We examine how the structural characteristics of entangled quantum states impact the achievable rates in entanglement-based quantum key distribution (QKD). Focusing on the performance differences between entangled states produced by entanglement distillation protocols and Werner states, we show that the structured nature of distilled states can yield significantly higher secure key rates, even when their fidelity matches that of Werner states. This suggests that while converting arbitrary entangled states into Werner states (through twirling) simplifies the analysis of protocol performance, it also limits potential secret key rates. Our findings underscore the potential of entanglement distillation protocols to enhance QKD performance by additionally improving the structure of entangled states, thus, broadening their utility beyond simple fidelity enhancement.

Quantum repeaters are a key component for the deployment of quantum communication networks. While the implementation of such repeaters is still ongoing research, some of its core components like, e.g., entanglement distillation and swapping, have been already well investigated. In this paper, we study the relevance of quantum repeaters for erroneous but lossless quantum channels. To do so, we assume a depolarization channel in an otherwise ideal scenario and compare the distribution rate, i.e., one over the number of entangled quantum states which are required to achieve a certain target fidelity, of a network with a repeater to one with a direct link only. We simulate regions of channel parameters for which a quantum repeater is beneficial or not. Moreover, we derive analytical bounds for these regions which can be used for efficient quantum network planning as well as for the design of quantum routing protocols.

Energy efficiency is a key requirement for meshed networks which demand a high battery life and low maintenance costs. A state-of-the-art method to decrease power consumption is the sleep mode technique. However, to fully exploit the benefits of this method, it is important that the sleep phases of all network nodes are synchronized. Synchronizing these phases via coexisting systems like, e.g., a GPS or LTE signal, would require additional hardware which contradicts the goal of an energy efficient and low-cost system.This paper introduces the sleeping firefly synchronization algorithm, i.e., a novel self-organized synchronization method which is based on pulse-coupled oscillators to synchronize the sleep phases of a meshed network where not all nodes have a direct connection to a master node. The algorithm not only synchronizes the network but also adapts the sleep phases in an autonomous manner, i.e., each node decides about phase changes and on the duration of a sleep phase by itself. Numerical results show that meshed networks synchronize mostly in a few cycles and that huge energy savings are possible in the synchronization phase when applying the proposed algorithm.

This paper addresses the assignment of transmission and sleep time slots between interfering transmitters with the objective of minimal power consumption. In particular, we address the constructive alignment of Discontinuous Transmission (DTX) time slots under link rate constraints. Due to the complexity of the combinatorial optimization problem at hand, we resort to heuristic assignment strategies. We derive four time slot alignment solutions (sequential alignment, random alignment, p-persistent ranking and DTX alignment with memory) and identify trade-offs. One of the proposed solutions, namely, DTX alignment with memory addresses identified issues of the other three solutions by maintaining memory of past alignment and channel quality to buffer short term changes in channel quality. All strategies are found to exhibit similar convergence behavior, but different power consumption and retransmission probabilities. DTX alignment with memory is shown to achieve up to 40% savings in power consumption and more than 20% lower retransmission probability than the State-Of-The-Art (SotA).

For MIMO interference networks, uncertainty in the spatial structure of interfering signals is a major source of performance degradation. In this work, we promote the use of linear unitary precoding, as it can be designed such that downlink transmission becomes more robust. Optimizing linear unitary precoding is a combinatorial and nonconvex problem, thus no efficient methods to compute global optimal solutions are available. Therefore, methods with reasonable complexity and acceptable performance are desired and have been investigated in research literature as well as for practical implementation. Contrary to existing work on unitary precoding, which considers receivers with a single antenna, we target scenarios with multiple receive antennas. We introduce and discuss a low-complexity method for successive user and precoder selection to enable unitary precoding for multi-antenna receivers. In addition to interference robustness, our novel method has several advantages for potential implementations, concerning the channel feedback and computation of optimal receive filters. Initial results by numerical simulations indicate that our approach has the potential to outperform existing methods.

