In this paper, we propose a data-driven algorithm to design rate- and length-flexible polar codes. While the algorithm is very general, a particularly appealing use case is the design of codes for automorphism ensemble decoding (AED), a promising decoding algorithm for ultra-reliable low-latency communications (URLLC) and massive machine-type communications (mMTC) applications. To this end, theoretic results on nesting of symmetric polar codes are derived, which give hope in finding a fully nested, rate-compatible sequence suitable for AED. Using the proposed algorithms, such a flexible polar code design for automorphism ensemble successive cancellation (SC) decoding is constructed, outperforming existing code designs for AED and also the 5G polar code under cyclic redundancy check (CRC)aided successive cancellation list (SCL) decoding.

The distributed nature of cellular networks is one of the main enablers for integrated sensing and communication (ISAC). For target positioning and tracking, making use of bistatic measurements is non-trivial due to their non-linear relationship with Cartesian coordinates. Most of the literature proposes geometric-based methods to determine the target's location by solving a well-defined set of equations stemming from the available measurements. The error covariance to be used for Bayesian tracking is then derived from local Taylor expansions. In our work we adaptively fuse any subset of bistatic measurements using a maximum likelihood (ML) framework, allowing to incorporate every possible combination of available measurements, i.e., transmitter angle, receiver angle and bistatic range. Moreover, our ML approach is intrinsically flexible, as it can be extended to fuse an arbitrary number of measurements by multistatic setups. Finally, we propose both a fixed and dynamic way to compute the covariance matrix for the position error to be fed to Bayesian tracking techniques, like a Kalman filter. Numerical evaluations with realistic cellular communications parameters at mmWave frequencies show that our proposal outperforms the considered baselines, achieving a location and velocity root mean square error of 0.25m and 0.83m/s, respectively.

For asynchronous transmission of short blocks, preambles for packet detection contribute a non-negligible overhead. To reduce the required preamble length, joint detection and decoding (JDD) techniques have been proposed that additionally utilize the payload part of the packet for detection. In this paper, we analyze two instances of JDD, namely hybrid preamble and energy detection (HyPED) and decoder-aided detection (DAD). While HyPED combines the preamble with energy detection for the payload, DAD also uses the output of a channel decoder. For these systems, we propose novel achievability and converse bounds for the rates over the binary-input additive white Gaussian noise (BI-AWGN) channel. Moreover, we derive a general bound on the required blocklength for JDD. Both the theoretical bound and the simulation of practical codebooks show that the rate of DAD quickly approaches that of synchronous transmission.

Distributed massive MIMO is considered a key advancement for improving the performance of next-generation wireless telecommunication systems. However, its efficacy in scenarios involving user mobility is limited due to channel aging. To address this challenge, channel prediction techniques are investigated to forecast future channel state information (CSI) based on previous estimates. We propose a new channel prediction method based on channel charting, a self-supervised learning technique that reconstructs a physically meaningful latent representation of the radio environment using similarity relationships between CSI samples. The concept of inertia within a channel chart allows for predictive radio resource management tasks through the latent space. We demonstrate that channel charting can be used to predict future CSI by exploiting spatial relationships between known estimates that are embedded in the channel chart. Our method is validated on a real-world distributed massive MIMO dataset, and compared to a Wiener predictor and the outdated CSI in terms of achievable sum rate.

Narrowing the performance gap between optimal and feasible detection in inter-symbol interference (ISI) channels, this paper proposes to use graph neural networks (GNNs) for detection that can also be used to perform joint detection and decoding (JDD). For detection, the GNN is build upon the factor graph representations of the channel, while for JDD, the factor graph is expanded by the Tanner graph of the parity-check matrix (PCM) of the channel code, sharing the variable nodes (VNs). A particularly advantageous property of the GNN is a) the robustness against cycles in the factor graphs which is the main problem for sum-product algorithm (SPA)-based detection, and b) the robustness against channel state information (CSI) uncertainty at the receiver. Consequently, a fully deep learning-based receiver enables joint optimization instead of individual optimization of the components, so-called end-to-end learning. Furthermore, we propose a parallel flooding schedule that also reduces the latency, which turns out to improve the error correcting performance. The proposed approach is analyzed and compared to state-of-the-art baselines for different modulations and codes in terms of error correcting capability and latency. The gain compared to SPA-based detection might be explained with improved messages between nodes and adaptive damping of messages. For a higher order modulation in a high-rate turbo detection and decoding (TDD) scenario the GNN shows a, at first glance, surprisingly high gain of 6.25 dB compared to the best, feasible non-neural baseline.

In wireless communication systems, nonlinearity is the root cause of many undesired effects. In order to compensate these effects, the nonlinearity must be estimated accurately. This article deals with nonlinearity estimation methods and especially focuses on sequences that are optimized for that purpose. Based on the Cramér-Rao bound of the nonlinearity estimator, we derive an objective function for sequence optimization. An algorithm is proposed to solve this optimization problem while satisfying constraints on the sequence format to produce sequences that are compatible to current wireless LAN standards. The obtained sequences are thoroughly analyzed and compared against sequences defined in IEEE 802.11ax. Their superiority confirms that dedicated sequences for nonlinearity estimation are valuable in future communication standards. Moreover, we provide an analysis of estimation error components to show that an optimal number of estimated polynomial coefficients can be found that minimizes estimation error. To further show the benefits of optimized sequences in the context of an application, a method for digital nonlinear self-interference cancellation suited for frequency-division duplex systems is proposed and evaluated. With that, we demonstrate that cancellation performance is significantly enhanced using optimized estimation sequences.

Row-merged polar codes are a family of pre-transformed polar codes (PTPCs) with little precoding overhead. Providing an improved distance spectrum over plain polar codes, they are capable to perform close to the finite-length capacity bounds. However, there is still a lack of efficient design procedures for row-merged polar codes. Using novel weight enumeration algorithms with low computational complexity, we propose a design methodology for row-merged polar codes that directly considers their minimum distance properties. The codes significantly outperform state-of-the-art cyclic redundancy check (CRC)-aided polar codes under successive cancellation list (SCL) decoding in error-correction performance. Furthermore, we present fast simplified successive cancellation list (Fast-SSCL) decoding of PTPCs, based on which we derive a high-throughput, unrolled architecture template for fully pipelined decoders. Implementation results of SCL decoders for row-merged polar codes in a 12nm technology additionally demonstrate the superiority of these codes with respect to the implementation costs, compared to state-of-the-art reference decoder implementations.

