In our recent work we have proposed a new class of graph signal expansions termed local graph Fourier frames (LGFFs). LGFFs have finite support in the vertex domain and hence entail computationally highly efficient signal analysis and synthesis algorithms. Furthermore, they are extremely flexible and can adapt to a multitude of graph signal types. In this paper, we formulate proof-of-concept approaches for the quantization and denoising of nonstationary graph processes based on LGFFs. We furthermore propose an adaptation of the best basis algorithm to optimally choose the LGFF parameters. Our methods involve simple scalar processing in the LGFF domain and are shown to outperform existing approaches despite having a substantially lower complexity.

Graph signal processing (GSP) has provided a wide range of powerful methodologies for diverse learning tasks. While the data domain in GSP is fundamentally non-Euclidean, the relation between graph signal samples has mostly been studied using Euclidean similarity metrics. In our recent work on signature graphs we have explored GSP models specifically suited for data featuring symmetries that can be characterized by the sign-flip involution. In this paper, we introduce a generalized GSP framework with models and tools that build on generalized similarity/dissimilarity metrics and on different involutions to capture domain-specific data symmetries. We illustrate the usefulness of our generalized signature graph framework in graph learning and clustering problems.

Cooperative connected automated mobility depends on sensing and wireless communication functions. With increasing carrier frequency both functions can be realized with the same hardware, however, the attenuation of radio signals increases quadratically with the carrier frequency. Hence, link setup becomes challenging in vehicular scenarios due to the required beam finding process. In this paper we investigate the multipath components of the vehicle-to-infrastructure (V2I) radio channel in three frequency bands with center frequencies of 3.2 GHz, 34.3 GHz and 62.35 GHz using measurement data with 155.5 MHz bandwidth and a sounding repetition rate of $31.25 \mu \mathrm{~s}$. The channel impulse responses are collected simultaneously at all three carrier frequencies. Using the high temporal sampling rate we apply the CLEAN algorithm, enabling the estimation of the weight, delay and Doppler frequency of multipath components. By analyzing the collinearity of the Doppler normalized scattering function between the frequency bands we found that the collinearity between the 3.2 GHz and 34.3 GHz band as well as between the 3.2 GHz and 62.35 GHz is smaller in the non-line of sight (NLOS) region but increases for the line-of-sight (LOS).

The novel concept of signature graphs extends signed graphs by admitting multiple types of partial similarity/agreement or dissimilarity/disagreement. Extending the concept of balancedness to signature graphs yields an explicit and efficient basis for multi-class clustering and classification. Contrary to existing two-stage approaches that consist of graph learning followed by graph clustering, we propose a one-step procedure that directly learns a perfectly clustered graph. We describe the algorithmic constituents for our approach and illustrate its superiority via numerical simulations.

Computational sleep scoring from multimodal neurophysiological time-series (polysomnography PSG) has achieved impressive clinical success. Models that use only a single electroencephalographic (EEG) channel from PSG have not yet received the same clinical recognition, since they lack Rapid Eye Movement (REM) scoring quality. The question whether this lack can be remedied at all remains an important one. We conjecture that predominant Long Short-Term Memory (LSTM) models do not adequately represent distant REM EEG segments (termed epochs), since LSTMs compress these to a fixed-size vector from separate past and future sequences. To this end, we introduce the EEG representation model ENGELBERT (electroEncephaloGraphic Epoch Local Bidirectional Encoder Representations from Transformer). It jointly attends to multiple EEG epochs from both past and future. Compared to typical token sequences in language, for which attention models have originally been conceived, overnight EEG sequences easily span more than 1000 30 s epochs. Local attention on overlapping windows reduces the critical quadratic computational complexity to linear, enabling versatile sub-one-hour to all-day scoring. ENGELBERT is at least one order of magnitude smaller than established LSTM models and is easy to train from scratch in a single phase. It surpassed state-of-the-art macro F1-scores in 3 single-EEG sleep scoring experiments. REM F1-scores were pushed to at least 86%. ENGELBERT virtually closed the gap to PSG-based methods from 4-5 percentage points (pp) to less than 1 pp F1-score.

Signed graphs have recently been found to offer advantages over unsigned graphs in a variety of tasks. However, the problem of learning graph topologies has only been considered for the unsigned case. In this paper, we propose a conceptually simple and flexible approach to signed graph learning via signed smoothness metrics. Learning the graph amounts to solving a convex optimization problem, which we show can be reduced to an efficiently solvable quadratic problem. Applications to signal reconstruction and clustering corroborate the effectiveness of the proposed method.

We consider discrete message passing (MP) decoding of low-density parity check (LDPC) codes based on information-optimal symmetric look-up table (LUT). A link between discrete message labels and the associated log-likelihood ratio values (defined in terms of density evolution distributions) is established. This link gives rise to an algebraic structure on the message labels and leads to an interpretation of LUT decoding as a form of quantized belief propagation. We then exploit the algebraic structure for low-complexity LUT decoder designs. Our LUT decoding framework is the first to also apply to irregular LDPC codes by taking into account the degree distribution in a joint LUT design. We exploit the relation between LUT decoding and belief propagation to obtain stability conditions and irregular LDPC code designs optimized for LUT decoding. The resulting decoders outperform floating-point precision min-sum decoders at LUT resolutions as low as 3 bit s for regular codes and 4 bits for irregular codes.

