Train localization during Global Navigation Satellite Systems (GNSS) outages presents challenges for ensuring failsafe and accurate positioning in railway networks. This paper proposes a minimalist approach exploiting track geometry and Inertial Measurement Unit (IMU) sensor data. By integrating a discrete track map as a Look-Up Table (LUT) into a Particle Filter (PF) based solution, accurate train positioning is achieved with only an IMU sensor and track map data. The approach is tested on an open railway positioning data set, showing that accurate positioning (absolute errors below 10 m) can be maintained during GNSS outages up to 30 s in the given data. We simulate outages on different track segments and show that accurate positioning is reached during track curves and curvy railway lines. The approach can be used as a redundant complement to established positioning solutions to increase the position estimate’s reliability and robustness.

In this paper, we investigate signal detection for HF skywave massive multiple-input multiple-output (MIMO) communications with orthogonal frequency division multiplexing (OFDM) modulation. We first introduce beam based channel models (BBCM) in the space domain at each subcarrier and in the space-frequency domain for all subcarriers. Based on the BBCM in the space domain, we propose a beam structured detector (BSD) for each subcarrier. Specifically, we prove that the space domain detector design can be transformed into that of a beam domain detector without sacrificing optimality, and the asymptotically optimal space domain detector is beam structured with a low-dimensional beam domain detector, thus significantly reducing the design and implementation complexities. Furthermore, we extend the BSD to the space-frequency domain based on the BBCM jointly for all subcarriers. The design of space-frequency domain detector is also converted to that of a low-dimensional beam domain detector, which enables a very efficient design and implementation of BSD. Simulation results demonstrate the low complexity and satisfactory performance of the proposed detectors.

In this paper, we investigate high frequency (HF) skywave massive multiple-input multiple-output (MIMO) communications with orthogonal frequency division multiplexing (OFDM) modulation. Based on the triple-beam (TB) based channel model and the channel sparsity in the TB domain, we propose a beam structured channel estimation (BSCE) approach. Specifically, we show that the space-frequency-time (SFT) domain estimator design for each TB domain channel element can be transformed into that of a low-dimensional TB domain estimator and the resulting SFT domain estimator is beam structured. We also present a method to select the TBs used for BSCE. Then we generalize the proposed BSCE by introducing window functions and a turbo principle to achieve a superior trade-off between complexity and performance. Furthermore, we present a low-complexity design and implementation of BSCE by exploiting the characteristics of the TB matrix. Simulation results validate the proposed theory and methods.

In this paper, we investigate signal detection for HF skywave massive multiple-input multiple-output (MIMO) communications with orthogonal frequency division multiplexing (OFDM) modulation. We first introduce beam based channel model (BBCM) in the space domain and reveal the sparsity of the channel in the space-beam domain. Based on the BBCM in the space domain, we propose a beam structured detector (BSD) for each subcarrier. Specifically, we prove that the space domain detector design can be transformed to that of a beam domain detector without sacrificing optimality, and the asymptotically optimal space domain detector is beam structured with a low-dimensional beam domain detector, thus significantly reducing the design and implementation complexities. Furthermore, we provide a beam selection criterion to choose the beams that are used for the BSD. Simulation results demonstrate the low complexity and satisfactory performance of the proposed detector.

The development of future railway systems is contingent on the evolution of wireless communications technologies and their ability to serve more sophisticated use cases. Recent proposals to extend the 3rd Generation Partnership Project (3GPP) 4G or 5G standard for use in next-generation railway wireless communications presents a problem in that they are still based on Orthogonal Frequency Division Multiplexing (OFDM), which is vulnerable to Doppler-related effects when traveling at high speed. Orthogonal Time Frequency Space (OTFS) is a promising new modulation technique that can handle commu-nication even in very high vehicle speed cases. In this paper, we investigate the performance of OTFS in terms of achievable rate under different High Speed Rail (HSR) environments, while taking into account the impact of practical but non-biorthogonal pulse shapes. Simulation results show that OTFS provides consistently high achievable rates regardless of the environment, and that the rates are relatively insensitive to the speed of travel.

Determination of train positions within a railway network must be fail-safe and of high accuracy. In train-bourne positioning, exploitation of geometrical map features is an important factor and uncertainties in the map information may affect the position estimate. In this paper, we present a method to estimate the position of a train in the track net and to identify the correct path behind a turnout, using absolute position estimates and geometrical map information of various accuracies. We evaluate the impact of uncertainties in the map representation on the correct identification of a path behind a turnout. We derive a formulation of a probabilistic track map and include the map information into a constrained multi-hypothesis Kalman filter. We show in numerical simulations on a crossover and a turnout that modelling existing map uncertainties significantly improves the track discrimination.

Although signal distortion-based peak-to-average power ratio (PAPR) reduction is a feasible candidate for orthogonal frequency division multiplexing (OFDM) to meet standard/regulatory requirements, the error vector magnitude (EVM) stemming from the PAPR reduction has a deleterious impact on the performance of high data-rate achieving multiple-input multiple-output (MIMO) systems. Moreover, these systems must constrain the adjacent channel leakage ratio (ACLR) to comply with regulatory requirements. Several recent works have investigated the mitigation of the EVM seen at the receivers by capitalizing on the excess spatial dimensions inherent in the large-scale MIMO that assume the availability of perfect channel state information (CSI) with spatially uncorrelated wireless channels. Unfortunately, practical systems operate with erroneous CSI and spatially correlated channels. Additionally, most standards support user-specific/CSI-aware beamformed and cell-specific/non-CSI-aware broadcasting channels. Hence, we formulate a robust EVM mitigation problem under channel uncertainty with nonconvex PAPR and ACLR constraints catering to beamforming/broadcasting. To solve this formidable problem, we develop an efficient scheme using our recently proposed three-operator alternating direction method of multipliers (TOP-ADMM) algorithm and benchmark it against two three-operator algorithms previously presented for machine learning purposes. Numerical results show the efficacy of the proposed algorithm under imperfect CSI and spatially correlated channels.

The weighted minimum mean square error (WMMSE) algorithm was proposed to provide a locally optimum solution to the otherwise NP-hard weighted sum rate maximization beamforming problem, but it can still be prohibitively complex for real-time implementation. With the success of deep unfolding in trading off complexity and performance, we propose to apply deep unfolding to the WMMSE algorithm. With respect to traditional end-to-end learning, deep unfolding incorporates expert knowledge, with the benefits of immediate and well-grounded architecture selection, fewer trainable parameters, and better explainability. However, the classical formulation of the WMMSE algorithm given by Shi et al. is not amenable for deep unfolding due to matrix inversions, eigendecompositions, and bisection searches. Therefore, we present an alternative formulation that circumvents these operations. By means of simulations, we show that the deep unfolded WMMSE algorithm performs on par with the original WMMSE algorithm, at a lower computational load.