This paper investigates multiple input multiple output (MIMO) transmission techniques based on realistic assumptions on feedback of channel state information. We consider three conventional techniques as the baseline: 3GPP long-term evolution (LTE) single user MIMO (SU-MIMO) based on implicit channel feedback, zero-forcing multiuser MIMO (ZF MU-MIMO) based on explicit channel feedback, and ZF MU-MIMO based on implicit channel feedback. SU-MIMO may not be able to exploit the full spatial dimension of the downlink MIMO channel. ZF MU-MIMO has the potential to improve the spectral efficiency, but the explicit channel feedback is not compatible with implicit feedback whereas implicit based ZF MU-MIMO is limited by performance and also the commonly assumed rank restriction makes it impossible to perform dynamic switching of SU/MU MIMO transmission. We propose a new hybrid scheme which enables such dynamic switching of SU/MU MIMO transmission by allowing UE to feed back the implicit channel information without any rank restriction. Computer simulation results show the benefits of the new hybrid scheme, which can properly switch to the better transmission mode in various correlation scenarios.

One major goal for future wireless communication systems is a uniform user experience. In order to solve this problem, additional relay nodes can be used to support the communication. Up to now mainly two relaying functions are considered, namely Amplify-Forward (AF) and Decode-Forward (DF). DF can either mean a channel decoding at the relay or a hard decision directly on the received signal which will be called DetF here to avoid confusion. But both have certain drawbacks: AF suffers from noise amplification whereas with DetF useful information is lost due to the hard decision. For this purpose a relay function minimizing the mean squared error called Estimate-Forward (EF) has been proposed in the literature combining the benefits of AF and DetF. If more than one relay is considered or if the signal received directly from the source contains useful information, these signals should be combined properly. In the case of nonlinear functions at the relay like for DetF or EF, the disturbance of the signal received from the relay is not Gaussian any more and simple weighted linear combining like Maximum Ratio Combining for Gaussian channels is suboptimal. In this paper we will derive a Maximum Likelihood detector for EF with higher order modulation schemes. This receiver results in significant gains in terms of bit error rate and mutual information and therefore leads to a higher user throughput compared to state-of-the-art techniques. Moreover, these gains are obtained without increasing the computational complexity of the terminals significantly.

The orthogonal multiple-access relay channel with two sources is considered. The goal of this paper is to show the applicability and effectiveness of a previously introduced quantize-and-forward scheme to a more realistic channel and system model, including orthogonal frequency division multiple access and multipath fading channels. Simulation results are provided to demonstrate the gain of quantize-and-forward relayed communication as opposed to the point-to-point links without the relay.

We consider coordination of transmission strategies in interference networks, where multiple antennas at the transmitters can be used to adjust the spatial signature of the transmitted signal. For single antenna receivers the interference power received can be constraint by so-called interference temperatures, which can be used to coordinate the amount of interference in the network. We recapitulate recent research results on this topic and discuss methods to select interference temperatures that lead to performance gains compared to uncoordinated transmission. A special configuration is to demand interference to be completely eliminated, so-called zero-forcing. Methods based on zero-forcing allow for simple computation of the transmit strategies, while for general temperatures iterative algorithms are required. Strictly enforcing completely orthogonalized transmission drastically reduces the number of active users in the network and is therefore too restrictive for larger networks. We suggest an efficient algorithm that enforces orthogonal transmission only in part, which leads to an increased number of users and significant performance gains, while maintaining the low complex computation of the transmit strategies. The method is based on successive user allocation, that avoids an exhaustive search for the active user set and the user transmitter pairs for which interference should be eliminated.

An interference management method for coordinating downlink transmission in a Multiple-Input Multiple-Output (MIMO) cellular network is proposed. The problem is to efficiently manage inter-cell interference in a multi-cell environment, by so-called transmitter cooperation, in order to reduce the diminishing effects of interference on the networks performance. To allow for application in deployable networks, an utmost concern of the presented algorithm is to provide a low-complexity solution avoiding costly combinatorial or non-convex optimization problems. The problem is solved by a network wide successive allocation of data streams and choosing linear transmit and receive filters for each data stream, such that interference is completely avoided. By embedding our new algorithm in a more general framework for interference coordination, we can show relevant gains for network performance where especially the cell-edge users profit.

The major problem of multiuser MIMO precoding and scheduling is the required Channel State Information (CSI) at the base station which needs to be provided to the base station via a feedback channel in case of frequency division duplex. Each user quantizes the channel direction information and computes a Channel Quality Indicator (CQI), e.g., based on the Signal-to-Interference-and-Noise Ratio (SINR), both fed back as CSI to the base station. Since the precoder is not known when the feedback information is computed, the SINR needs to be approximated where the quality of the approximation depends strongly on the number of finally scheduled data streams. In this paper, we propose limited feedback schemes which improve the performance of the scheduler by exploiting this dependency and adapting the feedback information accordingly. Three types of feedback schemes are presented: first, feeding back more than one approximation such that the base station can choose the more accurate one depending on the number of finally scheduled data streams, second, a time multiplexing of these approximations in order to decrease the feedback overhead, and third, feeding back the channel magnitude and estimating the approximations via additional statistical measures. Simulation results show that compared to state-of-the-art techniques, the proposed feedback schemes perform well for a wide range of correlation scenarios.

