two detectors are used with fixed, static channels. In our model, however, the effective channel is periodically time-varying, even when the component channels themselves are static. Consequently, we modify these two detector to account for cooperative ISI channels. Through simulations in frequency selective fading channels, we demonstrate the uncoded performance of the DFSE detector and the BP detector when compared to the optimal MLSE detector. In addition to quantifying the performance of these detectors, we also include an analysis of the implementation complexity as well as a discussion on complexity/performance tradeoffs

Persistent Localized Broadcasting in VANETs

We present a communication protocol, called LINGER, for persistent dissemination of delay-tolerant information to vehicular users, within a geographical area of interest. The goal of LINGER is to dispatch and confine information in localized areas of a mobile network with minimal protocol overhead and without requiring knowledge of the vehicles' routes or destinations. LINGER does not require roadside infrastructure support: it selects mobile nodes in a distributed, cooperative way and lets them act as "information bearers", providing uninterrupted information availability within a desired region. We analyze the performance of our dissemination mechanism through extensive simulations, in complex vehicular scenarios with realistic node mobility. The results demonstrate that LINGER represents a viable, appealing alternative to infrastructure-based solutions, as it can successfully drive the information toward a region of interest from a far away source and keep it local with negligible overhead. We show the effectiveness of such an approach in the support of localized broadcasting, in terms of both percentage of informed vehicles and information delivery delay, and we compare its performance to that of a dedicated, state-of-the-art protoco

Investigation of mode filtering as a preprocessing method for shallow-water acoustic communications

Author Posting. © IEEE, 2010. This article is posted here by permission of IEEE for personal use, not for redistribution. The definitive version was published in IEEE Journal of Oceanic Engineering 35 (2010): 744-755, doi:10.1109/JOE.2010.2045444.Acoustical array data from the 2006 Shallow Water Experiment (SW06) was analyzed to show the feasibility of broadband mode decomposition as a preprocessing method to reduce the effective channel delay spread and concentrate received signal energy in a small number of independent channels. The data were collected by a vertical array, which spans the water column from 12-m depth to the bottom in shallow water 80 m in depth. Binary-sequence data were used to phase-shift-keyed (PSK) modulate signals with different carrier frequencies. No error correction coding was used. The received signals were processed by a system that does not use training or pilot signals. Signals received both during periods of ordinary internal wave activity and during a period with unusually strong internal wave solitons were processed and analyzed. Different broadband mode-filtering methods were analyzed and tested. Broadband mode filtering decomposed the received signal into a number of independent signals with a reduced delay spread. The analysis of signals from the output of mode filters shows that even a simple demodulator can achieve a low bit error rate (BER) at a distance 19.2 km.This work was supported by the U.S. Office of Naval Research (ONR)

Advanced DSP Algorithms For Modern Wireless Communication Transceivers

A higher network throughput, a minimized delay and reliable communications are some of many goals that wireless communication standards, such as the fifthgeneration (5G) standard and beyond, intend to guarantee for its customers. Hence, many key innovations are currently being proposed and investigated by researchers in the academic and industry circles to fulfill these goals. This dissertation investigates some of the proposed techniques that aim at increasing the spectral efficiency, enhancing the energy efficiency, and enabling low latency wireless communications systems. The contributions lay in the evaluation of the performance of several proposed receiver architectures as well as proposing novel digital signal processing (DSP) algorithms to enhance the performance of radio transceivers. Particularly, the effects of several radio frequency (RF) impairments on the functionality of a new class of wireless transceivers, the full-duplex transceivers, are thoroughly investigated. These transceivers are then designed to operate in a relaying scenario, where relay selection and beamforming are applied in a relaying network to increase its spectral efficiency. The dissertation then investigates the use of greedy algorithms in recovering orthogonal frequency division multiplexing (OFDM) signals by using sparse equalizers, which carry out the equalization in a more efficient manner when the low-complexity single tap OFDM equalizer can no longer recover the received signal due to severe interferences. The proposed sparse equalizers are shown to perform close to conventional optimal and dense equalizers when the OFDM signals are impaired by interferences caused by the insertion of an insufficient cyclic prefix and RF impairments

Time-domain equalization for underwater acoustic OFDM systems with insufficient cyclic prefix

Master'sMASTER OF ENGINEERIN

Delay Alignment Modulation: Manipulating Channel Delay Spread for Efficient Single- and Multi-Carrier Communication

The evolution of mobile communication networks has always been accompanied by the advancement of ISI mitigation techniques, from equalization in 2G, spread spectrum and RAKE receiver in 3G, to OFDM in 4G and 5G. Looking forward towards 6G, by exploiting the high spatial resolution brought by large antenna arrays and the multi-path sparsity of mmWave and Terahertz channels, a novel ISI mitigation technique termed delay alignment modulation (DAM) was recently proposed. However, existing works only consider the single-carrier perfect DAM, which is feasible only when the number of BS antennas is no smaller than that of channel paths, so that all multi-path signal components arrive at the receiver simultaneously and constructively. This imposes stringent requirements on the number of BS antennas and multi-path sparsity. In this paper, we propose a generic DAM technique to manipulate the channel delay spread via spatial-delay processing, thus providing a flexible framework to combat channel time dispersion for efficient single- or multi-carrier transmissions. We first show that when the number of BS antennas is much larger than that of channel paths, perfect delay alignment can be achieved to transform the time-dispersive channel to time non-dispersive channel with the simple delay pre-compensation and path-based MRT beamforming. When perfect DAM is infeasible or undesirable, the proposed generic DAM technique can be applied to significantly reduce the channel delay spread. We further propose the novel DAM-OFDM technique, which is able to save the CP overhead or mitigate the PAPR issue suffered by conventional OFDM. We show that the proposed DAM-OFDM involves joint frequency- and time-domain beamforming optimization, for which a closed-form solution is derived. Simulation results show that the proposed DAM-OFDM outperforms the conventional OFDM in terms of spectral efficiency, BER and PAPR.Comment: 16 Pages, 15 figure

Machine Learning in Digital Signal Processing for Optical Transmission Systems

The future demand for digital information will exceed the capabilities of current optical communication systems, which are approaching their limits due to component and fiber intrinsic non-linear effects. Machine learning methods are promising to find new ways of leverage the available resources and to explore new solutions. Although, some of the machine learning methods such as adaptive non-linear filtering and probabilistic modeling are not novel in the field of telecommunication, enhanced powerful architecture designs together with increasing computing power make it possible to tackle more complex problems today. The methods presented in this work apply machine learning on optical communication systems with two main contributions. First, an unsupervised learning algorithm with embedded additive white Gaussian noise (AWGN) channel and appropriate power constraint is trained end-to-end, learning a geometric constellation shape for lowest bit-error rates over amplified and unamplified links. Second, supervised machine learning methods, especially deep neural networks with and without internal cyclical connections, are investigated to combat linear and non-linear inter-symbol interference (ISI) as well as colored noise effects introduced by the components and the fiber. On high-bandwidth coherent optical transmission setups their performances and complexities are experimentally evaluated and benchmarked against conventional digital signal processing (DSP) approaches. This thesis shows how machine learning can be applied to optical communication systems. In particular, it is demonstrated that machine learning is a viable designing and DSP tool to increase the capabilities of optical communication systems