Spectral precoding is a promising technique to suppress out-of-band emissions and comply with leakage constraints over adjacent frequency channels and with mask requirements on the unwanted emissions. However, spectral precoding may distort the original data vector, which is formally expressed as the error vector magnitude (EVM) between the precoded and original data vectors. Notably, EVM has a deleterious impact on the performance of multiple-input multiple-output orthogonal frequency division multiplexing-based systems. In this paper we propose a novel spectral precoding approach which constrains the EVM while complying with the mask requirements. We first formulate and solve the EVM-unconstrained mask-compliant spectral precoding problem, which serves as a springboard to the design of two EVM-constrained spectral precoding schemes. The first scheme takes into account a wideband EVM-constraint which limits the average in-band distortion. The second scheme takes into account frequency-selective EVM-constraints, and consequently, limits the signal distortion at the subcarrier level. Numerical examples illustrate that both proposed schemes outperform previously developed schemes in terms of important performance indicators such as block error rate and system-wide throughput while complying with spectral mask and EVM constraints.

Although spectral precoding is a propitious technique to suppress out-of-band emissions, it has a detrimental impact on the system-wide throughput performance, notably, in high data-rate multiple-input multiple-output (MIMO) systems with orthogonal frequency division multiplexing (OFDM), because of (spatially-coloured) transmit error vector magnitude (TxEVM) emanating from spectral precoding. The first contribution of this paper is to propose two mask-compliant spectral precoding schemes, which mitigate the resulting TxEVM seen at the receiver by capitalizing on the immanent degrees-of-freedom in (massive) MIMO systems and consequently improve the system-wide throughput. Our second contribution is an introduction to a new and simple three-operator consensus alternating direction method of multipliers (ADMM) algorithm, referred to as TOP-ADMM, which decomposes a large-scale problem into easy-to-solve subproblems. We employ the proposed TOP-ADMM-based algorithm to solve the spectral precoding problems, which offer computational efficiency. Our third contribution presents substantial numerical results by using an NR release 15 compliant simulator. In case of perfect channel knowledge at the transmitter, the proposed methods render similar block error rate and throughput performance as without spectral precoding yet meeting out-of-band emission (OOBE) requirements at the transmitter. Further, no loss on the OOBE performance with a graceful degradation on the throughput is observed under channel uncertainty.

In this research paper, fusion in the air (FIA) and fusion at the receiver (FAR) - two different approaches of multi-hypotheses distributed detection for wireless sensor networks with decision fusion center (DFC) - are investigated. The DFC is equipped with multiple antennas, whereas each of the sensors has a single antenna. The performance of these schemes is evaluated in two different scenarios; with identical sensors and non-identical sensors, in terms of their detection capabilities. For a global event, identical sensors observe an equal number of hypotheses, whereas the number of hypotheses detected by the non-identical sensors can be different. When all the sensors in the network are identical, the FIA based technique has a higher detection probability in transmit power constrained situations. However, the FAR scheme performs better when the transmit power budget is higher. Additionally, in the network with non-identical wireless sensors, the FAR based technique is unable to exploit the benefits from the local decisions of the low capability sensors. Therefore the FAR scheme has a lower detection probability than the FIA based approach.

This article investigates the wide-band channel characteristics at 24 GHz ISM band in a mobile radio environment. The mobility in the test environment is achieved by attaching the transmit antenna to a KUKA robot's arm. The radio measurements were carried out inside the robotics lab at the University of Gävle, Sweden. The radio channel measurements were carried out at various situations, e.g., line of sight (LOS), non-line of sight (NLOS), regular lab environment, reflective environment, and different velocities of the robot's arm. The influence of these situations on the power delay profile, Doppler spectral density, root mean square (RMS) delay spread, RMS Doppler spread, coherence bandwidth and coherence time, has been studied.

In this paper, we present a modulation design based on Spatial Modulation for the uplink in IoT applications. The proposed modulation design uses a Tabu search based deterministic heuristic to adapt the modulation link based on channel information fed back by the receiver. Our approach allows adaptivity to rate and energy constraints. We numerically validate the proposed method on a scenario with full channel state information available at the transceiver, showing clear performance gains compared to simpler heuristics and channel independent codebook designs.

In the context of wireless communications, we propose a deep learning approach to learn the mapping from the instantaneous state of a frequency selective fading channel to the corresponding frame error probability (FEP) for an arbitrary set of transmission parameters. We propose an abstract model of a bit interleaved coded modulation (BICM) orthogonal frequency division multiplexing (OFDM) link chain and show that the maximum likelihood (ML) estimator of the model parameters estimates the true FEP distribution. Further, we exploit deep neural networks as a general purpose tool to implement our model and propose a training scheme for which, even while training with the binary frame error events (i.e., ACKs / NACKs), the network outputs converge to the FEP conditioned on the input channel state. We provide simulation results that demonstrate gains in the FEP prediction accuracy with our approach as compared to the traditional effective exponential SIR metric (EESM) approach for a range of channel code rates, and show that these gains can be exploited to increase the link throughput.

Multiple-input multiple-output (MIMO) millimeter-wave (mm-wave) systems are vulnerable to hardware impairments due to operating at high frequencies and employing a large number of radio-frequency hardware components. In particular, nonlinear power amplifiers (PAs) employed at the transmitter distort the signal when operated close to saturation due to energy efficiency considerations. In this paper, we study the performance of an MIMO mm-wave hybrid beamforming scheme in the presence of nonlinear PAs. First, we develop a statistical model for the transmitted signal in such systems and show that the spatial direction of the inband distortion is shaped by the beamforming filter. This suggests that even in the large antenna regime, where narrow beams can be steered toward the receiver, the impact of nonlinear PAs should not be ignored. Then, by employing a realistic power consumption model for the PAs, we investigate the tradeoff between spectral and energy efficiency in such systems. Our results show that increasing the transmit power level when the number of transmit antennas grows large can be counter-effective in terms of energy efficiency. Furthermore, using numerical simulation, we show that when the transmit power is large, analog beamforming leads to higher spectral and energy efficiency compared to digital and hybrid beamforming schemes.

Cognitive radio (CR) systems need to detect the presence of a primary user (PU) signal by continuously sensing the spectrum area of interest. Radiowave propagation effects like fading and shadowing often complicate sensing of spectrum holes because the PU signal can be weak in a particular area. Cooperative spectrum sensing is seen as a prospective solution to enhance the detection of PU signals. In this paper we study distributed spectrum sensing, based on the largest eigenvalue of adaptively estimated correlation matrices (CMs) of received signals. The PU signal is assumed to be temporally correlated. In this paper an Combine and Adapt (CTA) least mean square (LMS) diffusion based mean vector estimation scheme is proposed. No fusion center (FC) for estimation or detection is used. We analyse the resulting detection performance and verify the theoretical findings through simulations.

In this paper we have proposed clock error mitigation from the measurements in the scheduled based self localization system. We propose measurement model with clock errors while following a scheduled transmission among anchor nodes. Further, RLS algorithm is proposed to estimate clock error and to calibrate measurements of self localizing node against relative clock errors of anchor nodes. A full-scale experimental validation is provided based on commercial off-the-shelf UWB radios under IEEE-standardized protocols.

