A standard reconfigurable intelligent surface (RIS) can be configured to reflect signals from an arbitrary impinging direction to an arbitrary outgoing direction. However, if a signal impinges from any other direction, said signal is reflected, with full beamforming gain, to a specific direction, which is easily determined. The goal of this paper is to propose a RIS which only reflects signals from the configured impinging direction. This can be accomplished by a RIS architecture that permutes the antenna elements in the sense that a signal is re-radiated from a different antenna than the one receiving the signal. We analytically prove this fact, and also discuss several variants and hardware implementations.

In this paper, we study integration strategies for reconfigurable intelligent surfaces (RISs) in distributed MIMO (D-MIMO) systems as one of the promising techniques for evolving 5G networks and beyond (6G). The scalability of D-MIMO systems to large networks in a practically feasible way is challenging. The exploitation of cost-effective and energy-efficient dynamic access point (AP) clustering techniques and densification enablers is crucial for such systems to sustain the required level of performance and reliability while mitigating the environmental and economic challenges related to future network operations. RIS is well regarded as a low-cost, rapidly deployable, energy-efficient candidate offering extra diversity in the spatial domain. This work explores RIS-aided multi-AP systems attaining certain prescribed key performance indicators (KPIs) while considering the energy consumption in the system.We concentrate on indoor use cases with large user equipment (UE) populations where the service coverage is low due to the high obstacle density. To that end, we propose dynamic user-centric AP clustering and RIS placement techniques adapted for serving multi-user indoor systems. Here, we use an alternating optimization method as a sub-optimal solution for RIS phase-shift configuration, keeping the computation complexity low. We show that the integration of RISs in D-MIMO systems is an attractive approach to enhance energy efficiency and provide the scalability required in 5G and beyond (6G).

Reconfigurable surface (RS) has been shown to be an effective solution for improving wireless communication links in general multi-user multiple-input multiple-output (MU-MIMO) setting. Current research efforts have been largely directed towards the study of reconfigurable intelligent surface (RIS), which corresponds to an RS made of passive reconfigurable elements with only phase shifting capabilities. RIS constitutes a cost- and energy- efficient solution for increased beamforming gain since it allows to generate constructive interference towards desired directions, e.g., towards a base station (BS). However, in many situations, multiplexing gain may have greater impact on the achievable transmission rates and number of simultaneously connected devices, while RIS has only been able to achieve minor improvements in this aspect. Recent work has proposed the use of alternative RS technologies, namely amplitude-reconfigurable intelligent surface (ARIS) and fully-reconfigurable intelligent surface (FRIS), to achieve perfect orthogonalization of MU-MIMO channels, thus allowing for maximum multiplexing gain at reduced complexity. In this work we consider the use of ARIS and FRIS for simultaneously orthogonalizing a MU-MIMO channel, while embedding extra information in the orthogonalized channel. We show that the resulting achievable rates allow for full exploitation of the degrees of freedom in a MU-MIMO system with excess of BS antennas.

Cell-free massive multiple-input multiple-output (MIMO) consists of a large set of distributed access points (APs) serving a number of users. The APs can be far from each other, and they can also have a big number of antennas. Thus, decentralized architectures have to be considered so as to reduce the interconnection bandwidth to a central processing unit (CPU) and make the system scalable. On the other hand, the APs in a heterogeneous network might have limited processing capabilities and fully-decentralized processing may not be available. In a recent paper, a trade-off between level of decentralization and decentralized processing complexity has been identified. Furthermore, a novel matrix decomposition – the WAX decomposition – which, if applicable to the channel matrix, allows for exploitation of said trade-off without loss of information. The results on WAX decomposition are only available for random channel matrices with-out specific structures, while in a cell-free massive MIMO scenario the channel can have sparse structures. In this work, we study the applicability of WAX decomposition to cell-free massive MIMO with its implications to the above-mentioned trade-off.

Large intelligent surfaces (LISs) is an evolution of massive MIMO systems allowing for huge capacity gains. To reduce implementation complexity, it is convenient to implement the LIS using panels that are either activated or deactivated, and associated to terminals according to their propagation characteristics to the panels. The associated spatial resource allocation to maximise the terminals’, as well as the overall, bit rates can lead to complex optimisation problems.In this paper we consider resource allocation for panel-based LIS surfaces. We present an iterative sequential algorithm for determining the set of active panels and the respective panel-terminal association for the maximisation of the minimum terminal rate. Our algorithm is decentralised and has low complexity. Moreover, it approaches the performance of much more complex, quasi-optimum algorithms.

Reflective reconfigurable intelligent surface (RIS) technology is regarded as an innovative, cost- and power-effective solution that aims at influencing the wireless channel through controlled scattering. The technology can be realized by using metamaterials and/or resonant elements that scatter electromagnetic waves with a configurable phase shift. Most of the previous work on beamforming techniques for RIS assumes ideal hardware and, thus, continuous phase shifts. However, hardware constraints limit the phase shift resolution, manifested into the amount of discrete phase shifts that can be configured into each RIS element. This paper aims to offer a discrete phase shift beamforming algorithm for reflective RISs that targets minimization of the quantization error resulting from discretization of continuous phase shifts. The beamforming solution proves to be optimal under perfect channel knowledge for any discrete set of uniformly distributed phase shifts. The required complexity to find the optimal beamforming vector for our approach is found to be linear with the number of RIS elements, the minimum needed to obtain optimal results. Simulated behavior is validated by measurements, showing robustness against angle misalignments and distance variations.

Large intelligent surface (LIS) is a technology that extends massive MIMO by considering an even greater number of antennas distributed throughout vast areas. In order to be able to implement this technology, it is crucial to consider decentralized architectures so as to make the whole system scalable. We consider a LIS divided into several LIS panels of smaller size, which can be located far away from each other. We present a modular architecture that allows combining different LIS panels using a binary tree. This architecture is also valid in a cell-free massive MIMO scenario. We make use of a newly defined matrix decomposition, the WAX decomposition, to define the modules that are used within our architecture. We also study the lossless dimensionality reduction in the data to be processed, which can be achieved using our proposed architecture.

In this paper, we study the effect of optimizing the per-antenna digital predistortion (DPD) sizes on the performance of the downlink massive MIMO system with residual hardware impairment. In particular, we first quantify the capacity after applying some per-antenna DPD with different numbers of coefficients at each antenna and then maximize the capacity by finding optimum values of the per-antenna DPD sizes under a constraint on the total number of DPD coefficients in the system. Two closed-form sub-optimal solutions are derived and numerical examples illustrate that their performance is very close to the optimal solution. It is shown that when the channel large-scale gains have high variation over the transmitter array, which is the case in practical scenarios, using our proposed optimized DPD sizes can improve the system capacity significantly. This allows us to scale down the massive MIMO system but still maintain performance. We also study the asymptotic behavior of the derived capacity and show that by using the optimized DPD sizes, the system performance can approach the asymptotic bound with a significantly smaller number of antennas.

A Large Intelligent Surface (LIS) is a recently proposed concept, especially suitable for high speed indoor communications and industrial internet of things (IoT) applications. Basing the LIS on smaller panels has clear advantages in terms of flexibility and mass production of its elements. In this paper we consider a panel-based LIS and we study the interplay of the panel size, the number of baseband outputs per square meter of deployed surface, the total activated surface area, the number of baseband outputs per panel, the terminal density and the ensuing minimum terminal rate. Our performance results show that it is desirable to employ smaller panels when the terminal density increases, but this means more outputs per m2, and higher overall LIS implementation complexity. It was observed that we can surpass such increase by working with higher fractions of the LIS area. Furthermore, we present an empirical equation stating the number of outputs per panel needed to ensure that all terminals are reasonably served. These results are useful for the LIS design in practical scenarios.

As an emerging technology and evolution that goes beyond massive multi-input multi-output (MIMO), large intelligent surface (LIS) has gained much interest. LIS acts as an electromagnetic surface that can transmit, redirect, and receive radiating signals across its entire contiguous surface. It allows for unprecedented energy-focusing, data-transmission and terminal-positioning, and can fulfill the most grand visions for future communication systems. Earlier proposed LISs are in two-dimensional (2D), i.e., planar shapes. In this paper, we extend LISs to be three-dimensional (3D) and deployed as spherical surfaces. Compared to 2D LIS, a spherical LIS has advantages in wide coverage, simple positioning technique, and flexible deployment as reflecting surface.