We consider the problem of semi-supervised clustering for multiple (more than two) classes. The proposed clustering algorithm uses the (dis)similarity of given data to learn the unknown cluster labels. We quantify label (dis)similarity in terms of the new concept of signed total variation (TV). The clustering task is formulated as a convex optimization problem with an ℓ1-norm regularization term that helps when only few labels are known. We solve the optimization problem by developing an ADMM-based algorithm whose per-iteration complexity scales linearly with the number of edges and the number of clusters. Our algorithm admits a distributed implementation and can therefore efficiently handle large-dimensional problems. Numerical experiments demonstrate the superiority of our scheme.

We consider the problem of learning the topology of a graph from a given set of smooth graph signals. We construct a weighted adjacency matrix that best explains the data in the sense of achieving the smallest graph total variation. For the case of noisy measurements of the graph signals we propose a scheme that simultaneously denoises the signals and learns the graph adjacency matrix. Our method allows for a direct control of the number of edges and of the weighted node degree. Numerical experiments demonstrate that our graph learning scheme is well suited for community detection.

An ultrahigh throughput low-density parity-check (LDPC) decoder with an unrolled full-parallel architecture is proposed, which achieves the highest decoding throughput compared to previously reported LDPC decoders in the literature. The decoder benefits from a serial message-transfer approach between the decoding stages to alleviate the well-known routing congestion problem in parallel LDPC decoders. Furthermore, a finite-alphabet message passing algorithm is employed to replace the VN update rule of the standard min-sum (MS) decoder with lookup tables, which are designed in a way that maximizes the mutual information between decoding messages. The proposed algorithm results in an architecture with reduced bit-width messages, leading to a significantly higher decoding throughput and to a lower area compared to an MS decoder when serial message transfer is used. The architecture is placed and routed for the standard MS reference decoder and for the proposed finite-alphabet decoder using a custom pseudo-hierarchical backend design strategy to further alleviate routing congestions and to handle the large design. Postlayout results show that the finite-alphabet decoder with the serial message-transfer architecture achieves a throughput as large as 588 Gb/s with an area of 16.2 mm2and dissipates an average power of 22.7 pJ per decoded bit in a 28-nm fully depleted silicon on isulator library. Compared to the reference MS decoder, this corresponds to 3.1 times smaller area and 2 times better energy efficiency.

This paper investigates the Multiple Description (MD) Chief Executive Officer (CEO) problem under logarithmic-loss distortion. The setup extends previous work of Courtade and Weissman (2014) by requiring the CEO to obtain a useful reconstruction also from a reduced set of descriptions. A single-letter characterization of the achievable region is derived under a suitable conditional independence assumption. Surprisingly, the resulting rate requirement is in general less than that required to ensure successful typicality decoding of the corresponding description.

This paper investigates the problem of distributed biclustering of memoryless sources and extends previous work [1] to the general case with more than two sources. Given a set of distributed stationary memoryless sources, the encoders' goal is to find rate-limited representations of these sources such that the mutual information between two selected subsets of descriptions (each of them generated by distinct encoders) is maximized. This formulation is fundamentally different from conventional distributed source coding problems since here redundancy among descriptions should actually be maximally preserved. We derive non-trivial outer and inner bounds to the achievable region for this problem and further connect them to the CEO problem under logarithmic loss distortion. Since information-theoretic biclustering is closely related to distributed hypothesis testing against independence, our results are also expected to apply to that problem.

Let (X,Y) be a doubly symmetric binary source. For n i.i.d. copies (Xn,Yn) of (X,Y) we show that max[I(f(Xn); g(Yn))]= I(X,Y), where the maximum is over all Boolean functions f, g: {0, 1}n→ {0, 1}. This positively resolves a conjecture published by Kumar and Courtade in 2013.

Average consensus is a well-studied method for distributed averaging. The convergence properties of average consensus depend on the averaging weights. Examples for commonly used weight designs are Metropolis-Hastings (MH) weights and constant weights. In this paper, we provide a complete convergence analysis for a generalized MH weight design that encompasses conventional MH as special case. More specifically, we formulate sufficient and necessary conditions for convergence. A main conclusion is that AC with MH weights is guaranteed to converge unless the underlying network is a regular bipartite graph.

We introduce an iterative solution to the problem of interference alignment (IA) over MIMO channels based on a message-passing formulation. We propose a parameterization of the messages that enables the computation of IA precoders by a min-sum algorithm over continuous variable spaces - under this parameterization, suitable approximations of the messages can be computed in closed-form. We show that the iterative leakage minimization algorithm of Gomadam et al. is a special case of our message-passing algorithm, obtained for a particular schedule. Finally, we show that the proposed algorithm compares favorably to iterative leakage minimization in terms of convergence speed, and discuss a distributed implementation.

We consider lossy compression of the output of a Gaussian vector channel. This is relevant for quantizer design in rate-limited feedback and in receiver front-ends. In particular, we study the trade-off between compression rate and mutual information between channel input and compressed channel output. Using the Gaussian information bottleneck we provide closed-form expressions for the information-rate function and the rate-information function. We prove that optimal compression in the rate distortion sense with squared-error distortion does not achieve the optimal rate-information trade-off. The suboptimality of the rate distortion approach is quantified and we give an upper bound on the gap to the optimal rate-information tradeoff. Finally, our results are corroborated by numerical examples.

It is well known that feedback does not increase the capacity of the AWGN channel. Schalkwijk and Kailath presented a feedback scheme that dramatically improves the error probability for finite block lengths. Unfortunately, the Schalkwijk-Kailath scheme requires perfect feedback, which is often not feasible. We study the performance of linear transmission schemes for AWGN channels with separate quantization of the feedback signal and the receiver input signal. The quantizers are designed in a rate-information-optimal manner using the Gaussian information bottleneck. We provide expressions for achievable rates and error probabilities in terms of the so-called information-rate function. It turns out the exploiting knowledge of the quantized feedback signal at the receiver is crucial for achieving strictly positive rates.