Although the benefits of precoding and combining of data streams are widely recognized, the potential of precoding the pilot signals at the user equipment (UE) side and combining them at the base station (BS) side has not received adequate attention. This paper considers a multiuser multiple input multiple output (MU-MIMO) cellular system in which the BS acquires channel state information (CSI) by means of uplink pilot signals and proposes pilot precoding and combining to improve the CSI quality. We first evaluate the channel estimation performance of a baseline scenario in which CSI is acquired with no pilot precoding. Next, we characterize the channel estimation error when the pilot signals are precoded by spatial filters that asymptotically maximize the channel estimation quality. Finally, we study the case when, in addition to pilot precoding at the UE side, the BS utilizes the second order statistics of the channels to further improve the channel estimation performance. The analytical and numerical results show that, specially in scenarios with large number of antennas at the BS and UEs, pilot precoding and combining has a great potential to improve the channel estimation quality in MU-MIMO systems.

MIMO systems in the lower part of the millimetre-wave (mmWave) spectrum band (i.e., below 28 GHz) do not exhibit enough directivity and selectively, as compared to their counterparts in higher bands of the spectrum (i.e., above 60 GHz), and thus still suffer from the detrimental effect of interference, on the system sum rate. As such systems exhibit large numbers of antennas and short coherence times for the channel, traditional methods of distributed coordination are ill-suited, and the resulting communication overhead would offset the gains of coordination. In this paper, we propose algorithms for tackling the sum-rate maximization problem that are designed to address the above-mentioned limitations. We derive a lower bound on the sum rate, a so-called difference of log and trace (DLT) bound, shed light on its tightness, and highlight its decoupled nature at both the transmitters and receivers. Moreover, we derive the solution to each of the subproblems that we dub non-homogeneous waterfilling (a variation on the MIMO waterfilling solution), and underline an inherent desirable feature: its ability to turn-OFF streams exhibiting low SINR, and contribute to greatly speeding up the convergence of the proposed algorithm. We then show the convergence of the resulting algorithm, max-DLT, to a stationary point of the DLT bound. Finally, we rely on extensive simulations of various network configurations, to establish the fast-converging nature of our proposed schemes, and thus their suitability for addressing the short coherence interval, as well as the increased system dimensions, arising when managing interference in lower bands of the mmWave spectrum. Moreover, our results suggest that interference management still brings about significant performance gains, especially in dense deployments.

Although the benefits of precoding and combining data signals are widely recognized, the potential of these techniques for pilot transmission is not fully understood. This is particularly relevant for multiuser multiple-input multiple-output (MU-MIMO) cellular systems using millimeter-wave (mmWave) communications, where multiple antennas have to be used both at the transmitter and the receiver to overcome the severe path loss. In this paper, we characterize the gains of pilot precoding and combining in terms of channel estimation quality and achievable data rate. Specifically, we consider three uplink pilot transmission scenarios in an mmWave MU-MIMO cellular system: 1) non-precoded and uncombined; 2) precoded but uncombined; and 3) precoded and combined. We show that a simple precoder that utilizes only the second-order statistics of the channel reduces the variance of the channel estimation error by a factor that is proportional to the number of user equipment (UE) antennas. We also show that using a linear combiner design based on the second-order statistics of the channel significantly reduces multiuser interference and provides the possibility of reusing some pilots. Specifically, in the large antenna regime, pilot precoding and combining help to accommodate a large number of UEs in one cell, significantly improve channel estimation quality, boost the signal-to-noise ratio of the UEs located close to the cell edges, alleviate pilot contamination, and address the imbalanced coverage of pilot and data signals.

Coordinated precoding based on interference alignment is a promising technique for improving the throughputs in future wireless multicell networks. In small networks, all base stations can typically jointly coordinate their precoding. In large networks, however, base station clustering is necessary due to the otherwise overwhelmingly high channel state information (CSI) acquisition overhead. In this work, we provide a branch and bound algorithm for finding the globally optimal base station clustering. The algorithm is mainly intended for benchmarking existing suboptimal clustering schemes. We propose a general model for the user throughputs, which only depends on the long-term CSI statistics. The model assumes intracluster interference alignment and is able to account for the CSI acquisition overhead. By enumerating a search tree using a best-first search and pruning sub-trees in which the optimal solution provably cannot be, the proposed method converges to the optimal solution. The pruning is done using specifically derived bounds, which exploit some assumed structure in the throughput model. It is empirically shown that the proposed method has an average complexity that is orders of magnitude lower than that of exhaustive search.

In this paper, we study virtual full-duplex (FD) buffer-aided relaying to recover the loss of multiplexing gain caused by half-duplex (HD) relaying in a multiple relay network, where each relay is equipped with a buffer and multiple antennas, through joint opportunistic relay selection (RS) and beamforming (BF) design. The main idea behind virtual FD buffer-aided relaying is that the source and one of the relays simultaneously transmit their own information to another relay and the destination, respectively. In such networks, interrelay interference (IRI) is a crucial problem, which has to be resolved like self-interference in the FD relaying. In contrast to previous work that neglected IRI, we propose joint RS and BF schemes taking IRI into consideration by using multiple antennas at the relays. To maximize average end-to-end rate, we propose a weighted sum-rate maximization strategy assuming that adaptive rate transmission is employed in both the source to relay and relay to destination links. Then, we propose several BF schemes cancelling or suppressing IRI in order to maximize the weighted sum-rate. Numerical results show that our proposed optimal, zero-forcing, and minimum mean square error BF-based RS schemes asymptotically approach the ideal FD relaying upper bound when increasing the number of antennas and/or the number of relays.

We consider the uplink of a cellular massive multiple-input multiple-output network. Acquiring channel state information at the base stations (BSs) requires uplink pilot signaling. Since the number of orthogonal pilot sequences is limited by the channel coherence, pilot reuse across cells is necessary to achieve high spectral efficiency. However, finding efficient pilot reuse patterns is non-trivial, especially in practical asymmetric BS deployments. We approach this problem using the coalitional game theory. Each BS has a few unique pilots and can form coalitions with other BSs to gain access to more pilots. The BSs in a coalition, thus, benefit from serving more users in their cells at the expense of higher pilot contamination and interference. Given that a cell's average spectral efficiency depends on the overall pilot reuse pattern, the suitable coalitional game model is in the partition form. We develop a low-complexity distributed coalition formation based on individual stability. By incorporating a BS intercommunication budget constraint, we are able to control the overhead in message exchange between the BSs and ensure the algorithm's convergence to a solution of the game called individually stable coalition structure. Simulation results reveal fast algorithmic convergence and substantial performance gains over the baseline schemes with no pilot reuse, full pilot reuse, or random pilot reuse pattern.

In this work, we study the design of a precoder on the user downlink of a multibeam satellite channel. The variations in channel due to phase noise introduced by on-board oscillators and the long round trip delay result in outdated channel information at the transmitter. The phase uncertainty is modelled and a robust design framework is formulated based on availability and power constraints. The optimization problem is cast into the convex paradigm after approximations and the benefits of the resulting precoder are highlighted.