Algorithms for Massive MIMO uplink detection are typically based on a centralized approach, by which baseband data from all antenna modules need to be routed to a central node for further processing. In the case of Massive MIMO, where hundreds or thousands of antennas are expected in the base-station, such architecture requires high interconnection bandwidth between antennas and the central node. Recently, decentralized architectures have been proposed to maintain low interconnection bandwidth, where channel-state-information (CSI) is obtained locally in each antenna node and not shared. Further, Massive MIMO performance is sensitive to CSI quality. However, in the literature, ideal CSI is typically assumed in decentralized systems, which is not only far from reality but also limits the generality of the analysis.This paper proposes a decentralized (a term that will be defined in the main body of the paper) architecture with the following main features: (i) the channel matrix is not made available at any single node, (ii) there is no inter-communication among antennas, (iii) the architecture used during the payload data phase, is reused to provide a certain statistic to a processing node, (iv) A non-standard channel estimation problem based on said statistic arises, (v) a matrix inversion is needed (in case of zero-forcing) at said processing node.A hefty share of the paper is devoted to (iv).

In this paper we present fully decentralized methods for calculating an approximate zero-forzing (ZF) equalizer in a large intelligent surface (LIS). A LIS is intended for wireless communication and facilitates unprecedented MU- MIMO performance, far superior to that of Massive MIMO. Antenna modules in the grid connect to their neighbors to exchange messages of information needed for interference cancellation in a fully-decentralized fashion, making the system scalable. By a careful design of how the messages are routed, we show that the proposed method is able to cancel inter-user interference sufficiently well without any centralized coordination, opening the door for the realization of this type of structures.

We consider time-of-arrival (ToA) estimation for a device working in narrowband Internet-of-Things (NB-IoT) systems. Due to a limited 180 kHz bandwidth, the time-domain auto-correlation function (ACF) of transmitted NB positioning reference signal (NPRS) has a wide main-lobe. Without considering that, the performance of ToA estimation can be degraded for two reasons. Firstly, the NPRS corresponding to different received paths are superimposed on each other under multipath propagation. Secondly, the measured peak-to-average power-ratio (PAPR) for detecting the presence of NPRS is inaccurate. Therefore, in this letter we propose a space-alternating generalized expectation-maximization (SAGE) based method to estimate the number of channel taps, coefficients, and corresponding delays, with taking the imperfect ACF of NPRS into consideration. The proposed ToA estimator only uses time-domain cross-correlations between the received signal and the transmitted NPRS, which yields a low computational-cost. We show through simulations that, it performs close to maximum likelihood (ML) estimator under flat-fading channels, and is superior than traditional estimators under frequency-selective fading channels.

We propose a modulus based zero-forcing (MZF) detector for multi-input multi-output (MIMO) channels. Traditionally, a ZF detector nulls out interference from other layers when detecting a certain layer. While this is conceptually simple, it can result in considerable noise-enhancement. In many communication systems, finite alphabets such asMquadrature-amplitude-modulation (QAM) are used, which comprises √M pulse-amplitude- modulation (PAM) symbols in both the real and imaginary components. With finite alphabets, one feasible way to improve ZF detection is to allow controllable interference that can be removed away by a modulus operation.

In this paper, we consider capacity degradations stemming from potential hardware impairments (HWI) of newly proposed Large Intelligent Surface (LIS) systems. Without HWI, the utility of surface-area (the first-order derivative of the capacity with respect to surface-area) is shown to be proportional to the inverse of it. With HWI, the capacity as well as the utility of surface-area are both degraded, due to a higher effective noise level caused by the HWI. After first modeling the HWI in a general form, we derive the effective noise density and the decrement of utility in closed-forms. With those the impacts of increasing the surface-area can be clearly seen. One interesting but also natural outcome is that both the capacity and utility can be decreased when increasing the surface-area in the cases with severe HWI. The turning points where the capacity and the utility start to decrease with HWI can be evaluated from the derived formulas for them. Further, we also consider distributed implementations of a LIS system by splitting it into multiple small LIS-Units, where the impacts of HWI can be significantly suppressed due to a smaller surface-area of each unit.

We consider a multipair two-way relay communication network, where pairs of user devices exchange information via a relay system. The communication between users employs time division duplex, with all users transmitting simultaneously to relays in one time slot and relays sending the processed information to all users in the next time slot. The relay system consists of a large number of single antenna units that can form groups. Within each group, relays exchange channel state information (CSI), signals received in the uplink and signals intended for downlink transmission. On the other hand, per-group CSI and uplink/downlink signals (data) are not exchanged between groups, which perform the data processing completely independently. Assuming that the groups perform zero-forcing in both uplink and downlink, we derive a lower bound for the ergodic sumrate of the described system as a function of the relay group size. By close observation of this lower bound, it is concluded that the sumrate is essentially independent of group size when the group size is much larger than the number of user pairs. This indicates that a very large group of cooperating relays can be substituted by a number of smaller groups, without incurring any significant performance reduction. Moreover, this result implies that relay cooperation is more efficient (in terms of resources spent on cooperation) when several smaller relay groups are used in contrast to a single, large group.

In this paper, we consider a wireless communication system where a large intelligent surface (LIS) is deployed comprising a number of small and distributed LIS-Units. Each LIS-Unit has a separate signal process unit (SPU) and is connected to a central process unit (CPU) that coordinates the behaviors of all the LIS-Units. With such a LIS system, we consider the user assignments both for sum-rate and minimum user-rate maximizations. That is, assuming M LIS-Units deployed in the LIS system, the objective is to select K(K ≤ M) best LIS-Units to serve K autonomous users simultaneously. Based on the nice property of effective inter-user interference suppression of the LIS-Units, the optimal user assignments can be effectively found through classical linear assignment problems (LAPs) defined on a bipartite graph. To be specific, the optimal user assignment for sum-rate and user-rate maximizations can be solved by linear sum assignment problem (LSAP) and linear bottleneck assignment problem (LBAP), respectively. The elements of the cost matrix are constructed based on the received signal strength (RSS) measured at each of the M LIS-Units for all the K users. Numerical results show that, the proposed user assignments are close to optimal both under line-of-sight (LoS) and scattering environments.

For a pair of closely located and cooperating user equipments (UEs), a precoder is designed at the base station (BS) which considers the UE cooperation. The UEs collaborate over an out-of-band side-link with a finite capacity. The side-link may be used for interference cancellation (IC) or for relaying decoded symbols. The precoder has two parts, a cooperative part based on channel inversion and a non- cooperative part based on the minimum mean squared error (MMSE) metric. It is the interference from the former part which is managed at the UEs in the cooperative IC phase. The latter part is included at the BS to further improve the performance if there is transmit power remaining at the BS after the cooperative phase; this due to the assumption of finite capacity side-link. To study the performance of the precoder design, various joint optimization problems that maximize a sum-rate objective are considered. The effects of power imbalance and correlation between the UEs are included into the problems. From the numerical results it is observed that the sum-rate increases with cooperation. Further, with an increase in the side-link capacity the objective value approaches the single-user water-filling capacity limit. By modifying the precoder structure and the user cooperation mechanism, a unidirectional side-link case, where only one of the users accesses the side-link, is also discussed.

Downlink beamforming in Massive multiple-input and multiple-output (MIMO) either relies on uplink pilot measurements-exploiting reciprocity and time-division duplexing operation, or on the use of a predetermined grid of beams with user equipments reporting their preferred beams, mostly in frequency-division duplexing operation. Massive MIMO in its originally conceived form uses the first strategy, with uplink pilots, whereas there is currently significant commercial interest in the second, grid-of-beams. It has been analytically shown that with isotropic scattering (independent Rayleigh fading) the first approach outperforms the second. Nevertheless, there remains controversy regarding their relative performance in practical channels. In this contribution, the performances of these two strategies are compared using measured channel data at 2.6 GHz.