We study energy management policies for the compression and transmission of source data collected by an energy-harvesting sensor node with a finite energy buffer (e.g., rechargeable battery) and a finite data buffer (memory) between source encoder and channel encoder. The sensor node can adapt the source and channel coding rates depending on the observation and channel states. In such a system, the absence of precise information about the amount of energy available in the future is a key challenge. We provide analytical bounds and scaling laws for the average distortion that depend on the size of the energy and data buffers. We furthermore design a resource allocation policy that achieves almost optimal distortion scaling. Our results demonstrate that the energy leakage of state of art energy management policies can be avoided by jointly controlling the source and channel coding rates.

We present a decode-and-forward transmission scheme based on spatially-coupled low-density parity-check (SC-LDPC) codes for a network consisting of two (possibly correlated) sources, one relay, and one destination. The links between the nodes are modeled as binary erasure channels. Joint source-channel coding with joint channel decoding is used to exploit the correlation. The relay performs network coding. We derive analytical bounds on the achievable rates for the binary erasure time-division multiple-access relay channel with correlated sources. We then design bilayer SC-LDPC codes and analyze their asymptotic performance for this scenario. We prove analytically that the proposed coding scheme achieves the theoretical limit for symmetric channel conditions and uncorrelated sources. Using density evolution, we furthermore demonstrate that our scheme approaches the theoretical limit also for non-symmetric channel conditions and when the sources are correlated, and we observe the threshold saturation effect that is typical for spatially-coupled systems. Finally, we give simulation results for large block lengths, which validate the DE analysis.

Average consensus (AC) is a popular method for distributed innetwork averaging that is closely related to diffusion processes. Recently, it has been suggested that AC designs inspired by physical advection processes feature improved performance. In this paper, we show how such advection-diffusion inspired AC designs can be obtained for realistic network topologies. The resulting AC algorithms act like a blender that mixes the measured data. Numerical simulations corroborate the performance improvements of our blending approach to the design of AC algorithms.

In our previous work, we developed efficient field reconstruction methods in wireless sensor networks. In this paper, we use an amplify-and-forward to transmit the sensor measurements to the fusion center and we derive the mean square error (MSE) of the reconstructed field as a function of the measurement and receive SNR and of the sensor positions. We propose to allocate the sensor node transmit powers such that the sum power is minimized subject to an MSE target and we phrase this approach as a convex optimization problem that can be numerically solved in an efficient manner. For the case of critical sampling we derive a closed-form expression for the optimal power allocation. We illustrate the power savings achieved with the proposed power allocation schemes both for Gaussian and Rayleigh fading channels.

We present a novel weight design for average consensus that improves its transient and stead-state performance. The idea is to blend Metropolis-Hastings weights and convex-optimization weights via signal-adaptive morphing coefficients. The resulting scheme is shown to be particularly useful in dynamic scenarios where the measurements feature abrupt changes or unknown noise levels.

Decentralized physics-based field estimation in clustered sensor networks requires the exchange of state vectors between neighboring clusters. We reduce the communication overhead between clusters by using a differential encoding of state vectors that exploits the spatio-temporal field dependencies. This encoding involves a Kalman prediction step that builds on the state-space equations governing the field's spatio-temporal evolution. The Kalman step keeps the computational complexity low. Simulation results for an acoustic field demonstrate the approach.

In this paper we consider the time-division multiple-access relay channel (MARC). We propose a low-complexity compress-and-forward-based transmission scheme that consists of a scalar quantization of log-likelihood ratios (LLRs), followed by a suitably defined network code. This scheme is well suited also for asymmetric source-relay channel conditions. We use the information bottleneck method (IBM) for designing the LLR quantizers and we propose a modified IBM algorithm with more favorable numerical properties. Finally, we assess the performance of the proposed scheme in AWGN and fading channels using numerical simulations, including a comparison with existing transmission schemes.

We derive bounds on the error probability of optimal and sub- optimal detectors in an uncoded decode-and- forward relay system with two correlated information sources. This setup is relevant to wireless sensor networks where nearby sensors collect spatially correlated data. We show that taking into account the source correlation at the relay and at the destination leads to significant performance gains. Simulation results corroborate the tightness of our analytical bounds.

In our previous work we have proposed a dynamic version of the consensus propagation (CP) algorithm introduced by Moallemi and Van Roy. Here, we pursue a system theoretic approach to the analysis of CR Specifically, we first develop a state-space model for CP and then use this model to prove stability of CP when applied to time-varying processes. We further show how the state-space model can be used to describe the transfer characteristics (spatio-temporal filtering) of CP in terms of attenuation and group delay, both for pure CP and an extended version that uses local linear predictors at the processing nodes. Numerical simulations illustrate our findings.

We study efficient algorithms for soft-input soft-output (SISO) encoding of convolutional codes. While the BCJR algorithm has been suggested for SISO encoding, we show that a forward recursion on the code's trellis is sufficient to compute the a posteriori probabilities of the code bits. We further propose a shift-register based SISO encoding algorithm for non-recursive convolutional encoders, whose complexity scales linearly with constraint length and block length. Finally, we assess the complexity of the proposed algorithms and we discuss approximations to facilitate practical implementation.