We investigate energy-efficient communications for time-division multiple access (TDMA) multiple-input multiple-output (MIMO) cognitive radio (CR) networks operating in underlay mode. In particular, we consider the joint optimization over both the time resource and the transmit precoding matrices to minimize the overall energy consumption of a single cell secondary network with multiple secondary users (SUs), while ensuring their quality of service (QoS). The corresponding mathematical formulations turn out to be non-convex, and thus of high complexity to solve in general. We give a comprehensive treatment of this problem, considering both the cases of perfect channel state information (CSI) and statistical CSI of the channels from the SUs to the primary receiver. We tackle the non-convexity by applying a proper optimization decomposition that allows the overall problem to be efficiently solved. In particular, we show that when the SUs only have statistical CSI, the optimal solution can be found in polynomial time. Moreover, if we consider additional integer constraints on the time variable which is usually a requirement in practical wireless system, the overall problem becomes a mixed-integer non-convex optimization which is more complicated. By exploring the special structure of this particular problem, we show that the optimal integer time solution can be obtained in polynomial time with a simple greedy algorithm. When the SUs have perfect CSI, the decomposition based algorithm is guaranteed to find the optimal solution when the secondary system is under-utilized. Simulation results show that the energy-optimal transmission scheme adapts to the traffic load of the secondary system to create a win-win situation where the SUs are able to decrease the energy consumption and the PUs experience less interference from the secondary system. The effect is particularly pronounced when the secondary system is under-utilized.

We consider optimized design of training sequences, given knowledge of the channel and noise statistics. Recently, pilot designs considering the end performance of the channel estimate, have been proposed, both optimizing the average performance and the performance at a certain outage level. Unfortunately, these problems, as well as previously proposed designs optimizing the channel estimation MSE, are non-convex for arbitrary channel and noise correlations so additional assumptions have been introduced in the literature to be able to find tractable solutions. Here, we show that arbitrarily correlated scenarios can easily be handled by resorting to alternating optimization, for all the previously mentioned problem formulations. Furthermore, we numerically compare the average and outage performance of the proposed algorithms, to alternative solutions adopted from the literature.

Physical transceivers exhibit distortions from hardware impairments, of which traces remain even after compensation and calibration. Multicell MIMO coordinated beamforming methods that ignore these residual impairments may suffer from severely degraded performance. In this work, we consider a general model for the aggregate effect of the residual hardware impairments, and propose an iterative algorithm for finding locally optimal points to a weighted sum rate optimization problem. The importance of accounting for the residual hardware impairments is verified by numerical simulation, and a substantial gain over traditional time-division multiple access with impairments-aware resource allocation is observed.

In this paper, we propose a robust transmit beampattern design for multiple-input multiple-output (MIMO) radar systems. The objective considered here is minimization of the beampattern sidelobes, subject to constraints on the transmit power where the waveform co-variance matrix is the optimization variable. Motivated by the fact that the steering vectors are subject to uncertainties in practice, we propose a worst-case robust beampattern design where the uncertainties are parameterized by a deterministic set. We show that the resulting non-convex maximin problem can be translated into a convex problem. We numerically illustrate that the steering vector uncertainty yields a severe degradation in the array performance, i.e., the transmit beampattern. Also, we show that the proposed robust design improves the transmit beampattern by reducing the worst case sidelobe peak levels.

Recent studies have shown that, while the available licensed radio spectrum becomes more occupied, the assigned spectrum is significantly underutilized. To alleviate the situation, cognitive radio (CR) technology has been proposed to provide an opportunistic access to the licensed spectrum areas. CR systems are able to serve the secondary users for detecting and utilizing so called spectrum holes by sensing and adapting to the environment without causing harmful effects or interference to the licensed primary users (PU). CR systems need to detect the presence of a primary user by continuously sensing the spectrum area of interest. Radiowave propagation effects like fading and shadowing often complicate sensing of spectrum holes because the PU signal can be weak in a particular area. Cooperative spectrum sensing is seen as a prospective solution to enhance the detection of PU signals. This paper studies distributed spectrum sensing in a cognitive radio context. We investigate a distributed energy detection scheme without using any fusion center. Due to reduced communication such a topology is more energy efficient. The PU signal is assumed to be in slow fading. A recursive distributed power estimation and detection scheme is proposed. The theoretical findings are verified through simulations.

In this work, we study the so-called leakage minimization problem, within the context of interference alignment (IA). For that purpose, we propose a novel approach based on controlled perturbations of the leakage function, and show how the latter can be used as a mechanism to control the algorithm's convergence (and thus tradeoff convergence speed for reliability). Although the proposed scheme falls under the broad category of stochastic optimization, we show through simulations that it has a quasi-deterministic convergence that we exploit to improve on the worst case performance of its predecessor, resulting in significantly better sum-rate capacity and average cost function value.

In this paper, the problem of robust training sequence design for multiple-input single-output (MISO) channel estimation is investigated. The mean-squared error (MSE) of the channel estimates is considered as a performance criterion to design an optimized training sequence which is a function of channel covariance matrix. In practice, the channel covariance matrix is not perfectly known at the transmitter side. Our goal is to take such imperfection into account and propose a robust design following the worst-case philosophy which results in finding the optimal training sequences for the least favorable channel covariance matrix within a deterministic uncertainty set. In this work, we address the formulated minimax design problem under different assumptions of the uncertainty set, and we show that for a unitarily-invariant uncertainty set, the optimally robust training sequence shares its eigenvectors with the channel covariance matrix. Furthermore, we give analytical closed-form solutions for robust training sequences if the spectral norm or nuclear norm are considered as constraints to bound the existing uncertainty.

In this paper, we study virtual full-duplex (FD) buffer-aided relaying to recover the multiplexing loss of half-duplex (HD) relaying in a network with multiple buffer-aided relays, each of which has multiple antennas, through opportunistic relay selection and beamforming. The main idea of virtual FD buffer-aided relaying is that a source and a relay simultaneously transmit their own information to another relay and a destination, respectively. In this network, inter-relay interference (IRI) is a crucial problem which has to be resolved like self-interference in the FD relaying. In contrast to previous work that neglected the IRI, we propose two buffer-aided relay selection and beam-forming schemes taking the IRI into consideration. Numerical results show that our proposed relay selection scheme with zero-forcing beamforming (ZFB)-based IRI cancellation approaches the average end-to-end capacity of IRI-free upper bound as the numbers of relays and antennas increase.

This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as “massive MIMO”. Unlike previous works on this topic, which mainly considered the impact of inter-cell disturbance due to pilot reuse (so-called pilot contamination), we are concerned with the computational complexity. The conventional minimum mean square error (MMSE) and minimum variance unbiased (MVU) channel estimators rely on inverting covariance matrices, which has cubic complexity in the multiplication of number of antennas at each side. Since this is extremely expensive when there are hundreds of antennas, we propose to approximate the inversion by an L-order matrix polynomial. A set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced. The coefficients of the polynomials are optimized to yield small mean square error (MSE). We show numerically that near-optimal performance is achieved with low polynomial orders. In practice, the order L can be selected to balance between complexity and MSE. Interestingly, pilot contamination is beneficial to the PEACH estimators in the sense that smaller L can be used to achieve near-optimal MSEs.