In this paper, we consider positioning with observed-time-difference-of-arrival (OTDOA) for a device deployed in long-term-evolution (LTE) based narrow-band Internet-of-things (NB-IoT) systems. We propose an iterative expectation- maximization based successive interference cancellation (EM-SIC) algorithm to jointly consider estimations of residual frequency- offset (FO), fading-channel taps and time-of- arrival (ToA) of the first arrival-path for each of the detected cells. In order to design a low complexity ToA detector and also due to the limits of low-cost analog circuits, we assume an NB-IoT device working at a low-sampling rate such as 1.92 MHz or lower. The proposed EM-SIC algorithm comprises two stages to detect ToA, based on which OTDOA can be calculated. In a first stage, after running the EM-SIC block a predefined number of iterations, a coarse ToA is estimated for each of the detected cells. Then in a second stage, to improve the ToA resolution, a low-pass filter is utilized to interpolate the correlations of time-domain PRS signal evaluated at a low sampling-rate to a high sampling-rate such as 30.72 MHz. To keep low-complexity, only the correlations inside a small search window centered at the coarse ToA estimates are upsampled. Then, the refined ToAs are estimated based on upsampled correlations. If at least three cells are detected, with OTDOA and the locations of detected cell sites, the position of the NB-IoT device can be estimated. We show through numerical simulations that, the proposed EM-SIC based ToA detector is robust against impairments introduced by inter-cell interference, fading-channel and residual FO. Thus significant signal-to-noise (SNR) gains are obtained over traditional ToA detectors that do not consider these impairments when positioning a device.

In this paper, we consider precoder design for multiuser multiple-input-multiple-output (MIMO) Gaussian broadcast (BC) channels and propose a generalized zero-forcing (GZF) precoder based on successive dirty-paper coding (DPC), i.e., the GZF-DP precoder. The GZF-DP precoder is an extension of the GZF-DP precoder designed earlier for multi-input-single-output broadcast (MISO-BC) channels, and also a generalization of both the linear block-diagonalization ZF (BD-ZF) and the successive ZF with DPC (SZF-DPC) precoders. With the GZF-DP precoder, the depth of the inter-user interference after precoding (and before the DPC) can be specified at will by a parameter ν, which provides a trade-off between the optimal rates and the DPC implementation-complexity. Utilizing DPC, the known non-causal inter-user interferences from the other (up to) ν users are canceled through successive encoding. Within the class of GZF-DP, we analyze the optimal precoder designs both for sum-rate and minimum user-rate maximizations, which are solved in closed-forms in conjunction with water-filling algorithms depending on ν. We show through numerical results that, the proposed GZF-DP precoder with a small ν renders significant rate increments compared to the linear BD-ZF precoder, and is close to the SZF-DP preocder with a much less DPC complexity.

We consider channel estimation (CE) in narrowband Internet-of-Things (NB-IoT) systems. Due to the fluctuations in phase within receiver and transmitter oscillators, and also the residual frequency offset (FO) caused by discontinuous receiving of repetition coded transmit data-blocks, random phase noises are presented in received signals. Although the coherent-time of fading channel can be assumed fairly long due to the low-mobility of NB-IoT user-equipments (UEs), such phase noises have to be considered before combining the the channel estimates over repetition copies to improve their accuracies. In this paper, we derive a sequential minimum-mean-square-error (MMSE) channel estimator in the presence of random phase noise that refines the CE sequentially with each received repetition copy, which has a low-complexity and a small data storage. Further, we show through simulations that, the proposed sequential MMSE estimator improves the mean-square-error (MSE) of CE by around 1 dB in the low signal-to-noise ratio (SNR) regime, compared to a traditional sequential MMSE estimator that does not thoroughly consider the impact of random phase noises.

Non-Orthogonal Multiple Access (NOMA) for a multi-user single- input single-output (SISO) setup is studied in the power and the frequency domains simultaneously. The problem of sum-bandwidth minimization under perfect channel state information is solved for various combinations of rate requirements and user pairings. In this process, an iterative Tabu-search based algorithm is applied to avoid an exhaustive search over all possible user pairing combinations. It is assumed that each constituent user of the pair has a required quality of service and a flat power spectrum. Further, for each user pair, the NOMA operating region is defined by dividing the allocated bandwidth into two non-overlapping Orthogonal Multiple Access (OMA) sub-bands and an overlapping NOMA sub-band. Such an assumption achieves a greater capacity region when compared to the conventional power domain only NOMA. Also for most of the rate requirements, only one of the OMA sub-bands is active in addition to the NOMA sub-band. This simplifies the NOMA user rate expressions and power allocation process. To verify the performance gain, NOMA is compared to an OMA technique.

Non-Orthogonal Multiple Access (NOMA) is studied under statistical Channel State Information (CSI) and probabilistic constraints. Unlike the conventional power domain only NOMA, the definition of NOMA here considers both the power and the frequency domains simultaneously, where a flat power spectrum is assumed for each UE. This increases the capacity region when compared to the conventional definition. The problem of minimizing the number of consumed resource elements (REs) while satisfying the outage constraints is solved. An RE here is a frequency slot of unit bandwidth resolution, so the considered problem translates to a saving in bandwidth. The solution techniques involve a Gaussian Approximation of NOMA user rates and an offline empirical approach based on tail distributions. Numerical results show that the former is a good approximation while the latter provides exact results. In any case, these methods outperform the orthogonal multiple access techniques.

In this paper, we consider capacities of single-antenna terminals communicating to large antenna arrays that are deployed on surfaces. That is, the entire surface is used as an intelligent receiving antenna array. Under the condition that the surface area is sufficiently large, the received signal after matched-filtering (MF) can be well approximated by an intersymbol interference (ISI) channel where channel taps are closely related to a sinc function. Based on such an approximation, we have derived the capacities for both one-dimensional (terminals on a line) and high dimensional (terminals on a plane or in a cube) terminal-deployments. In particular, we analyze the normalized capacity C̅, measured in nats/s/Hz/m2, under the constraint that the transmit power per m2, P̅, is fixed. We show that when the user-density increases, the limit of C̅, achieved as the wavelength λ approaches 0, is P̅/(2N0) nats/s/Hz/m2, where N0is the spatial power spectral density (PSD) of noise. In addition, we also show that the number of signal dimensions is 2/λ per meter deployed surface for the one-dimensional case, and π/λ2per m2deployed surface for two and three dimensional terminal-deployments.

We consider the potential for positioning with a system where antenna arrays are deployed as a large intelligent surface (L'S). We derive Fisher-informations and Cramέr-Rao lower bounds (CRLB) in closed-form for terminals along the central perpendicular line (CPL) of the L'S for all three Cartesian dimensions. For terminals at positions other than the CPL, closed-form expressions for the Fisher-informations and CRLBs seem out of reach, and we alternatively provide approximations (in closed-form) which are shown to be very accurate. We also show that under mild conditions, the CRLBs in general decrease quadratically in the surface-area for both the and dimensions. For the -dimension (distance from the L'S), the CRLB decreases linearly in the surface-area when terminals are along the CPL. However, when terminals move away from the CPL, the CRLB is dramatically increased and then also decreases quadratically in the surface-area. We also extensively discuss the impact of different deployments (centralized and distributed) of the L'S.

We consider optimal channel shortener design for a reduced-state soft-output Viterbi equalizer (RS-SOVE) in single-carrier systems. To use RS-SOVE, three receiver filters need to be designed: a prefilter, a target response, and a feedback filter. The collection of these three filters are commonly referred to as the “channel shortener.” Conventionally, the channel shortener is designed to transform an intersymbol interference (ISI) channel into an equivalent minimum-phase equivalent form. In this paper, we design the channel shortener to maximize a mutual information lower bound based on a mismatched detection model. By taking the decision-feedback quality in the RS-SOVE into consideration, the prefilter and feedback filter are found in closed forms, while the target response is optimized via a gradient-ascending approach with the gradient explicitly derived. The information theoretical properties of the proposed channel shortener are analyzed. Moreover, we show through numerical results that the proposed channel shortener design achieves superior detection performance compared with previous channel shortener designs at medium and high code rates.

In this paper, we consider precoder designs for multiuser multiple-input-single-output broadcasting channels. Instead of using a traditional linear zero-forcing (ZF) precoder, we propose a generalized ZF (GZF) precoder in conjunction with successive dirty-paper coding (DPC) for data transmissions, namely, the GZF-DP precoder, where the suffix “DP” stands for “dirty-paper.” The GZF-DP precoder is designed to generate a band-shaped and lower triangular effective channel F, such that only the entries along the main diagonal and the v first lower-diagonals can take non-zero values. Utilizing the successive DPC, the known non-causal inter-user interferences from the other (up to) v users are canceled through successive encoding. We analyze optimal GZF-DP precoder designs both for sumrate and minimum user-rate maximizations. Utilizing Lagrange multipliers, the optimal precoders for both cases are solved in closed-forms in relation to optimal power allocations. For the sum-rate maximization, the optimal power allocation can be found through water filling, but with modified water levels depending on the parameter v, while for the minimum user-rate maximization that measures the quality of the service, the optimal power allocation is directly solved in closed-form, which also depends on v. Moreover, we propose two low-complexity userordering algorithms for the GZF-DP precoder designs for both maximizations, respectively. We show, through numerical results, that the proposed GZF-DP precoder with a small v value (≤ 3) renders significant rate increments compared with the previous precoder designs, such as the linear ZF and the user-groupingbased DPC precoders.