The use of distributed space-time codes in cooperative communications promises to increase the rate and reliability of data transmission. These gains were mostly demonstrated for ideal scenarios, where all nodes are perfectly synchronized. Considering a cooperative uplink scenario with asynchronous nodes, the system suffers from two effects: timing errors and individual carrier frequency offsets. In effect, timing errors can completely cancel the advantages introduced by space-time codes, while individual carrier frequency offsets provide a great challenge to receivers. Indeed, frequency offsets are perceived as a time-variant channel (even if the individual links are static) in distributed cooperative communications. We show that using OFDM, space-time codes (STCs) become tolerant to timing errors. Channel estimation and tracking takes care of frequency offsets. Our simulations demonstrate that the bit error rate performance improves by an order of magnitude, when using a cooperative system design, which takes these two effects into account.

We propose a novel pilot-aided algorithm for estimation of rapidly varying wireless channels in OFDM systems. Our approach is specifically designed for channels varying on the scale of a single OFDM symbol duration, which occur, for example, in mobile WiMAX, WAVE, and DVB-T. From the pilot information, we recover information about the channel taps in the framework of the Basis Expansion Model (BEM). We derive explicit formulas for the BEM coefficients in terms of the receive signal. Algebraically, the algorithm is FFT-based, and can be easily implemented in hardware. For a system with L channels taps, our method uses O(L log L) operations and O(L) memory per OFDM symbol. This complexity is the best possible up to the order of magnitude. Previously published methods require O(L2) operations and O(L2) memory. Numerical simulations illustrate performance gains achieved by our estimator at sufficiently high Doppler frequencies. Our approach does not assume any prior statistical information.

This paper considers a wireless relay network with one source, one relay, and one destination. We propose a low-complexity quantize-and-forward (QF) scheme in which the relay calculates log-likelihood ratios (LLRs) for the code bits transmitted by the source and passes quantized versions of these LLRs on to the destination. The destination combines the LLRs from the source-destination link and the quantized LLRs from the source-relay link to obtain improved information bit estimates. We verify the usefulness of the proposed scheme via numerical simulations in block and fast fading.

This work deals with the distributed measurement and reconstruction of time-varying spatial fields using wireless sensor networks (WSN).We use basis functions to formulate a low-dimensional subspace model for the field and estimate the field coefficients using a suitably modified version of consensus propagation (CP), which is a distributed asynchronous averaging algorithm with favorable convergence. Simulation results confirm the excellent performance of the proposed method in static and dynamic environments.

This paper focuses on perturbation-based distributed beamforming with 1-bit feedback for wireless amplify-and-forward relay networks. We propose to use multiplicative perturbations based on Givens rotations to adapt the beamforming weights while guaranteeing a sum power constraint for the relays. This perturbation scheme is shown to be computationally efficient and easy to design, thus allowing for low-complexity relay nodes. An adaptation of the Givens rotation angle allows to approach optimum performance arbitrarily close. Numerical simulations demonstrate noticeable performance gains over additive perturbation schemes that have been exclusively considered up to now.

In this paper we consider the vector perturbation (VP) precoding scheme for the multiuser MISO broadcast channel proposed by Hochwald et al. under the practical assumption that the receivers have limited dynamic range. In this case, VP precoding is shown to suffer from an error floor at high signal-to-noise ratio (SNR). As an alternative, we propose precoding with restricted VP (RVP), which takes the limited dynamic range of the receivers explicitly into account by restricting to a finite set of possible perturbation vectors at the transmitter side. We derive the diversity order of this RVP scheme and show that no error floor occurs and that the performance is superior to VP for the entire range of SNRs.

We present a factor graph based design of a receiver for pilot-assisted OFDM-IDMA systems transmitting over frequency-selective channels. The receiver performs joint iterative multiuser data detection and channel estimation with a complexity that is linear in the number of users, and it includes estimation of the channel length. Simulation results demonstrate large performance gains compared to OFDM-IDMA receivers using separate MMSE channel estimation.

We use the theory and algorithms developed for so-called shift-invariant spaces to develop a novel distributed architecture for sampling and reconstructing non-bandlimited fields in wireless sensor networks. Our scheme groups neighboring sensors into clusters that locally perform highly accurate field reconstruction with limited communication overhead. The overall complexity of our method scales only linearly with the number of sensors. Numerical simulations illustrate that the proposed field reconstruction scheme outperforms band-limited reconstruction, even though the latter has much larger complexity.

The clipping of log-likelihood ratios (LLRs) in soft demodulators for multiple-input multiple-output (MIMO) systems with bit-interleaved coded modulation (BICM) was recently observed to allow for enormous complexity savings. In this paper we first provide an information-geometric interpretation of LLR clipping as information projection onto a log-convex manifold. Then we study the system capacity of MIMO-BICM systems that use LLR clipping. Our results show that strong LLR clipping is possible without significant capacity loss. We finally propose an LLR transformation scheme which is necessary for approaching capacity in case of strong clipping. The usefulness of this LLR transformation is illustrated by numerical simulations for MIMO-BICM systems employing low-density parity check (LDPC) codes.

We study quantization of log-likelihood ratios (LLR) in bit-interleaved coded modulation (BICM) systems in terms of an equivalent discrete channel. We propose to design the quantizer such that the quantizer outputs become equiprobable. We investigate semi-analytically and numerically the ergodic and outage capacity over single- and multiple-antenna channels for different quantizers. Finally, we show bit error rate simulations for BICM systems with LLR quantization using a rate 1/2 low-density parity-check code.