Inter-cell interference diminishes the performance of wireless cellular networks, hence interference management by cooperation of basestations should be employed to combat interference and increase spectral efficiency. Contrary to full cooperation, which renders the network into a super-cell with distributed antennas, we investigate a form of weak cooperation: transmission strategies among the basestations are coordinated, which requires a minor overhead, while the users treat interference of other cells as noise. Although our results are not restricted to reuse partitioning, we assume a set of strategies, each corresponding to a different reuse factor, and assign orthogonal resources to each strategy. Basestation cooperation is realized by dynamically adjusting the resource allocation, so-called fractional reuse partitioning, while the capacity achieving single-cell strategies are employed in each cell in order to optimally manage intra-cell interference exploiting all degrees of freedom offered by multiple antennas at the transmitter and receiver. Efficient operation of a cellular communications network requires interference management in order to achieve high data rates including rate assignment matched to the user demands, which we formulate as network utility maximization problem. We put special emphasis on the popular utilities sum-rate and proportional fairness, either with or without additional quality of service constraints. Finally, we illustrate the performance gain of our method by providing system level simulation results for a three sectorized cellular network with nineteen sites.

Solving Quality of Service constrained optimization problems in the Multiple-Input Multiple-Output (MIMO) broadcast channel usually requires the iterative solution of a weighted sum rate maximization, which exhibits a considerable amount of numerical complexity itself, especially in Orthogonal Frequency Multiplexing (OFDM) systems. In this paper a low complexity framework for these problems is presented, where the allocation of data streams to users and carriers is done successively. An efficient rule for choosing the user and carrier to be allocated in each step is presented for both linear and non-linear precoding leading to small performance losses compared to the optimum.

We investigate enhanced downlink multiuser multiple input multiple output (MU-MIMO) transmission schemes for 3GPP LTE-Advanced based on system level simulations. As compared to Rel. 8 LTE single user MIMO (SU-MIMO), MU-MIMO has the potential to better exploit the spatial dimension of MIMO channels in some scenarios. Although Rel. 8 LTE defines a simple MU-MIMO mode, more advanced MU-MIMO techniques are currently discussed towards Rel. 10 LTE-Advanced to further improve the spectral efficiency. In this paper, we focus on zero-forcing (ZF) MU-MIMO precoding with an explicit channel quantization mechanism called channel vector quantization (CVQ). Moreover, we consider two different criteria of CVQ at the receiver: either minimizing Euclidean distance or maximizing the signal to interference plus noise power ratio (SINR). A number of system level simulations reveal significant potential gains of ZF MU-MIMO as compared to those of Rel. 8 LTE SU/MU-MIMO in terms of both cell throughput and cell-edge user throughput when the spatial correlations at the base station (eNB) are relatively high. The potential gain of ZF MU-MIMO is shown to be further improved when the CVQ is based on the SINR maximization criterion instead of Euclidean distance minimization.

For downlink transmission in a multiuser multiple-input multiple-output (MIMO) communication system, quantized Channel State Information (CSI) is fed back to the base station in an uplink channel of finite rate. The quantized CSI is obtained via Channel Vector Quantization (CVQ) of the so-called composite channel vector, i.e., the product of the channel matrix and an estimation of the receive filter, which cannot be computed exactly at the stage of quantization because of its dependency on the finally chosen precoder. Here, the state-of-the-art approach estimates the receive filter and quantize the composite channel vector such that its Euclidean distance to the estimated composite channel vector is minimized. In this paper, we propose an alternative CVQ method which determines the estimated receive filter vector and the quantized composite channel vector such that the resulting Signal-to-Interference-and-Noise Ratio (SINR), or an approximation thereof, is maximized. Since the SINR is related to the individual user rates, and therefore related to the sum rate of the system, the presented solution aims at maximizing the system sum rate. Simulation results of a multiuser MIMO system with linear zero-forcing preceding show that the proposed schemes achieve significant performance improvements compared to the state-of-the-art method, especially in the low signal-to-noise ratio region.