This paper presents a mutual coupling-based calibration method for time-division-duplex massive MIMO systems, which enables downlink precoding based on uplink channel estimates. The entire calibration procedure is carried out solely at the base station (BS) side by sounding all BS antenna pairs. An expectation-maximization (EM) algorithm is derived, which processes the measured channels in order to estimate calibration coefficients. The EM algorithm outperforms the current state-of-the-art narrow-band calibration schemes in a mean squared error and sum-rate capacity sense. Like its predecessors, the EM algorithm is general in the sense that it is not only suitable to calibrate a co-located massive MIMO BS, but also very suitable for calibrating multiple BSs in distributed MIMO systems. The proposed method is validated with experimental evidence obtained from a massive MIMO testbed. In addition, we address the estimated narrow-band calibration coefficients as a stochastic process across frequency, and study the subspace of this process based on measurement data. With the insights of this study, we propose an estimator which exploits the structure of the process in order to reduce the calibration error across frequency. A model for the calibration error is also proposed based on the asymptotic properties of the estimator, and is validated with measurement results.

In massive MIMO performance evaluations it is often assumed that the terminal has a single antenna. The combination of multiple antennas in a terminal and massive MIMO precoding at the base station side can further improve overall system performance. We present measurement results for multi antenna terminals operating in different transmission schemes and how they perform under varying loading conditions. Gain expressions are derived that enable easy comparison between the transmission schemes. The evaluation is performed on realistic antennas integrated into Sony Xperia handsets tuned to 3.7 GHz and operated together with the Lund University massive MIMO (LuMaMi) test bed. It is concluded that the approach used in today's mobile systems, where up link and down link are addressed independently, will not provide the best performance. The performance can be improved by the selection of transmission schemes optimized for massive MIMO.

The second generation (2G) cellular networks are the current workhorse for machine-to-machine (M2M) communications. Diversity in 2G devices can be present both in form of multiple receive branches and blind repetitions. In presence of diversity, intersymbol interference (ISI) equalization and co-channel interference (CCI) suppression are usually very complex. In this paper, we consider the improvements for 2G devices with receive diversity. We derive a low-complexity receiver based on a channel shortening filter, which allows to sum up all diversity branches to a single stream after filtering while keeping the full diversity gain. The summed up stream is subsequently processed by a single stream Max-log-MAP (MLM) equalizer. The channel shortening filter is designed to maximize the mutual information lower bound (MILB) with the Ungerboeck detection model. Its filter coefficients can be obtained mainly by means of discrete-Fourier transforms (DFTs). Compared with the state-of-art homomorphic (HOM) filtering based channel shortener which cooperates with a delayed-decision feedback MLM (DDF-MLM) equalizer, the proposed MILB channel shortener has superior performance. Moreover, the equalization complexity, in terms of real-valued multiplications, is decreased by a factor that equals the number of diversity branches.

We investigate antenna correlation of an M-antenna massive multiple-input multiple-output (MIMO) setup with the purpose of obtaining a low-rank representation of the instantaneous massive MIMO channel. Low-rank representation bases using short-term and long-term antenna correlation statistics are defined, and their performance is evaluated with data sets obtained from channel measurements in both indoor and outdoor environments at 2.6 GHz. Our results indicate that the short-term bases can capture a larger amount of the channel energy compared to the long-term ones, but they have a limited timespan, one coherence time or less. On the other hand, the long-term bases are stable over time-spans of a few seconds. Hence, they can be obtained relatively easily. We also investigate a rank-p vector-scalar LMMSE channel estimator that exploits antenna correlation. Our results show that the investigated estimator can achieve a performance similar to that of full-rank LMMSE at a (2p + 1)/M times lower cost. The investigated estimator may be used in conjunction with estimators that exploit correlation in the frequency and time domains or, alternatively, in situations in which these estimators cannot be used, e.g., when pilot separation is larger than the channel coherence bandwidth or time.

We consider channel shortening (CS) algorithms for communication systems where multiple single antenna nodes are transmitting single carrier signals to a single antenna receiver over known intersymbol interference channels. We discuss seven methods to shorten the intersymbol interference (ISI) channels, and the parameters are optimized from a generalized mutual information (GMI) perspective. The motivation for dealing with seven methods is that each one may come across as the “natural” CS receiver, and we therefore consider them all in order to compare their performances. A favorable outcome is that the strongest method is also the one that is easiest to optimize.

This paper presents a calibration technique for massive MIMO base stations, where the frequency responses of the transmit and/or receive analog front-ends are individually estimated and compensated for. Calibration is achieved by a first-round of channel sounding between base station antennas, followed by post-processing and a compensation stage. The proposed technique is general in the sense that is does not use external sources, nor internal dedicated circuits for calibration purposes. The only requirement of the technique is that mutual coupling between all pairs of sounded base station antennas exists and is known. Our analysis suggests that mutual coupling can be conveniently used for calibration purposes, and that multipath propagation during calibration is the most prominent source for calibration inaccuracies.

We consider a multiple-input multiple-output (MIMO) channel with inter-symbol interference (ISI) where signal detection is highly complex due to the large signal state-space dimensionality. A common strategy is to apply a front-end filter (FEF) to eliminate the ISI dimension (i.e. full ISI equalization). This FEF is then followed by a frequency non-selective MIMO detector. However, another, much less researched, strategy is to apply an FEF that eliminates the MIMO dimension and results in a set of parallel ISI channels followed by a bank of parallel single-input single-output (SISO) detectors. Which of the two strategies is better in a Shannon capacity sense? In this paper, we show that the answer to this question depends on system parameters such as SNR, number of antennas, ISI duration, and spatial correlation properties.

We consider optimal precoder design for multiuser multiple-input multiple-output broadcasting channels in single-carrier systems. Instead of linear detection, we assume that the advanced nonlinear channel shortening detectors are utilized at the receivers. Such a scenario is challenging for precoder design as the uplink-downlink duality is inapplicable. The target of our linear precoder design is to maximize the sum of the achievable information rate (sum-AIR), with AIR of each user being explicitly derived. We analyze such a precoder design in general, and provide an efficient per-user based optimization algorithm for the design of block-diagonalization precoder.

Optimal data detection of data transmitted over a linear channel can always be implemented through the Viterbi algorithm (VA). However, in many cases of interest the memory of the channel prohibits direct application of the VA. A popular and conceptually simple method in this case, studied since the early 1970s, is to first filter the received signal in order to shorten the memory of the channel, and then to apply a VA that operates with the shorter memory. We shall refer to this general concept as a channel shortening (CS) receiver. Although studied for almost four decades, an information theoretic understanding of what such a simple receiver solution is actually doing is not available. In this paper, we show that an optimized CS receiver has a direct correspondance to the chain rule of mutual information. Furthermore, we show that the tools for analyzing the ensuing achievable rates from an optimized CS receiver are precisely the same as those used for analyzing the achievable rates of a minimum mean-square-error (MMSE) receiver.

Fully-synchronous measurements of a massive multi-user multiple-input multiple-output (MU-MIMO) radio propagation channel are presented. We evaluate the ability of a massive MIMO system to spatially separate users located close to each other in line-of-sight (LOS) propagation conditions. The system consists of a base-station (BS) antenna array equipped with 64 dual-polarized antenna elements (128 ports) arranged in a cylindrical configuration, and eight single-antenna users. The users are confined to a five-meter diameter circle and move randomly at pedestrian speeds. The BS antenna array is located on top of a 20 m tall building and has LOS to the users. We examine user separability by studying singular value spread of the MU-MIMO channel matrix for several subsets of BS antenna array ports, along with sum-rate capacity and achievable sum-rates with both zero-forcing and matched-filtering linear precoders. We also analyze the performance of the user with the lowest rate. Finally, a comparison between the performance offered by the massive MIMO system and that of a conventional MU-MIMO system is provided. To the best of our knowledge, this is the first report of fully-synchronous dynamic measurements of a massive MIMO system. Our investigation shows that even users located close to each other in LOS propagation conditions can be spatially separated in a massive MIMO system.