For array processing, we consider the problem of estimating signals of interest, and their directions of arrival (DOA), in unknown colored noise fields. We develop an estimator that efficiently utilizes a set of noise-only samples and, further, can incorporate prior knowledge of the DOAs with varying degrees of certainty. The estimator is compared with state of the art estimators that utilize noise-only samples, and the Cramér-Rao bound, exhibiting improved performance for smaller sample sets and in poor signal conditions.

We study low-signalling overhead scheduling for downlink coordinated multi-point (CoMP) transmission with multi-antenna base stations (BSs) and single-antenna users. By exploiting the asymmetric channel feature, i.e., the path-loss differences towards different BSs, we derive a metric to judge orthogonality among users only using their average channel gains, based on which we propose a semi-orthogonal scheduler that can be applied in a two-stage transmission strategy. Simulation results demonstrate that the proposed scheduler performs close to the semi-orthogonal scheduler with full channel information, especially when each BS is with more antennas and the cell-edge region is large. Compared with other overhead reduction strategies, the proposed scheduler requires much less training overhead to achieve the same cell-average data rate.

We consider precoder design for maximizing the weighted sum rate (WSR) of successive zero-forcing dirty paper coding (SZF-DPC). For this problem, the existing precoder designs often assume a sum power constraint (SPC) and rely on the singular value decomposition (SVD). The SVD-based designs are known to be optimal but require high complexity. We first propose a low-complexity optimal precoder design for SZF-DPC under SPC, using the QR decomposition. Then, we propose an efficient numerical algorithm to find the optimal precoders subject to per-antenna power constraints (PAPCs). To this end, the precoder design for PAPCs is formulated as an optimization problem with a rank constraint on the covariance matrices. A well-known approach to solve this problem is to relax the rank constraints and solve the relaxed problem. Interestingly, for SZF-DPC, we are able to prove that the rank relaxation is tight. Consequently, the optimal precoder design for PAPCs is computed by solving the relaxed problem, for which we propose a customized interior-point method that exhibits a superlinear convergence rate. Two suboptimal precoder designs are also presented and compared to the optimal ones. We also show that the proposed numerical method is applicable for finding the optimal precoders for block diagonalization scheme.

We consider the beamformer design for multiple-input multiple-output (MISO) broadcast channels (MISO BCs) using zero-forcing dirty paper coding (ZF-DPC). Assuming a sum power constraint (SPC), most previously proposed beamformer designs are based on the QR decomposition (QRD), which is a natural choice to satisfy the ZF constraints. However, the optimality of the QRD-based design for ZF-DPC has remained unknown. In this paper, first, we analytically establish that the QRD-based design is indeed optimal for any performance measure under a SPC. Then, we propose an optimal beamformer design method for ZF-DPC with per-antenna power constraints (PAPCs), using a convex optimization framework. The beamformer design is first formulated as a rank-1-constrained optimization problem. Exploiting the special structure of the ZF-DPC scheme, we prove that the rank constraint can be relaxed and still provide the same solution. In addition, we propose a fast converging algorithm to the beamformer design problem, under the duality framework between the BCs and multiple access channels (MACs). More specifically, we show that a BC with ZF-DPC has the dual MAC with ZF-based successive interference cancellation (ZF-SIC). In this way, the beamformer design for ZF-DPC is transformed into a power allocation problem for ZF-SIC, which can be solved more efficiently.

Physical wireless transceivers suffer from a variety of impairments that distort the transmitted and received signals. Their degrading impact is particularly evident in modern systems with multiuser transmission, high transmit power, and low-cost devices, but their existence is routinely ignored in the optimization literature for multicell transmission. This paper provides a detailed analysis of coordinated beamforming in the multicell downlink. We solve two optimization problems under a transceiver impairment model and derive the structure of the optimal solutions. We show numerically that these solutions greatly reduce the impact of impairments, compared with beamforming developed for ideal transceivers. Although the so-called multiplexing gain is zero under transceiver impairments, we show that the gain of multiplexing can be large at practical SNRs.

We consider a worst-case robust precoding design for multi-input multi-output (MIMO) communication systems with imperfect channel state information at the transmitter (CSIT). Instead of a particular choice, we consider a general imperfect CSIT model that only assumes the channel errors to be within a convex set, which includes most common imperfect CSIT models as special cases. The robust precoding design is formulated as a maximin problem, aiming at maximizing the worst-case received signal-to-noise ratio or minimizing the worst-case error probability. It is shown that the robust precoder can be easily obtained by solving a convex problem. We further provide an equivalent but more practical form of the convex problem that can be efficiently handled with common optimization methods and software packages.

We consider the beamformer design for zero-forcing dirty paper coding (ZF-DPC), a suboptimal transmission technique for MISO broadcast channels (MISO BCs). Beamformers for ZF-DPC are designed to maximize a performance measure, subject to some power constraints and zero-interference constraints. For the sum rate maximization problem under a total power constraint, the existing beamformer designs in the literature are based on the QR decomposition (QRD), which is used to satisfy the ZF constraints. However, the optimality of the QRD-based design is still unknown. First, we prove that the QRD-based design is indeed optimal for ZF-DPC for any performance measure under a sum power constraint. For the per-antenna power constraints, the QRD-based designs become suboptimal, and we propose an optimal design, using a convex optimization framework. Low-complexity suboptimal designs are also presented.

This paper considers the precoder designs for successive zero-forcing dirty paper coding (SZF-DPC), a suboptimal transmission technique for MIMO broadcast channels (MIMO BCs). Existing precoder designs for SZF-DPC often consider a sum power constraint. In this paper, we address the precoder design for SZF-DPC with per-antenna power constraints (PAPCs), which has not been well studied. First, we formulate the precoder design as a rank-constrained optimization problem, which is generally difficult to handle. To solve this problem, we follow a relaxation approach, and prove that the optimal solution of the relaxed problem is also optimal for the original problem. Considering the relaxed problem, we propose a numerically efficient algorithm to find the optimal solution, which exhibits a fast convergence rate. Suboptimal precoder designs, with lower computational complexity, are also presented, and compared with the optimal ones in terms of achievable sum rate and computational complexity.

Successive zero-forcing dirty paper coding (SZF-DPC) is a simplified alternative to DPC for MIMO broadcast channels (MIMO BCs). In the SZF-DPC scheme, the noncausally-known interference is canceled by DPC, while the residual interference is suppressed by the ZF technique. Due to the ZF constraints, the precoders are constrained to lie in the null space of a matrix. For the sum rate maximization problem under a sum power constraint, the existing precoder designs naturally rely on the singular value decomposition (SVD). The SVD-based design is optimal but needs high computational complexity. Herein, we propose two low-complexity optimal precoder designs for SZF-DPC, all based on the QR decomposition (QRD), which requires lower complexity than SVD. The first design method is an iterative algorithm to find an orthonormal basis of the null space of a matrix that has a recursive structure. The second proposed method, which will be shown to require the lowest complexity, results from applying a single QRD to the matrix comprising all users' channel matrices. We analytically and numerically show that the two proposed precoder designs are optimal.