Communication systems are usually designed by assuming perfect channel state information (CSI). However, in many practical scenarios, only a noisy estimate of the channel is available, which may strongly differ from the true channel. This imperfect CSI scenario is addressed by introducing the notion ofestimation-induced outage (EIO). We derive a single-letter characterization of the maximal EIO rate and prove an associated coding theorem and its strong converse for discrete memoryless channels (DMCs). The transmitter and the receiver rely on the channel estimate and the statistics of the estimate to construct codes that guarantee reliable communication with a certain outage probability. This ensures that in the non-outage case the transmission meets the target rate with small error probability, irrespective of the quality of the channel estimate. Applications of the EIO capacity to a single-antenna (nonergodic) Ricean fading channel are considered. The EIO capacity for this case is compared to the EIO rates of a communication system in which the receiver decodes by using a mismatched maximum-likelihood (ML) decoder. The effects of rate-limited feedback to provide the transmitter with quantized CSI are also investigated.

This paper deals with distributed beamforming techniques for wireless networks with half-duplex amplify-and- forward relays. Existing schemes optimize the beamforming weights based on the assumption that channel state information (CSI) is available at the relays. We propose to use adaptive beamforming based on deterministic perturbations and limited feedback (1-bit) from the destination to the relays in order to avoid CSI at the relays. Two scalable perturbation schemes are considered and practical implementation aspects are addressed. Simulation results confirm that the proposed techniques closely approach optimum performance and have satisfactory tracking properties in time-varying environments.

There have recently been a large number of papers that derive the diversity order of various, low complexity, suboptimal receiver structures for MIMO communications. In almost all analyses the MIMO channel is assumed to be i.i.d. Rayleigh fading. It is of interest to investigate how these results generalize to other fading models (e.g., correlated Ricean fading). We show in this paper that the diversity achieved by virtually any receiver is preserved within a very general class of fading models (including i.i.d. Rayleigh fading and correlated Ricean fading). This result obviates the need to recalculate the diversity of various receivers for different fading distributions in a piecemeal fashion.

Lattice reduction by means of the LLL algorithm has been previously suggested as a powerful preprocessing tool that allows to improve the performance of suboptimal detectors and to reduce the complexity of optimal MIMO detectors. The complexity of the LLL algorithm is often cited as polynomial in the dimension of the lattice. In this paper we argue that this statement is not correct when made in the MIMO context. Specifically, we demonstrate that in typical communication scenarios the worst-case complexity of the LLL algorithm is not even finite. For i.i.d. Rayleigh fading channels, we further prove that the average LLL complexity is polynomial and that the probability for an atypically large number of LLL iterations decays exponentially.

We consider a pilot-assisted interleave-division multiple access (IDMA) system transmitting over block-fading channels. We describe this system in terms of a factor graph and use the sum-product algorithm to develop a receiver that performs joint data detection and channel estimation. Suitable approximations to the messages passed by the sum-product algorithm yield an implementation with a complexity that scales linearly with the number of users. Simulation results demonstrate large performance gains compared to classical receivers performing separate channel estimation and data detection.

Interleave-division multiple access (IDMA) has recently been introduced as an attractive alternative to CDMA. IDMA employs user-specific interleavers combined with low-rate channel coding for user separation. In this paper, we consider a MIMO-IDMA system with increased spectral efficiency due to the use of higher-order symbol constellations. Based on a factor graph framework and the sum-product algorithm, we develop an iterative turbo multiuser receiver. Gaussian approximations for certain messages propagated through the factor graph lead to a complexity that scales only linearly with the number of users. To further reduce complexity, we introduce a selective message update scheme. Numerical simulations demonstrate the performance of the proposed receiver algorithms.

This paper considers multiuser OFDMA uplink transmissions over doubly selective channels. We propose a pilot-aided channel estimator based on irregular sampling techniques. Our novel estimator features several benefits: it has low complexity, excellent performance, and enables highly flexible subcarrier allocation. Simulation results show that our scheme significantly outperforms conventional least-squares channel estimation and allows to support high-rate users with reduced pilot overhead.

In this paper, we consider MIMO spatial multiplexing systems and elaborate the impact of the channel condition number on the performance of ML and ZF detection. In particular, we show that for channels with bounded condition number ZF detection achieves the same diversity as ML detection. Motivated by this, we propose a novel threshold receiver that uses simple ZF detection for well-conditioned channels and ML detection for poorly conditioned channels. We show that this receiver achieves full diversity and we provide an upper bound on its SNR gap to ML detection. We further investigate cost-reduced versions of the threshold receiver and examine their performance in terms of simulation results.

Interleave-division multiple access (IDMA) has recently been proposed as an alternative to CDMA. IDMA employs user-specific interleavers combined with low-rate channel coding for user separation. It can outperform coded CDMA when iterative receivers are used, and it allows the design of multiuser detectors with moderate complexity. In this paper, we extend IDMA to MIMO multiuser systems employing spatial multiplexing. We also develop an iterative receiver for MIMO-IDMA that incorporates an efficient soft multiuser detector whose complexity is linear in the number of users. Both flat-fading and frequency-selective MIMO channels are considered. The performance of the proposed MIMO-IDMA system is assessed through simulation results.

Lattice reduction (LR) is a powerful technique for improving the performance of suboptimum MIMO data detection methods. For LR-assisted data detection, the LLL algorithm has been considered almost exclusively so far. In this paper, we propose and develop the application of Seysen's algorithm (SA) to LR-assisted MIMO detection, and we show that the SA is a promising alternative to the LLL algorithm. Specifically, the SA outperforms the LLL algorithm in that it finds better lattice bases for MIMO systems of practical interest, which is reflected by an improved performance of SA-assisted detectors relative to their LLL-assisted counterparts. We present an efficient implementation of the SA whose per-iteration complexity is linear in the number of antennas, and we demonstrate that the SA requires significantly fewer iterations than the LLL algorithm.