This study describes a high throughput constant envelope (CE) pre-coder for Massive MIMO systems. A large number of antennas (M), in the order of 100s, serve a relatively small number of users (K) simultaneously. The stringent amplitude constraint (only phase changes) in the CE scheme is motivated by the use of highly power-efficient non-linear RF power amplifiers. We propose a scheme that computes the CE signals to be transmitted based on box-constrained regression (coordinate-descent), with an O(2MK) complexity per iteration per user symbol. A highly scalable systolic architecture is implemented, where M Processing Elements (PEs) perform the pre-coding for a system with up to K=16 users. This systolic architecture results in a very high throughput of 500 Msamples/sec (at 500 MHz clock rate) with a gate count of 14K per PE in 65nm technology.

We consider the problem of designing demodulators for channels with memory that use reduced-size trellis descriptions for the received signal. We assume an overall iterative receiver, and for the parts of the signal not covered by the trellis description, we use interference cancellation based on the soft information provided by the outer decoder. In order to reach a trellis description, a linear filter is applied as front-end to compress the signal structure into a small trellis. This process requires three parameters to be designed: (i) the front-end filter, (ii) the feedback filter through which the interference cancellation is done, and (iii) a target response which specifies the trellis. While (i) and (ii) can be found in closed form, a numerical search is required for (iii). The numerical search is, however, very efficient and stable. Demodulators of this form have been studied before under the name channel shortening (CS), but the interplay between CS and interference cancellation has not been adequately addressed in the literature.

This paper investigates linear precoding over nonsingular linear channels with additive white Gaussian noise, with lattice-type inputs. The aim is to maximize the minimum distance of the received lattice points, where the precoder is subject to an energy constraint. It is shown that the optimal precoder only produces a finite number of different lattices, namely perfect lattices, at the receiver. The well-known densest lattice packings are instances of perfect lattices, but are not always the solution. This is a counter-intuitive result as previous work in the area showed a tight connection between densest lattices and minimum distance. Since there are only finite many different perfect lattices, they can theoretically be enumerated offline. A new upper bound on the optimal minimum distance is derived, which significantly improves upon a previously reported bound, and is useful when actually constructing the precoders.

Massive MIMO, also known as very-large MIMO or large-scale antenna systems, is a new technique that potentially can offer large network capacities in multi-user scenarios. With a massive MIMO system, we consider the case where a base station equipped with a large number of antenna elements simultaneously serves multiple single-antenna users in the same time-frequency resource. So far, investigations are mostly based on theoretical channels with independent and identically distributed (i.i.d.) complex Gaussian coefficients, i.e., i.i.d. Rayleigh channels. Here, we investigate how massive MIMO performs in channels measured in real propagation environments. Channel measurements were performed at 2.6 GHz using a virtual uniform linear array (ULA), which has a physically large aperture, and a practical uniform cylindrical array (UCA), which is more compact in size, both having 128 antenna ports. Based on measurement data, we illustrate channel behavior of massive MIMO in three representative propagation conditions, and evaluate the corresponding performance. The investigation shows that the measured channels, for both array types, allow us to achieve performance close to that in i.i.d. Rayleigh channels. It is concluded that in real propagation environments we have characteristics that can allow for efficient use of massive MIMO, i.e., the theoretical advantages of this new technology can also be harvested in real channels.

In this paper we consider time-division-duplex (TDD) reciprocity calibration of a massive MIMO system. The calibration of a massive MIMO system can be done entirely at the base station (BS) side by sounding the BS antennas one-by-one while receiving with the other BS antennas. With an M antenna BS, this generates M(M - 1) signals that can be used for calibration purposes. In this paper we study several least-squares (LS) based estimators, differing in the number of received signals that are being used. We compare the performance of the estimators, and we conclude that is possible to accurately calibrate an entire BS antenna array using the mutual coupling between antennas as the main propagation mechanism.

This paper describes a hardware efficient linear precoder for Massive MIMO Base Stations (BSs) comprising a very large number of antennas, say, in the order of 100s, serving multiple users simultaneously. To avoid hardware demanding direct matrix inversions required for the Zero-Forcing (ZF) precoder, we use low complexity Neumann series based approximations. Furthermore, we propose a method to speed-up the convergence of the Neumann series by using tri-diagonal precondition matrices, which lowers the complexity even further. As a proof of concept a flexible VLSI architecture is presented with an implementation supporting matrix inversion of sizes up-to 16×16. In 65 nm CMOS, a throughput of 0.5M matrix inversions per sec is achieved at clock frequency of 420MHz with a 104K gate count.

The possibility of using the channel reciprocity between the uplink and downlink channels in Frequency Division Duplex (FDD) systems to improve the efficiency has been deeply investigated. Previous studies have come to different conclusions for the characterization of the dissimilarity in uplink and downlink channel properties. This paper analyzes the mismatch in directional properties of the uplink and downlink channels of FDD systems based on the power of their multipath clusters. At a system level, due to the limited directional resolution, the multipath components arriving at the base station are seen as clusters, rather than individual signal paths. This fact is used to describe the mismatch of directional properties between uplink and downlink. The contribution of this paper is the use of a spectral dissimilarity metric as a measure to characterize this mismatch; a detailed study of this dissimilarity metric is also presented. It is found that under favorable propagation conditions, for both actual channel measurement data and ray-tracing simulations, the directional and power properties of the downlink multipath clusters can be estimated from the uplink channel with high reliability. Therefore, directional-based beamforming transmission techniques for FDD systems will be able to benefit from such similarity in order to improve the system performance.

This paper deals with MIMO detection for rank 4 3GPP Long-Term-Evolution (LTE) systems. The paper revolves around a previously known detector [1], which we shall refer to as RCSMLD (Reduced-Constellation-Size-Maximum-Likelihood-Detector). However, a direct application of the scheme in [1] to LTE/LTE-A rank 4 test cases results in unsatisfactory performance. The first contribution of the paper is to introduce several modifications that can jointly be applied to the basic RCSMLD scheme which, taken together, result in excellent performance. Our second contribution is the development of a highly efficient hardware structure for RCSMLD that allows for an implementation with very few multiplications.

We consider physical layer security of massive MIMO systems in TDD mode. We show that with massive MIMO a passive eavesdropper is not very dangerous and must therefore be active and attack the training phase. An attack on the training phase is potentially very harmful to the physical layer security, and we therefore investigate three different schemes for detecting the presence of an active eavesdropper. The three schemes differ in the location where the detection is done (base station, intended user, or jointly), and also in the level of system parameters that are assumed known to the base station and/or intended user.

In this paper we investigate the highly bandwidth-efficient Faster-than-Nyquist (FTN) signaling scheme under high order modulations. The FTN system is an emerging technology which has drawn attention in the contemporary spectrum-saving communication environment. Since FTN traditionally achieves high bandwidth efficiency through increased baud-rate, binary modulation is assumed in most research of FTN. The contribution of this paper lies in the extension into high order modulations and its assessment. This enables the communication systems to achieve higher data rates for the same bandwidth and receiver complexity than binary Nyquist signaling systems. Moreover, it is shown that an additional efficiency gain can be achieved by replacing the LDPC codes from the DVB-S2 standard by new optimized quasi-cyclic (QC) LDPC codes whose parameters are matched with FTN signaling.

We consider intersymbol interference channels with reduced-complexity, mutual information optimized, channel-shortening detectors. For a given channel and receiver complexity, we optimize the transmit filter to use. The cost function we consider is the (Shannon) achievable information rate of the entire transceiver system. By functional analysis, we can establish a general form of the optimal transmit filter, which can then be optimized by standard numerical methods. As a side result, we also obtain an insight of the behaviour of the standard waterfilling algorithm for intersymbol interference channels.

Heterogeneous network (HetNet) deployment is a key feature to increase the network capacity in LTE- Advanced and systems beyond. One major obstacle is the interference from neighbor base-stations which can significantly degrade the system performance. In this paper, we present downlink interference mitigation and cancellation algorithms for HetNets in the so-called almost blank subframe (ABS) scenario. In the ABS scenario, one must differentiate between two cases, namely (1) the non- colliding case: the common reference symbols (CRS) of the serving and the dominant interfering cell are not overlapped, and (2) the colliding case: the CRS of the serving cell and the dominant interfering cell are overlapped. For case (1) we propose a robust equalizer and a low-complexity variant of it. For case (2) we present the application of the space alternating generalized expectation-maximization (SAGE) with a maximum a-posteriori (MAP) criterion. Based on extensive realistic link-level simulations, the outcome for case (1) is that the proposed robust equalization technique is almost as good as the receiver with traditional CRS interference cancellation (IC) but with lower complexity and latency. For case (2), we find that the SAGE-MAP with three SAGE cycles/iterations is sufficient to achieve the same performance as the receiver with ideal CRS-IC.