This paper proposes to use graph neural networks (GNNs) for equalization, that can also be used to perform joint equalization and decoding (JED). For equalization, the GNN is build upon the factor graph representations of the channel, while for JED, the factor graph is expanded by the Tanner graph of the parity-check matrix (PCM) of the channel code, sharing the variable nodes (VNs). A particularly advantageous property of the GNN is the robustness against cycles in the factor graphs which is the main problem for belief propagation (BP)-based equalization. As a result of having a fully deep learning-based receiver, joint optimization instead of individual optimization of the components is enabled, so-called end-to-end learning. Furthermore, we propose a parallel flooding schedule that further reduces the latency, which turns out to improve also the error correcting performance. The proposed approach is analyzed and compared to state-of-the-art baselines in terms of error correcting capability and latency. At a fixed low latency, the flooding GNN for JED demonstrates a gain of 2.25 dB in bit error rate (BER) compared to an iterative Bahl-Cocke-Jelinek-Raviv (BCJR)-BP baseline.

Neural network (NN)-based receivers for orthogonal frequency division multiplex (OFDM) excel through promising performance and benefits in their applicability. In this paper we analyze their capabilities when they are imposed with practical constraints that have to be considered when implementing such a receiver on hardware. Specifically, we focus on the effects of uniform linear affine quantization and it is shown which performance can be achieved by utilizing quantization-aware training (QAT) with trainable quantizers. In order to reduce the computational complexity of the NN-based receiver different pruning methods are investigated. We showcase that a reduction of the number of floating-point operations (FLOPs) by more than 50% is possible at the cost of less than 0.25 dB difference. Finally, an intuition on joint pruning and quantization is given.

Nonlinear characteristics in a wireless transmitter can cause various undesired effects like spectral regrowth or signal quality degradation. To compensate these effects, e.g., via digital predistortion, an accurate estimation of the nonlinear characteristic is required. This work focuses on methods and sequences that allow accurate and robust estimation of a non-linearity. Based on the Cramér- Rao bound of the nonlinearity estimator, we derive an objective function for sequence optimization. An algorithm is proposed to solve this optimization problem while satisfying constraints on the sequence format to obtain sequences that are compatible to current wireless LAN standards. The performance of the optimized sequences is evaluated using a power amplifier measurement. Results show that the optimized sequences are superior to conventional estimation sequences defined in the IEEE 802.11ax standard. Thus, dedicated sequences for nonlinearity estimation should be considered in future communication standards. Moreover, we show that depending on the noise power an optimal number of estimated polynomial coefficients can be found that minimizes estimation error.

The challenging propagation environment, combined with the hardware limitations of mmWave systems, gives rise to the need for accurate initial access beam alignment strategies with low latency and high achievable beamforming gain. Much of the recent work in this area either focuses on one-sided beam alignment, or, joint beam alignment methods where both sides of the link perform a sequence of fixed channel probing steps. Codebook-based non-adaptive beam alignment schemes have the potential to allow multiple user equipments (UEs) to perform initial access beam alignment in parallel whereas adaptive schemes are favourable in achievable beamforming gain. This work introduces a novel deep learning based joint beam alignment scheme that aims to combine the benefits of adaptive, codebook-free beam alignment at the UE side with the advantages of a codebook-sweep based scheme at the basestation (BS). The proposed end-to-end trainable scheme is compatible with current cellular standard signaling and can be readily integrated into the standard without requiring significant changes to it. Extensive simulations demonstrate superior performance of the proposed approach over purely codebook-based ones.

Error correction coding (i.e., channel coding) is a key ingredient of any digital communications system. In mobile wireless communications, channel codes have evolved from simple convolutional codes in Global System for Mobile Communications (GSM) (2G), parallel concatenated (turbo) codes in Universal Mobile Telecommunications Service (UMTS) (3G), and long-term evolution (LTE) (4G), to carefully designed multirate/multilength low-density parity-check (LDPC) codes in 5G, combined with polar codes for short messages on the synchronization channel. Based on this rich history, and by accounting for the technological advances in very large-scale integration, this article will outline some recent trends in channel coding as they may be applied in 6G systems, ranging from novel approaches for short blocklengths such as automorphism ensemble decoding, via ideas of coding for multiple access, to concepts for unified coding schemes that may simplify encoding/decoding hardware at competitive error-correcting performance.

Channel charting is a self-supervised learning technique whose objective is to reconstruct a map of the radio environment, called channel chart, by taking advantage of similarity relationships in high-dimensional channel state information. We provide an overview of processing steps and evaluation methods for channel charting and propose a novel dissimilarity metric that takes into account angular-domain information as well as a novel deep learning-based metric. Furthermore, we suggest a method to fuse dissimilarity metrics such that both the time at which channels were measured as well as similarities in channel state information can be taken into consideration while learning a channel chart. By applying both classical and deep learning-based manifold learning to a dataset containing sub-6 GHz distributed massive MIMO channel measurements, we show that our metrics outperform previously proposed dissimilarity measures. The results indicate that the new metrics improve channel charting performance, even under non-line-of-sight conditions.

We propose and practically demonstrate a joint detection and decoding scheme for short-packet wireless communications in scenarios that require to first detect the presence of a message before actually decoding it. For this, we extend the recently proposed serial Turbo-autoencoder neural network (NN) architecture and train it to find short messages that can be, all “at once”, detected, synchronized, equalized and decoded when sent over an unsynchronized channel with memory. The conceptional advantage of the proposed system stems from a holistic message structure with superimposed pilots for joint detection and decoding without the need of relying on a dedicated preamble. This results not only in a higher spectral efficiency, but also translates into the possibility of shorter messages compared to using a dedicated preamble. We compare the detection error rate (DER), bit error rate (BER) and block error rate (BLER) performance of the proposed system with a hand-crafted state-of-the-art conventional baseline and our simulations show a significant advantage of the proposed autoencoder-based system over the conventional baseline in every scenario up to messages conveying$k\!=\!96$information bits. Finally, we practically evaluate and confirm the improved performance of the proposed system over-the-air (OTA) using a software-defined radio (SDR)-based measurement testbed.