This paper describes the first VLSI implementation of lattice reduction (LR) aided multi-antenna broadcast precoding with vector perturbation. The considered LR, scheme is based on Brun's algorithm for finding integer relations. We analyze its high-level architectural issues, we devise a corresponding low-complexity implementation, and, finally, we develop a suitable VLSI architecture. The resulting circuit provides reference for the true silicon complexity of LR, for broadcast precoding with vector perturbation

We present multiuser space-time receiver algorithms for synchronization, channel estimation, and data detection in the downlink of a universal mobile telecommunications system (UMTS)/time-division duplex (TDD) cellular communication system with multiple receive antennas. These algorithms were designed for use in a network monitoring device that analyzes the interference situation present, thereby allowing the operators to improve their networks. For interference analysis, we decode the broadcast channels (BCHs) of surrounding base stations. To cope with the widely differing power levels of signals received from different base stations, we combine multiuser space-time signal processing techniques with reestimation and successive cancellation schemes. Simulation results demonstrate that our algorithms enable reliable BCH data detection even at low SINR.

This paper considers pulse-shaping multicarrier (MC) systems that transmit over doubly dispersive fading channels. We provide exact and approximate expressions for the intersymbol and intercarrier interference occurring, in such systems. This analysis reveals that the time and frequency concentration of the transmit and receive pulses is of paramount importance for low interference. We prove the (nonobvious) existence of such jointly concentrated pulse pairs by adapting recent mathematical results on Weyl-Heisenberg frames to the MC context. Furthermore, pulse optimization procedures are proposed that aim at low interference and capitalize on the design freedom existing for redundant MC systems. Finally, we present efficient FFT-based modulator and demodulator implementations. Our numerical results demonstrate that for realistic system and channel parameters, optimized pulse-shaping MC systems can outperform conventional cyclic-prefix OFDM systems

We propose an iterative receiver for horizontally encoded MIMO systems like the PARC proposal for MIMO-HSDPA. Our receiver uses a K-best-MAP demodulator to provide the channel decoder with approximate log-likelihood ratios. The complexity of K-best-MAP is reduced by exploiting the CRC present in each encoded layer. We show that K-best-MAP with list update is superior to demodulation using a fixed candidate list. Finally, our numerical results demonstrate significant SNR gains as compared to a receiver using MMSE-based successive interference cancelation.

Time-frequency-autoregressive (TFAR) models allow the parsimonious modeling of underspread nonstationary random processes and are physically meaningful due to their formulation in terms of delays and Doppler frequency shifts. Here, we derive least-squares (LS) and maximum-likelihood (ML) methods for TFAR parameter estimation as well as approximative LS and ML methods specifically suited for the underspread case. We show that the LS, under-spread LS, and underspread ML estimators are equivalent to estimators based on linear time-frequency Yule-Walker (TFYW) equations. The exact ML estimator, on the other hand, requires numerical maximization but yields better estimation accuracy than TFYW techniques. We also discuss the application of block-based TFAR estimation to the spectral analysis of signals with arbitrary length

MIMO-OFDM using bit-interleaved coded modulation (BICM) is an attractive scheme for wireless communications in frequency-selective fading channels. The BICM decoder requires log-likelihood ratios (LLRs) whose exact computation is extremely costly. In this paper, we present a novel method termed soft sphere-projection algorithm (SSPA) that provides approximate LLRs for the case of constant modulus symbol alphabets. The SSPA has very low computational complexity and performs nearly as well as the list sphere decoder. These properties are demonstrated by numerical simulations using synthetic and measured MIMO channels

We present a unified framework for time-varying or time-frequency (TF) spectra of nonstationary random processes in terms of TF operator symbols. We provide axiomatic definitions and TF operator symbol formulations for two broad classes of TF spectra, one of which is new. These classes contain all major existing TF spectra such as the Wigner-Ville, evolutionary, instantaneous power, and physical spectrum. Our subsequent analysis focuses on the practically important case of nonstationary processes with negligible high-lag TF correlations (so-called underspread processes). We demonstrate that for underspread processes all TF spectra yield effectively identical results and satisfy several desirable properties at least approximately. We also show that Gabor frames provide approximate Karhunen-Loeve (KL) functions of underspread processes and TF spectra provide a corresponding approximate KL spectrum. Finally, we formulate simple approximate input-output relations for the TF spectra of underspread processes that are passed through underspread linear time-varying systems. All approximations are substantiated mathematically by upper bounds on the associated approximation errors. Our results establish a TF calculus for the second-order analysis and time-varying filtering of underspread processes that is as simple as the conventional spectral calculus for stationary processes

The time-frequency ARMA (TFARMA) model is introduced as a time-varying ARMA model for nonstationary random processes that is formulated in terms of time shifts and frequency (Doppler) shifts. We present Akaike and minimum description length information criteria for the practically important task of selecting the TFARMA model orders. Because the estimated inverse filter used by the resulting order selection procedures is not guaranteed to be stable, we propose an iterative stabilization algorithm that is based on the concepts of instantaneous roots and root reflection/shrinkage. The performance of the proposed order selection and stabilization techniques is assessed through simulation.

Bit-interleaved coded modulation (BICM) is an attractive transmission scheme for MIMO wireless communications over fast fading channels. BICM receivers employing maximum-likelihood decoding require a soft demodulator (demapper) that calculates log-likelihood ratios (LLRs) for the coded bits. Because in the MIMO case the calculation of LLRs tends to he excessively complex, there is a strong demand for efficient soft demodulation algorithms that calculate approximate LLRs. Here, we develop the novel soft line-search demodulator (SLSD) by extending the recently introduced line-search detector (LSD) such that approximate LLRs are obtained with little extra computations. We show that the SLSD's BER performance Ls close to that of the list extension of the sphere decoding algorithm even though the complexity is significantly smaller.