Achieving the capacity region in the MIMO broadcast channel requires the use of dirty paper coding (DPC). When it cannot be afforded to satisfy the requirements of all users by DPC based approaches, it is necessary to identify the users which exhibit the highest performance gain compared to simpler approaches. In this paper we present a user grouping method that aims to identify those users with highest weighted sum rate gain. First some users are excluded by a simple criterion leading to a reduced user set, from which the final user group is selected by a more sophisticated criterion.

A random non-line-of-sight environment with stationary transmitter and receiver is considered. In such an environment movement of a scatterer will lead to perturbations of the otherwise static channel with a resulting Doppler spectrum. This is quite a general situation in outdoor environments with moving traffic or indoor situations with moving people. Here we study the latter situation in detail with experimental results from a large office environment. A general theory of Doppler spectra is developed. The impact of a scatterer depends on the angular distribution of scattered energy, and uniform as well as sharply peaked distributions are considered in the theory. The Doppler spectra are in all cases sharply peaked at zero frequency due to forward scattering, but the actually measured distribution depends on the degree and type of activity in the environment, as well as the spectrum estimation accuracy.

Finding the matrix with the maximum singular value amongst a set of matrices is a common problem occurring in transmit signal processing algorithms for multiuser multiple-input multiple-output (MIMO) systems. However, computing the principal singular value of a matrix is a rather numerically complex task. Furthermore, in many practical scenarios, the number of users is large and for each user this task has to be conducted. In this paper we therefore propose a novel user preselection method which reduces the computational complexity at no performance loss. This is achieved by deselecting some users based on a simple criterion and thus avoiding explicit computations of the singular values of those users. This criterion is based on easily computable bounds for the principal singular values. Finally, a statistical analysis is provided and the application to the Successive Encoding Successive Allocation Method (SESAM) is shown.

The downlink of amultiusermultiple-inputmultiple-outputsystem is considered. Compared to nonlinear precoding strategies which are designed to achieve the channel capacity in case of perfectchannelstateinformation(CSI) at the transmitter, we focus on systems which are restricted to use only linear precoders due to complexity constraints and where only partial CSI is available at the transmitter due to limited feedback. Here, we compare two different feedback approaches: in the first, users feed back the best entry of a precoder codebook, and in the second, users provide quantized channel information based on a channel codebook. The presented transmitters exploit the available feedback information to select the users for transmission (scheduling) and to compute the corresponding precoder. Sum rate investigations show that channel codebook based feedback should be preferred in systems with a very low feedback rate.

Interleave division multiple access (IDMA) recently attracted many research activities because of its excellent performance despite its reasonable low complexity. The low complexity is usually realized by the multiuser detector that applies an approximation similar to the rake receiver for CDMA systems. So far, this type of detector has been most frequently considered in IDMA literature. In this paper we investigate the performance of IDMA based on linearminimummeansquareerror(MMSE) detection. The MMSE detector is more complex than the rake-like approximation. At the price of the complexity, however, it is shown that the MMSE detector brings several advantages over the rake-like approach such as the superior performance on channels with spectrally poor characteristics, effective iterative processing for lower SNR values, faster convergence and therefore shorter decoding delays, and better performance for short block length. We also confirm that the complexity can be drastically reduced by the low rank approximation of the MMSE filter by its multistage representation without compromising on the performance.

In this paper, we present two extensions of the block conjugate gradient (BCG) algorithm, a method which exploits the concept of block Krylov subspaces. First, we extend the BCG algorithm such that it is more flexible concerning the dimension of the block Krylov subspace. Second, a computationally efficient preconditioned BCG (PBCG) algorithm is introduced which turns out to outperform the standard BCG algorithm concerning the complexity-performance ratio. Hence, we provide a powerful implementation for reduced-rank signal processing in the minimum mean square error (MMSE) sense. Simulation results show the gain in rank-flexibility and convergence speed

We derive a hybrid of beam-forming (BF) and space-time block coding (STBC), where the space-time code is transmitted over the beams generated by the steering vectors corresponding to the channel path directions. This is for the practical case where the transmit array may have adequate information on the departure angles of the dominant paths between transmitter and receiver, but unreliable information on the associated complex path gains. We compute analytically the signal-to-noise ratio (SNR) of the proposed hybrid for the specific case of a two-path channel model and using the orthogonal Alamouti code, and compare the result to the SNR of optimal linear precoding (LP) and the theoretically possible SNR of orthogonal STBC (OSTBC). Simulation results show that the performance of the BF/STBC hybrid can be very close to LP /sup n/der certain conditions - or even better in the practical case where there are phase estimation errors in the path gain estimates employed at the transmitter.