In communication systems, autoencoder refers to a system that replaces parts of the traditional transmitter and receiver of the baseband processing chain with artificial neural networks (ANNs). This allows to jointly train the system for an underlying channel model by reconstructing the input symbols at the output. Since the actual behavior of a real communication channel cannot be perfectly reproduced by an abstract model, it is necessary for the autoencoder to adapt to the changing conditions at runtime. Thus, online fine-tuning, in the form of ANN-retraining is of great importance. A platform able to satisfy the low-latency and low-power requirements of embedded communication systems are Field-programmable gate arrays (FPGAs). In this paper, we present an online-trainable low-power FPGA architecture for the receiver of an autoencoder-based communication chain. The architecture is embedded into an exploration framework that automatically determines the optimal degree of parallelism to minimize latency or power consumption. Our solutions achieve 2000×higher throughput than a high-performance GPU, draw 5×less power than an embedded CPU and are 5800×more energy efficient compared to an embedded GPU, for a batch size of one. To the best of our knowledge, this is the first FPGA-based autoencoder implementation for communication systems.

Permutation decoding gained recent interest as it can exploit the symmetries of a code in a parallel fashion. Moreover, it has been shown that by viewing permuted polar codes as polar subcodes, the set of usable permutations in permutation decoding can be increased. We extend this idea to pre-transformed polar codes, such as cyclic redundancy check (CRC)-aided polar codes, which previously could not be decoded using permutations due to their lack of automorphisms. Using belief propagation (BP)-based subdecoders, we showcase a performance close to CRC-aided SCL (CA-SCL) decoding. The proposed algorithm outperforms the previously best performing iterative CRC-aided belief propagation list (CA-BPL) decoder both in error-rate performance and decoding latency.

We consider a frequency division duplex (FDD) scheme in which two wireless communication devices simultaneously transmit and receive on adjacent channels. Inevitable out-of-band (OOB) emissions caused by the transmission on one channel induce self-interference on the adjacent channel. As a result, receiver sensitivity severely degrades by self-interference from the transmitter of the same device. Therefore, we propose a novel self-interference cancellation (SIC) method, that has a lower complexity compared to existing approaches. It comprises digital linear SIC in frequency domain and power amplifier backoff adaption to mitigate both linear and nonlinear components. We further present and evaluate an OOB emission model of a transmitter which is subsequently used to analyze the performance of the proposed SIC method. Our simulation results highlight capabilities and limitations of the proposed SIC method in different scenarios. It turns out that the proposed method can significantly reduce the error vector magnitude of a received signal in FDD operation. Prerequisites of the cancellation method and impact to protocol design are thoroughly discussed.

Future cellular networks are intended to have the ability to sense the environment by utilizing reflections of transmitted signals. Multi-dimensional sensing brings along the crucial advantage of being able to resort to multiple domains to resolve targets, enhancing detection capabilities compared to one-dimensional (1D) estimation. However, estimating parameters jointly in 5G New Radio systems poses the challenge of limiting the computational complexity while preserving a high resolution. To that end, we make use of channel state information (CSI) decimation for MUltiple SIgnal Classification (MUSIC)-based joint range-angle of arrival estimation. We further introduce multi-peak search routines to achieve additional detection capability improvements. Simulation results with orthogonal frequency-division multiplexing (OFDM) signals show that we attain higher detection probabilities for closely spaced targets than with 1D range-only estimation. Moreover, we demonstrate that for our considered 5G setup, we are able to significantly reduce the required number of computations due to CSI decimation.

The automorphism group of a code is the set of permutations of the codeword symbols that map the whole code onto itself. For polar codes, only a part of the automorphism group was known, namely the lower-triangular affine group (LTA), which is solely based upon the partial order of the code's synthetic channels. Depending on the design, however, polar codes can have a richer set of automorphisms. In this paper, we extend the LTA to a larger subgroup of the general affine group (GA), namely the block lower-triangular affine group (BLTA) and show that it is contained in the automorphism group of polar codes. Furthermore, we provide a low complexity algorithm for finding this group for a given information/frozen set and determining its size. Most importantly, we apply these findings in automorphism-based decoding of polar codes and report a comparable error-rate performance to that of successive cancellation list (SCL) decoding with significantly lower complexity.

We compare the potential of neural network (NN)-based channel estimation with classical linear minimum mean square error (LMMSE)-based estimators, also known as Wiener filtering. For this, we propose a low-complexity recurrent neural network (RNN)-based estimator that allows channel equalization of a sequence of channel observations based on independent time- and frequency-domain long short-term memory (LSTM) cells. Motivated by Vehicle-to-Everything (V2X) applications, we simulate time- and frequency-selective channels with orthogonal frequency division multiplex (OFDM) and extend our channel models in such a way that a continuous degradation from line-of-sight (LoS) to non-line-of-sight (NLoS) conditions can be emulated. It turns out that the NN-based system cannot just compete with the LMMSE equalizer, but it also can be trained w.r.t. resilience against system parameter mismatch. We thereby showcase the conceptual simplicity of such a data-driven system design, as this not only enables more robustness against, e.g., signal-to-noise-ratio (SNR) or Doppler spread estimation mismatches, but also allows to use the same equalizer over a wider range of input parameters without the need of re-building (or re-estimating) the filter coefficients. Particular attention has been paid to ensure compatibility with the existing IEEE 802.11p piloting scheme for V2X communications. Finally, feeding the payload data symbols as additional equalizer input unleashes further performance gains. We show significant gains over the conventional LMMSE equalization for highly dynamic channel conditions if such a data-augmented equalization scheme is used.

Universal Filtered Orthogonal Frequency Division Multiplexing (UF-OFDM) is one of the main candidate wave-form for the next generation of mobile communication due to its advantages in terms of spectral efficiency and the robustness against frequency offsets and Doppler spread. UF-OFDM suffers from the problem of having a high Peak to Average Power Ratio (PAPR) compared to conventional OFDM systems. Therefore, the development of efficient PAPR reduction methods is crucial. In this paper, we apply the Partial Transmit Sequence (PTS) method to reduce the PAPR in UF-OFDM systems as it does not suffer from spectral regrowth; also it does not impact the Bit Error Rate (BER). Due to the computational complexity of PTS, the Harmony Search Algorithm (HSA) is proposed where the proposed HSA will save about 84% of complexity compared with the conventional PTS. Moreover, a novel “adaptive HSA” technique is presented that gives the same performance as HSA with PTS while it saves about 48.3% in run time.

Reed–Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an open problem. In this work, we present a versatile decoding architecture for RM codes based on their rich automorphism group. The decoding algorithm can be seen as a generalization of multiple-bases belief propagation (MBBP) and may use any polar or RM decoder as constituent decoders. We provide extensive error-rate performance simulations for successive cancellation (SC)-, SC-list (SCL)- and belief propagation (BP)-based constituent decoders. We furthermore compare our results to existing decoding schemes and report a near-ML performance for the RM(3,7)-code (e.g., 0.04 dB away from the ML bound at BLER of 10−3) at a competitive computational cost. Moreover, we provide some insights into the automorphism subgroups of RM codes and SC decoding and, thereby, prove the theoretical limitations of this method with respect to polar codes.