We propose decision-directed channel predictors for orthogonal frequency-division multiplexing (OFDM) communications over time-varying channels. Channel prediction is capable of yielding up-to-date channel state information even without regular transmission of pilot symbols. It is thus potentially useful for delay-free equalization, antenna combining, space-time decoding, adaptive modulation, adaptive power control, and adaptive transmit antenna diversity. We derive a minimum mean-square error channel predictor and its efficient discrete Fourier transform implementation. Furthermore, we develop adaptive predictors that do not require any statistical prior knowledge and are able to track nonstationary channel and noise statistics. Simulation results involving an OFDM receiver in which channel prediction is used for delay-free equalization demonstrate the excellent performance of the proposed techniques even for fast time-varying channels.

We introduce a multipulse multicarrier (MPMC) transceiver for packet transmissions over time-varying fading channels. The core of this system is an efficient Zak-transform implementation of the MPMC modulator/demodulator that uses optimized transmit/receive pulses. This implementation suggests a simple precoder that allows us to exploit the multipath/Doppler diversity offered by the channel. The transmit symbols are recovered via an MMSE equalizer and decoder. To obtain the required channel state information, we propose efficient LS and MMSE channel estimators that are based on pilot symbols. Numerical simulations verify the diversity gain of our MPMC transceiver as well as its superiority over conventional multicarrier systems for the case of highly dispersive channels.

In bit-interleaved coded modulation (BICM) systems employing maximum-likelihood decoding, a demodulator (demapper) calculates a log-likelihood ratio (LLR) for each coded bit, which is then used as a bit metric for Viterbi decoding. In the MIMO case, the computational complexity of LLR calculation tends to be excessively high, even if the log-sum approximation is used. Thus, there is a strong demand for efficient suboptimum MIMO-BICM demodulation algorithms with near-optimum performance. We propose an efficient MIMO-BICM demodulator that is derived by means of a Gaussian approximation for the post-detection interference. Our derivation results in an MMSE equalizer followed by per-layer LLR calculation (i.e., LLRs are calculated separately for each layer). The novel demodulator can be interpreted as an MMSE analogue of a recently proposed ZF-equalization based demodulator, as well as an extension of ZF-equalization based demodulation to correlated post-detection interference. Because it performs per-layer LLR calculation, it has the same (low) computational complexity as the ZF-equalization based demodulator. Simulation results demonstrate that the performance of our demodulator is close to that of LLR calculation using all layers jointly, and significantly better than that of the ZF-equalization based demodulator.

We present an interference and noise analysis for multipulse multicarrier (MPMC) transmission over time-varying fading channels. Based on this analysis, we propose algorithms and guidelines for system optimization (transmit and receive pulse shapes, time-frequency lattice parameters, and power allocation). Numerical simulations illustrate the optimization gain and the superiority of MPMC systems over traditional (single-pulse) multicarrier systems for highly dispersive channels.

We introduce the time-frequency-moving-average (TFMA) model as a highly parsimonious time-varying MA model formulated in terms of time-frequency (TF) shifts. For estimation of the TFMA model parameters, we develop a computationally efficient nonlinear technique based on a novel complex TF cepstrum, TF cepstral recursions, and an underspread approximation. Simulation results demonstrate significant performance advantages of the proposed TFMA model and parameter estimation technique over an existing method for time-varying MA modeling and estimation.

Assuming PSK modulation, we derive the system capacity of pulse-shaped orthogonal frequency division multiplexing (OFDM) communications over time-frequency selective fading channels in the absence of channel state information at the transmitter and the receiver. We show that capacity tends to zero in the large bandwidth limit and quantify the impact of spread and shape of the scattering function on finite bandwidth capacity

We propose two related iterative algorithms for computing the capacity of discrete memoryless channels. The celebrated Blahut-Arimoto algorithm is a special case of our framework. The formulation of these algorithms is based on the natural gradient and proximal point methods. We also provide interpretations in terms of notions from information geometry. A theoretical convergence analysis and simulation results demonstrate that our new algorithms have the potential to significantly outperform the Blahut-Arimoto algorithm in terms of convergence speed.

We introduce a reduced-detail paradigm for nonstationary statistical signal processing with enhanced performance. Time-frequency localized subspace signal components (called robustons) are used as atomic entities for statistical signal modeling and processing. Robuston signal processing employs special time-varying filters that allow an efficient on-line implementation, and statistical signal descriptors that can be estimated in a stable manner by means of intra-subspace averaging. We develop the principles of robuston signal processing and consider optimal nonstationary signal estimation as a specific application. The performance advantages of the resulting "robuston Wiener filters" are assessed by means of simulations.

We present a novel formulation of nonstationary autoregressive (AR) models in terms of time-frequency (TF) shifts. The parameters of the proposed TFAR model are determined by "TF Yule-Walker equations" that involve the expected ambiguity function and can be solved efficiently due to their block-Toeplitz structure. For moderate model orders, we also propose approximate TF Yule-Walker equations that have Toeplitz/block-Toeplitz structure and thus allow a further reduction of computational complexity. Simulation results demonstrate that the TFAR model is parsimonious and accurate and that the performance of our parameter estimation methods compares favorably with that of Y. Grenier's method (see IEEE Trans. Acoust., Speech, Sig. Processing, vol.31, p.899-911, 1983).