In very-large multiple-input multiple-output (MIMO) systems, the base station (BS) is equipped with very large number of antennas as compared to previously considered systems. There are various advantages of increasing the number of antennas, and some schemes require handling large matrices for joint processing (pre-coding) at the BS. The dirty paper coding (DPC) is an optimal pre-coding scheme and has a very high complexity. However, with increasing number of BS antennas, linear pre-coding performance tends to that of the optimal DPC. Although linear pre-coding is less complex than DPC, there is a need to compute pseudo inverses of large matrices. In this paper we present a low complexity approximation of down-link Zero Forcing (ZF) linear pre-coding for very-large multi-user MIMO systems. Approximation using a Neumann series expansion is opted for inversion of matrices over traditional exact computations, by making use of special properties of the matrices, thereby reducing the cost of hardware. With this approximation of linear pre-coding, we can significantly reduce the computational complexity for large enough systems, i.e., where we have enough BS antenna elements. For the investigated case of 8 users, we obtain 90% of the full ZF sum rate, with lower computational complexity, when the number of BS antennas per user is about 20 or more.

In this paper, we survey faster-than-Nyquist (FTN) signaling, an extension of ordinary linear modulation in which the usual data bearing pulses are simply sent faster, and consequently are no longer orthogonal. Far from a disadvantage, this innovation can transmit up to twice the bits as ordinary modulation at the same bit energy, spectrum, and error rate. The method is directly applicable to orthogonal frequency division multiplex (OFDM) and quadrature amplitude modulation (QAM) signaling. Performance results for a number of practical systems are presented. FTN signaling raises a number of basic issues in communication theory and practice. The Shannon capacity of the signals is considerably higher.

We consider channels affected by intersymbol interference with reduced-complexity, mutual information optimized, channel-shortening detection. For such settings, we optimize the transmit filter, taking into consideration the reduced receiver complexity constraint. As figure of merit, we consider the achievable information rate of the entire system and with functional analysis, we establish a general form of the optimal transmit filter, which can then be optimized by standard numerical methods. As a corollary to our main result, we obtain some insight of the behavior of the standard waterfilling algorithm for intersymbol interference channels. With only some minor changes, the general form we derive can be applied to multiple-input multiple-output channels with intersymbol interference. To illuminate the practical use of our results, we provide applications of our theoretical results by deriving the optimal shaping pulse of a linear modulation transmitted over a bandlimited additive white Gaussian noise channel which has possible applications in the faster-than-Nyquist/time packing technique.

Consider the communication system model y = HFx + n, where H and F are the channel and precoder matrices, x is a vector of data symbols drawn from some lattice-type constellation, such as M-QAM, n is an additive white Gaussian noise vector and y is the received vector. It is assumed that both the transmitter and the receiver have perfect knowledge of the channel matrix H and that the transmitted signal Fx is subject to an average energy constraint. The columns of the matrix HF can be viewed as the basis vectors that span a lattice, and we are interested in the precoder F that maximizes the minimum distance of this lattice. This particular problem remains open within the theory of lattices and the communication theory. This paper provides the complete solution for any nonsingular M × 2 channel matrix H. For real-valued matrices and vectors, the solution is that HF spans the hexagonal lattice. For complex-valued matrices and vectors, the solution is that HF, when viewed in four-dimensional real-valued space, spans the Schlafli lattice D4.

In this paper, we present a novel approach for the design of rate-maximizing channel shortening detectors with soft feedback side information for frequency-selective channels. The detector is a soft-input soft-output detector and constitutes one of the components of an iterative receiver. The design optimization is performed from an information-theoretic perspective where we maximize the achievable rate during each step of the iterative process. Our proposed detector consists of a front-end filter whose coefficients are given in closed form in addition to a convex optimization procedure which provides the branch labels of the trellis and the feedback filter coefficients. The detector can be implemented as a BCJR-type algorithm operating on a trellis where the number of states is a user-defined parameter.

We consider the effect of signaling rate (baud rate) on the information rate of single carrier linear transmission systems with Gaussian inputs. Several different communication scenarios are investigated: correlated or uncorrelated symbols, a fixed modulation pulse or a modulation pulse varying with the signaling rate and frequency selective or flat channels. For uncorrelated symbols, we show that the information rate grows monotonically with signaling rate for some cases while it can in fact decrease in other cases. Sufficient conditions on the modulation pulse and the channel impulse response are derived so that the information rate is increasing with increased signaling rate. Especially, these conditions give criterias for when non-orthogonal signaling is beneficial compared to orthogonal signaling in the case of flat fading. For modulation pulses varying with the signaling rate, it is shown that there are pulses for which the information rate is non-decreasing with increasing signaling rate. When correlation between symbols is allowed, we show that one can guarantee increasing information rate with increased signaling rate, no matter the pulse-channel shape (except for some hypothetical special cases), by signaling with an SNR above a certain finite threshold.

We perform a minimum distance analysis of a class of two-dimensional intersymbol interference (ISI) channels applicable to multitrack magnetic recording and orthogonal frequency division multiplex transmission systems. Exact minimum distance for a wide class of ISI responses is derived. The fundamental analytical technique is to transform the channel into an equivalent minimum phase channel. The results improve upon the prior work of Soljanin and Georghiades.

We consider the problem of bounding the information rate of intersymbol interference channels via simulation-based algorithms. The adopted approach, which is based on a general class of reduced-complexity receivers that includes several previously studied receivers as special cases, leads to provable upper and lower bounds on the information rate of interest. As a by-product of the information-theoretic investigations, novel insights on the design of efficient reduced-complexity receivers are also provided, since the proposed lower bounds are known to be achievable by practical receivers. In many scenarios, our novel approach significantly outperforms the existing ones, for all practical values of the signal-to-noise ratio.

We present a method to compute, quickly and efficiently, the mutual information achieved by an independent identically distributed (IID) complex Gaussian signal on a block Rayleigh-faded channel without side information at the receiver. The method accommodates both scalar and multiple-input multiple-output (MIMO) settings. Operationally, this mutual information represents the highest spectral efficiency that can be attained using Gaussian codebooks. Examples are provided that illustrate the loss in spectral efficiency caused by fast fading and how that loss is amplified when multiple transmit antennas are used. These examples are further enriched by comparisons with the channel capacity under perfect channel-state information at the receiver, and with the spectral efficiency attained by pilot-based transmission.

In this paper, a number of channel estimation algorithms for iterative receivers are compared for the case of an up-link orthogonal frequency division multiplexing interleave division multiple access (OFDM-IDMA) system. Both pilot based algorithms, used to obtain an initial estimate, as well as semi-blind decision-directed algorithms working as a component of the iterative receiver are considered. Algorithms performing either joint minimum mean square error (MMSE) channel estimation, or iterative estimation using space-alternating expectation maximization (SAGE), are evaluated. The considered algorithms differ in terms of complexity, as well as performance. The main contribution of this paper is to give an overview of different channel estimation approaches for OFDM-IDMA, where the complexity versus performance tradeoff is at the focal point. There is no single channel estimator providing the best tradeoff and our analysis shows how the system load (number of users) and the SNR influence the estimator choice.

Consider receivers that do not exploit any knowledge of the channel distribution in non-coherent block-fading multiple-input multiple-output (MIMO) channels. The main contribution of this letter is to derive a semi-analytical semi-numerical lower bound to the achieveble rate of such receivers. The bound is of operational meaning since practical receivers can achieve the lower bound. Several numerical examples with Gaussian block fading channels, which illuminate that the lack of channel distribution at the receiver imposes a significant penalty if the coherence time (counted in symbol times) is not much larger than the number of transmit antennas, are provided.

We deal with the construction of optimal channel shortening, also known as combined linear Viterbi detection, algorithms for ISI and MIMO channels. In the case of MIMO channel shortening, the tree structure to represent MIMO signals is replaced by a trellis. The optimization is performed from an information theoretical perspective and the achievable information rates of the shortened models are derived and optimized. Closed form expressions for all components of the optimal detector of the class are derived. Furthermore, we show that previously published channel shortening algorithms can be seen as special cases of the derived model.