Although iterative decoding of polar codes has recently made huge progress based on the idea of permuted factor graphs, it still suffers from a non-negligible performance degradation when compared to state-of-the-art CRC-aided successive cancellation list (CA-SCL) decoding. In this work, we show that iterative decoding of polar codes based on the belief propagation list (BPL) algorithm can approach the error-rate performance of CA-SCL decoding and, thus, can be efficiently used for decoding the standardized 5G polar codes. Rather than only utilizing the cyclic redundancy check (CRC) as a stopping condition (i.e., for error-detection), we also aim to benefit from the error-correction capabilities of the outer CRC code. For this, we develop two distinct soft-decision CRC decoding algorithms: a Bahl-Cocke-Jelinek-Raviv (BCJR)-based approach and a sum product algorithm (SPA)-based approach. Further, an optimized selection of permuted factor graphs is analyzed and shown to reduce the decoding complexity significantly. Finally, we benchmark the proposed CRC-aided belief propagation list (CA-BPL) decoding to state-of-the-art 5G polar codes under CA-SCL decoding and, thereby, showcase an error-rate performance not just close to the CA-SCL but also close to the maximum likelihood (ML) bound as estimated by ordered statistic decoding (OSD).

We consider a trainable point-to-point communication system, where both transmitter and receiver are implemented as neural networks (NNs), and demonstrate that training on the bit-wise mutual information (BMI) allows seamless integration with practical bit-metric decoding (BMD) receivers, as well as joint optimization of constellation shaping and labeling. Moreover, we present a fully differentiable neural iterative demapping and decoding (IDD) structure which achieves significant gains on additive white Gaussian noise (AWGN) channels using a standard 802.11n low-density parity-check (LDPC) code. The strength of this approach is that it can be applied to arbitrary channels without any modifications. Going one step further, we show that careful code design can lead to further performance improvements. Lastly, we show the viability of the proposed system through implementation on software-defined radios (SDRs) and training of the end-to-end system on the actual wireless channel. Experimental results reveal that the proposed method enables significant gains compared to conventional techniques.

Massive MIMO uses a large number of antennas to increase the spectral efficiency (SE) through spatial multiplexing of users, which requires accurate channel state information. It is often assumed that regular pilots (RP), where a fraction of the time-frequency resources is reserved for pilots, suffices to provide high SE. However, the SE is limited by the pilot overhead and pilot contamination. An alternative is superimposed pilots (SP) where all resources are used for pilots and data. This removes the pilot overhead and reduces pilot contamination by using longer pilots. However, SP suffers from data interference that reduces the SE gains. This paper proposes the Massive-MIMO Iterative Channel Estimation and Decoding (MICED) algorithm where partially decoded data is used as side-information to improve the channel estimation and increase SE. We show that users with precise data estimates can help users with poor data estimates to decode. Numerical results with QPSK modulation and LDPC codes show that the MICED algorithm increases the SE and reduces the block-error-rate with RP and SP compared to conventional methods. The MICED algorithm with SP delivers the highest SE and it is especially effective in scenarios with short coherence blocks like high mobility or high frequencies.

We establish a multiuser extrinsic information transfer (EXIT) chart area theorem for the interleave-division multiple access (IDMA) scheme, a special form of superposition coding, in multiple access channels (MACs). A low-cost multi-user detection (MUD) based on the Gaussian approximation (GA) is assumed. The evolution of mean-square errors (MSE) of the GA-based MUD during iterative processing is studied. We show that the K-dimensional tuples formed by the MSEs of K users constitute a conservative vector field. The achievable rate is a potential function of this conservative field, so it is the integral along any path in the field with value of the achievable rate solely determined by the two path terminals. Optimized error correcting codes can be found given the integration paths in the MSE fields by matching EXIT type functions. The above findings imply that i) low-cost GA detection can provide MAC capacity-approaching performance, ii) the sum-rate capacity can be achieved independently of the integration path in the MSE fields; and iii) the integration path determining achievable rate tuples of all users can be an extra degree of freedom for code design.

We establish a multi-user extrinsic information transfer (EXIT) chart area theorem for the interleave-division multiple-access (IDMA) scheme, a special form of superposition coding, in multiple access channels (MACs). A low-cost multi-user detection (MUD) based on the Gaussian approximation (GA) is assumed. The evolution of mean-square errors (MSE) of the GA-based MUD during iterative processing is studied. We show that the K-dimensional tuples formed by the MSEs of K users constitute a conservative vector field. The achievable rate is a potential function of this conservative field, so it is the integral along any path in the field with value of the integral solely determined by the two path terminals. Optimized codes can be found given the integration paths in the MSE fields by matching EXIT type functions. The above findings imply that i) low-cost GA-based MUD can provide near capacity performance; ii) the sum-rate capacity (region) can be achieved independently of the integration path in the MSE fields; and iii) the integration path can be an extra degree of freedom for code design.

Previous work showed that polar codes can be decoded using off-the-shelf LDPC decoders by imposing special constraints on the LDPC code structure, which, however, resulted in some performance degradation. In this paper we show that this loss can be mitigated; in particular, we demonstrate how the gap between LDPC-style decoding and Arıkan's Belief Propagation (BP) decoding of polar codes can be closed by taking into account the underlying graph structure of the LDPC decoder while jointly designing the polar code and the parity-check matrix of the corresponding LDPC-like code. The resulting polar codes under conventional LDPC-style decoding are shown to have similar error-rate performance when compared to some well-known and standardized LDPC codes. Moreover, we obtain performance gains in the high SNR region.

We showcase the practicability of an indoor positioning system (IPS) solely based on neural networks (NNs) and the channel state information (CSI) of a (Massive) multiple-input multiple-output (MIMO) communication system, i.e., only build on the basis of data that is already existent in today's systems. As such our IPS system promises both, a good accuracy without the need of any additional protocol/signaling overhead for the user localization task. In particular, we propose a tailored NN structure with an additional phase branch as feature extractor and (compared to previous results) a significantly reduced amount of trainable parameters, leading to a minimization of the amount of required training data. We provide actual measurements for indoor scenarios with up to 64 antennas covering a large area of 80m2. In the second part, several robustness investigations for real-measurements are conducted, i.e., once trained, we analyze the recall accuracy over a period of several days. Further, we analyze the impact of pedestrians walking in-between the measurements and show that finetuning and pre-training of the NN helps to mitigate effects of hardware drifts and alterations in the propagation environment over time. This reduces the amount of required training samples at equal precision and, thereby, decreases the effort of the costly training data acquisition.