Space-time transmit structures for multi-antenna systems have received considerable interest. Circulant structures were among the first space-time coding techniques ever used for multiple-input multiple-output (MIMO) systems due to their simplicity and full rate. The fact that a circulant matrix is diagonalized by the discrete Fourier transformation matrix suggests that the circulant structure can be combined with an inverse fast Fourier transform (IFFT) at the transmitter and a fast Fourier transform (FFT) at the receiver. Using this method, the spatial mixing effect of the MIMO channel is decoupled but the diversity gain is lost. To recover the diversity advantage, we propose to spread the transmitted symbols over the diagonalized channel using the constellation rotation matrix for signal diversity designs. After spreading, every symbol experiences all the components of the frequency counterpart of the channel vector which makes our scheme provide full diversity. The proposed scheme is full rate and can be easily applied to any number of transmit antennas. Our simulation results show that the performance of our scheme is close to the performance of the ideal orthogonal space-time code and much better than the conventional circulant space-time code.

The multi-stage transmit Wiener filter (MSTxWF) is presented, an approach to reducing the complexity of the transmit Wiener filter (TxWF). The MSTxWF is found by applying the multi-stage decomposition known from the receive multi-stage Wiener filter (MSWF) to the TxWF. Complexity reduction is achieved by truncating the decomposition. We show that the resulting reduced rank MSTxWF can be interpreted as an approximation of the TxWF in a Krylov subspace, allowing for an efficient computation of the MSTxWF with the Lanczos algorithm. The reduced rank MSTxWF shows near-optimum performance for relatively low rank, making it an interesting alternative to eigenspace-based methods for complexity reduction.

Compared to the conventional full-rank Wiener filter (WF), reduced-rank processing in the minimum mean square error sense is a well-known strategy in order to reduce computational complexity and enhance performance in case of low sample support. In this paper, we reveal the relationship between block Krylov methods and the multi-stage matrix WF (MSMWF) as a reduced-rank matrix WF which estimates a signal vector instead of a scalar. The new insights lead to an implementation of the MSMWF based on Rune's variant of the block Lanczos algorithm which is more flexible with respect to rank selection compared to existing algorithms. Finally, the application to a time-dispersive multiple-input multiple-output (MIMO) system demonstrates the ability of the new algorithm to lessen receiver complexity while maintaining the same level of system performance or even improve it if second order statistics are not perfectly known. Moreover, the MSMWF outperforms the parallel implementation of multi-stage vector WFs with a comparable computational complexity.

Compared to wired channels, time dispersive radio channels possess more frequent nulls in their spectral characteristics. Thus, the performance of linear filters to compensate intersymbol interference degrades dramatically. The well-known nonlinear decision feedback equalizer (DFE) is one approach to improve this behavior. However, in systems with observations of high dimensionality, the optimum DFE structure is computational intensive. In this paper, we apply the method of the multi-stage Wiener filter (MSWF) to a conventional minimum mean square error (MMSE) DFE in order to reduce computational complexity. The application of the new algorithm to an Enhanced Data rates for GSM Evolution (EDGE) system demonstrates the ability to outperform the even more computational intensive linear Wiener filter (WF).

The Wiener filter solves the Wiener-Hopf equation and may be approximated by the multi-stage nested Wiener filter (MSNWF) which lies in the Krylov subspace of the covariance matrix of the observation and the cross-correlation vector between the observation and the desired signal. Moreover, since the covariance matrix is Hermitian, the Lanczos algorithm can be used to compute the Krylov subspace basis. The conjugate gradient (CG) method is another approach to solving a system of linear equations. We derive the relationship between the CG method and the Lanczos based MSNWF and finally transform the formulas of the MSNWF into those of the CG algorithm. Consequently, we present a CG based MSNWF where the filter weights and the mean square error (MSE) are updated at each iteration step. The resulting algorithm is used for linear equalization of the received signal in an enhanced data rates for GSM evolution (EDGE) system. Simulation results demonstrate the ability of the MSNWF to reduce receiver complexity while maintaining the same level of system performance.