Consider the communication model ȳ = HF x̄ + n̄, where H; F are real-valued matrices, x̄ is a data vector drawn from some real-valued lattice (e.g. M-PAM), n̄ is additive white Gaussian noise and ȳ is the received vector. It is assumed that the transmitter and the receiver have perfect knowledge of the channel matrix H (perfect CSI) and that the transmitted signal F x̄ is subject to an average energy constraint. The columns of the matrix HF can be viewed as basis vectors that span a lattice, and we are interested in the minimum distance of this lattice. More precisely, for a given H, which F under an average energy constraint will maximize the minimum distance of the lattice HF? This particular question remains open within the theory of lattices. This work provides the solution for 2×2 matrices H; F. The answer is an F such that HF is a hexagonal lattice.

Wireless communication using very-large multiple-input multiple-output (MIMO) antennas is a new research field, where base stations are equipped with a very large number of antennas as compared to previously considered systems. In theory, as the number of antennas increases, propagation properties that were random before start to become deterministic. Theoretical investigations with independent identically distributed (i.i.d.) complex Gaussian (Rayleigh fading) channels and unlimited number of antennas have been done, but in practice we need to know what benefits we can get from very large, but limited, number of antenna elements in realistic propagation environments. In this study we evaluate properties of measured residential-area channels, where the base station is equipped with 128 antenna ports. An important property to consider is the orthogonality between channels to different users, since this property tells us how advanced multi-user MIMO (MU-MIMO) pre-coding schemes we need in the downlink. We show that orthogonality improves with increasing number of antennas, but for two single-antenna users there is very little improvement beyond 20 antennas. We also evaluate sum-rate performance for two linear pre-coding schemes, zero-forcing (ZF) and minimum mean squared error (MMSE), as a function of the number of base station antennas. Already at 20 base station antennas these linear pre-coding schemes reach 98% of the optimal dirty-paper coding (DPC) capacity for the measured channels.

Consider the transmission of complex-valued symbols over $N$ parallell channels in additive white Gaussian noise. It is well known that linear precoding of the complex-valued data improves system performance (e.g. symbol error rate, information rate, MMSE, etc.) at a cost of increased decoding complexity at the receiver. This work constructs precoders that are constrained to have a decoding complexity which equals that of no precoding, while still improving the system performance significantly compared with the no precoding case. This is achieved by designing the precoder so that it precodes the complex data streams separately, by utilizing the latest result from optimal real-valued precoding, and transmitting the real and complex parts of one symbol over different antennas.

This work studies the design of linear precoder codebooks for NxM MIMO channels with MMSE detection at the receiver. A natural split of precoder-design is unitary precoding and non-unitary precoding. Unitary precoding is only performing rotation of the data in a way beneficial for the channel. Non-unitary precoding additionally also uses power-loading to further improve the performance. Somewhat surprisingly, unitary precoding facilitates a performance boosting by a re-enumeration of the antenna elements at the receiver side that can not be accomodated in the non-unitary precoding setting. This operation leads to substantial performance gains. The question investigated in this paper is whether this re-enumeration can compensate for the lack of power-loading. The outcome is that for small precoder codebooks, unitary precoding performs as good as non-unitary, while for larger codebooks non-unitary precoding outperforms unitary precoding.

An iterative decoder for time-frequency compressed multicarrier system is presented in this paper. The inner detector consists of a sub-optimal maximum a-posteriori symbol-by-symbol decoding algorithm with a successive interference cancellation (SIC) scheme. The complexity of the inner detector is not more complex than the corresponding detector for a memoryless modulation scheme. The inner decoder together with a standard BCJR forms the iterative decoding loop. The SIC scheme is used to eliminate the intentional interference caused by symbols stacked beyond their orthogonality limit. As compared to prior work, the iterative decoder has been adapted to make the FTN technique feasible for hardware implementation. The results show that such modifications does not affect the performance of the receiver. The receiver has been evaluated under various other FTN system parameters to determine the performance.

Next generation wireless systems have to be able to efficiently deal with fast fading environments in order to achieve high spectral efficiency. Using multiple-input multiple-output (MIMO) systems and exploiting receive diversity, the spectral efficiency can be greatly increased. Commonly, the channel is estimated via training symbols, before data detection is carried out based on the obtained channel estimate. While this significantly simplifies the process of data detection, it leads in general to suboptimal results. A better approach is to carry out joint channel estimation and data detection; we turn our attention to joint maximum-likelihood (ML) detection which is the optimal strategy. In this paper, the BEAST - Bidirectional Efficient Algorithm for Searching code Trees - is proposed as an alternative algorithm for joint ML channel estimation and data detection and its complexity is compared with recently published algorithms in the literature.

We consider the problem of constructing linear precoders for quasi-stationary multiple-input multiple-output channels. Maximum-likelihood detection is assumed and the objective of the precoding is to maximize the minimum Euclidean distance of the signaling. Since the channel remains constant for some time, the precoding is performed spatially as well as across time. As will be shown, the precoder design is tightly connected to the theory of partial response signaling and precoders can be designed by usage of existing methods. The decoding complexity will be controlled and can be maintained small.

In this paper we propose a novel trellis based soft-input soft-output MIMO detector with significantly reduced search space. The performance of the detector is measured by evaluating the ultimate communication rate that is achievable for a system employing the novel detector; this limit corresponds to a mutual information that can be determined by standard methods. We also derive an expression that bounds the mutual information of interest and that can be optimized by numerical methods. Numerical results for many MIMO setups that illustrate the performance of the detector are also provided.

We present a method to compute, quickly and efficiently, the mutual information achieved by an IID (independent identically distributed) complex Gaussian input on a block Rayleigh-faded channel without side information at the receiver. The method accommodates both scalar and MIMO (multiple-input multiple-output) settings. Operationally, the mutual information thus computed represents the highest spectral efficiency that can be attained using standard Gaussian codebooks. Examples are provided that illustrate the loss in spectral efficiency caused by fast fading and how that loss is amplified by the use of multiple transmit antennas. These examples are further enriched by comparisons with the channel capacity under perfect channel-state information at the receiver, and with the spectral efficiency attained by pilot-based transmission.

In this paper we evaluate, by means of Extrinsic Information Transfer (EXIT) charts, an iterative receiver that has emerged as a promising candidate for non-coherent multi-user multi-antenna OFDM systems. The receiver performs parallel interference cancellation (followed by linear filtering) and channel estimation, using soft symbols obtained from a bank of single-user decoders. For the sake of conceptual clarity we study a system with two single antenna users and a receiver with two antennas, and we demonstrate how the convergence behavior of the receiver can be visualized using paired three dimensional EXIT surfaces. Our results show that the actual decoder trajectories obtained through simulations are well predicted from the EXIT charts. For the iterative receiver under investigation we identify a very specific problem with EXIT chart generation; the EXIT curve for the inner component decoder depends on the outer encoder. To handle this problem we propose a modification to the iterative receiver which solves the aforementioned problem; the performance degradation is demonstrated to be small.

This paper presents the complexity analysis of a transmitter architecture for a faster-than-Nyquist (FTN) system. Complexity issues in terms of computations and memory requirements to achieve an FTN system are dealt with. An OFDM based multi-carrier system is considered as it is one of the most widely used in upcoming wireless standards. Retaining the modules within the OFDM transmitter helps in exploiting the already optimized and hardware efficient structures, the IFFT being one. From an implementation perspective the introduction of FTN introduces negligible overhead for the transmitter.

A critical component in detection under intersymbol interference (ISI) and in turbo equalization is the BCJR algorithm. We combine three approaches to reducing its computation. First, energy seen by the receiver is focused by a phase-maximizing all pass filter; an improvement on this older idea is proposed. Then the state used by the BCJR is broken into an offset state and a main state. Finally, some reduced-state BCJR procedures are evaluated. These receivers are tested by ISI detection and turbo equalization over strongly bandlimited channels.

We consider the problem of lower bounding the information rate of intersymbol interference channels via Monte Carlo algorithms. We adopt a novel approach based on the Ungerboeck observation model, unlike the existing ones that are all based on the Forney model. The two approaches, yet equivalent in the case of full-complexity detection, lead to different results in the case of reduced-complexity detection, which is the only viable option when the channel memory is large. The proposed approach significantly outperforms the existing ones for all practical values of the signal-to-noise ratio.