We present a new framework for constructing polar codes (i.e., selecting the frozen bit positions) for arbitrary channels, tailored to a given decoding algorithm rather than assuming the (not necessarily optimal) successive cancellation (SC) decoding. The proposed framework is based on the genetic algorithm (GenAlg), where populations (i.e., collections) of information sets evolve via evolutionary transformations based on their individual error-rate performance. These populations converge toward an information set that fits both the decoding behavior and the defined channel. We construct polar codes, without the CRC-aid, tailored to plain successive cancellation list (SCL) decoding, achieving the same error-rate performance as the CRC-aided SCL decoding over both the AWGN channel and the Rayleigh channel, respectively. Furthermore, a proposed belief propagation (BP)-tailored construction approaches the SCL error-rate performance without any modifications in the decoding algorithm itself. The performance gains can be attributed to the significant reduction in the number of low-weight codewords. We show that, when required, the GenAlg can also be set up to find codes that reduce the decoding complexity. This way, the SCL list size or the number of BP iterations can be reduced while maintaining the same error-rate performance.

Multi-soliton pulses are potential candidates for fiber optical transmission where the information is modulated and recovered in the so-called nonlinear Fourier domain. While this is an elegant technique to account for the channel nonlinearity, the obtained spectral efficiency, so far, is not competitive with classic Nyquist-based schemes. This is especially due to the observation that soliton pulses generally exhibit a large time-bandwidth product. We consider the phase modulation of spectral amplitudes of higher order solitons, taking into account their varying spectral and temporal behavior when propagating along the fiber. For second- and third-order solitons, we numerically optimize the pulse shapes to minimize the time-bandwidth product. We study the behavior of multi-soliton pulse duration and bandwidth, and generally observe two corner cases where we approximate them analytically. We use these results to give an estimate on the minimal achievable time-bandwidth product per eigenvalue.

Soliton pulses are special waveforms to account for nonlinearity in fiber optical communication. They can be represented in a nonlinear spectrum by eigenvalues and spectral amplitudes which have simple transformation equations along the ideal link. This motivates to encode data in the nonlinear spectrum. In this paper, we consider dual-polarization modulation of spectral amplitudes, and show that they become highly correlated during propagation along a noisy fiber link. Thus, joint equalization is generally needed for detection at the receiver. We propose a simple precoding scheme that almost removes these correlations. This allows to significantly improve the detection performance even without any complex equalization. The spectral amplitudes are transformed into pairs of common and differential information part. We show that the differential part is almost preserved along the link, even in the presence of noise. Thus, it can be directly detected from the received spectral amplitudes with high reliability. Exploiting the differential gain of the precoding allows much higher bit rates at comparable error rates. We analyze our precoding scheme and verify its performance gain in split-step-Fourier simulations by comparing it to the conventional independent modulation of spectral amplitudes for first and second order solitons.

This paper considers the forward error correction (FEC) code design for approaching the capacity of adynamicmultiple access channel (MAC) where both the number of users and their respective signal powers keep constantly changing, resembling the scenario of an actual wireless cellular system. To obtain a low-complexity non-orthogonal multiple access (NOMA) scheme, we propose a serial concatenation of a low-density parity-check (LDPC) code and a repetition code (REP), this way achieving near Gaussian MAC (GMAC) capacity performance while coping with the dynamics of the MAC system. The joint optimization of the LDPC and REP codes is addressed by matching the analytical extrinsic information transfer (EXIT) functions of the sub-optimal multi-user detector (MUD) and the channel code for a specific and static MAC system, achieving near-GMAC capacity. We show that the near-capacity performance can be flexibly maintained with the same LDPC code regardless of the variations in the number of users and power levels. This flexibility (or elasticity) is provided by the REP code, acting as “user-load and power equalizer”, dramatically simplifying the practical implementation of NOMA schemes, as only a single LDPC code is needed to cope with the dynamics of the MAC system.

We introduce the Scattered Extrinsic Information Transfer (S-EXIT) chart as a tool for optimizing degree profiles of short length Low-Density Parity-Check (LDPC) codes under iterative decoding. As degree profile optimization is typically done in the asymptotic length regime, there is space for further improvement when considering the finite length behavior. We propose to consider the average extrinsic information as a random variable, exploiting its specific distribution properties for guiding code design. We explain, step-by-step, how to generate an S-EXIT chart for short-length LDPC codes. We show that this approach achieves gains in terms of bit error rate (BER) of 0.5 dB and 0.6 dB over the additive white Gaussian noise (AWGN) channel for codeword lengths of 128 and 180 bits, respectively, at a target BER of 10-4 when compared to conventional Extrinsic Information Transfer (EXIT) chart-based optimization. Also, a performance gain for the Binary Erasure Channel (BEC) for a block (i.e., codeword) length of 180 bits is shown.

We describe a novel approach to interpret a polar code as a low-density parity-check (LDPC)-like code with an underlying sparse decoding graph. This sparse graph is based on the encoding factor graph of polar codes and is suitable for conventional belief propagation (BP) decoding. We discuss several pruning techniques based on the check node decoder (CND) and variable node decoder (VND) update equations, significantly reducing the size (i.e., decoding complexity) of the parity-check matrix. As a result, iterative polar decoding can then be conducted on a sparse graph, akin to the traditional well-established LDPC decoding, e.g., using a fully parallel sum-product algorithm (SPA). This facilitates the systematic analysis and design of polar codes using the well-established tools known from analyzing LDPC codes. We show that the proposed iterative polar decoder has a negligible performance loss for short-to-intermediate codelengths compared to Arikan's original BP decoder. Finally, the proposed decoder is shown to benefit from both reduced complexity and reduced memory requirements and, thus, is more suitable for hardware implementations.