In this paper, we introduce a general convex framework for robust beamforming, which is valid for both deterministic and stochastic uncertainty models, and provides robustness against errors both in the channel and in the interference co-variance matrix estimations. Furthermore, we extend our design to a multiple-state interference model and show the performance gains obtained by exploiting the interference structure.

This paper addresses coordinated downlink beamforming optimization in multicell time division duplex (TDD) systems where a small number of parameters are exchanged between cells but with no data sharing. With the goal to reach the point on the Pareto boundary with max-min rate fairness, we first develop a two-step centralized optimization algorithm to design the joint beamforming vectors. This algorithm can achieve a further sum-rate improvement over the max-min optimal performance, and is shown to guarantee max-min Pareto optimality for scenarios with two base stations (BSs) each serving a single user. To realize a distributed solution with limited intercell communication, we then propose an iterative algorithm by exploiting an approximate uplink-downlink duality, in which only a small number of positive scalars are shared between cells in each iteration. Simulation results show that the proposed distributed solution achieves a fairness rate performance close to the centralized algorithm while it has a better sum-rate performance, and demonstrates a better tradeoff between sum-rate and fairness than the Nash Bargaining solution especially at high signal-to-noise ratio.

Spectrum sharing between two independent, co-existing transmit-receive pairs (TRPs) is formulated as a non-cooperative game with the TRPs as players, their individual link rates as payoffs and power allocation over the utilized spectral bands as the strategy. A Nash Equilibrium (NE) corresponds to the outcome of such a game and TRPs iteratively use the water-filling algorithm according to an agreed order for achieving the NE. Dynamics of this distributed algorithm is studied to determine the conditions for convergence and characterize the resulting NE. A sufficient condition on global convergence is derived and is shown to be tighter than existing ones. Further, a novel characterization of the globally achievable NE based on necessary conditions is presented. Some of these results are also extended to multiple NE scenarios where local convergence is exhibited.

In this paper, we propose a multiple-state other-cell interference (OCI) model, which takes into account the interference variability and uncertainty created by scheduling and other fast resource allocation adaptivity. This situation is modeled by a set of states, each described by a spatial covariance matrix and a probability. In order to illustrate the usefulness of such a model, we study two receive beamforming design problems, one maximizing the average data rate and one maximizing the worst-case data rate. We compare the resulting performance with what can be obtained when state information is not available. We show theoretically and numerically that exploring the multiple-state OCI structure can improve the receive beamforming design efficiency, especially for cell-edge users in a interference-limited system.

Methods for spatially diagonalizing wideband multiple-input multiple-output channels using linear finite impulse response (FIR) filters are investigated. The PSVD approach by applying the PQRD-BC algorithm for approximate singular value decomposition (SVD) of polynomial matrices is compared to the approach of performing a set of conventional SVDs in the Discrete Fourier Transform (DFT) domain, in terms of complexity and approximation error. Reduced order filters, based on the DFT-SVDs, are then obtained by optimizing the phases of the filters. Applying the phase optimized filters as linear filters then forms a benchmark on the accuracy attainable for any PSVD factorization, for the given filter length. Simulations show that the DFT-SVD method has significantly lower complexity than the PSVD by PQRD-BC, but results in higher order filters. On the other hand, the PSVD by PQRD-BC yields filters which are close to being perfectly unitary for all frequencies. To achieve good performance, the reduced order filters are around one order of magnitude longer than the channel impulse response length. Therefore there is no gain in performing time domain diagonalization using a polynomial SVD, compared to using a multicarrier solution.

Base station cooperative transmission is an effective strategy to mitigate inter-cell interference. Centralized multi-cell transmission provides considerable performance gains but is impractical in large cellular systems, due to its prohibitive complexity and large amount of overhead. Dividing cells into small clusters enables practical channel acquisition and coordination within each cluster but still suffers from out-of-cluster interference. In this paper, we propose a dynamic cooperative framework for large cellular systems, which divides cells into groups such that neighboring cells belong to different groups. Based on the cell-grouping, a distributed scheduling strategy is proposed which can effectively coordinate the interference between cell-groups. With limited signalling among BSs and lower complexity, the cell-grouping based distributed scheduling and beamforming shows performance advantages over the fixed clustering based centralized scheduling and beamforming.

In this paper, we study the design of optimal robust training sequences for multiple-input multiple-output (MIMO) channel estimation, based on known second order statistics of both the channel and the colored disturbance, but with an uncertainty in the channel covariance matrix. More specifically, the training sequences are designed by taking the least-favorable channel covariance component into account throughout an iterative algorithm. Numerical experiments are carried out to demonstrate the performance gained by employing the proposed design procedure and to compare it with other relevant schemes.

To exploit the full benefit of base station (BS) cooperative transmission, also known as coordinated multi-point (CoMP) transmission, large amount of feedback is required to gather the channel information. In this paper, we analyze the impact of channel asymmetry, which is inherent in CoMP systems, on downlink coherent BS cooperative transmission using zero-forcing beamforming with limited feedback. Per-cell quantization of multicell channels is considered, which quantizes the local channel and cross channels separately and is more feasible in practice. We analyze the per-user rate of limited feedback multi-user CoMP systems, and provide approximate expressions for both the inter-cell and intra-cell residual multi-user interference introduced by the quantization errors. When the desired user is at the cell center, the former is weak, but the latter is strong and depends not only on the signal to noise ratio but also on the location of its co-scheduled users. Simulation results validate our theoretical analysis.

We consider a robust MIMO transceiver design to minimize mean square errors, by taking into account the imperfect channel state information from a worst-case robustness perspective. We show that for a given precoder, the optimal robust equalizer is obtained through channel diagonalization, and vice versa. Thus, a joint but usually suboptimal transceiver design can be readily obtained through alternately optimizing the equalizer and precoder, where in each iteration only a scalar problem is to be solved. We further propose efficient algorithms for the scalar optimization problems.

Base station cooperation can theoretically improve the throughput of multicell systems by coordinating interference and serving cell edge terminals through multiple base stations. In practice, the extent of cooperation is limited by the increase in backhaul signaling and computational demands. To address these concerns, we propose a novel distributed cooperation structure where each base station has responsibility for the interference towards a set of terminals, while only serving a subset of them with data. Weighted sum rate maximization is considered, and conditions for beamforming optimality and the optimal transmission structure are derived using Lagrange duality theory. This leads to distributed low-complexity transmission strategies, which are evaluated on measured multiantenna channels in a typical urban multicell environment.