In this work we study the problem of constructing precoders for spatially multiplexed multiple-input multiple output (MIMO) channels with close to optimal minimum Euclidean distance. In order to exploit the full potential of such designs, an ML detector must be used. Our design takes the decoding complexity into account and constrains it to a reasonable level. For our simplest case, the ML detector can be implemented by a Viterbi algorithm operating on a state space of size equal to the size of the modulation alphabet. The design problem will be relaxed by using precoders F such that F*H*HF is a cyclic Toeplitz matrix. Within this class of precoders, the optimal precoder can be found via linear programming. Of uttermost practical importance is the discovery that there only exist very few different effective channels HF even for large MIMO setups; thus, the optimization at the transmitter side reduces into choosing the best precoder from a small list. Receiver tests verify that our method improves upon the currently best precoder designs.

We extend Mazo's concept of faster-than-Nyquist (FTN) signaling to pulse trains that modulate a bank of subcarriers, a method called two dimensional FTN signaling. The signal processing is similar to orthogonal frequency division multiplex(OFDM) transmission but the subchannels are not orthogonal. Despite nonorthogonal pulses and subcarriers, the method achieves the isolated-pulse error performance; it does so in as little as half the bandwidth of ordinary OFDM. Euclidean distance properties are investigated for schemes based on several basic pulses. The best have Gaussian shape. An efficient distance calculation is given. Concatenations of ordinary codes and FTN are introduced. The combination achieves the outer code gain in as little as half the bandwidth. Receivers must work in two dimensions, and several iterative designs are proposed for FTN with outer convolutional coding.

This paper deals with capacity computations of faster-than-Nyquist (FTN) signaling. It shows that the capacity of FTN is higher than the orthogonal pulse linear modulation capacity for all pulse shapes except the sinc. FTN signals can in fact achieve the ultimate capacity for the signal power spectral density (PSD). The paper lower- and upper-bounds the FTN capacity under the constraint of finite input alphabet. It is often higher than the capacity for comparable orthogonal pulse systems; sometimes it is superior to all forms of orthogonal signaling with the same PSD.

Mazo, in 1975, showed that the signaling rate of a linear modulation can be significantly higher than the maximum rate for orthogonal signaling without any loss of minimum square Euclidean distance. In subsequent literature the highest such rate is referred to as the Mazo-limit. In this letter we ask whether there exists a Mazo-limit also on MIMO channels. The answer is yes, but it applies to the largest pairwise error probability rather than to minimum square Euclidean distance. Moreover, it occurs at exactly the same rate as in the AWGN case. As a special case results for single-input single-output fading channels are obtained.

Faster-than-Nyquist (FTN) signaling is a trellis coding method that maintains the error rate while reducing signal bandwidth. The combined effect is to move closer to capacity. We study some basic receiver issues: How to model the signaling efficiently in discrete time, how much the Viterbi receiver can be truncated, and how to combine the method with an outer code. The methods are modeling for minimum phase, minimum distance calculation and receiver tests. Concatenated FTN in a turbo equalization scenario proves to be a strong coding method.

In this paper we perform a minimum distance analysis of a class of two dimensional intersymbol interference channels. In particular, some important cases of multitrack multihead magnetic recording systems fall into the studied class. Previously, Soljanin and Georghiades have studied the same problem as we do. The results derived in this paper are more conclusive and they improve upon theirs. The fundamental proof technique that we will use is to transform the channel into an equivalent minimum phase channel.

We consider the effect of symbol rate on the constrained capacity of linear modulation with a fixed spectral density. We show that constrained capacity grows with the symbol rate for some modulation pulses but shrinks with others. Sufficient conditions on the pulse are derived for the constrained capacity to be monotonically increasing with faster symbol rate. Most standard pulses fulfill these.

Faster than Nyquist (FTN) signaling is an important method of narrowband coding. The concept is extended here to non binary signal constellations; these are much more bandwidth efficient than binary ones. A powerful method of finding the minimum distance for binary and non binary FTN is presented. Preceding FTN transmissions with short linear filters proves to be an effective way to gain distance. A Shannon limit to bit error rate is derived that applies for FTN. Tests of an M-algorithm receiver are performed and compared to this limit.

This paper investigates the performance of reduced- state trellis-based ISI equalizers, which are based on the so- called Ungerboeck and Forney observation models. Although the two models are equivalent when the Viterbi or BCJR equalizer is employed, their performances differ significantly when using reduced-complexity methods. It is demonstrated that practical equalizers operating on the Forney model outperform those operating on the Ungerboeck model for high signal-to-noise ratios (SNRs), while the situation is reversed for low SNR levels. A novel theoretical reduced-complexity equalization strategy that improves on previous Ungerboeck-based equalizers is proposed.

In this paper we investigate partial response signaling (PRS) systems that are intended to operate close to capacity. We show that finding PRS systems with maximal capacity is a rather easy optimization task. We give an alternate way of defining bandwidth for PRS systems based on capacity considerations; this differs considerably from the traditional method based on transmission power. Practical PRS schemes are derived, based on these ideas. Their bit error rate is significantly better than earlier, distance-optimizing schemes.

We minimize the frequency and time occupancy of multicarrier binary linear modulation based on two-dimensional faster than Nyquist (FTN) signaling. FTN analysis provides the asymptotic time-frequency consumption per bit and prolate spheroidal wave analysis minimizes the side lobe occupancy. For both problems, an excellent choice is a Gaussian pulse, with some adjustment of the side lobes.

In this paper we consider the least time-frequency product necessary to transmit a small finite symbol packet such that the symbols can be independently detected. The system model assumed is offset QAM-OFDM, based on a finite duration pulse shape. The outcome is that the optimal pulse shape is of very short duration and that the optimal symbol allocation strategy is often to use as many subcarriers as there are symbols to transmit. Symbol packets up to 150 symbols are considered.

In this paper we investigate MIMO systems where faster-than-Nyquist (FTN) signaling is used as modulation. On the AWGN channel, the main characteristic of FTN is the so called Mazo limit; it is possible to signal considerably faster than conventional without loss in minimum Euclidean distance. We show that MIMO-FTN systems inherit this property from the AWGN-FTN systems. Moreover, not only does it exist a Mazo limit in MIMO, but it occurs at exactly the same signaling rate as for the AWGN channel. We also discuss information rates of MIMO-FTN systems.

In this paper we consider the information rates of faster than Nyquist (FTN) signaling schemes. We consider binary, quaternary and octal schemes that use root raised cosine pulses. Lower and upper bounds to the information rates are given. The main result is that the lower bounds are often above the information rates for standard Nyquist signaling schemes. This implies that FTN must be superior to Nyquist signaling in some cases. Test results for one coding scheme are given; these show that high throughput communication based on FTN is indeed practical.

We investigate the performance of concatenated coding schemes based on faster than Nyquist (FTN) signaling over the AWGN channel. We test both serial and parallel concatenations. In serial concatenation the FTN signaling is considered as the inner encoder and the outer code is a rate b/c convolutional code. In parallel schemes we use two parallel Gaussian channels and transmit FTN pulse trains in both; here a precoding device turns out to be crucial. The convergence behaviour is analysed using EXIT charts. The overall spectral density of the schemes varies but is roughly 1-2 bit/s/Hz. The results, in terms of needed Eb/N0for reliable communication versus spectral density, are very good

In earlier work we have extended Mazo's concept of faster-than-Nyquist signaling to pulse trains that modulate adjacent subcarriers, a method we called two dimensional Mazo signaling. The signal processing is similar to orthogonal frequency division multiplex (OFDM) transmission. Despite pulses that are faster than the Nyquist limit and subcarriers that significantly overlap, the transmission achieves the isolated pulse error performance. In this paper we review the method and test a receiver based on successive interference cancellation. It virtually achieves the matched filter bound.

The decision depth L/sub d/ for finite and infinite partial response signaling (PRS) schemes is investigated. New measures are proposed that take into account error event multiplicity. We conclude that small to moderate decoder decision depths achieve performance near MLSE even for near catastrophic codes. Under some constraints, the decision depth should be an increasing function of the signal to noise ratio.

Faster than Nyquist (FTN) signaling is extended. We send FTN pulse trains that overlap in both time and frequency; this is called two dimensional Mazo signaling. The minimum time and frequency separation that achieves dmin2= 2 for root raised cosine pulses is found. Two dimensional signaling is more bandwidth efficient than one dimensional. A simple decoder is tested and it verifies the distance results

Optimal finite partial response signals based on 2 and 4 PAM were found by Said and Anderson. The encoder is a simple discrete-time filter, whose combination of bandwidth and Euclidian distance is optimized. Here we extend the idea to the case when the modulated symbols are first encoded by a convolutional encoder. Good narrowband codes are the result.