We show that the performance of iterative belief propagation (BP) decoding of polar codes can be enhanced by decoding over different carefully chosen factor graph realizations. With a genie-aided stopping condition, it can achieve the successive cancellation list (SCL) decoding performance which has already been shown to achieve the maximum likelihood (ML) bound provided that the list size is sufficiently large. The proposed decoder is based on different realizations of the polar code factor graph with randomly permuted stages during decoding. Additionally, a different way of visualizing the polar code factor graph is presented, facilitating the analysis of the underlying factor graph and the comparison of different graph permutations. In our proposed decoder, a high rate Cyclic Redundancy Check (CRC) code is concatenated with a polar code and used as an iteration stopping criterion (i.e., genie) to even outperform the SCL decoder of the plain polar code (without the CRC-aid). Although our permuted factor graph-based decoder does not outperform the SCL-CRC decoder, it achieves, to the best of our knowledge, the best performance of all iterative polar decoders presented thus far.

The training complexity of deep learning-based channel decoders scales exponentially with the codebook size and therefore with the number of information bits. Thus, neural network decoding (NND) is currently only feasible for very short block lengths. In this work, we show that the conventional iterative decoding algorithm for polar codes can be enhanced when sub-blocks of the decoder are replaced by neural network (NN) based components. Thus, we partition the encoding graph into smaller sub-blocks and train them individually, closely approaching maximum a posteriori (MAP) performance per sub-block. These blocks are then connected via the remaining conventional belief propagation decoding stage(s). The resulting decoding algorithm is non-iterative and inherently enables a highlevel of parallelization, while showing a competitive bit error rate (BER) performance. We examine the degradation through partitioning and compare the resulting decoder to state-of-the art polar decoders such as successive cancellation list and belief propagation decoding.

The decoding performance of polar codes strongly depends on the decoding algorithm used, while also the decoder throughput and its latency mainly depend on the decoding algorithm. In this work, we implement the powerful successive cancellation list (SCL) decoder on a GPU and identify the bottlenecks of this algorithm with respect to parallel computing and its difficulties. The inherent serial decoding property of the SCL algorithm naturally limits the achievable speed-up gains on GPUs when compared to CPU implementations. In order to increase the decoding throughput, we use a hybrid decoding scheme based on the belief propagation (BP) decoder, which can be intra- and inter-frame parallelized. The proposed scheme combines excellent decoding performance and high throughput within the signal-to-noise ratio (SNR) region of interest.

Multi-soliton pulses are potential candidates for fiber optical transmission where the information is modulated and recovered in the so-called nonlinear Fourier domain. While this is an elegant technique to account for the channel nonlinearity, the obtained spectral efficiency, so far, is not competitive with the classic Nyquist-based schemes. In this paper, we study the evolution of the time-bandwidth product of multi-solitons as they propagate along the optical fiber. For second and third order soliton pulses, we numerically optimize the pulse shapes to achieve the smallest time-bandwidth product when the phase of the spectral amplitudes is used for modulation. Moreover, we analytically estimate the pulse-duration and bandwidth of multi-solitons in some practically important cases. Those estimations enable us to approximate the time-bandwidth product for higher order solitons.

Universal Filtered OFDM (UF-OFDM) exhibits better spectral properties compared to the classic OFDM modulation technique. One of the drawbacks of multicarrier modulation (MCM) is its high Peak to Average Power Ratio (PAPR), challenging power amplifier design. In this paper, the PAPR of UF-OFDM signals is analyzed mathematically and then verified by numerical simulations. It is shown, analytically as well as by simulation, that the PAPR of UF-OFDM signals is higher than that of OFDM signals due to the FIR-filtering. Moreover, a simple approximated PAPR relation between both signals is found and accurately matches with simulation. To reduce the PAPR, a simple clipping algorithm along with DFT precoding is investigated in UF-OFDM systems with low complexity transceiver implementation, and compared with classic CP-OFDM/SC-FDMA systems under various system settings of both synchronous and asynchronous multiuser transmission. The link level simulation with typical LTE parameters shows that UF-OFDM performs slightly worse than OFDM with perfect time and frequency synchronization, while significant SNR gain of more than 2 dB can be achieved with relaxed synchronization.

In this paper, a novel iterative MIMO subspace detection method is proposed to approach the maximum-likelihood (ML) receiver performance while keeping the computational complexity scalable for MIMO systems with large number of transmit and receive antennas. By dividing the signal detection problem for a large MIMO system into subspaces with smaller size, the complexity of applying a per-subspace ML receiver is much lower while near ML performance may still be achieved in combination with an iterative parallel interference cancellation unit. It is shown that, for equal number of transmit and receive antennas, the complexity of the proposed method is cubic with the number of transmit antennas. A flexible complexity#x002F;performance trade-off can be obtained by varying the subspace size. Even for small subspace dimensions, close to ML performance can be achieved, resulting in low complexity. The performance of this method is assessed in terms of bit error rate and achievable mutual information, and compared to conventional MIMO detection methods using the zero-forcing (ZF) or minimum mean squared error (MMSE) criterion, as well as the successive interference cancellation (SIC) approach. Furthermore, the convergence behavior of this iterative detection method is analyzed using a new variant of the EXIT-Chart based on the mutual information of equivalent hard output channels, i.e., a binary symmetric channel (BSC) model.

This paper considers channel estimation for multiple-input multiple-output (MIMO) channels and revisits two competing concepts of including training data into the transmit signal, namely, orthogonal pilot (OP) that periodically transmits alternating pilot-data symbols, and superimposed pilot (SP) that overlays pilot-data symbols over time. We investigate rates achievable by both schemes when the channel undergoes time-selective bandlimited fading and analyze their behaviors with respect to the MIMO dimension and fading speed. By incorporating the multiple-antenna factors, we demonstrate that the widely known trend in which the OP is superior to the SP in the regimes of high signal-to-noise ratio (SNR) and slow fading, and vice versa, does not hold in general. As the number of transmit antennas (nt) increases, the range of operable fading speeds for the OP is significantly narrowed due to limited time resources for channel estimation and insufficient fading samples, which results in the SP being competitive in wider speed and SNR ranges. For a sufficiently small nt, we demonstrate that as the fading variation becomes slower, the estimation quality for the SP can be superior to that for the OP. In this case, the SP outperforms the OP in the slow-fading regime due to full utilization of time for data transmission.

For finite length polar codes, channel polarization leaves a significant number of channels not fully polarized. Adding a Cyclic Redundancy Check (CRC) to better protect information on the semi-polarized channels has already been successfully applied in the literature, and is straightforward to be used in combination with Successive Cancellation List (SCL) decoding. Belief Propagation (BP) decoding, however, offers more potential for exploiting parallelism in hardware implementation, and thus, we focus our attention on improving the BP decoder. Specifically, similar to the CRC strategy in the SCL-case, we use a short-length “auxiliary” LDPC code together with the polar code to provide a significant improvement in terms of BER. We present the novel concept of “scattered” EXIT charts to design such auxiliary LDPC codes, and achieve net coding gains (i.e. for the same total rate) of 0.4dB at BER of 10-5compared to the conventional BP decoder.