We address the problem of combining limited feedback information with long-term channel statistical information in the design of downlink SDMA schemes. A novel combining method is developed to improve the quality of channel knowledge at the base station. More specifically, a set of novel feedback parameters is proposed and a related method is developed to estimate a representation of the multiuser channel vectors at the base station. This method utilizes the hybrid information by combining instantaneous channel feedback and long-term channel statistics, and is based on a channel phase codebook designed using the generalized Lloyd algorithm. The estimated channel knowledge at the base station can be used for joint design of multiuser precoding and opportunistic scheduling. The advantage of the proposed scheme over existing CSI quantization based SDMA schemes is further confirmed by computer simulations.

In this paper, we address the problem of user scheduling in downlink coordinated multi-point transmission (CoMP) systems, where multiple users are selected and then served with zero forcing beamformer simultaneously by several cooperative base stations (BSs). To reduce the enormous overhead led by obtaining full channel state information at the transmitter, a low-feedback user scheduling method called channel norm-based user scheduler (NUS), is proposed by exploiting the asymmetric channel feature of CoMP systems. Simulation results show that the channel norm provides sufficient information for user scheduling when each BS has one antenna, where the performance gap between the NUS and the greedy user selection (GUS) is negligible with respect to both the cell average throughput and the cell edge throughput. When each BS has multiple antennas, NUS is inferior to GUS, but still significantly outperforms the uncoordinated systems.

We consider the interaction of several transmit-receive pairs coexisting in the same area and communicating using the same portion of the spectrum. Using a game theoretic framework, each pair is regarded as a player whose payoff function is the individual link rate and power is allocated using the iterative water-filling algorithm. We find properties of the resulting Nash equilibria and derive conditions for when various operating points are achievable. The analysis presented herein extends previous work by characterizing the set of stable solutions for a multi-user system. Also, we show how the game can be modified to obtain better operating points in terms of sum rate compared to the iterative water-filling algorithm. The increase in performance corresponding to one such modification is evaluated and compared to the iterative water-filling algorithm by numerical simulations.

A scenario consisting of two transmitter-receiver pairs coexisting in the same area and communicating using the same portion of the spectrum is considered. Decentralized coding strategies are employed at the transmitter side and no cooperation is assumed between the two systems. We investigate the structure of Nash equilibria corresponding to simultaneous water-filling solutions and propose a scheme that improves overall performance of systems with weak mutual interference. The resulting scheme provides a spectrum sharing rule in the form of a modified utility function. The conditions for optimality are presented and a numerical example illustrates the performance compared to a scheme employing the link rate as utility function.

A simple structure to exploit both long-term and partial short-term channel state information at the transmitter (CSIT) over a family of correlated multiple-antenna channels is proposed. Partial short-term CSIT in the form of a weighting matrix is combined with a unitary transformation based on the long-term channel statistics. The heavily quantized feedback link is directly optimized to maximize the expected achievable rate under different power constraints, using vector quantization and convex optimization techniques on a sample channel distribution. Robustness against errors in the feedback link is also pursued with tools in channel optimized vector quantization. Simulations indicate the benefits of the proposed scheme.

Spatial division multiple access (SDMA) systems efficiently take advantage of the spatial dimensions of the channel to increase the performance of the system. A major difficulty, common to all SDMA systems, is the requirement of channel knowledge at the transmitter to enable transmission of multiple streams without catastrophic interference. Herein we show that, in wide area scenarios, statistical channel information combined with the Euclidean norm of the channel realization, fed back from the users, provide sufficient information for SDMA systems to efficiently allocate users in time and space. A joint beamforming and scheduling algorithm is proposed for the downlink, which extends the proportional fair scheduling criterion to an SDMA setting, resulting in a weighted sum rate maximization.

Low-rate feedback design for multiple-input multiple-output broadcast channels is studied under a vector quantization framework. Iterative algorithms are proposed to design the partial feedback link, the scheduler, and the linear precoding codebook. It is demonstrated that the gain due to multi-user diversity can be significant even with heavily quantized channel state information at the transmitter. Our results highlight the potential of multi-user diversity, even with simple schemes and extremely-low-rate feedback.

We study the downlink of a system with multiple antennas at the base stations and propose two different schemes for admission control and beamforming selection when a new user enters the system. To keep the complexity low, only the power control, not the spatial signatures of beamformers for the already admitted users, are adjusted. Numerical examples illustrate the performance compared to joint optimization of all users

A simple structure to exploit both long-term and partial short-term channel state information at the transmitter (CSIT) over a family of correlated multiple-antenna channels is proposed. Partial short-term CSIT in the form of a weighting matrix is obtained via a resolution-constrained feedback link, combined with a unitary transformation based on the long-term channel statistics. The feedback link is optimized to maximize the expected achievable rate under different power constraints, using vector quantization techniques. Simulation indicate the benefits of the proposed scheme in all scenarios considered.

In wireless systems with multiple antennas at the access points, the downlink power has to be spatially optimized to allow several simultaneous users. We consider two different MMSE criteria for a multi-user downlink CDMA system and determine the optimal transmit beamforming weights. The MMSE criteria with and without receiver gain control are compared for a system where the transmitter is equipped with an antenna array and the receivers have single antennas. The MMSE and SINR versus different number of users is shown and the effect of including the gain control in the MMSE criteria is clearly demonstrated

In opportunistic SDMA, the base station forms several random beams simultaneously and relies on fast but limited feedback for scheduling users on the beams. In this paper, opportunistic SDMA is applied to an OFDMA downlink by having independent beamformers run in parallel on different frequency bands (SD-OFDMA). A method for improving the performance of completely random beamforming is proposed and evaluated. It exploits the temporal channel correlation and the partial channel state information available at the transmitter to keep "successful" beams over longer periods of time than the default block duration. Extensive simulation results show a significant improvement in cell throughput compared to a completely random scheme. The results also show that in order to gain more from the multiple simultaneous beams than what is lost in additional interference, the system load must be high.

We investigate the use of congestion control and joint optimal downlink beamforming, power control, and access point allocation, in a multi-cell wireless communication system. The access points of the system employ smart antennas and single antennas are used at the terminals. The possibility to send messages to multiple terminals at the same frequency in the same time slot is exploited. We show how previously proposed algorithms for optimal downlink beamforming easily can be extended to determine also the optimal access point for each mobile terminal. In order to assign resources, optimal beamforming requires a feasible set of mobiles, i.e. that all admitted users can be offered the required signal-to-interference-and-noise ratio. Therefore, an algorithm for deciding which mobile terminals to admit or reject from a congested system is proposed and evaluated. Using the proposed congestion algorithm, joint optimal downlink beamforming is evaluated and the throughput increase as compared to decentralized beamforming algorithms and other congestion control strategies is assessed from a system point of view. The results show that the proposed strategy can almost double the throughput compared to decentralized beamforming algorithms and give a fivefold increase in throughput compared to conventional beamforming without any interference suppression.

By imposing additional constraints in the downlink beamforming optimization, more general quality of service (QoS) measures than the average signal to interference and noise ratio (SINR) alone, can be introduced. Herein a rapidly converging algorithm solving the downlink beamforming problem with additional indefinite quadratic constraints on the beamforming vector is presented. The proposed algorithm is significantly faster than the previously proposed solution, which involves semidefinite programming. Also, the algorithm is easy to implement, since it only involves eigenvalue problems.