We present two robust detectors for nonstationary random signals that belong to p-point uncertainty classes, one being based on an estimator-correlator approach, the other using the deflection criterion. Apart from stable performance, these robust detectors have the advantage of requiring only reduced prior knowledge. Using local cosine bases, we provide an intuitive and highly efficient time-frequency implementation of these robust detectors along with an extension that permits signal-adaptive operation. Simulation results illustrate the robustness of the proposed detectors.

In wireless OFDM systems, the time-varying channel is often estimated by a Wiener filter-type MMSE estimator based on pilot symbols. Such an estimator, however, requires statistical prior knowledge that is not easily obtained. Here, we propose adaptive Wiener filters for channel estimation that do not require statistical prior knowledge. We also calculate the performance limits of finite-length and infinite-length MMSE estimation. Simulation results demonstrate the good performance of our adaptive estimators.

We present space-time methods for channel estimation in the downlink of a UMTS/TDD system. The channels associated to all base stations near the mobile receiver are estimated by a multiuser, multi-antenna technique. We develop a minimum mean-square error (MMSE) channel estimator that incorporates midamble detections/estimation and least-squares channel estimation as preparatory stages. Combination of this MMSE channel estimator with a successive interference cancellation scheme allows to cope with strong co-channel interference. Simulation results indicate the good performance of our space-time channel estimator for various realistic propagation scenarios.

We present several novel tools for statistical characterization of fading dispersive channels that do not satisfy the usual WSSUS assumption. A local scattering function, describing the time- and frequency-dependent average scatterer power, is introduced. Furthermore, a novel channel correlation function, we introduce the practically important class of doubly underspread channels. Numerical results involving a simulated and a measured channel illustrate the usefulness of our framework.

This paper presents methods for synchronization In the downlink of a UMTS/TDD system. Space-time processing based on multiple receive antennas is used to suppress potentially strong co-channel interference caused by other base stations. We develop a detection-based synchronization procedure exploiting the structure of UMTS/TDD, and we present three alternative detection algorithms. Simulation results using various propagation scenarios indicate the good performance of our synchronization methods in the presence of strong co-channel interference.

We propose an online time-frequency (TF) projection filter with reasonable computational complexity for signals of arbitrary length. The filter uses local projections and TF subspace tracking based on an efficient iterative eigendecomposition. The high TF selectivity of the online TF projection filter is shown to be advantageous for interference excision in spread-spectrum communications.

We propose adaptive channel predictors for orthogonal frequency division multiplexing (OFDM) communications over time-varying channels. Successful application of the normalized least-mean-square (NLMS) and recursive least-squares (RLS) algorithms is demonstrated. We also consider the use of adaptive channel predictors for delay-free equalization, thereby avoiding the need for regular transmission of pilot symbols. Simulation results demonstrate the good performance of the proposed techniques.

This paper considers practically relevant aspects and advantages of pulse-shaping orthogonal/biorthogonal frequency division multiplexing (OFDM/BFDM) systems. We analyze the intersymbol/intercarrier interference (ISI/ICI) in such systems when they operate over time-varying channels. Two methods for an ISI/ICI-minimizing pulse design are proposed, and efficient FFT-based modulator and demodulator implementations are presented. Simulations show that for fast time-varying channels, optimized BFDM systems can outperform conventional OFDM systems with respect to ISI/ICI.

We show that measurements of time-varying mobile radio channels obtained with uncalibrated correlative channel sounders are affected by four different types of systematic errors (commutation, pulse-compression, aliasing, and misinterpretation error). We analyze these errors and provide upper error bounds that are formulated in terms of channel and sounder parameters. Based on these error bounds, we provide guidelines for a judicious choice of important sounder parameters. Computer simulations using a simple two-path channel illustrate our theoretical results. Finally, we show how our results can be used to assess the accuracy of measured channel data.

We propose a signal-adaptive robust time-varying Wiener filter for nonstationary signal estimation/enhancement. This filter uses projections onto local cosine subspaces and a novel "best subspace" algorithm. It allows efficient online operation including stable online estimation of design parameters. A statistical analysis is provided, and a speech enhancement example is considered.

We present two POCS (projections onto convex sets) algorithms for deterministic blind equalization of linear time-varying (LTV) channels. Our approach is based on a multichannel LTI representation of LTV channels. We prove a theorem on unique reconstruction/equalization, formulate a POCS algorithm for the resolution of a matrix ambiguity, and show how to cope with unequal subchannel lengths. We also present an alternative POCS algorithm for equalization that avoids a singular value decomposition. Both algorithms are guaranteed to converge to the desired solution.

We propose a novel receiver for coded orthogonal/biorthogonal frequency division multiplexing (OFDM/BFDM) communications over time-varying mobile radio channels. The receiver uses decision-directed predictive equalization and thus does not require regular transmission of pilot symbols. An optimum channel predictor and its efficient implementation are discussed, and simulation results are presented.

We introduce minimax robust time-varying Wiener filters and show a result that facilitates their calculation. Reformulation in the time-frequency domain yields simple closed-form expressions of minimax robust time-frequency Wiener filters based on three different uncertainty models. For one of these filters, an efficient implementation using the multi-window Gabor transform is proposed.

We extend the approximate transfer function calculus of "underspread" linear time-varying (LTV) systems introduced by W. Kozek (1992). Our extension is based on a new, generalized definition of underspread LTV systems that does not assume finite support of the systems' spreading function. We establish explicit bounds on various error quantities associated with the transfer function approximation. Our results yield a simple and convenient transfer function calculus for a significantly wider and practically more relevant class of LTV systems than that previously considered.