Universal Filtered Multi-Carrier (UFMC, a.k.a. UF-OFDM) is a novel multi-carrier modulation technique, which aims at replacing OFDM for next generation wireless communication systems (5G). It is a generalization of OFDM and filter bank based multi-carrier (FBMC-FMT), which combines the advantages of OFDM and FBMC while avoiding its main drawbacks. UFMC is shown to be more robust in relaxed synchronization conditions i.e. time-frequency misalignment compared to conventional CP-OFDM systems. As required in potential scenarios of 5G systems, UFMC is more efficient to support short uplink bursts communications. Without the insertion of cyclic prefix, we investigate the procedure and performance of pilot-aided channel estimation for UFMC in an uplink multi-user FDMA scenario and show that almost the same performance as CP-OFDM can be achieved despite the lack of cyclic prefix. In case of timing and frequency offset, UFMC shows its robustness over CP-OFDM in terms of symbol error rate (SER). Simulation results show that the error floor is reduced applying UFMC for considered different types of channels.

In order to reduce pilot overhead for Multiple-Input Multiple-Output (MIMO) communications, we present a trellis-based joint channel tracking and data detection approach that allows reliable communications at fast fading rates. The trellis tracking algorithm predicts multiple channel coefficients in parallel while simultaneously performing a posteriori Probability (APP) detection of the transmitted bits. Different variants are compared based on different pilot training strategies, using discrete pilots, superimposed pilots, or no pilots at all by employing Differential Phase Shift Keying (DPSK) across multiple antenna channels.

We propose a time division duplex (TDD) based network architecture where a macrocell tier with a “massive” multiple-input multiple-output (MIMO) base station (BS) is overlaid with a dense tier of small cells (SCs). In this context, the TDD protocol and the resulting channel reciprocity have two compelling advantages. First, a large number of BS antennas can be deployed without incurring a prohibitive overhead for channel training. Second, the BS can estimate the interference covariance matrix from the SC tier which can be leveraged for downlink precoding. In particular, the BS designs its precoding vectors to transmit independent data streams to its users while being orthogonal to the subspace spanned by the strongest interference directions; thereby minimizing the sum interference imposed on the SCs. In other words, the BS “sacrifices” some of its antennas for interference cancellation while the TDD protocol allows for an implicit coordination across both tiers. Simulation results suggest that, given a sufficiently large number of BS antennas, the proposed scheme can significantly improve the sum-rate of the SC tier at the price of a small macro performance loss.

The interference limitation of cellular systems can be addressed by coordinated multi-point (CoMP) transmission and reception, where different base stations act together as a distributed antenna system, sharing data. CoMP has been shown to be sensitive to accuracy of channel knowledge. This work deals with practical channel estimation in an uplink joint reception scenario for multiple users across multiple cells. In most academic work, the parameter knowledge, like second order statistics of the channel and noise, is assumed to be perfectly known. In contrast to that, in this paper, we fully estimate all parameters using pilots. Practical algorithms are designed here to achieve fast convergence of parameter estimation, avoiding the need for too many samples, with manageable complexity. This is done in a multi-stage way, where the outputs of simpler estimators provide the parameters for the more advanced stages. Even for large coordination set sizes, like 7 cells, we show that our multi-stage approach is roughly just 1 dB below perfect channel knowledge in terms of post-combining SINR.

LTE and LTE-Advanced have been optimized to deliver high bandwidth pipes to wireless users. The transport mechanisms have been tailored to maximize single cell performance by enforcing strict synchronism and orthogonality within a single cell and within a single contiguous frequency band. Various emerging trends reveal major shortcomings of those design criteria: (1) The fraction of machine-type-communications (MTC) is growing fast. Transmissions of this kind are suffering from the bulky procedures necessary to ensure strict synchronism. (2) Collaborative schemes have been introduced to boost capacity and coverage (CoMP), and wireless networks are becoming more and more heterogeneous following the non-uniform distribution of users. Tremendous efforts must be spent to collect the gains and to manage such systems under the premise of strict synchronism and orthogonality. (3) The advent of the Digital Agenda and the introduction of carrier aggregation are forcing the transmission systems to deal with fragmented spectrum. 5GNOW will question the design targets of LTE and LTE-Advanced having these shortcomings in mind. The obedience of LTE and LTE-Advanced to strict synchronism and orthogonality will be challenged. It will develop new PHY and MAC layer concepts being better suited to meet the upcoming needs with respect to service variety and heterogeneous transmission setups. A demonstrator will be built as Proof-of-Concept relying upon continuously growing capabilities of silicon based processing. Wireless transmission networks following the outcomes of 5GNOW will be better suited to meet the manifoldness of services, device classes and transmission setups being present in envisioned future scenarios like smart cities. The integration of systems relying heavily on MTC, e.g. sensor networks, into the communication network will be eased. The per-user experience will be more uniform and satisfying. To ensure this 5GNOW will contribute to upcoming 5G standardization.

We consider the uplink (UL) and downlink (DL) of non-cooperative multi-cellular time-division duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot contamination, and an arbitrary path loss and antenna correlation for each link. We derive approximations of achievable rates with several linear precoders and detectors which are proven to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations. It is known from previous work assuming uncorrelated channels, that as N→∞ while K is fixed, the system performance is limited by pilot contamination, the simplest precoders/detectors, i.e., eigenbeamforming (BF) and matched filter (MF), are optimal, and the transmit power can be made arbitrarily small. We analyze to which extent these conclusions hold in the more realistic setting where N is not extremely large compared to K. In particular, we derive how many antennas per UT are needed to achieve η% of the ultimate performance limit with infinitely many antennas and how many more antennas are needed with MF and BF to achieve the performance of minimum mean-square error (MMSE) detection and regularized zero-forcing (RZF), respectively.

We consider the downlink of a time-division duplexing (TDD) multicell multiuser MIMO system where the base stations (BSs) are equipped with a very large number of antennas. Assuming channel estimation through uplink pilots, arbitrary antenna correlation and user distributions, we derive approximations of achievable rates with linear precoding techniques, namely eigenbeamforming (BF) and regularized zero-forcing (RZF). The approximations are tight in the large system limit with an infinitely large number of antennas and user terminals (UTs), but match our simulations for realistic system dimensions. We further show that a simple RZF precoding scheme can achieve the same performance as BF with one order of magnitude fewer antennas in both uncorrelated and correlated fading channels.