In this paper, we address the problem of transmit beamforming, power allocation, bit loading, and admission control in a multi-user scenario, where several single antenna mobile terminals are served by one base station equipped with an antenna array. In particular, we explore the impact of using either optimal or zero-forcing transmit beamforming schemes in combination with different bit allocation strategies, namely the maximization of the sum rate (MSR), the maximization of the minimum rate (MMR) and a modified version of the latter, for a finite set of modulation schemes. The performance evaluation is conducted by means of system-level simulations, using a realistic channel model for urban micro cells, with an emphasis not only on the aggregated cell throughput but also on the associated fairness issues.

For any given single link strategy for transmission over a MIMO channel with channel knowledge at both transmitter and receiver, we propose a general approach to reduce the interference when the strategy is used in an interference limited system. This solution has several interesting interpretations. The structure of the solution is shown to include the global optimum, even though it may be difficult to determine all parameters. However, a suboptimal choice is presented that can be implemented in practical systems using only local information. A numerical example illustrates the performance when trying to minimize the summed mutual information.

Using ideas from power control and downlink beamforming, we suggest a pragmatic approach for spatial multiplexing in systems with several access points, each serving one or more mobile terminals. We assume that all channels are known globally, but in the case of fast fading, it is sufficient to know the second order statistics of the channels. Robustness to channel estimation errors is easily incorporated in the algorithm. Since global channel knowledge is required, the algorithm is mainly intended for system simulations where it provides a benchmark for the performance of any spatial multiplexing scheme with equal rate on the spatial channels.

Herein, results of 5.2 GHz wideband indoor multiple input multiple output (MIMO) channel measurements under the EU IST SATURN project are reported. Our investigation shows that for non-line-of-sight (NLOS) cases, the average power delay profiles fit the exponentially decaying curve quite well, therefore a simple wideband model for single-input single-output (SISO) proposed in COST259 has been used in our model. Furthermore, the investigations show that the MIMO channel covariance matrix of each normalized tap of the impulse response could be well approximated by the Kronecker product of the covariance matrices seen from the transmitter and receiver respectively. Based on the above results, a wideband statistical model is presented. Monte-Carlo simulations show reasonably good agreement between the measured data and our model. Finally, we use this model to show some capacity characteristics of Hiper-LAN/2 channels in NLOS indoor scenarios.

Downlink beamforming in a WLAN-type system employing access points and mobiles equipped with multiple antennas and associated receivers and transmitters are considered. The beamforming aims at maximizing the performance under constraints on transmit power or equivalent isotropic radiated power (EIRP). Solutions for the two constraints are derived and investigated using simulated and measured channels. Our simulation and experimental results shows that performance gains of 8-10 dB when using four directional transmitter antennas and two receive antennas (as compared with a base-line one-transmit two-receive), are possible under both constraints. For simulated channels, a delay between channel estimation and use of the same channel of up to 10% of the (inverse of the) Doppler frequency only degrades performance some tenths of a dB. In our measurements, very small degradations are seen with delays of up to 130 ms. The measurements were made under relatively stationary conditions with only occasionally moving people. Two different strategies for updating the beamforming vectors: sounding and ping-pong, are also considered in the paper.

Herein, results from measurements conducted by the University of Bristol are presented. The channel characteristics of multiple input multiple output (MIMO) indoor systems at 5.2 GHz are studied. Our investigation shows that the envelope of the channel for non-line-of-sight (NLOS) indoor situations are approximately Rayleigh distributed and consequently we focus on a statistical description of the first and second order moments of the narrowband MIMO channel. Furthermore, it is shown that for NLOS indoor scenarios, the MIMO channel covariance matrix can be well approximated by a Kronecker product of the covariance matrices describing the correlation at the transmitter and receiver side respectively. A statistical narrowband model for the NLOS indoor MIMO channel based on this covariance structure is presented.

We present an algorithm that jointly determines the optimal downlink beamformers and the optimal assignment of each mobile to a base station. The optimality criterion is based on a systems perspective; provide sufficient quality of service for all users, transmitting as little excess power as possible. Since the algorithm is centralized and requires knowledge about all the channels in the system, it may be infeasible in a practical implementation. However, it provides the ultimate benchmark in system evaluations. Numerical examples show substantial gain compared to ordinary base station assignment.

The increased popularity of array antennas for wireless communication, has inspired investigations of the spatio-temporal properties of the radio channel, among others the azimuthal shape of the scattering clusters. Based on a statistical analysis, we show that trying to estimate the shape of the scattering is an ill-posed problem and that the heavy-tailed power azimuth spectra reported in the literature may be an artifact stemming only from the measurement procedure.

We investigate the use of joint optimal downlink beamforming, power control and access point allocation, in a multicell SDMA system. Smart antennas are used at the access points and single antennas are used at the terminals. The possibility to send messages to multiple terminals on the same frequency in the same time slot is exploited. An algorithm for removing users from a congested system, in order to avoid outage is proposed and evaluated Results show that the proposed algorithm gives substantial increase of the system performance compared to random removal of users.

A WLAN-type scenario where a base-station (access point) equipped with multiple antennas is transmitting and a mobile with only a single antenna is receiving, is considered. Three approaches are investigated: grid-of-beams (GOB), maximal-ratio (MR) and equal-gain (EG), each with one of the following constraints 1) total transmit power over all antenna elements, 2) maximum power on any antenna element 3) equivalent isotropic radiated power (EIRP). The median diversity gain for the MR approach is estimated to be 14.8 dB, 10.6 dB, and 11.4 dB using constraint 1-3, respectively at 5.2 GHz in a modern university building at 5-50 meter range. For GOB corresponding numbers are 9.4 dB, 9.4 dB, 2.3 dB and for EG 13.9 dB, 13.9 dB, 10.3 dB, respectively. These results are virtually independent of delay between channel estimation and use of the same estimate, when the delay is less than 130 ms. This result is obtained although there were people moving in the environment. The diversity gain under the EIRP constraint is encouraging and shows that coverage improvements are possible even under EIRP limitations.

We present an application of a Potts glass to the clustering problem. Simulated annealing in the mean field approximation is used in order to avoid local minima. The resulting updating equations are completely parallel, and very easy to implement. The model has no free parameters except for the annealing parameters. We show how the model can be implemented for some special clustering problems. The T-->0 limit of the Potts glass is identical to the vector quantization algorithm with certain increments. A comparative study of the Potts glass and vector quantization is also made, and it is shown that for difficult clustering problems, the Potts glass is far better than vector quantization.

We have investigated the storage capacity in the limit of large N (the network size) for a third order recurrent artificial neural network with Hebbian learning. Numerical results for the relation between the overlap to stored patterns, and the fraction of the number of stored patterns and N2 (the m—α relation), agree well with replica symmetric predictions. A comparative study is made of the m—α relation for a third and a second order network. Large differences exist between these two models, usually to the favour of the third order network. This result stands in some contrast to previous investigations. The phase transition temperature is investigated numerically and compared with mean field theory predictions.