A low-complexity detection algorithm is proposed for Multiple-Input Multiple-Output (MIMO) systems with many transmit and receive antennas. We involve QR Decomposition (QRD) to triangularize the effective MIMO channel matrix so that several MIMO sub-systems can be individually established, which allow detecting several (possibly overlapping) groups of data streams separately. This method is referred to as MIMO Overlapped Subspace Detection (OSD). Further, we propose an OSD based non-iterative (i.e., without feedback from an outer channel decoder) Interference Cancellation (IC) approach where some streams are cancelled out as reliable interference. Link layer simulations for an 8×8 configuration show that this algorithm not only inherits the feature of OSD, yielding a scalable performance/complexity trade-off, but can also closely approach the MIMO ergodic capacity.

This paper presents a low complexity detection algorithm for Multiple-Input Multiple-Output (MIMO) systems. The novel subspace approach involves QR Decomposition (QRD) or Cholesky decomposition to triangularize the effective channel matrix so that several (possibly overlapping) groups of data streams can be detected separately. Link layer simulations show that the ergodic MIMO capacity can be closely approached by exploiting an Overlapped Subspace Detection (OSD) strategy. The OSD algorithm offers a scalable performance/complexity trade-off between Zero-Forcing (ZF) and Maximum a posteriori Probability (APP) detection. The proposed algorithm can be straightforwardly applied to large MIMO systems, as prevalent with recent advances in the field such as network MIMO and Coordinated Multi-Point (CoMP) transmission and reception.

The "writing on dirty paper"-channel model offers an information-theoretic framework for precoding techniques for canceling arbitrary interference known at the transmitter. It indicates that lossless precoding is theoretically possible at any signal-to-noise ratio (SNR), and thus dirty-paper coding may serve as a basic building block in both single-user and multiuser communication systems. We design an end-to-end coding realization of a system materializing a significant portion of the promised gains. We employ multidimensional quantization based on trellis shaping at the transmitter. Coset decoding is implemented at the receiver using "virtual bits." Combined with iterative decoding of capacity-approaching codes we achieve an improvement of 2dB over the best scalar quantization scheme. Code design is done using the EXIT chart technique.

An information theoretic framework for the study of efficient known interference cancellation technique is presented in this paper. The dirty paper channel model is given where the arbitrary interference is known at the transmitter is a statistically independent Gaussian random variable with variance. The link to precoding was made and it was shown that the full capacity might be achieved using lattices and MMSE scaling for arbitrary interference. A BCJR detector computes the a posteriori probability (APP) values of the channel code bits, summing over the corresponding coset. Extrinsic information is iteratively passed between BCJR detector and channel decoder. Code design is done using the EXIT chart, achieving an improvement over optimal scalar quantization (SQ).

A coding and modulation technique is studied where the coded bits of an irregular low-density parity-check (LDPC) code are passed directly to a modulator. At the receiver, the variable nodes of the LDPC decoder graph are connected to detector nodes, and iterative decoding is accomplished by viewing the variable and detector nodes as one decoder. The code is optimized by performing a curve fitting on extrinsic information transfer charts. Design examples are given for additive white Gaussian noise channels, as well as multiple-input, multiple-output (MIMO) fading channels where the receiver, but not the transmitter, knows the channel. For the MIMO channels, the technique operates within 1.25 dB of capacity for various antenna configurations, and thereby outperforms a scheme employing a parallel concatenated (turbo) code by wide margins when there are more transmit than receive antennas.

Extrinsic information transfer (EXIT) charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems. A model is introduced that applies to decoding problems, including the iterative decoding of parallel concatenated (turbo) codes, serially concatenated codes, low-density parity-check (LDPC) codes, and repeat-accumulate (RA) codes. EXIT functions are defined using the model, and several properties of such functions are proved for erasure channels. One property expresses the area under an EXIT function in terms of a conditional entropy. A useful consequence of this result is that the design of capacity-approaching codes reduces to a curve-fitting problem for all the aforementioned codes. A second property relates the EXIT function of a code to its Helleseth-Klove-Levenshtein information functions, and thereby to the support weights of its subcodes. The relation is via a refinement of information functions called split information functions, and via a refinement of support weights called split support weights. Split information functions are used to prove a third property that relates the EXIT function of a linear code to the EXIT function of its dual.

Recent advancements in iterative processing of channel codes and the development of turbo codes have allowed the communications industry to achieve near-capacity on a single-antenna Gaussian or fading channel with low complexity. We show how these iterative techniques can also be used to achieve near-capacity on a multiple-antenna system where the receiver knows the channel. Combining iterative processing with multiple-antenna channels is particularly challenging because the channel capacities can be a factor of ten or more higher than their single-antenna counterparts. Using a "list" version of the sphere decoder, we provide a simple method to iteratively detect and decode any linear space-time mapping combined with any channel code that can be decoded using so-called "soft" inputs and outputs. We exemplify our technique by directly transmitting symbols that are coded with a channel code; we show that iterative processing with even this simple scheme can achieve near-capacity. We consider both simple convolutional and powerful turbo channel codes and show that excellent performance at very high data rates can be attained with either. We compare our simulation results with Shannon capacity limits for ergodic multiple-antenna channel.

Mutual information transfer characteristics of soft in/soft out decoders are proposed as a tool to better understand the convergence behavior of iterative decoding schemes. The exchange of extrinsic information is visualized as a decoding trajectory in the extrinsic information transfer chart (EXIT chart). This allows the prediction of turbo cliff position and bit error rate after an arbitrary number of iterations. The influence of code memory, code polynomials as well as different constituent codes on the convergence behavior is studied for parallel concatenated codes. A code search based on the EXIT chart technique has been performed yielding new recursive systematic convolutional constituent codes exhibiting turbo cliffs at lower signal-to-noise ratios than attainable by previously known constituent codes.

We present a channel estimation method for coherent detection of multicarrier signals which is based on the a posteriori probability calculation algorithm (APP estimator). A two-dimensional channel estimation is performed by applying a concatenation of two one-dimensional APP estimators. The combination with an outer soft in/soft out channel decoder allows one to further improve the bit error rate by means of iterative estimation and decoding. The robustness of the new channel estimator permits one to reduce the number of pilot symbols which are required as phase references for coherent detection. It is readily applicable to current multicarrier systems (e.g. DVB-T) without changing the transmission format. A combination with an inner convolutional code is suggested to further improve the performance.